Glossary: finance terms from A to Z

Euro short-term rate: the rate for unsecured overnight borrowing between banks, published by the ECB since 2019. Successor to EONIA and the usual risk-free rate for euro investors.

More: Sharpe ratio: return per unit of risk · Methodology: Metrics methodology: how Portfolio Lab measures return and risk

Rule of thumb for the equity allocation: 110 minus your age, as a percentage, so 70% equities at age 40. It describes a glide path but takes no account of wealth, income or risk tolerance.

More: Equity allocation by age: rules of thumb, glide paths and what theory says · Methodology: Financial goals methodology: how Portfolio Lab simulates a life plan

Mandatory filing with the US Securities and Exchange Commission (SEC) for investment managers with discretion over at least US$100 million in reportable securities. Every quarter it shows the long positions in US stocks, ETFs and certain options and convertible bonds, no later than 45 days after quarter-end; short positions are not included. On request, positions may be kept confidential for a time.

Example: Quarter-end June 30, filing due by August 14, i.e. 45 days later.

Source: SEC, Form 13F (2026)

More: Legendary investors: the investment styles of the most famous investors, from Graham to Simons

Rule of thumb from US studies in the 1990s: withdraw 4% of your wealth in the first year of retirement and then raise the amount in line with inflation; historically, in the US, this would mostly have lasted 30 years. For other countries and periods the limit is often lower.

More: Safe withdrawal rate: how good is the 4% rule?

A diversification requirement for UCITS funds: a single position may make up at most 10%, and all positions above 5% together at most 40%. Extended limits apply to index funds.

More: ETF basics: costs, replication and distributions

Inflation rate that the market prices in for the five years starting five years from now, calculated from the 5- and 10-year breakevens. Because the near future drops out, it is often regarded as a measure of whether long-term inflation expectations are anchored.

Example: 10-year breakeven 2.30%, 5-year 2.40%: (1.023¹⁰ / 1.024⁵)^(1/5) − 1 = 2.20%.

More: Market expectations: what the yield curve, inflation-linked bonds and options reveal about the future

The classic mix of 60% equities and 40% bonds. It is the benchmark for balanced portfolios; how well it works depends heavily on the correlation between equities and bonds.

More: 60/40 portfolio: the classic mix of equities and bonds

A 60/40 portfolio with leverage of 1.5: 90% equities and 60% bonds on 100% of capital, usually via bond futures. The return is roughly 1.5 × the 60/40 return − 0.5 × the money market rate.

Example: Equities +8%, bonds +4%, money market 3%: 60/40 +6.4%, 90/60 1.5 × 6.4 − 0.5 × 3 = +8.1%.

More: Leveraged ETFs and return stacking: path dependence, costs and research

The actual return minus the normal, expected return, usually from a market model (α + β × market return). Summed over several days, this gives the cumulative abnormal return (CAR), the standard measure in event studies.

Example: With a beta of 1.2, a stock return of 1.5% and a market return of 0.5%, the abnormal return is 1.5 − 1.2 × 0.5 = 0.90%.

Source: Fama et al. (1969)

More: Insider trading: what is prohibited, what is allowed and what insider purchases reveal

Principle that in insolvency and restructuring, a junior creditor or owner receives nothing as long as a senior one has not been paid in full. In US law, it is part of confirming a plan over a dissenting class; in Germany, it appears in the StaRUG (Corporate Stabilization and Restructuring Act) as the absolute priority rule with limited exceptions; in practice there are deviations.

Source: US Bankruptcy Code (1978); StaRUG (2020); Eberhart et al. (1990)

More: Distressed debt: strategies, bankruptcy law, recovery rates and returns when investing in crises

The share of total variance explained by the few largest principal components. When it rises, markets move more closely together. This points to greater vulnerability to broad declines.

Source: Kritzman et al. (2011)

Methodology: Asset analysis: methodology from correlation to cointegration

Companies whose earnings consist largely of accruals rather than cash flows have subsequently delivered lower returns on average. Such earnings are less persistent, and prices took this into account only with a delay.

Source: Sloan (1996)

More: Fundamental analysis: valuing a company like an investor

Interest that has built up on a bond since its last coupon date. The buyer pays it to the seller on top of the price, because the buyer receives the full coupon on the next date.

Example: 3% coupon, 226 of 365 days since the last coupon date (act/act): 3 × 226 / 365 = €1.86 per €100 face value.

Source: Tuckman and Serrat (2012)

More: Bond math: calculating price, yield, duration, convexity and spreads

A fund that reinvests its income instead of paying it out. In Germany, taxed every year through the Vorabpauschale.

More: ETF basics: costs, replication and distributions

Exchange-traded fund whose manager selects and weights securities at their own discretion instead of following an index. Usually cheaper than traditional active funds but more expensive than index ETFs; it too has to beat its benchmark after costs first.

Source: Easley et al. (2021)

More: Active ETFs: how they work and what they deliver

A fund whose manager selects and weights securities in order to beat a benchmark. Over long periods, most active funds lag behind their benchmark index after costs.

Source: French (2008); Fama and French (2010)

More: Active or passive investing: ETFs versus fund managers

The difference between the return of a portfolio and that of its benchmark. Its average divided by its volatility (tracking error) gives the information ratio.

More: Tracking error and information ratio: deviation from the index

How far a portfolio may deviate from its benchmark, measured as tracking error. It is divided between tactical allocation and selection; because variances add up, the budgets grow with the square root.

Example: If the return difference between equities and bonds has a volatility of 16.28%, a budget of 1% tracking error allows the equity weight to deviate by at most 6.1 percentage points.

Source: Grinold and Kahn (2000)

More: Strategic and tactical asset allocation and the total portfolio approach

Half the sum of the absolute weight differences between a fund and its index. 0% means a copy of the index, 100% no overlap at all. A high value shows active selection, but not yet skill.

More: Active or passive investing: ETFs versus fund managers

Investor, often a hedge fund, that buys a minority stake and pushes for changes, publicly or behind closed doors: higher payouts, a new strategy, the sale of divisions or a change of management. If necessary, this happens via a proxy fight, a contested vote at the annual general meeting.

Example: According to Brav et al. (2008), the excess return around the announcement of a campaign in the US from 2001 to 2006 was about 7%.

Source: Brav et al. (2008)

More: Legendary investors: the investment styles of the most famous investors, from Graham to Simons

A mandatory announcement by an issuer under Art. 17 MAR: it must disclose inside information that directly concerns it without delay, and may delay disclosure only under strict conditions. Since June 5, 2026, for protracted processes such as takeovers, only the final event has to be disclosed.

Source: MAR (2014); Gleiss Lutz (2026)

More: Insider trading: what is prohibited, what is allowed and what insider purchases reveal

Tactical rule that each month picks the assets with the strongest momentum and then weights them by minimum variance or inverse volatility.

More: Tactical allocation: momentum, dual momentum and trend following

A market maker's risk of trading mainly with better-informed traders: it buys before prices fall and sells before they rise. The bid-ask spread compensates for these losses.

Example: Value 99 or 101 with equal probability, 20% informed orders: ask 100.20, bid 99.80.

Source: Glosten and Milgrom (1985)

More: Market making and bond trading: spread, inventory, axes, RFQ, cross trades and matrix pricing

Medium-sized tanker with a deadweight of about 80,000 to 120,000 t, smaller than Suezmax and VLCC. Portfolio Lab classifies tankers from 230 to under 265 m in length this way.

Source: EIA (2014); Notteboom et al. (2026)

Methodology: Ships at chokepoints (beta): methodology

Automatic Identification System: radio system for safety at sea. Ships automatically transmit their identity, position, course and speed over VHF, along with name, type, dimensions, draft and destination. Under SOLAS, it is mandatory for ships of 300 GT and above on international voyages; the range at sea is typically 20 to 30 nautical miles.

Source: IMO (2015); ITU (2026)

More: Ship tracking data and satellite images: what they reveal about commodities · Methodology: Ships at chokepoints (beta): methodology

Losses from selling individual stocks can only be offset against gains from individual stocks. Losses from ETFs, by contrast, go into the general loss offset pot.

A portfolio designed to be ready for every combination of growth and inflation: equities, long-term bonds, inflation-linked bonds, gold and commodities, weighted by risk rather than by capital.

More: All Weather portfolio: ready for every economic climate?

The part of the active return that comes from differing segment weights. Under Brinson-Fachler it is (wᵢ − Wᵢ) × (bᵢ − B): an overweight pays off if the segment beats the overall benchmark.

Example: A 10 percentage point overweight in a segment returning 8% against a benchmark return of 6.8%: 0.10 × 1.2 = 0.12 percentage points.

Source: Brinson and Fachler (1985)

More: Performance attribution: Brinson decomposition, factors and linking over time

The part of a fund's return that cannot be explained by its market risk (beta) or other factors. Positive means: better than the risk taken would have led you to expect.

More: Beta and alpha: how closely a fund moves with the market

The decline in a signal's return once it becomes known and more investors use it. Published return predictors delivered on average 58% less after publication than in the original sample.

Source: McLean and Pontiff (2016)

More: Alternative data: job ads, Reddit, X, satellites and card payments

Information about companies and markets beyond prices, financial statements and official statistics, e.g. job ads, social media posts, satellite images, card payments or location data. It is often available earlier, but has to be processed first and is frequently expensive.

Source: Zhu (2019)

More: Alternative data: job ads, Reddit, X, satellites and card payments

State-subsidized investment account with no guarantee requirement that replaces the Riester pension for new contracts from January 1, 2027. Every provider must offer a standard account with costs capped at 1.0%; the basic subsidy is 50 cents per euro up to €360 and 25 cents per euro up to €1,800 of own contributions.

Example: With €1,800 of own contributions: 360 × 0.5 + 1,440 × 0.25 = €540 basic subsidy.

Source: Federal Government, pension reform (2026); Bundestag, Altersvorsorgedepot (2026)

Option that may be exercised at any time up to expiry, unlike a European option, which can only be exercised on the expiry date. For calls without dividends, early exercise never pays, but for deep in-the-money puts it can; the right to do so costs a premium.

Example: Put with price and strike 100, one year, 5% interest rate and 20% volatility: European 5.57, American 6.09.

Source: Merton (1973)

More: Option pricing: where fair option prices come from · Methodology: Option pricer: how Portfolio Lab values options

An illiquidity measure based on daily data: the average ratio of the absolute daily return to daily trading value. The higher the value, the more one euro of turnover moves the price; it can be calculated for any stock with prices and turnover.

Example: Returns of +1.2%, −0.8% and +2.0% on turnover of €2.0 million, €1.6 million and €2.5 million: (0.6 + 0.5 + 0.8) / 3 = 0.63% per million euros of turnover.

Source: Amihud (2002)

More: Liquidity risk: measuring market liquidity, liquidity premiums and the tools of open-ended funds

A random or irrelevant number, such as your own purchase price or a previous high, influences judgments. The purchase price says nothing about whether an investment is a good one today.

Income tax return form for investment income. Needed, for example, for the most-favorable assessment, for offsetting losses across several banks or if income was received without tax being deducted.

Increasing the contribution every year by a fixed rate, for example to keep pace with your salary. With an annual increase d, the monthly contribution in year k (counting from 0) is R × (1 + d)^k; over long periods, this raises the total amount paid in considerably.

Example: €150 a month with a 3% annual increase: in the eleventh year €150 × 1.03¹⁰ = €201.59 a month.

More: Compound interest: how returns on returns make wealth grow · Methodology: Methodology of the free calculators: savings plan, withdrawal and leveraged ETF

Certificate from the bank showing a year's investment income, taxes withheld, exemption order used and losses. The basis for Anlage KAP in the tax return.

Scaling metrics up to one year: returns with compounding, volatilities with the square root of time (monthly values × √12, daily values × √252).

More: Volatility: how much a portfolio fluctuates

Return pattern that a standard model such as the CAPM does not explain, for example momentum or the low-volatility effect. Many anomalies weaken after they are published.

Source: McLean and Pontiff (2016)

More: The efficient market hypothesis: why it is so hard to beat the market

A fee charged only to the transacting investors on days with large inflows or outflows, which is paid into the fund. It is meant to cover the estimated trading costs so that the remaining investors are not diluted; unlike with swing pricing, the unit price stays the same for everyone else.

Source: IOSCO (2023)

More: Liquidity risk: measuring market liquidity, liquidity premiums and the tools of open-ended funds

Contract clause that protects earlier investors in a round at a lower price (down round): their conversion price is lowered, either all the way to the new price (full ratchet) or by a weighted average. The additional dilution is borne mainly by founders and employees.

More: Venture capital: funding rounds, valuation, the power law and what research knows about returns

Theory according to which expected returns depend on several common risk factors. It leaves open which factors these are and is the foundation of all multi-factor models.

Source: Ross (1976)

More: CAPM: the capital asset pricing model and the security market line

Autoregressive conditional heteroskedasticity: today's variance depends on the squared surprises of the previous days. The model captures volatility clustering; Robert Engle received the Nobel Prize for it in 2003.

Source: Engle (1982)

A time series model following Box and Jenkins that combines autoregression (AR), differencing (I) and a moving average of past shocks (MA). For returns the estimated weights are usually small, and the forecast quickly reverts to the mean.

Example: AR(1) with φ = 0.10: a monthly return of 3% with a mean of 0.6% raises the forecast for the following month only to 0.84%.

Source: Box and Jenkins (1970)

More: Return forecasting models: ARIMA, GARCH, LSTM and machine learning

The simple average of period returns. It overstates actual wealth growth as soon as returns fluctuate; on the other hand, it is the right measure for the expected return of a single period.

Example: +50% and −50% average 0%, but wealth falls to 75%.

More: Volatility drag: why volatility costs you return

A fund that makes no sustainability claim within the meaning of the SFDR. It only discloses whether and how sustainability risks are factored into its investment decisions.

Source: SFDR (2019)

More: ESG ETFs: index rules, ratings, returns and the limits of sustainable funds

A fund that promotes environmental or social characteristics, colloquially “light green”. The SFDR does not prescribe how strictly it has to select. Anything from a few exclusions to strict filters is possible.

Source: SFDR (2019)

More: ESG ETFs: index rules, ratings, returns and the limits of sustainable funds

A fund that has sustainable investment as its objective, colloquially “dark green”. If it has a climate objective, it must refer to an EU climate benchmark or explain how it will achieve that objective.

Source: SFDR (2019)

More: ESG ETFs: index rules, ratings, returns and the limits of sustainable funds

Option on the average price over several fixings instead of the closing price. It is cheaper than the standard option and harder to manipulate; common for commodities and currencies. There is no exact formula for the arithmetic average.

Source: Kemna and Vorst (1990); Levy (1992)

More: Option pricing: where fair option prices come from · Methodology: Option pricer: how Portfolio Lab values options

Group of investments with similar risk and return, such as equities, government bonds, corporate bonds, commodities, real estate or the money market.

Which asset is held in which account when accounts are taxed differently, e.g. a private pension plan and a regular brokerage account. The same allocation, distributed more cleverly, can save tax.

Source: Dammon et al. (2004)

The spread over a floating reference rate that a fixed-rate bond earns when its interest rate risk is exchanged via an interest rate swap. It measures the bond's credit risk and, alongside the Z-spread, serves as a point of comparison for the CDS premium.

More: Basis trades: positive and negative basis in bonds, CDS and futures

GmbH (German limited company) that invests its own assets (stocks, funds, bonds or real estate) instead of running an operating business. Capital gains on shares are 95% tax-exempt within it, whereas interest and dividends from small holdings are fully taxable; when profits are distributed to the shareholder, flat-rate withholding tax (Abgeltungsteuer) is due once more.

Example: Capital gain on shares at a municipal multiplier of 400%: 5% × 29.825% = 1.49% tax in the GmbH.

Source: KStG (2002); GewStG (2002)

Planning that sets assets against future payments: present value of the liabilities, funding ratio and required return.

More: Asset-liability management: aligning your wealth with future spending

A crypto-asset under MiCA that aims to maintain a stable value by referencing another value or a basket, e.g. gold, several currencies or crypto-assets (ART). The issuer needs authorization, a white paper and a reserve of assets; issues of up to €5 million on average over twelve months are exempt from authorization.

Source: BaFin, ART and EMT guidance notice (2025)

More: Digital assets: tokenization, stablecoins, crypto securities and the digital euro

Equities are more strongly correlated in falling markets than in rising ones. Diversifying across equity markets therefore offers less protection precisely in a crash than the average correlation promises.

Source: Longin and Solnik (2001); Ang and Chen (2002)

More: Correlation and diversification: why mixing assets reduces risk

Settlement in which delivery and payment take place in a single, indivisible step: either both sides change hands or neither does. On a shared register this eliminates the settlement risk between trade and settlement; in return, cash and securities have to be in place beforehand.

Example: Share purchase of €10 million at 1.5% daily volatility: with T+2, the replacement risk at the 99% level is about €10 million × 2.326 × 1.5% × √2 = €493,419; with atomic settlement it is €0.

More: Digital assets: tokenization, stablecoins, crypto securities and the digital euro

An extended Dickey-Fuller test for a unit root: the regression also includes lagged differences so that autocorrelation does not distort the test. A strongly negative test statistic points to a stationary series, such as a spread that reverts to its mean.

Source: Said and Dickey (1984); Dickey and Fuller (1979)

More: Pairs trading and statistical arbitrage: idea, methods, research · Methodology: Long/short and statistical arbitrage: methodology

An approved market participant, usually a large bank, that may create or redeem units directly with the ETF provider. It uses price deviations for arbitrage.

More: ETF basics: costs, replication and distributions

Correlation of a time series with a lagged copy of itself: is a good month more likely to be followed by another good one? Equity returns show hardly any autocorrelation; smoothed valuations (property funds) show a lot.

Payment by the public sector to the operator of an infrastructure asset for keeping it usable, regardless of how many people use it; typical of public-private partnerships for roads, schools or hospitals. The counterpart is a concession with demand risk, where tolls or user charges determine revenue. Social infrastructure projects with such payments had the lowest default rate after ten years in Moody's data, at 1.1%.

Source: Moody's (2020)

More: Infrastructure investing: equity and debt, revenue models, valuation and research

A dealer's specific interest in buying (bid axe) or selling (ask or offer axe) a security, usually because the dealer wants to reduce or cover a position. Under the ICMA standard the quantity has to be stated, while the price is optional.

Source: ICMA and FIX Trading Community (2025)

More: Market making and bond trading: spread, inventory, axes, RFQ, cross trades and matrix pricing

Test of an investment strategy on historical prices: how would a portfolio have performed in the past? It shows return and risk, but is no guarantee for the future.

More: CAGR: how to calculate the average annual return correctly

Downward-sloping futures curve: near-term contracts are more expensive than longer-dated ones. For the VIX, a sign of acute fear.

More: VIX: how to read the stock market's fear gauge

Voyage without cargo. To keep the empty ship stable, it takes on ballast water; even so, its draft is considerably smaller than when loaded. Portfolio Lab classifies a draft of up to 65% of the reference value as “probably in ballast”.

Source: Cerdeiro et al. (2020)

Methodology: Ships at chokepoints (beta): methodology

A variant of FIRE in which a part-time job covers part of the expenses and the portfolio covers only the gap. This lowers the capital required considerably and dampens the sequence risk of the first years.

Example: €30,000 in expenses, €12,000 in part-time income: at a 3.5% withdrawal rate, €514,286 is enough instead of €857,143.

More: FIRE (Financial Independence, Retire Early): Lean, Fat, Coast and Barista FIRE

Option that comes into existence (knock-in) or is extinguished (knock-out) when the price touches a threshold. It is cheaper than the standard option; in plus out gives the standard option again. If the barrier is monitored only daily rather than continuously, it is shifted in the calculation.

Example: Call with price and strike 100, one year, 5% interest rate and 20% volatility: standard 10.45, down-and-out at 90 still 8.67, down-and-in 1.79.

Source: Merton (1973); Broadie et al. (1997)

More: Option pricing: where fair option prices come from · Methodology: Option pricer: how Portfolio Lab values options

Distortion of a rate of change by an unusual value in the comparison period: after a deep slump, the year-on-year comparison a year later shows strong growth even though the level is still below its starting value, and vice versa.

Example: An index falls from 100 to 80 in the previous year and then rises to 88: the year-on-year comparison shows +10%, but the index is still 12% below its starting value.

Methodology: Economic pulse: how Portfolio Lab calculates early indicators

One hundredth of a percentage point (0.01%). Changes in interest rates and spreads are usually quoted in basis points: from 2.50% to 2.75% is 25 basis points.

Change in a bond's price in euros when its yield rises by one basis point (DV01). Approximately market value × modified duration × 0.0001.

Example: €100,000 of bonds with a modified duration of 7: 100,000 × 7 × 0.0001 = €70 per basis point.

More: Duration: how strongly bonds react to interest rates

The risk that the hedged asset and the hedging instrument perform differently, e.g. because the future is on a different index, the hedge ratio has been estimated wrongly or the basis fluctuates until expiry.

More: Short selling, hedge funds and hedging: types and how they work

A fund's redemption price at the start of the year times 70% of the base rate. The Vorabpauschale is the amount by which the year's distributions fall short of the base return, but at most the increase in value plus distributions.

Example: Unit value €10,000 at the start of the year, base rate 3.20%: 10,000 × 0.032 × 0.7 = €224.00.

Source: InvStG (2016)

Private life annuity insurance under § 10(1) no. 2(b) EStG, colloquially known as the Rürup pension. Contributions are deductible as special expenses up to the maximum contribution to the miners' pension insurance (knappschaftliche Rentenversicherung); in return, there is only a lifelong monthly pension from age 62 at the earliest, with no lump-sum payment, not inheritable and not usable as loan collateral.

Example: Maximum amount 2026: €124,800 × 24.7% = €30,826 (rounded up), minus contributions to the statutory pension insurance.

Source: EStG §§ 10, 10a, 10c (2009); EStG § 22 (2009)

Interest rate used to calculate the Vorabpauschale. The Federal Ministry of Finance publishes it every January; for 2026 it is 3.20%.

A total return swap on a custom basket: the bank pays the return of the basket, the investor a reference rate plus a spread. Also called a portfolio swap; from the outside, the positions are barely visible.

Source: SEC, Archegos (2022)

More: Basket swaps, total return swaps or futures: building market exposure efficiently

A method for estimating a hidden Markov model, a special case of the EM algorithm. The E-step uses the forward-backward algorithm to calculate how likely each regime was in each period and how likely each switch was; the M-step re-estimates the transition matrix, means and variances with these weights. No iteration lowers the likelihood, but only a local maximum is found. That is why the calculation is run from several starting values.

Source: Baum et al. (1970); Rabiner (1989)

More: Regime models: hidden Markov, Markov switching and more · Methodology: Regime methodology: how the hidden Markov model works

An estimator for expected returns that shrinks the individual means toward a common value. It accepts a little bias in order to remove a lot of variance, and so improves portfolio selection compared with the simple mean.

Source: Jorion (1986)

More: Michaud resampled optimization: more stable portfolio weights through simulation

An approach that combines a prior assumption (the prior) with new data or views to form an updated assumption (the posterior). This is how the Black-Litterman model blends market equilibrium with your own forecasts.

Source: Black and Litterman (1992)

More: Black-Litterman: incorporating your own views cleanly

A phase of sharply falling prices, often defined as a decline of at least 20% from the peak. A correction, by contrast, is a decline of 10 to 20%.

More: Maximum drawdown: the largest loss from a peak

The highest income on which social security contributions are levied; anything above it is contribution-free. It is adjusted to wage growth every year and serves as the reference for many limits in retirement provision.

Example: 2026: pension insurance €101,400 a year (€8,450 a month), health and long-term care insurance €69,750 (€5,812.50 a month).

Source: Deutsche Rentenversicherung (2025)

Yardstick for a portfolio, usually an index such as the MSCI World. Only the comparison shows whether return and risk were good or bad.

More: Tracking error and information ratio: deviation from the index

Option that may only be exercised on a few fixed dates before expiry, such as monthly. Its value lies between that of a European and an American option; common in callable bonds and interest rate derivatives.

Methodology: Option pricer: how Portfolio Lab values options

An ESG approach that selects only the companies with the best ESG ratings in each industry. Sector weights remain similar to those of the parent index, while the number of stocks falls considerably.

More: ESG ETFs: index rules, ratings, returns and the limits of sustainable funds

How strongly a fund moves with the market on average. A beta of 1.2 means: about 12% for a 10% market move.

Example: A covariance of 12.22 divided by a market variance of 10.97 gives a beta of 1.11.

More: Beta and alpha: how closely a fund moves with the market

Factor that buys low-beta stocks with leverage and sells high-beta stocks. It has delivered positive risk-adjusted returns in many markets.

Source: Frazzini and Pedersen (2014)

More: The low-volatility anomaly and betting against beta

The gap between the price at which you can sell (bid) and the price at which you can buy (ask). For large ETFs often below 0.1%, considerably more in thin markets and outside the main exchange trading hours.

More: ETF basics: costs, replication and distributions · Methodology: Backtest methodology: data, process, rebalancing and costs

Model in which the price rises or falls in each time step; the option value is built backwards as the discounted risk-neutral expected value. With many steps, it converges to Black-Scholes, and it can also value American options. Variants: Cox-Ross-Rubinstein, Jarrow-Rudd, Leisen-Reimer.

Source: Cox et al. (1979); Leisen and Reimer (1996)

More: Option pricing: where fair option prices come from · Methodology: Option pricer: how Portfolio Lab values options

Variant of Black-Scholes for options on futures and forwards: the futures price replaces the spot price, and the cost of carry is zero. Standard for interest rate, commodity and index options on futures and for reading implied volatilities off the forward.

Source: Black (1976)

Methodology: Option pricer: how Portfolio Lab values options

Optimization model that starts from the market-implied returns and blends in your own views according to how confident you are in them. Produces more stable weights than pure Markowitz optimization.

More: Black-Litterman: incorporating your own views cleanly

Formula for the fair price of European options based on price, strike price, time to maturity, interest rate and volatility. Applied in reverse, it extracts the implied volatility from market prices.

Source: Black and Scholes (1973); Merton (1973)

More: Option pricing: where fair option prices come from · Methodology: Option pricer: how Portfolio Lab values options

A bootstrap variant for time series: instead of individual months, contiguous blocks are drawn, e.g. twelve consecutive months. This preserves trends, volatility phases and autocorrelation.

Source: Kunsch (1989)

More: Bootstrap: future scenarios from your own history · Methodology: Monte Carlo methodology: how Portfolio Lab simulates wealth paths

Bands usually two standard deviations above and below a 20-period moving average. They widen when volatility rises; chartists treat touches and breakouts as signals.

More: Technical analysis, chart patterns and candlesticks from a quant perspective

Return of a bond if the yield curve stays unchanged: coupon plus roll-down, often measured over the money market rate. With a steep curve, long maturities earn more carry but also bear more interest rate risk; that is why carry per unit of duration is compared as well.

Source: Koijen et al. (2018)

More: Carry trade: earning interest with currencies and bonds · Methodology: Carry backtest: methodology for FX and bond carry

Conversion of the discount rate at which US Treasury bills (T-bills) are quoted into a yield that can be compared with bond yields. For 3-month bills with 91 days to maturity: 365 · d / (360 − 91 · d).

Example: Discount 5.10%: 365 × 0.051 / (360 − 91 × 0.051) = 5.24%.

Source: Estrella and Trubin (2006)

More: Market expectations: what the yield curve, inflation-linked bonds and options reveal about the future · Methodology: Macro dashboard and regime analysis: methodology

A certificate that pays at least the bonus amount at maturity as long as the underlying never touches the barrier, and otherwise the price. Decomposed: the underlying without dividends plus a down-and-out put struck at the bonus level; with a cap, also minus a call.

Example: Share €100, bonus €120, barrier €75, one year, 25% volatility, 2% interest rate, 3% dividend yield: the fair value is 97.04 + 10.63 = €107.67.

Methodology: Option pricer: how Portfolio Lab values options

Simulation method that randomly draws historical monthly returns instead of generating them from a normal distribution. Captures crises and skewed distributions more realistically.

More: Monte Carlo simulation: how safe is your plan?

Fee for borrowing a security that is to be sold short (short selling), usually in percent p.a. of the borrowed value. Low for easy-to-borrow large caps, sometimes high for names in demand; fees can rise and securities can be recalled.

Source: Engelberg et al. (2018)

More: Pairs trading and statistical arbitrage: idea, methods, research · Methodology: Long/short and statistical arbitrage: methodology

The markup on a reference rate, such as the money market rate, that a lender charges for a securities-based loan. With leverage L it applies to (L − 1) × own capital. In the Portfolio Lab backtest such a spread over the money market rate applies to the financed part of leveraged securities; the default is 1% p.a.

More: Leverage in a portfolio: return, risk, costs and margin calls · Methodology: Backtest methodology: data, process, rebalancing and costs

Parameter B in the Takahashi-Alexander model: the distribution rate (t / L)^B rises with the fund's age t and reaches 100% in the final year L. The larger B, the later and more bunched the money flows back.

Example: Fund life 12 years, year 6: with B = 1, 50.00% of NAV flows back; with B = 2.5, only 17.68%.

Source: Takahashi and Alexander (2002)

More: Takahashi-Alexander model: forecasting the cash flows of private markets funds

Price of the underlying at which an option position makes neither a profit nor a loss on the expiry date. For a bought call, it is the strike plus the premium; for a bought put, the strike minus the premium.

More: Option pricing: where fair option prices come from · Methodology: Option pricer: how Portfolio Lab values options

Difference between the yield of a conventional and an inflation-linked government bond of the same maturity. It shows the inflation expected by the market plus a risk premium.

Example: Nominal 2.6%, real 0.4%: breakeven about 2.6 − 0.4 = 2.2%.

Source: Bekaert and Wang (2010)

More: Real return: what is left after inflation · Methodology: Macro dashboard and regime analysis: methodology

Performance attribution according to Brinson, Hood and Beebower or Brinson and Fachler: the active return in each segment is broken down into allocation, selection and interaction effects, which add up exactly to the difference between portfolio and benchmark returns.

Source: Brinson et al. (1986); Brinson and Fachler (1985)

More: Performance attribution: Brinson decomposition, factors and linking over time

Brownfield assets are already built and have a revenue history; greenfield projects still have to be built and carry construction, cost and schedule risk. For project finance loans, annual default rates according to Moody's (2020) fall as projects age and reach roughly the level of A-rated companies in about the seventh year.

Source: Moody's (2020)

More: Infrastructure investing: equity and debt, revenue models, valuation and research

Basis Trade at Index Close: an index future is traded as a spread (basis) to the official index close; the futures price is the closing level plus the agreed basis. On Eurex this trade type is called TAIC (Trade at Index Close) and is available for index futures and total return futures.

Example: Agreed basis +12.5 points, index close 5,000 points: futures price 5,012.5 points.

Source: CME Group, BTIC (2026); Eurex, TAIC (2026); Eurex (2026)

More: Order types and execution: from limit orders to MOC, VWAP, TAS and BTIC

Band around an index boundary within which a security keeps its existing status. This stops companies at the boundary from moving back and forth at every review, which lowers the turnover and costs of index funds.

Example: Solactive cuts off large and mid caps at 85% of cumulative free-float capitalization, with a buffer between 80 and 90%.

Source: MSCI GIMI Methodology (2024); Solactive GBS Guideline (2026)

More: Index providers and valuation points: why the same index is calculated differently

Buying a call with a low strike and selling a call with a higher strike. Cheaper than a single call, but the profit is limited to the difference between the strikes minus the cost. The counterpart for falling prices is the bear put spread.

Example: Calls 95/105, 91 days, price 100: cost 5.07, maximum profit 4.93.

More: Option pricing: where fair option prices come from

A phase of persistently rising prices, often measured from the trough of a bear market to the next peak.

Weakness of market-value-weighted bond indices: whoever takes on more debt gets more weight. Such an index steers the money of those tracking it toward the most heavily indebted issuers, not the soundest ones.

Source: Bloomberg Methodology (2026)

More: Active or passive in bonds and commodities: why the rules differ from equities

A division of the business cycle into four phases based on the level and direction of a leading indicator: upswing, boom, downturn and recession. For each phase you can analyze how asset classes have performed historically.

Methodology: Macro dashboard and regime analysis: methodology

US investment company that provides capital, mainly loans, to small and mid-sized companies; created by a 1980 law. Its debt-to-equity ratio is legally capped at 2 to 1. Listed BDCs fluctuate like stocks.

Source: Cai and Haque (2024); Avalos et al. (2025)

More: Private debt in practice: direct lending, unitranche, mezzanine, loan structure and fund vehicles

A smile is inconsistent if a butterfly (one call each with a low and a high strike bought, two in the middle sold) would have a negative price. The implied probability density would be negative there. With SVI, this is checked with a function g(k) ≥ 0.

Source: Gatheral and Jacquier (2014)

Methodology: Option pricer: how Portfolio Lab values options

The positions chosen at the start are never reallocated; the weights drift with prices. The winner thus gains more and more weight, and risk usually rises over time.

Source: Perold and Sharpe (1988)

More: Rebalancing: getting your portfolio back on course

Credit portfolio that, as a rule, holds bonds to maturity and only trades when an issuer's credit quality threatens to deteriorate. The core of many CDI strategies: it saves trading costs and earns the spread as long as defaults stay below those budgeted for.

Source: PLSA (2023)

More: Liability-driven investing and cash flow driven investing: covering liabilities with bonds

A long-term abnormal return calculated as the difference between two compounded returns: the stock's increase in value minus that of a benchmark portfolio over the same period. Unlike the CAR, it measures how much more or less an investor would actually have earned by buying and holding.

Source: Barber and Lyon (1997); Lyon et al. (1999)

More: Event studies: how to measure and test price reactions to events

Surcharge that the buyer at an auction pays to the auction house on top of the hammer price, usually tiered by price. At the major international houses, in spring 2026 it was 27 to 29% of the hammer price in the lowest tier and 15% above US$8 million. The seller also pays a commission.

Example: Hammer price €100,000 and a 25% buyer's premium: the buyer pays €125,000.

Source: Grossman LLP (2026)

More: Collectibles as an investment: what art, wine, watches and classic cars really return

Compound annual growth rate: the average annual return including compounding.

Example: €10,000 grows to €16,105.10 in five years. That corresponds to a CAGR of 10.00%.

More: CAGR: how to calculate the average annual return correctly

A return pattern tied to a fixed date (half-year, month, day of the week, turn of the month or holiday) rather than to new information. Because a great many such rules can be tested, chance findings are common; effects that are significant on their own often do not survive a correction for the search.

Source: Sullivan et al. (2001)

More: Stock market seasonality: Sell in May, the January effect and how to test calendar effects

Returning to the target weights at fixed intervals, e.g. once a year. Simple and predictable, but blind to large deviations between the dates; the alternative is tolerance-band rebalancing.

Source: Perold and Sharpe (1988)

More: Rebalancing: getting your portfolio back on course

Call option: makes money when the underlying rises above the strike price plus the premium paid. The buyer's loss is limited to the premium.

More: Option pricing: where fair option prices come from

CAGR divided by the absolute value of the maximum drawdown.

Example: A 6% CAGR and a −20% maximum drawdown give 0.30.

More: Sortino ratio and Calmar ratio: measuring downside risk

Attribution for fixed income portfolios following Campisi: the return is broken down into income, a treasury effect from changes in government bond yields, a spread effect from changes in risk premiums, and selection, each relative to the benchmark.

Source: Campisi (2000)

More: Multi-asset attribution: weighting schemes, top-down and bottom-up, currencies and overlays

A Japanese candlestick display showing the open, high, low and close for each period. Patterns such as the doji, hammer, engulfing or morning star are said to signal reversals; research finds mixed evidence for this, and weak evidence after costs.

Source: Caginalp and Laurent (1998); Marshall et al. (2006)

More: Technical analysis, chart patterns and candlesticks from a quant perspective

Cyclically adjusted price-to-earnings ratio: price divided by the inflation-adjusted average earnings of the last ten years.

More: Shiller P/E (CAPE): how expensive is the stock market?

Capital call (drawdown, contribution): the fund requests part of the commitment, usually at short notice, for purchases, costs and fees; the total is called paid-in or called capital. Distribution: money flowing back to investors from sales, dividends or interest. The Yale model by Takahashi and Alexander plans both flows.

Source: Takahashi and Alexander (2002)

More: Measuring private markets: J-curve, cash flows, smoothing and public proxies

Amount an investor bindingly commits to a closed-end fund (commitment). The fund draws it down step by step; the part still outstanding (unfunded commitment) must be kept available. Allocation and liquidity planning therefore depend on commitments, called capital and NAV at the same time.

More: Measuring private markets: J-curve, cash flows, smoothing and public proxies

Sale proceeds minus acquisition costs and the costs of buying and selling. For funds, the Vorabpauschalen already taxed are deducted so that nothing is taxed twice.

Source: InvStG (2016)

The straight line from the risk-free rate to the tangency portfolio in the risk-return diagram. Its slope is the Sharpe ratio of the market portfolio; mixes of money market and market portfolio lie on it.

Source: Sharpe (1964)

More: CAPM: the capital asset pricing model and the security market line

A certificate that repays at least the nominal value at maturity and participates in price gains. Decomposed: a zero-coupon bond of the issuer plus a call. The protection only holds as long as the issuer pays.

Example: 2% interest rate, five years: the zero-coupon bond costs 1,000 / 1.02⁵ = €905.73; €94.27 remains for the call and the margin.

Capital Asset Pricing Model: expected return = risk-free rate + beta × market risk premium. Only market risk, which cannot be diversified away, is rewarded.

Source: Sharpe (1964); Lintner (1965); Mossin (1966)

More: CAPM: the capital asset pricing model and the security market line

A company's emissions per million euros of revenue or enterprise value. For funds, the weighted average (WACI) is common: the sum of weight times emissions divided by revenue.

Example: 10% in a utility with 1,200 t per €m of revenue and 90% in companies with 100 t: 0.1 × 1,200 + 0.9 × 100 = 210 t per €m.

More: ESG ETFs: index rules, ratings, returns and the limits of sustainable funds

Four-factor model of market, size, value and momentum. With it, many apparent successes of active funds disappear, because the funds simply held momentum stocks.

Source: Carhart (1997)

More: Factor investing: understanding the Fama-French factors · Methodology: Factor regression, factor allocation and factor statistics: methodology

The fund manager's share of profits, according to Kaplan and Strömberg (2009) almost always 20% of the profits, usually only after the capital and a preferred return have been paid back. In the European model (whole fund), it applies to the fund as a whole; in the American model (deal by deal), to each holding, then with a clawback in case losses follow later.

Example: Capital 100, proceeds 200 after five years, 8% hurdle, full catch-up, 20% carry: manager 20.00, investors 180.00.

Source: Kaplan and Strömberg (2009); Metrick and Yasuda (2010)

More: Private equity explained: strategies, fund structure, fees and what research shows about returns

Income an asset generates if prices do not change: for bonds, coupon and roll-down; for currencies, the interest rate differential; for futures, the roll yield. Researched as a factor across asset classes.

Source: Ilmanen (2011); Koijen et al. (2018)

More: Carry trade: earning interest with currencies and bonds · Methodology: Carry backtest: methodology for FX and bond carry

Sudden large loss on carry trades when many investors unwind their positions at the same time and funding currencies appreciate strongly. This typically happens when risk appetite and funding liquidity decline. It makes carry returns negatively skewed.

Source: Brunnermeier et al. (2008)

More: Carry trade: earning interest with currencies and bonds · Methodology: Carry backtest: methodology for FX and bond carry

Strategy that borrows in low-interest currencies and invests in high-interest currencies, usually via currency forwards. It earns the interest rate differential as long as the high-yielding currency does not depreciate by more than that, and in crises it often loses a lot very quickly.

Source: Lustig and Verdelhan (2007); Brunnermeier et al. (2008)

More: Carry trade: earning interest with currencies and bonds · Methodology: Carry backtest: methodology for FX and bond carry

Buying index futures equal to a fund's cash so that inflows, dividends or a liquidity reserve participate in the market until they are invested. The cash remains invested at the money market rate and serves as collateral; what remains are basis risk and roll costs.

Example: €12 million of cash, index at 5,000 points, €10 per point: 12,000,000 / 50,000 = 240 contracts.

Source: Hull (2021)

More: Overlay management with futures: beta, duration and currency overlays, contract numbers and liquidity needs

Investment approach in which the coupons and redemptions of a bond portfolio cover the future payouts of a pension plan or insurer as closely in time as possible, usually with corporate bonds on a buy-and-maintain basis. It complements liability-driven investing rather than replacing it: interest rate, inflation and liquidity risks are still hedged by an LDI component.

Source: PLSA (2023)

More: Liability-driven investing and cash flow driven investing: covering liabilities with bonds

Selecting bonds whose payments cover at least the liabilities due on each date; surpluses are parked until the next date. Unlike immunization, this protects against any interest rate movement, but it costs more if suitable maturities are missing.

Example: Five payments of €10 million each, covered with three bonds (1, 3 and 5 years): because two gaps are bridged with non-interest-bearing cash, the portfolio costs €46.312 million instead of €45.797 million at 3% interest.

More: Liability-driven investing and cash flow driven investing: covering liabilities with bonds

The state of a CPPI after a crash down to the floor: everything is held in safe assets, and with no cushion left the rule buys no more equities. If the floor grows with the interest rate, this often remains so during the recovery as well.

More: CPPI: portfolio insurance with cushion, floor and multiplier · Methodology: CPPI backtest: methodology

The CDS premium minus the spread of a bond from the same debtor, usually the Z-spread or asset swap spread. Negative means that default protection is cheaper than the bond's spread. After the collapse of Lehman in 2008, the basis became strongly negative.

Example: CDS premium 1.80%, asset swap spread 2.50%: basis −0.70%.

Source: Bai and Collin-Dufresne (2019); Choi and Shachar (2013)

More: Basis trades: positive and negative basis in bonds, CDS and futures

Comparison portfolio of stocks with the same characteristics as a fund's holdings, such as size, valuation and momentum. It separates style from genuine stock-picking skill.

Source: Daniel et al. (1997)

More: Look-through: what is really inside your ETFs

The bond that is cheapest for the party with the delivery obligation to deliver: for bond futures, among all deliverable bonds according to their conversion factor; for CDS, among the debtor's deliverable bonds. This choice has a value that is reflected in prices.

Source: Hull (2021)

More: Basis trades: positive and negative basis in bonds, CDS and futures

Strait or canal through which a large share of seaborne trade has to pass, such as the Straits of Malacca and Hormuz, the Suez Canal or the Panama Canal. In 2024, around 20 million barrels of oil a day flowed through Hormuz alone; if a chokepoint is closed, ships have to make long detours.

Source: EIA (2024); Dunn and Barden (2025)

More: Ship tracking data and satellite images: what they reveal about commodities · Methodology: Ships at chokepoints (beta): methodology

For church members, 8% (Bavaria, Baden-Württemberg) or 9% of the flat-rate tax. Because it counts as a special expense, the flat-rate tax falls slightly in return; the bank automatically queries the membership status from the Federal Central Tax Office (BZSt).

Example: With 8% church tax: 25% / (1 + 0.25 × 0.08) × (1 + 0.055 + 0.08) = 27.82% total rate.

The clean price is a bond's quoted price without accrued interest; the dirty price (full price) is the price actually paid: clean price plus accrued interest. The dirty price is the present value of the future payments; the clean price does not jump on the coupon date.

More: Bond math: calculating price, yield, duration, convexity and spreads

EU climate transition benchmark: a greenhouse gas intensity at least 30% below that of the investment universe, then at least 7% lower each year; controversial weapons, tobacco and companies violating the UN Global Compact or the OECD Guidelines are excluded.

Source: EU Climate Benchmarks Regulation (2020)

More: ESG ETFs: index rules, ratings, returns and the limits of sustainable funds

A period of 30 calendar days before the announcement of an interim or year-end report during which managers may not trade in the issuer's financial instruments under Art. 19(11) MAR, either on their own account or for third parties. The issuer may allow exceptions only in narrowly defined cases.

Source: MAR (2014)

More: Insider trading: what is prohibited, what is allowed and what insider purchases reveal

The auction at the end of the trading day that determines the official closing price. Index funds trade there because net asset value and index are calculated from closing prices; on Xetra the call phase begins at 17:30 and ends at a random time.

Source: Deutsche Börse, trading parameters (2026); Bogousslavsky and Muravyev (2021)

More: Order types and execution: from limit orders to MOC, VWAP, TAS and BTIC

Conservative minus aggressive: return of companies that invest little minus those that expand their balance sheets strongly. Part of the five-factor model.

Source: Fama and French (2015); Hou et al. (2015)

More: Factor investing: understanding the Fama-French factors · Methodology: Factor regression, factor allocation and factor statistics: methodology

The point from which your existing portfolio will grow to the FIRE number by the planned exit date without further contributions. The coast number is the discounted FIRE number: FIRE number / (1 + r)^n, with real return r and n years.

Example: €750,000 in 30 years at a 4% real return: 750,000 / 1.04^30 = €231,239.

More: FIRE (Financial Independence, Retire Early): Lean, Fat, Coast and Barista FIRE

A risk measure that satisfies four axioms, including subadditivity: the risk of two portfolios combined is never greater than the sum of their risks. Expected shortfall is coherent; value at risk is not always.

Source: Artzner et al. (1999); Acerbi and Tasche (2002)

More: Value at risk and conditional VaR: how much you could lose in a bad case

Two price series that each wander randomly on their own but keep a stable distance in the long run. The basis of pairs trading strategies; the spread reverts to its mean. It is tested, for example, with the Engle-Granger test.

Source: Engle and Granger (1987)

More: Pairs trading and statistical arbitrage: idea, methods, research · Methodology: Long/short and statistical arbitrage: methodology

Storing private keys without a connection to the internet, e.g. on a hardware device or on paper in a safe. This is hard to attack, but slow. Day-to-day trading uses a hot wallet with a network connection, which is easier to use and easier to attack.

More: Crypto in institutional portfolios: access, custody, regulation and risk budget

A hedge consisting of an asset held, a put bought below the current price and a call sold above it. The call premium pays for the put in full or in part; in return, the upside is capped.

Example: Index 100, put at 90 for 3.65, call at 110 for 3.07: net cost 0.58; the result at expiry lies between −10.58% and +9.42%.

More: Tail hedging: what put protection costs, when it pays off and what short-vol strategies teach · Methodology: Option pricer: how Portfolio Lab values options

Interest income on the cash that a fully collateralized futures index or fund holds alongside its futures, usually in short-dated government paper. Part of a commodity index's total return, alongside spot and roll return.

Example: Spot +5.00%, roll −5.81%, collateral 2%: total return 1.05 × 0.9419 × 1.02 − 1 = 0.88%.

Source: BCOM methodology (2026)

More: Active or passive in bonds and commodities: why the rules differ from equities

A method for estimating the probability of backtest overfitting: the period is divided into S contiguous blocks of equal length, and each selection of S/2 blocks forms a split into an in-sample part and an out-of-sample part of equal size. For each split, the variant that is best in-sample is chosen and its out-of-sample rank determined.

Example: S = 16 blocks give C(16, 8) = 12,870 splits, S = 4 blocks only 6.

Source: Bailey et al. (2016)

More: Probability of backtest overfitting: does the best variant deliver what the backtest promises?

Planning annual commitments to private markets funds over many vintages so that the invested share (NAV) reaches and holds a target allocation without overstretching liquidity. It is based on a forecast of calls and distributions, for example using the Takahashi-Alexander model.

Example: In the article's example, a target allocation of 15% requires commitments of 3.77% of assets per year.

Source: de Zwart et al. (2012)

More: Takahashi-Alexander model: forecasting the cash flows of private markets funds

A measure of crowding in momentum strategies developed by Lou and Polk: the correlation of the excess returns of the stocks that a typical momentum strategy bets on. When it is low, momentum has a stabilizing effect; when it has been high, the returns of momentum stocks have subsequently reversed sharply.

Source: Lou and Polk (2022)

More: Momentum crashes: why momentum collapses rarely but violently, and what volatility scaling and crowding measures show

A payment with which a seller who delivers a share only after the dividend date, or a borrower, replaces the missed dividend. In cum-ex trades, no withholding tax was deducted from it, yet it was certified all the same.

Source: Spengel (2020)

Every investment idea has to show that it improves the total portfolio, rather than filling a fixed budget for its asset class. Formally, an investment is worthwhile if its Sharpe ratio is greater than its correlation with the portfolio times the portfolio's Sharpe ratio.

Example: Portfolio with a Sharpe ratio of 0.40: an investment with a correlation of 0.5 must exceed 0.5 × 0.40 = 0.20.

Source: Filbeck and Bok (2025)

More: Strategic and tactical asset allocation and the total portfolio approach

Grouping of all mandates or funds with the same strategy under the GIPS standards. All actual, fee-paying, discretionary mandates must be included in at least one composite, so that a manager cannot show only its best accounts.

Source: CFA Institute (2019)

More: Portfolio reporting: how to report return, risk, attribution and costs properly

Income itself earns further income. That is why wealth grows exponentially: at 7% a year, it doubles in just over ten years.

More: CAGR: how to calculate the average annual return correctly

Too large a share in a single position, sector or region. Often builds up unnoticed through overlaps between several ETFs.

More: Look-through: what is really inside your ETFs

The average of the worst drawdowns beyond a threshold, analogous to CVaR for returns. It can be used as a constraint in optimizations.

Source: Chekhlov et al. (2005)

More: Maximum drawdown: the largest loss from a peak

In a stress test, the value you expect on average for the factors that are not shocked when the shocked factors take exactly their shock values: E[f₂ | f₁ = s] = Σ₂₁ Σ₁₁⁻¹ s for jointly normally distributed factors with zero mean. This keeps a scenario with few inputs internally consistent.

Example: Equities fluctuate by 4.5% a month and the yield on ten-year bonds by 0.20 percentage points, with a correlation of 0.3. An equity move of −30% is consistent, on average, with a yield change of 0.3 × 0.20 / 4.5 × (−30) = −0.40 percentage points.

Source: Kupiec (1998); Breuer et al. (2009)

More: Scenario analysis and sensitivity analysis: stress testing equity, interest rate, credit and currency risk

Average loss in the worst cases beyond the value at risk, for example in the worst 5% of months.

More: Value at risk and conditional VaR: how much you could lose in a bad case

A range that contains the true value with a chosen level of confidence (often 95%). For returns and Sharpe ratios these ranges are surprisingly wide, even with decades of data.

Information that supports your own opinion gets more attention than information that contradicts it. In investment decisions, this leads to one-sided research.

A strategy that always returns to fixed weights: it sells after rises and buys after falls. It gains in volatile sideways markets and loses against buy-and-hold in long trends.

Source: Perold and Sharpe (1988)

More: Rebalancing: getting your portfolio back on course

Upward-sloping futures curve: later contracts cost more than near-term ones. For the VIX, the normal state in calm markets.

Example: M1 at 19.6 and M2 at 20.2 give 3.1% contango.

More: VIX: how to read the stock market's fear gauge

The growth rate with continuous compounding: g = log(1 + CAGR), i.e. the mean log return per year. Unlike CAGR values, continuous growth rates can be weighted and added up over periods; that is why return decompositions like to use them.

Example: CAGR 8%: log(1.08) = 7.70% continuously compounded; two years give 2 × 7.70% = 15.39% = log(1.08²).

More: CAGR: how to calculate the average annual return correctly

Buying when most people are selling, and selling when most are buying. Behind it lies the assumption that exaggerated sentiment pushes prices away from value. John Templeton bought at the point of maximum pessimism; Howard Marks describes acting against the cycle. The difficulty is that a trend often lasts longer than you expect.

Source: Templeton and Phillips (2008); Marks (2011)

More: Legendary investors: the investment styles of the most famous investors, from Graham to Simons

Technique that reduces the random error of a Monte Carlo simulation: you also simulate a closely related quantity whose exact value is known and correct the estimator by its deviation. For Asian options, the geometric average serves as the control variate.

Example: Arithmetic Asian call with 12 fixings and 40,000 paths: standard error 0.0297 without and 0.0012 with the control variate.

Source: Kemna and Vorst (1990); Glasserman (2003)

Methodology: Option pricer: how Portfolio Lab values options

States how many units of the underlying a warrant, turbo or certificate refers to. To compare prices with options, you convert the warrant's price to one unit of the underlying by dividing it by the ratio.

Example: Ratio of 0.1: ten warrants refer to one share; €0.53 per warrant corresponds to €5.30 per share.

A rebalancing rule that buys more after gains and sells after losses, e.g. CPPI. It comes out ahead in long trends and loses in sideways markets; a concave strategy such as constant mix behaves the other way round.

Source: Perold and Sharpe (1988)

More: CPPI: portfolio insurance with cushion, floor and multiplier

Curvature of the price-yield relationship of bonds: price gains when rates fall are larger than the losses when rates rise by the same amount.

More: Duration: how strongly bonds react to interest rates

Buying the reported positions of well-known investors or funds, for example from 13F filings. The copycat saves on research and fees, but buys with a delay, sees only part of the portfolio and does not find out when the role model sells. Studies have found partly positive results in the past.

Source: Frank et al. (2004); Martin and Puthenpurackal (2005)

More: Legendary investors: the investment styles of the most famous investors, from Graham to Simons

Inflation rate excluding the volatile prices of energy and food (in the euro area usually also excluding alcohol and tobacco). It shows the underlying price trend better than the headline rate.

Methodology: Macro dashboard and regime analysis: methodology

A split into a broad, low-cost core (e.g. a global ETF) and smaller satellite holdings for themes, factors or active ideas. The core determines the risk, the satellites the deviation.

Common classification of real estate and infrastructure funds by risk. Core: existing, well-let or regulated assets with little debt, returns mainly from current income. Core-plus: somewhat more risk. Value-add: value creation through refurbishment, letting or expansion. Opportunistic: new development, special situations, high leverage. The boundaries are not standardized.

More: Infrastructure investing: equity and debt, revenue models, valuation and research

Adjusts the quantile of the normal distribution for the skewness and kurtosis of returns. This makes value at risk more realistic in the presence of negative skewness and fat tails (modified VaR).

Source: Cornish and Fisher (1938)

More: Value at risk and conditional VaR: how much you could lose in a bad case

Measure from −1 to +1 of how closely two investments move together. The lower it is, the stronger the diversification effect.

More: Correlation and diversification: why mixing assets reduces risk

The change in correlations during stress phases compared with calm periods, usually an increase, so that diversification protects less than expected. Stress tests using correlations from calm years then turn out too mild; Kim and Finger therefore estimate separate correlations for hectic days.

Source: Kim and Finger (2000); Longin and Solnik (2001)

More: Historical stress testing: how to apply past crises to your portfolio today

With a fixed contribution, you buy more units when prices are low and fewer when they are high. This lowers the average price per unit below the average market price, but it is no return advantage over a lump-sum investment.

Costs minus income from holding an underlying, expressed as a rate b: for stocks, the interest rate minus the dividend yield; for futures, zero; for currencies, the domestic minus the foreign interest rate. With b, Black-Scholes, Black 76 and Garman-Kohlhagen can be written as a single formula.

Source: Haug (2007)

Methodology: Option pricer: how Portfolio Lab values options

Where a group's net position lies between its minimum (0) and maximum (100) over recent years. Values close to 100 indicate positioning that has rarely been this one-sided.

Example: Net 120,000 contracts, range −40,000 to 160,000: (120,000 + 40,000) / 200,000 × 100 = 80.

Methodology: Sentiment: methodology for the fear and greed index, put/call ratio and COT

A weekly report by the US futures market regulator on the positions of market participants, broken down into groups such as dealers, asset managers, hedge funds and hedgers. The reference date is Tuesday; publication follows on Friday.

Source: Wang (2003)

Methodology: Sentiment: methodology for the fear and greed index, put/call ratio and COT

Risk that the counterparty to a derivative, a securities loan or a repo defaults while the transaction has a positive value for you. Collateral, netting and central clearing limit it; funds may only put a small part of their assets at risk with any single counterparty.

Source: DerivateV (2013); Gregory (2020)

More: Counterparty and issuer risk: CVA, ETCs, certificates and swaps

Classification of a country by an index provider as a developed, emerging or frontier market, based on criteria including market size and access for foreign investors. The providers judge differently: South Korea is a developed market at FTSE Russell, but an emerging market at MSCI.

Source: FTSE Russell Country Classification (2026); MSCI Market Classification (2026)

More: Index providers and valuation points: why the same index is calculated differently

A bond's annual interest as a percentage of its face value. A higher coupon lowers the duration.

More: Duration: how strongly bonds react to interest rates

Joint variation of two returns: the correlation times both volatilities. A building block of portfolio volatility and beta.

More: Correlation and diversification: why mixing assets reduces risk

A table of all variances (diagonal) and covariances (other cells) of several assets. Together with the weights it gives the portfolio variance; optimizers are very sensitive to its estimation errors.

More: Covariance estimation: why optimizers need shrinkage

Contractual condition in a loan: metrics such as debt to EBITDA must not exceed a limit (financial covenant), or certain actions such as taking on new debt or making distributions are prohibited (negative covenant). A breach allows the lender to renegotiate; loans with few conditions are called covenant-lite.

Source: Block et al. (2024)

More: Private credit and public credit compared: returns, risks and what the research shows

Holding stocks and selling calls on them. The premiums provide ongoing income, but strong price gains are capped; losses largely remain.

More: Option pricing: where fair option prices come from

The forward rate of a currency deviates from today's spot rate by exactly the interest rate differential; otherwise there would be risk-free profits. That is why a hedge costs or earns roughly this differential. It does not hold exactly: Du et al. (2018) find persistent deviations for major currencies.

Source: Du et al. (2018)

More: Carry trade: earning interest with currencies and bonds · Methodology: Carry backtest: methodology for FX and bond carry

Constant Proportion Portfolio Insurance: a fixed multiple (the multiplier) of the cushion above a lower limit, the floor, is held in equities; the rest is held in safe assets. The rule buys after gains and sells after losses.

Source: Black and Jones (1987); Black and Perold (1992)

More: CPPI: portfolio insurance with cushion, floor and multiplier · Methodology: CPPI backtest: methodology

The issue and redemption of ETF units in large blocks by authorized participants in exchange for the underlying securities or cash. This mechanism keeps the market price close to the net asset value.

Source: Ben-David et al. (2017)

More: ETF basics: costs, replication and distributions

Sensitivity of a bond fund to the excess return of corporate or high-yield bonds over government bonds. Additional credit beta relative to the benchmark brings excess return in calm years that looks like skill, and losses in crises.

Example: Additional credit beta of 0.2 and a 4% excess return on high yield: 0.2 × 4% = 0.80% excess return; with −20% in a crisis, −4.00%.

Source: Brooks et al. (2020)

More: Active or passive in bonds and commodities: why the rules differ from equities

A credit derivative in which the protection buyer pays a regular premium and the protection seller covers the loss if the debtor suffers a credit event: nominal value minus recovery rate. The premium is regarded as the market price of default risk.

Source: Hull (2021)

More: Basis trades: positive and negative basis in bonds, CDS and futures

Excess return of corporate bonds over government bonds of the same maturity as compensation for default risk. Used as the factor DEF in factor models for bonds.

Source: Fama and French (1993)

Methodology: Factor regression, factor allocation and factor statistics: methodology

Assessment of an issuer's creditworthiness by a rating agency, from AAA (best) to D (defaulted). Ratings often react sluggishly to changes.

Yield premium of a corporate or riskier government bond over a safe government bond of the same maturity. It widens in crises and reflects default risk and liquidity.

Source: Fama and French (1993)

Methodology: Risk factors in the look-through: methodology

Deduction from the value of derivative transactions for the counterparty's default risk: loss given default times the sum, over all periods, of expected exposure, probability of default and discount factor. Since Basel III, banks also hold capital against fluctuations in CVA.

Source: Hull and White (2012); Basel Committee (2011)

More: Counterparty and issuer risk: CVA, ETCs, certificates and swaps

An industry term for a strategy's gains precisely during crises in other assets, above all those of trend followers in prolonged downturns. Not guaranteed protection: sudden crashes after long rallies often catch trend followers positioned long.

Source: Fung and Hsieh (2001); Dao et al. (2017)

More: CTAs and managed futures: industry, position sizing, costs and crisis protection

In the LPPLS model, the point in time at which a bubble ends. It is the most likely crash date, not a certain one: the crash can come earlier, and the bubble can also fade out without a crash. Estimates of tc are highly uncertain.

Source: Johansen, Ledoit and Sornette (2000)

More: Speculative bubbles: what they are and how the LPPLS model detects them · Methodology: Bubble indicator (LPPLS): methodology

Hedging with a related but not identical instrument because none exists for the risk itself or it is too illiquid. How well it works is shown by the square of the correlation between portfolio and hedge.

Example: With a correlation of 0.9, the cross hedge eliminates 81% of the variance; at 20% volatility, 8.72% remains.

Source: Hull (2021)

More: Short selling, hedge funds and hedging: types and how they work

A trade between two funds or mandates of the same manager without going through the market. It saves the spread and market impact but is a conflict of interest; US Rule 17a-7 and the KAMaRisk (BaFin's risk management requirements for fund managers) require an independent, fair market price.

Source: SEC Rule 17a-7 (2005); KAMaRisk (2017); Eisele et al. (2020)

More: Market making and bond trading: spread, inventory, axes, RFQ, cross trades and matrix pricing

The data are split several times into estimation and validation parts; each piece serves once as the validation set. With time series the parts must stay separated in time, so that no future information leaks into the estimate.

Source: López de Prado (2018)

Overcrowded trades: many investors hold the same positions, e.g. the same factor portfolios. If one of them has to sell, it pushes down the prices of everyone else's positions and can trigger a chain of forced sales. The risk then lies less in the strategy itself than in who else is running it.

Source: Lou and Polk (2022); Khandani and Lo (2011)

More: Momentum crashes: why momentum collapses rarely but violently, and what volatility scaling and crowding measures show

The safekeeping, administration and securing of crypto-assets or private cryptographic keys for others. In Germany this has been a financial service requiring a license under the KWG (Banking Act) since 2020. Under MiCA the comparable service is called “providing custody and administration of crypto-assets on behalf of clients” and requires authorization.

Source: BaFin, crypto custody business (2020); BaFin, MiCAR guidance notice (2025)

More: Crypto in institutional portfolios: access, custody, regulation and risk budget

An electronic security under the Electronic Securities Act (eWpG, 2021) that is issued by entry in a crypto securities register instead of by a physical certificate. The register is a tamper-proof recording system, usually a blockchain. Whoever keeps the register needs a license from BaFin under the KWG.

Source: BaFin, crypto securities (2023)

More: Digital assets: tokenization, stablecoins, crypto securities and the digital euro

A digital representation of a value or a right that is transferred and stored using distributed ledger technology such as a blockchain. MiCA distinguishes e-money tokens, asset-referenced tokens and other crypto-assets such as bitcoin or ether; tokenized financial instruments are not covered.

Source: BaFin, MiCAR (2024)

More: Crypto in institutional portfolios: access, custody, regulation and risk budget

Change in value of a bond or bond portfolio in euros when the credit spread rises by one basis point. Approximately market value × spread duration × 0.0001; the counterpart of DV01 for the level of interest rates.

Example: €150,000 of corporate bonds with a spread duration of 5: 150,000 × 5 × 0.0001 = €75 per basis point.

More: Scenario analysis and sensitivity analysis: stress testing equity, interest rate, credit and currency risk

Commodity Trading Advisor: under US law, a person or firm that advises on futures trading or manages accounts for a fee; registered with the NFA, to which the regulator, the CFTC, has delegated registration. Most CTAs follow trends systematically across many markets.

Source: NFA (2026)

More: CTAs and managed futures: industry, position sizing, costs and crisis protection

Transferring shares from foreign owners, shortly before the dividend date, to domestic investors who can fully credit the withholding tax (Kapitalertragsteuer), and transferring them back afterward. Since 2016, Section 36a EStG (Income Tax Act) has limited the credit for short holding periods without the holder bearing any price risk.

Source: § 36a EStG (2016); Spengel (2020)

Share trades around the dividend date in which a short sale with delivery after that date produced two tax certificates for withholding tax (Kapitalertragsteuer) that had been withheld only once. In 2021 the Federal Court of Justice (Bundesgerichtshof) confirmed that claiming such tax is tax evasion.

Source: BGH (2021); BFH (2022)

The sum of the abnormal returns over the days of an event window. Averaged over many events (CAAR), it shows how strongly and how quickly prices react to a particular type of news.

Example: Abnormal returns of +0.4%, +2.1% and −0.3% on three days give a CAR of +2.2%.

Source: MacKinlay (1997)

More: Event studies: how to measure and test price reactions to events

The total change in value over a period, without converting it to an annual figure. 100% in ten years sounds like a lot, but corresponds to just over 7% a year.

More: CAGR: how to calculate the average annual return correctly

The part of an international portfolio's active return that is attributable to exchange rates. Without a separate effect, it remains hidden in allocation or selection; it is split into the interest rate differential and the unexpected exchange rate movement.

Source: Ankrim and Hensel (1994)

More: Performance attribution: Brinson decomposition, factors and linking over time

Contract to exchange a currency on a later date at a rate fixed today, the forward rate. Under covered interest parity, the forward rate is the spot rate adjusted for the interest rate differential; currency hedges and carry trades usually run through such contracts.

Source: Hull (2021)

More: Carry trade: earning interest with currencies and bonds · Methodology: Carry backtest: methodology for FX and bond carry

Eliminating exchange rate fluctuations, usually through currency forwards that are renewed every month. Common for bonds in foreign currencies, disputed for equities.

Source: Campbell et al. (2010); Perold and Schulman (1988)

More: Currency risk: how exchange rates change your return

Fluctuation caused by exchange rates: if the euro rises against the dollar, US equities lose value in euro terms. What matters is the currency of the securities, not that of the fund.

A share class that hedges the exchange rate risk against the share class currency, e.g. a global ETF in “EUR Hedged”. It costs or earns roughly the interest rate differential and usually comes with slightly higher fees.

More: Currency risk: how exchange rates change your return

The distance between the portfolio value and the floor, in euros or as a percentage of the value. In CPPI, the cushion times the multiplier determines how much is held in equities.

More: CPPI: portfolio insurance with cushion, floor and multiplier · Methodology: CPPI backtest: methodology

Companies whose profits fluctuate strongly with the business cycle, e.g. industrials, materials or carmakers. They rise more than average in an upswing and fall more sharply in recessions.

Leveraged ETFs and factor certificates restore their leverage every trading day: after gains they buy more, after losses they sell. This keeps leverage constant, but makes the return path-dependent over longer periods. The leverage per security in the Portfolio Lab backtest works the same way, adjusted every day using daily prices.

Example: Index +10%, then −10% (−1% in total): 2x leverage reset daily −4%, in a margin account without adjustment −2%.

Source: Cheng and Madhavan (2009); Avellaneda and Zhang (2010)

More: Leverage in a portfolio: return, risk, costs and margin calls · Methodology: Backtest methodology: data, process, rebalancing and costs

Repeatedly analyzing the same historical data until patterns emerge. The effects found are then partly due to chance and weaken out of sample.

Source: McLean and Pontiff (2016)

More: Backtest overfitting: when the past looks too good

Rule for how days and the year are counted in interest calculations: act/act (actual days divided by the actual days of the coupon period, common for government bonds), 30/360 (every month 30 days, the year 360) or act/360 (actual days divided by 360, common in the money market).

Source: Tuckman and Serrat (2012)

More: Bond math: calculating price, yield, duration, convexity and spreads

Time by which orders for fund units must reach the fund company in order to be settled at the next net asset value. Because this value is only determined afterward, nobody knows the settlement price when placing the order.

More: Index providers and valuation points: why the same index is calculated differently

Debt service coverage ratio: cash flow available for debt service (CFADS) divided by the period's interest and principal payments. Values above 1 mean debt service is covered. Lenders size the loan to a minimum DSCR and tie covenants to thresholds; the path of the DSCR is the basis of structural credit risk models for project finance.

Example: CFADS of €13 million and a minimum DSCR of 1.30 allow €10 million of debt service a year; if CFADS falls by more than 23.08%, it is no longer covered.

Source: Blanc-Brude and Hasan (2016); Blanc-Brude et al. (2018)

More: Infrastructure investing: equity and debt, revenue models, valuation and research

The Vorabpauschale for a year is deemed to have been received on the first working day of the following calendar year. The bank then collects the tax from the settlement account, unless an exemption order covers it.

Source: InvStG (2016)

Companies with stable demand even in downturns, e.g. utilities, consumer staples or healthcare. They usually have a low beta.

Retirement contributions remain tax-free or deductible during the saving phase; in return, the benefits are taxed in retirement at the personal tax rate that applies then. This is how the state pension, company pensions, the Basisrente and the Altersvorsorgedepot work; the advantage depends on the difference between your marginal tax rate today and in retirement.

Source: EStG § 22 (2009)

A Sharpe ratio corrected for the number of strategies tried, the length of the series, and the skewness and kurtosis of the returns. It indicates how likely it is that the observed Sharpe ratio reflects genuine skill rather than luck.

Source: Bailey and López de Prado (2014)

More: Backtest overfitting: when the past looks too good

Reducing leverage through sales or repayment. When many leveraged investors sell at the same time, e.g. after margin calls, they push prices down and trigger further sales. The result is a liquidity spiral of the kind seen in financial crises.

Source: Geanakoplos (2010); Brunnermeier and Pedersen (2009)

More: Leverage in a portfolio: return, risk, costs and margin calls

How much the option price changes when the underlying rises by one unit. A call with a delta of 0.5 gains about 50 cents when the stock rises by €1.

More: Option pricing: where fair option prices come from · Methodology: Option pricer: how Portfolio Lab values options

Hedging an option position with the underlying in proportion to the delta, so that small price moves barely change the result. Because delta changes with the price (gamma), the hedge has to be adjusted continuously.

Example: 1,000 calls with a delta of 0.57 are hedged by selling 570 shares short.

More: Short selling, hedge funds and hedging: types and how they work · Methodology: Option pricer: how Portfolio Lab values options

Statutory protection of bank balances in a bank failure: in the EU, up to €100,000 per depositor and bank, and temporarily higher for certain credits such as the proceeds of a property sale. Securities such as ETFs are not deposits; they are protected as segregated assets.

Source: EinSiG § 8 (2015); Directive (EU) 2026/804 (2026)

A high-income country with a developed capital market, such as the US, Japan or Germany. Indices such as the MSCI World contain only developed markets.

More: World portfolio: the whole world in one or two ETFs

A test of whether two forecasts are equally accurate. It relates the mean difference between their losses, e.g. the squared errors, to its standard error and allows any loss function as well as autocorrelated, non-normally distributed errors.

Source: Diebold and Mariano (1995)

More: Return forecasting models: ARIMA, GARCH, LSTM and machine learning

The planned digital central bank money of the Eurosystem for payments, as a complement to cash. The regulation is in the legislative process (as of October 2026); the ECB wants to be ready for a possible first issuance in 2029 if the law is adopted in 2026.

Source: ECB (2025); European Parliament (2026)

More: Digital assets: tokenization, stablecoins, crypto securities and the digital euro

Option with a fixed payout if the price at maturity is above (call) or below (put) the strike, and nothing otherwise. Its price is the discounted amount times the risk-neutral probability of ending in the money.

Methodology: Option pricer: how Portfolio Lab values options

Decline in the percentage stake of existing shareholders when new shares are issued (in financing rounds, options or conversions). It costs nothing as long as the value per share at least stays the same; in a down round, by contrast, the value falls too.

Example: Someone holding 7 of 10 million shares who accepts 4 million new shares falls from 70% to 7 / 14 = 50%.

More: Venture capital: funding rounds, valuation, the power law and what research knows about returns

The largest strategy in private credit: a fund lends directly to a company, often to finance a takeover by a private equity firm. Often structured as a unitranche, i.e. a single loan instead of several senior and junior tranches.

Source: Block et al. (2024)

More: Private credit and public credit compared: returns, risks and what the research shows

Transactions by persons discharging managerial responsibilities at an issuer, such as members of the management and supervisory boards, and by persons closely associated with them, in the issuer's shares, debt instruments or derivatives. Under Art. 19 MAR (Market Abuse Regulation) they must be reported no later than three business days after the transaction; in Germany a threshold of €50,000 per calendar year has applied since January 1, 2026.

Source: MAR (2014); BaFin, managers' transactions (2025)

More: Insider trading: what is prohibited, what is allowed and what insider purchases reveal

A certificate that is bought below the price of the underlying and pays out the price at maturity, but no more than the cap. Decomposed: the underlying without dividends minus a call struck at the cap. The discount is made up of dividends and option premium.

Example: Share €100, cap €90, ask price €84: discount 16%, maximum return 90 / 84 − 1 = 7.14%.

Source: Wilkens et al. (2003); Baule et al. (2008)

Methodology: Option pricer: how Portfolio Lab values options

A valuation method that discounts a company's expected free cash flows to today at the cost of capital (WACC) and adds a terminal value for the period after the detailed forecast. Subtracting net financial debt leaves the value of the equity.

Source: Damodaran (2012)

More: Fundamental analysis: valuing a company like an investor

A pattern looks the same when the scale is stretched by certain factors λ, λ², …, but not by arbitrary factors. The physical basis of the log-periodic oscillations before a critical point such as a crash.

Source: Feigenbaum and Freund (1996); Johansen, Sornette and Ledoit (1999)

More: Speculative bubbles: what they are and how the LPPLS model detects them

Tendency to sell winners too early and hold on to losers too long, so as not to have to admit a loss. Usually unfavorable in terms of both tax and returns.

Pair selection following Gatev, Goetzmann and Rouwenhorst: prices are normalized to 1, and each security is matched with the partner that has the smallest sum of squared distances. A trade is opened when the distance exceeds two standard deviations of the formation period.

Source: Gatev et al. (2006)

More: Pairs trading and statistical arbitrage: idea, methods, research · Methodology: Long/short and statistical arbitrage: methodology

A shared register that many computers maintain together and reconcile through a consensus mechanism. The best-known design is the blockchain, in which transactions are recorded in linked blocks. Public networks (permissionless) are open to everyone, private ones (permissioned) only to approved participants.

More: Digital assets: tokenization, stablecoins, crypto securities and the digital euro

A fund that pays dividends and interest out to investors, usually quarterly or annually. The opposite is accumulating.

More: ETF basics: costs, replication and distributions

Spreading money across investments that do not move in lockstep. It pushes the portfolio's volatility below the average of the individual volatilities.

More: Correlation and diversification: why mixing assets reduces risk

A proposal by Ayres and Nalebuff: when you are young, you have little capital but a lot of future income. Using leverage in your early years and holding fewer equities later in life spreads equity risk more evenly over your working life than a fixed allocation applied to a portfolio that starts out small.

Source: Ayres and Nalebuff (2008); Ayres and Nalebuff (2010)

More: Leverage in a portfolio: return, risk, costs and margin calls

The weighted sum of the individual volatilities divided by the volatility of the portfolio. 1 means no diversification effect; the higher it is, the more the fluctuations offset each other.

Source: Choueifaty and Coignard (2008)

More: Risk parity: equal risk contributions instead of equal weights

Payment from a derivative that refers to the dividend of a US stock and, under Section 871(m), can be subject to US withholding tax like a dividend. A qualified index, by contrast, counts as a security in its own right. This is where the tax advantage of swap ETFs on broad US indices comes from.

Source: US Section 871(m) Rules (2015); Mellor (2022)

More: Index replication: full replication, optimized sampling and swaps

Dividends paid over the last twelve months divided by the price. It is only one part of the total return; since the 1980s, share buybacks have increasingly replaced dividends.

More: Shiller P/E (CAPE): how expensive is the stock market?

Average excess return of an equally weighted basket of all foreign currencies against the US dollar; it captures the common movement of currencies against the dollar. Alongside it stands the slope factor HML-FX (high- minus low-interest currencies), which according to Lustig et al. (2011) explains most of the differences in returns.

Source: Lustig et al. (2011)

More: Carry trade: earning interest with currencies and bonds · Methodology: Carry backtest: methodology for FX and bond carry

Treaty between two countries that governs which of them may tax income. For dividends, it usually caps the withholding tax, often at 15%, which can then be credited against German tax.

The share of a benchmark's losses that a portfolio takes part in during the benchmark's negative periods. Below 100 means it lost less than the index. A good ratio relative to upside capture matters more than either value on its own.

Source: Bacon (2008)

More: Beta and alpha: how closely a fund moves with the market

Volatility on the downside only: the square root of the average squared shortfall below a minimum return. The basis of the Sortino ratio.

More: Sortino ratio and Calmar ratio: measuring downside risk

Distributed to paid-in: distributions divided by paid-in capital. Shows how much a fund has already returned in cash and, unlike TVPI, does not depend on valuations. Early distributions funded by NAV financing can, however, pull it forward.

Example: Paid in 95, distributed 35: DPI = 35 / 95 = 0.37.

Source: ILPA (2024)

More: Measuring private markets: J-curve, cash flows, smoothing and public proxies

Distance from the keel to the waterline. The more cargo, the lower a ship sits in the water, which is why the draft is used to estimate whether it is loaded. In AIS, the crew enters the draft by hand, often late; errors are common.

Source: IMO (2015); Cerdeiro et al. (2020)

More: Ship tracking data and satellite images: what they reveal about commodities · Methodology: Ships at chokepoints (beta): methodology

Decline from the previous peak to the current value, in percent. The deepest point in the period is the maximum drawdown.

More: Maximum drawdown: the largest loss from a peak

The time from a peak until the value returns to that level. For investors it is often harder to bear than the depth: after 2000, broad equity indices in euros needed many years to regain their old highs.

More: Maximum drawdown: the largest loss from a peak

Capital committed to private markets funds but not yet called (for one fund or the whole market). A lot of dry powder means a lot of money that has to be invested; according to Kaplan and Strömberg (2009), high inflows into private equity go hand in hand with lower subsequent returns.

Source: Kaplan and Strömberg (2009)

More: Measuring private markets: J-curve, cash flows, smoothing and public proxies

Rule by Gary Antonacci: the asset with the best 12-month return is held, but only if it has also beaten the money market; otherwise bonds or the money market.

More: Tactical allocation: momentum, dual momentum and trend following

Standardized set of questions (DDQ) that investors use to vet a manager: organization, ownership, processes, risk management, valuation, compliance, service providers, costs. Common templates are the ILPA DDQ for private markets and the AIMA model questionnaire.

Source: ILPA DDQ (2021); AIMA (2025)

More: RFP and mandate awards: how institutional investors select asset managers

An explanatory variable in a regression that takes only the values 0 or 1, e.g. 1 for periods in the winter half-year. Its coefficient measures the average difference between the two groups; its t-test is equivalent to the two-sample t-test with pooled variance.

Example: r = μ + α × S: with S = 1 in winter, α is the excess return of winter over summer.

More: Stock market seasonality: Sell in May, the January effect and how to test calendar effects

How strongly a bond's price reacts to changes in interest rates. A modified duration of 8 means: about −8% for a one percentage point rise in rates.

Example: A 10-year bond with a 3% coupon at a 3% yield has a modified duration of 8.53.

More: Duration: how strongly bonds react to interest rates

Position of bought and sold bonds of different maturities with the same duration on both sides. A parallel shift of the yield curve then roughly cancels out and what counts is the steepness: long the short end and short the long end is a steepener, the reverse a flattener.

Example: 5 years of duration per side: two-year par bond at 3% with semi-annual coupon, duration 1.93 → weight 259%; ten-year bond at 4% with duration 8.18 → 61%.

More: Carry trade: earning interest with currencies and bonds · Methodology: Carry backtest: methodology for FX and bond carry

A crypto-asset under MiCA that aims to maintain a stable value by referencing a single official currency (EMT). Only credit institutions and e-money institutions may issue it; holders can redeem it at par at any time, and paying interest is prohibited. At least 30% of the funds received are held in segregated accounts with credit institutions.

Example: €500 million in circulation: at least 0.3 × 500 = €150 million as deposits with credit institutions, the remainder of up to €350 million in secure, highly liquid assets in the same currency.

Source: MiCA (2023); BaFin, MiCAR (2024)

More: Digital assets: tokenization, stablecoins, crypto securities and the digital euro

Inverse of the P/E: earnings per share divided by the price. A P/E of 25 corresponds to a 4% earnings yield; comparing it with bond yields is common but imprecise, because earnings grow in real terms.

More: Shiller P/E (CAPE): how expensive is the stock market?

A durable competitive advantage that keeps competitors away and protects high returns on capital for years, e.g. network effects, switching costs, cost advantages of scale, or protected brands, patents and licenses.

More: Fundamental analysis: valuing a company like an investor

Electronic Data Gathering, Analysis, and Retrieval: the SEC's electronic filing and retrieval system. Company annual and quarterly reports, insider filings and public 13F filings all go through it, and all of them can be searched free of charge. For the holdings of well-known investors, EDGAR is the primary source.

Source: SEC, Form 13F (2026)

More: Legendary investors: the investment styles of the most famous investors, from Graham to Simons

A measure of how many uncorrelated, equally sized risks a portfolio takes: the exponential of the entropy of the variance shares that uncorrelated building blocks (principal components or minimum-torsion factors) contribute to portfolio risk. 1 means a single risk, N means N equally sized ones.

Example: Variance shares of 50% and 50%: exp(−2 × 0.5 × ln 0.5) = 2 bets; shares of 90% and 10%: 1.38 bets.

Source: Meucci (2009)

More: Beyond Markowitz: estimation error, noise and true diversification · Methodology: Dimensions methodology: how Portfolio Lab counts independent risks

1 divided by the sum of the squared weights: how many equally sized positions would give the same diversification?

Example: Weights of 40, 30, 20 and 10% give 3.33.

More: Look-through: what is really inside your ETFs

The number of truly independent variants tried in a strategy search. Similar variants, such as neighboring parameters, are highly correlated and together count for less than their number; López de Prado and Lewis (2019) estimate the effective number with a clustering method. It is the N that goes into the deflated Sharpe ratio.

Source: López de Prado and Lewis (2019); Bailey and López de Prado (2014)

More: Backtest overfitting: when the past looks too good

All portfolios that offer the highest expected return for their level of risk (Markowitz, 1952).

More: Efficient frontier: Markowitz portfolio optimization

The thesis that prices reflect all available information, so that this information cannot be used to earn systematic excess returns. Fama distinguished a weak, a semi-strong and a strong form.

Source: Fama (1970); Malkiel (2003)

More: The efficient market hypothesis: why it is so hard to beat the market

In principal component analysis, the variance explained by a principal component. The share of the largest eigenvalue in the total shows how strongly a single factor drives all assets together.

Source: Pearson (1901)

Methodology: Asset analysis: methodology from correlation to cointegration

European Long-Term Investment Fund: an EU fund type for unlisted companies, loans, infrastructure and real estate. Since ELTIF 2.0 (from January 10, 2024), at least 55% must be held in eligible assets; retail investors may buy after a suitability assessment and without a statutory minimum investment.

Source: Regulation (EU) 2023/606 (2023)

Expectation-maximization: a method for maximum likelihood estimation with missing or hidden data. It alternates between the E-step, which uses the current parameters to estimate the hidden variables as probabilities, and the M-step, which re-estimates the parameters with these weights. Typical applications are mixture distributions such as the Gaussian mixture model, and hidden Markov models.

Source: Dempster et al. (1977)

More: Regime models: hidden Markov, Markov switching and more · Methodology: Regime methodology: how the hidden Markov model works

A middle-income country whose capital market is not yet fully developed, e.g. China, India or Brazil. Higher volatility, with its own political and currency risks.

More: World portfolio: the whole world in one or two ETFs

Bond issued by an emerging market country, either in hard currency (usually US dollars) or in local currency. With local currency, exchange rate risk comes on top of credit quality.

Benefit that owning a real asset provides in itself: pleasure in a painting, the joy of driving, prestige. It replaces part of the financial return: according to Mandel (2009), this is why the financial returns of art are low; Dimson et al. (2015) find a growing non-financial benefit in mature fine wines.

Source: Mandel (2009); Dimson et al. (2015)

More: Collectibles as an investment: what art, wine, watches and classic cars really return

Shares of the company you work for, e.g. from employee share schemes. Income and wealth then depend on the same risk; according to studies, the lack of diversification costs a large part of the market value.

Source: Benartzi (2001); Meulbroek (2005)

More: Your whole wealth: total wealth from portfolio, home, human capital and car

Investment approach of large university endowments, shaped by David Swensen at Yale: broad diversification across many asset classes, few bonds and a high share of illiquid assets such as private equity, real estate and hedge funds, to profit from illiquidity premiums and good managers. Requires a very long investment horizon.

Source: Swensen (2000)

More: Legendary investors: the investment styles of the most famous investors, from Graham to Simons

A two-step test for cointegration: first a regression estimates the relationship between two series, then a unit root test checks whether the residuals are stationary. Because the relationship is estimated, stricter critical values apply; MacKinnon's formulas provide the p-values.

Source: Engle and Granger (1987); MacKinnon (1994)

More: Pairs trading and statistical arbitrage: idea, methods, research · Methodology: Long/short and statistical arbitrage: methodology

Part of the gross salary goes into a company pension scheme instead of into your account. Up to 8% of the contribution assessment ceiling of the pension insurance, this is tax-free, and up to 4% also free of social security contributions; the employer must add 15% to the extent that it saves social security contributions. In retirement, the benefits are fully taxable and usually subject to contributions.

Example: 2026: 8% × €101,400 = €8,112 tax-free, 4% × €101,400 = €4,056 also free of social security contributions.

Source: BetrAVG § 1a (1974); EStG § 3 No. 63 (2009); SvEV (2006)

Euro OverNight Index Average, the former reference rate for overnight money in the euro area until 2021. For long time series it is chained with the €STR.

Methodology: Metrics methodology: how Portfolio Lab measures return and risk

Every asset receives the same share (1/N). In out-of-sample studies this simple rule beats many optimization models because it picks up no estimation error.

Source: DeMiguel et al. (2009)

More: Risk parity: equal risk contributions instead of equal weights

An index in which every stock has the same weight. It tilts toward smaller companies and requires regular rebalancing back to equal weights.

Fund that, according to its investment terms, continuously invests more than 50% of its value in equities. For private investors, it qualifies for a 30% partial exemption.

Source: InvStG (2016)

The puzzle that the historical equity premium was far higher than standard economic models with reasonable risk aversion can explain. Proposed explanations range from loss aversion to rare disasters.

Source: Mehra and Prescott (1985); Benartzi and Thaler (1995)

More: Equity risk premium: how much more equities return and why it is a puzzle

The excess return of equities over safe assets as compensation for their risk. Historically, in many countries, it amounted to several percentage points a year over decades, with large differences between countries and periods.

Source: Dimson et al. (2002); Mehra and Prescott (1985)

More: Equity risk premium: how much more equities return and why it is a puzzle

A criticism of mean-variance optimization: it favors precisely those assets whose return has been overestimated and whose risk has been underestimated. As a result, the optimized weights are often extreme and unstable.

Source: Michaud (1989); Chopra and Ziemba (1993)

More: Efficient frontier: Markowitz portfolio optimization

If the bank does not know the acquisition costs, for example after a transfer to another broker without the cost data being passed on, it treats 30% of the sale proceeds as the gain. This can be corrected via the tax return.

Example: Sale for €10,000 with no known acquisition costs: 10,000 × 0.3 = €3,000 counts as gain.

Source: EStG (2009)

For private life annuities, for example from a private pension insurance converted into an annuity, only this flat-rate interest portion of the pension is taxed. It depends on the age at the start of the pension and is set out in a table in § 22 EStG.

Example: Pension starting at 65: 18%; at 67: 17% of the pension is taxable.

Source: EStG § 22 (2009)

Method of valuing income-producing property under the ImmoWertV (German Property Valuation Ordinance): the income value follows from the income achievable at market rates, operating costs, land value, remaining useful life and the property yield rate (Liegenschaftszinssatz). The property yield rate is a capitalization rate derived from purchase prices and net income; if it rises, the value falls.

Example: Greatly simplified as a perpetuity: €9,600 of net income gives a value of €300,000 at 3.2% and €259,459 at 3.7%.

Source: ImmoWertV (2021)

More: Real estate as an investment: rental property, REITs, open-end funds and private real estate

Short for environmental, social and governance, i.e. the environment, social issues and good corporate governance. An umbrella term for the criteria investors use to assess companies beyond their financial metrics.

More: ESG ETFs: index rules, ratings, returns and the limits of sustainable funds

A rating provider's score for how well a company meets ESG criteria. Ratings from different providers diverge widely, mainly because they measure the same categories differently and include different categories.

Source: Berg et al. (2022)

More: ESG ETFs: index rules, ratings, returns and the limits of sustainable funds

The gap between a quantity estimated from data, such as an expected return, and its true value. For average returns it shrinks only with the square root of the number of years, and it often drives the weights of an optimization more than the information does.

Source: Michaud (1989); Chopra and Ziemba (1993)

More: Michaud resampled optimization: more stable portfolio weights through simulation

Exchange-traded commodity: an exchange-traded debt security on a commodity, often physically backed, as with gold. It is not a segregated fund: there is issuer risk, which the collateral reduces.

Exchange-traded fund: an investment fund traded on a stock exchange that usually tracks an index. It can be bought and sold like a share during trading hours and is protected as segregated assets (Sondervermögen).

Source: Ben-David et al. (2017)

More: ETF basics: costs, replication and distributions

Exchange-traded note: an unsecured debt security whose repayment depends on an index. If the issuer defaults, the money is gone, even if the index has risen.

The mathematical reason why risk contributions add up exactly: volatility is homogeneous of degree one in the weights, so it equals the sum of each weight times its partial derivative.

Source: Roncalli (2013)

More: Risk contribution: breaking portfolio risk down into its parts

Enterprise value (market capitalization plus net financial debt) divided by earnings before interest, taxes, depreciation and amortization. Unlike the P/E ratio, this metric hardly depends on how a company is financed; however, it easily makes companies with heavy capital expenditure look cheaper than they are.

More: Fundamental analysis: valuing a company like an investor

A contract whose payout depends on whether an event occurs, usually 1 for yes and 0 for no. Economically, it is a digital option on an event. In the US the CFTC treats such contracts as swaps, which may only be offered on registered trading venues.

Source: CFTC (2022)

More: Prediction markets as bets on events: what they can and cannot do

A method that measures the price reaction to an event such as an earnings release, a takeover or an index inclusion: the normal return is estimated from an estimation window before the event, and the abnormal return is measured in the event window and tested across many events.

Source: MacKinlay (1997); Fama et al. (1969)

More: Event studies: how to measure and test price reactions to events

The first trading day on which a share trades without entitlement to the declared dividend. The price then falls by roughly the amount of the dividend; exactly how much also depends on investors' tax rates.

Source: Elton and Gruber (1970)

Annual, individual statement of all costs and charges actually incurred under MiFID II, as an amount in euros and as a percentage, with an illustration of how the costs reduce the return cumulatively.

Source: European Commission (2017)

More: Portfolio reporting: how to report return, risk, attribution and costs properly

Earnings yield of the equity market (1 / CAPE) minus the real yield on ten-year government bonds: the extra yield of equities over bonds.

More: Shiller P/E (CAPE): how expensive is the stock market?

A concept from stochastic portfolio theory: the amount by which a portfolio's growth rate exceeds the weighted average of its components' growth rates, per period log(Σ wᵢ × (1 + Rᵢ)) − Σ wᵢ × log(1 + Rᵢ). With positive weights it is never negative by Jensen's inequality and is approximately half the weighted dispersion of the log returns around their mean; with short sales or leverage at portfolio level this does not hold (Qian 2012).

Example: 60% equities at +10% and 40% bonds at −5%: log(1.04) − (0.6 × 9.531% + 0.4 × (−5.129%)) = 3.922% − 3.667% = 0.255%.

Source: Fernholz and Shay (1982); Fernholz (2002); Qian (2012)

In stochastic portfolio theory, the gap between a portfolio's growth rate and the weighted average of its positions' growth rates: ½ × (Σ wᵢσᵢ² − σ_p²). Never negative with positive weights, and the less the positions are correlated, the larger it is.

Example: Two uncorrelated assets, each with 20% volatility, 50/50: ½ × (0.04 − 0.02) = 0.01, i.e. 1 percentage point of growth rate a year.

Source: Fernholz (2002)

More: Beyond Markowitz: estimation error, noise and true diversification · Methodology: Dimensions methodology: how Portfolio Lab counts independent risks

The return above a reference point, usually the risk-free rate. Measured against an index, it is called active return.

More: Sharpe ratio: return per unit of risk

Robert Shiller's finding: share prices fluctuate far more than the dividends actually paid later would justify. An argument against strict market efficiency.

Source: Shiller (1980)

More: The efficient market hypothesis: why it is so hard to beat the market

Rules under which a fund does not buy certain companies, e.g. makers of controversial weapons, tobacco companies, coal companies or firms with serious violations of the UN Global Compact.

More: ESG ETFs: index rules, ratings, returns and the limits of sustainable funds

Assumption that long-term interest rates merely reflect the average of expected short-term rates, so that forward rates are exactly the expected rates. It does not hold in the data: forward rates contain term premiums that vary over time.

Source: Campbell and Shiller (1991); Fama (1984)

More: Market expectations: what the yield curve, inflation-linked bonds and options reveal about the future

Expected positive market value of the transactions with a counterparty at a future point in time, i.e. the amount that would be at stake on average in a default. Potential future exposure (PFE), by contrast, is a high quantile of this value, such as 95%.

Source: Gregory (2020)

More: Counterparty and issuer risk: CVA, ETCs, certificates and swaps

The Sharpe ratio that the best of N independent variants with no real edge can be expected to reach by chance alone: SR₀ = dispersion × ((1 − γ) × Φ⁻¹(1 − 1/N) + γ × Φ⁻¹(1 − 1/(N × e))), with the Euler-Mascheroni constant γ. It is the hurdle of the deflated Sharpe ratio and rises with the number and the dispersion of the variants.

Example: Ten variants, dispersion of their Sharpe ratios 0.3 p.a.: 0.3 × (0.4228 × 1.282 + 0.5772 × 1.789) = 0.47 p.a.

Source: Bailey and López de Prado (2014)

More: Deflated Sharpe ratio: how much skill is in a Sharpe ratio?

Probability-weighted average of all possible outcomes; in a simulation, the mean across all paths. For skewed distributions such as final wealth after many years, it is above the median: a few very good paths pull it up.

Example: Lognormal distribution with median 1 and σ = 0.5: expected value e^(0.5² / 2) = 1.13.

More: Volatility drag: why volatility costs you return · Methodology: Methodology of the free calculators: savings plan, withdrawal and leveraged ETF

Day on which an option or a future ends. VIX futures expire on a Wednesday 30 days before the third Friday of the following month, the expiry of the corresponding S&P 500 options.

Methodology: Volatility dashboard: methodology

A price that for a time grows faster than a random walk allows. Tests such as the PSY test by Phillips, Shi and Yu check for this with right-tailed unit root tests over changing windows and date the start and end of such phases.

Source: Phillips, Wu and Yu (2011); Phillips, Shi and Yu (2015)

More: Speculative bubbles: what they are and how the LPPLS model detects them

Weight of a segment according to its economic exposure rather than its market value: futures and swaps at their notional value, options at delta times the underlying, plus a financing line so that the weights add up to 100%.

Example: 50% equities plus equity futures worth 10% of assets: exposure weight of equities 50% + 10% = 60%, financing −10%.

More: Multi-asset attribution: weighting schemes, top-down and bottom-up, currencies and overlays

A certificate that is redeemed early with a coupon if the underlying is above a threshold on an observation date. Otherwise it continues; at maturity a barrier protects you, and below it you bear the price loss. Decomposed: a bond plus digital calls minus a down-and-in put.

The statistics of rare, very large events. It models only the tails of a distribution and uses them to estimate losses beyond anything ever observed in short data series.

A score from 0 to 9 devised by Piotroski, based on nine accounting signals covering profitability, leverage and liquidity, and operating efficiency. Among cheaply valued stocks, it separated winners from losers in the study.

Source: Piotroski (2000)

More: Fundamental analysis: valuing a company like an investor

Breaking down the excess return with a factor regression: each factor's contribution equals its loading times the factor return, plus alpha and a residual.

Example: A loading of 0.95 on the market with a market return of 8% above the risk-free rate: contribution 0.95 × 8 = 7.6 percentage points.

Source: Fama and French (1993)

More: Performance attribution: Brinson decomposition, factors and linking over time

Bank-issued debt security that multiplies the daily return of an underlying by a fixed factor and, like a leveraged ETF, resets its leverage every day. Unlike an ETF, it is not a segregated fund: if the issuer defaults, you risk losing your stake.

More: Leverage in a portfolio: return, risk, costs and margin calls

How strongly a fund responds to a factor such as size or value, measured as the coefficient from the factor regression.

More: Factor investing: understanding the Fama-French factors

Long-term excess return that a factor delivers on average, such as small versus large or cheap versus expensive stocks. It fluctuates strongly and can be negative for many years.

Source: Fama and French (1993); Ilmanen (2011)

More: Factor investing: understanding the Fama-French factors · Methodology: Factor regression, factor allocation and factor statistics: methodology

Regression of a fund's excess returns on factor returns. The slopes are the factor loadings; the intercept is the alpha that the factors do not explain.

Source: Fama and French (1993); Carhart (1997)

More: Factor investing: understanding the Fama-French factors · Methodology: Factor regression, factor allocation and factor statistics: methodology

The multitude of published factors (several hundred) that supposedly explain returns. Many are variants of one another or chance findings from multiple testing.

Source: Cochrane (2011); Harvey et al. (2016)

More: Backtest overfitting: when the past looks too good

Adjusting the prices of closed exchanges within a fund's price for what has happened since their close in markets that are still open. Prevents investors from trading at stale prices at the expense of the other unitholders.

Source: Zitzewitz (2003)

More: Index providers and valuation points: why the same index is calculated differently

Bond downgraded from investment grade to high-yield status. Because many investors may hold only limited amounts of high-yield bonds, forced selling follows; studies find weak prices at first and then a recovery over up to two years.

Source: Ellul et al. (2011); Ben Dor and Xu (2011)

More: Distressed debt: strategies, bankruptcy law, recovery rates and returns when investing in crises

Explains equity returns with market, size (SMB) and value (HML); the five-factor version adds profitability (RMW) and investment (CMA).

More: Factor investing: understanding the Fama-French factors

A two-step procedure: each month, a cross-sectional regression of returns on characteristics is run; the monthly coefficients are then averaged. This is how factor risk premia are estimated.

Source: Fama and MacBeth (1973)

Contribution-free co-insurance of spouses and children in a member's statutory health insurance. It requires that their own total income does not regularly exceed one seventh of the monthly reference value (Bezugsgröße); investment income counts after deduction of the saver's allowance.

Example: 2026: €3,955 / 7 = €565 a month.

Source: SGB V (1988); GKV-Spitzenverband (2022)

A way of presenting a simulation as a fan of percentiles, e.g. 10%, 50% and 90%. The fan shows the range of possible paths: not a forecast, but the uncertainty.

More: Monte Carlo simulation: how safe is your plan?

Rules of the DAX indices for changes between the semi-annual reviews: each quarter, a company enters the DAX if it ranks 33rd or better by free-float market capitalization, and must leave it if it ranks worse than 60th.

Source: DAX Methodology (2026)

More: The index effect: what happens to prices when stocks join or leave an index

Extreme returns occur far more often than the normal distribution predicts. A daily loss of five standard deviations would be almost impossible under a normal distribution, yet it happens again and again in equity markets.

Source: Mandelbrot (1963); Cont (2001)

More: Skewness and kurtosis: why market crashes are more frequent than the normal distribution says

A systematic distortion of betting odds: outsiders are priced too expensively, favorites too cheaply. Documented in horse racing and in prediction markets with a long time to resolution; it is mainly explained by misperceived small probabilities.

Source: Snowberg and Wolfers (2010); Page and Clemen (2013)

More: Prediction markets as bets on events: what they can and cannot do

A sentiment index from 0 (extreme fear) to 100 (extreme greed) built from several market series such as momentum, volatility and demand for safe havens. Portfolio Lab calculates its own index using an open method with six components.

Methodology: Sentiment: methodology for the fear and greed index, put/call ratio and COT

Exchange-traded futures on the US Federal Reserve's overnight rate (fed funds rate); the priced-in path of the key interest rate is read off their prices. Their excess returns were positive on average and varied with the business cycle. The prices therefore contain a risk premium.

Source: Piazzesi and Swanson (2004)

More: Market expectations: what the yield curve, inflation-linked bonds and options reveal about the future

Over the long run, a small fraction of stocks accounts for almost all of the market's wealth creation; the majority return less than money market instruments. Investors who diversify broadly are sure to hold these few winners.

Source: Bessembinder (2018)

More: Correlation and diversification: why mixing assets reduces risk

First in, first out: in a partial sale, the units bought first count as sold first for tax purposes.

The filtered probability of a regime uses only data up to the point in time in question, the smoothed probability all data up to the end of the sample. Only the filtered probability was known at the time. Using smoothed values in a backtest means looking into the future.

Source: Kim (1994)

More: Regime models: hidden Markov, Markov switching and more · Methodology: Regime methodology: how the hidden Markov model works

Combines many market series, such as yield spreads, volatility and funding costs, into a single number. Zero usually stands for average stress, positive values for more stress than usual.

Source: Kliesen et al. (2012); Monin (2019)

Methodology: Sentiment: methodology for the fear and greed index, put/call ratio and COT

A measure of unusual market phases developed by Kritzman and Li: the Mahalanobis distance of a period's returns from their mean. It rises when markets fluctuate strongly or move against their usual correlations, and so ranks historical crisis windows by their severity.

Source: Kritzman and Li (2010)

More: Historical stress testing: how to apply past crises to your portfolio today

Financial Independence, Retire Early: the goal of using a high savings rate to build wealth whose withdrawals cover your expenses, so that you no longer have to work long before the state retirement age. Variants include Lean, Fat, Barista, Coast and Slow FIRE.

Source: Dominguez and Robin (1992)

More: FIRE (Financial Independence, Retire Early): Lean, Fat, Coast and Barista FIRE

The level of wealth from which your annual expenses can be withdrawn from your portfolio indefinitely: expenses divided by the withdrawal rate (at 4%, 25 times your expenses; at 3.5%, 28.6 times).

Example: Annual expenses of €30,000 give a FIRE number of €750,000 at 4% and €857,143 at 3.5%.

Source: Bengen (1994)

More: FIRE (Financial Independence, Retire Early): Lean, Fat, Coast and Barista FIRE · Methodology: Financial goals methodology: how Portfolio Lab simulates a life plan

Relationship between the nominal interest rate, the real interest rate and inflation: (1 + i) = (1 + r) × (1 + π). Named after Irving Fisher.

Source: Fisher (1930)

More: Real return: what is left after inflation

Converts an estimated correlation r into z = artanh(r) = ½ ln((1 + r) / (1 − r)). The value z is approximately normally distributed with a standard error of 1 / √(n − 3); this makes it possible to calculate confidence intervals and tests for correlations that do not extend beyond −1 or +1.

Example: r = −0.3 from 60 monthly returns: tanh(artanh(−0.3) ± 1.96 / √57) gives a 95% interval of −0.51 to −0.05.

More: Stock-bond correlation: regimes, drivers and what it means for 60/40, risk parity and hedging

Extension of the three-factor model by profitability (RMW) and investment (CMA). In it, the value factor becomes partly redundant.

Source: Fama and French (2015)

More: Factor investing: understanding the Fama-French factors · Methodology: Factor regression, factor allocation and factor statistics: methodology

Tax of 25% on investment income in Germany, plus a 5.5% solidarity surcharge on that tax and church tax where applicable. Without church tax, this adds up to 26.375%.

Example: On €1,000 of taxable gain, the tax comes to €263.75.

Large oil tank whose roof floats on the oil and rises and falls with the fill level. Seen from above, the tank wall casts a shadow on the roof; analysts of high-resolution satellite images estimate from its width how full the tank is.

Source: Mukherjee et al. (2021)

More: Ship tracking data and satellite images: what they reveal about commodities

Loaded tankers that store oil at sea instead of delivering it. Under a definition by the EIA, this applies when they lie at anchor or drift slowly for at least seven days. It pays off when onshore storage is full and futures prices are well above the spot price (contango).

Source: EIA (2020)

More: Ship tracking data and satellite images: what they reveal about commodities

The value a portfolio insurance strategy aims never to fall below, e.g. 80% of the starting capital. It can be fixed, grow with the interest rate or be ratcheted up; it is not a guarantee.

More: CPPI: portfolio insurance with cushion, floor and multiplier · Methodology: CPPI backtest: methodology

A US tax form with which an investor certifies residence outside the US. If the bank has it on file, the US withholds 15% on dividends instead of 30%; German banks usually have it signed when the account is opened.

Difference between the forward and spot rate of a currency. The higher-yielding currency trades at a forward discount, the lower-yielding one at a premium (forward premium); the size follows from the interest rate differential.

Example: 150 yen per dollar, dollar rate 4.5%, yen rate 0.5%: one-year forward rate 150 × 1.005 / 1.045 = 144.26 yen, a discount on the dollar of 3.83%.

More: Carry trade: earning interest with currencies and bonds · Methodology: Carry backtest: methodology for FX and bond carry

Finding that high-interest currencies on average do not depreciate by the full interest rate differential, as uncovered interest parity would require. The forward discount is a poor predictor of the subsequent exchange rate change; the forward rate contains a time-varying premium.

Source: Fama (1984); Froot and Thaler (1990)

More: Carry trade: earning interest with currencies and bonds

Interest rate agreed today for an investment that only starts in the future, derived from the yield curve. If the curve is steep, forward rates are above today's rates.

A calculation method for hidden Markov models: the forward pass runs from the first period to the last and delivers the filtered probabilities and the likelihood; the backward pass runs back and adds what later observations reveal about each period. Together they give the smoothed probabilities. So that the numbers do not shrink toward zero in long series, they are normalized in each period (scaling), and the logarithms of the normalizing factors are summed to give the log-likelihood.

Source: Rabiner (1989)

More: Regime models: hidden Markov, Markov switching and more · Methodology: Regime methodology: how the hidden Markov model works

Staking only part of the Kelly fraction, often half. With normally distributed returns, half Kelly delivers about three quarters of the maximum growth at half the volatility.

Source: MacLean et al. (2010)

More: The Kelly criterion: how much to bet for maximum growth

The money a company has left after investing in fixed assets and working capital and could pay out to shareholders and lenders; roughly operating cash flow minus capital expenditure. The free cash flow yield relates it to market capitalization.

More: Fundamental analysis: valuing a company like an investor

The mistake of seeing dividends as extra income, even though the price falls by the amount of the distribution on the ex-date. The term comes from Hartzmark and Solomon; according to their study, demand for dividend stocks is particularly high in periods of low interest rates and weak markets.

Source: Hartzmark and Solomon (2019)

More: Dividend strategies and dividend ETFs under scrutiny: irrelevance, factors, risks

The share of a company's stock that trades freely on the exchange, not held by long-term major shareholders. Index providers usually weight by the market value of the free float.

Index of prices for sea transport, for example for dry bulk such as iron ore, coal and grain. Because shipping capacity hardly grows in the short term, rates rise with demand for commodities; Kilian uses such an index as a measure of global economic activity.

Source: Kilian (2009); Bakshi et al. (2011)

More: Ship tracking data and satellite images: what they reveal about commodities

Instruction to your bank not to tax investment income up to the saver's allowance. It can be split across several banks.

A one-off fee when buying fund units through the fund company or a bank, often up to 5% for active funds. It does not apply when you buy ETFs on an exchange, where you pay an order fee and the spread instead.

More: Active or passive investing: ETFs versus fund managers

In the narrow sense, prohibited trading by a dealer ahead of known client orders. In the context of index changes, it refers to legal trading ahead of the publicly foreseeable purchases and sales of index funds, which comes at the expense of the fund investors.

Source: Chen et al. (2006)

More: Smart indexing: added value for index funds around corporate actions and index changes

Small, illiquid capital markets on the fringes of the emerging markets, e.g. Vietnam or Kenya. Usually not included in broad global indices.

State contribution of €10 a month for children aged 6 to 18, paid into a funded retirement investment account, starting with children born in 2020. The Bundestag passed the law on October 16, 2026; as a rule, nothing is paid out before the 65th birthday, and the returns remain tax-free until then.

Example: 12 years × 12 months × €10 = €1,440 of state support per child.

Source: Bundestag, Frühstartrente (2026); Finance Committee (2026)

Each security is revalued with the scenario's market data, instead of multiplying sensitivities such as duration or delta by the move. More accurate for large shocks, options and cross effects between factors.

Example: Ten-year bond with a 3% coupon at a 3% yield: for +100 bp, duration estimates −8.53%, while full revaluation gives −8.11%.

More: Scenario analysis and sensitivity analysis: stress testing equity, interest rate, credit and currency risk

A portfolio whose weights result from a function of the market weights, e.g. diversity-weighted indices. Given market diversity and sufficient volatility, such portfolios are the only portfolio functions that reliably beat the market portfolio in the long run.

Source: Fernholz (2002); Pal and Wong (2016)

More: Beyond Markowitz: estimation error, noise and true diversification · Methodology: Dimensions methodology: how Portfolio Lab counts independent risks

A fund is liquidated or merged into another, usually because it was too small or performed too poorly. Statistics that show only existing funds leave these cases out.

Source: Brown et al. (1992)

The currency in which a fund calculates its net asset value. For currency risk, what matters is neither this currency nor the trading currency on the exchange, but the currencies of the securities held.

More: Currency risk: how exchange rates change your return

Country in which a fund is established; for ETFs usually Ireland or Luxembourg. Among other things, it affects the withholding tax on dividends.

More: ETF basics: costs, replication and distributions

The total assets a fund manages. Very small ETFs are closed or merged more often; a size of a few hundred million is considered solid.

More: ETF basics: costs, replication and distributions

Information ratio ≈ information coefficient (forecasting skill) × square root of the number of independent decisions. Managers who trade rarely need very high forecasting accuracy to achieve a good information ratio.

Source: Grinold (1989); Grinold and Kahn (2000)

More: Tracking error and information ratio: deviation from the index

Two structures of swap ETFs. With an unfunded swap, the fund buys its own basket of securities and swaps its return for the index return. With a funded swap, it hands the money to the bank and receives collateral in a blocked account, of which it is not the owner.

Source: Ramaswamy (2011)

More: Index replication: full replication, optimized sampling and swaps

Pension financing from saved and invested capital: every contribution is invested, and the later pension comes from capital and returns. Examples are occupational pensions, private provision or state funds such as the Swedish premium pension. The return depends on the capital market, with fluctuations and costs.

Source: Sinn (2000)

Low-interest currency in which a carry trade borrows or which it sells forward; for a long time, for example, the yen and the Swiss franc. Such currencies often appreciate in turbulent times and then amplify the losses.

Source: Menkhoff et al. (2012)

More: Carry trade: earning interest with currencies and bonds

Assets divided by the present value of future payments. Above 100%, the goal can be reached with safe investments.

More: Asset-liability management: aligning your wealth with future spending

Exchange-traded contract to buy or sell an underlying on a fixed date at a price agreed today. Gains and losses are settled daily through margin.

Curve of futures prices across maturities. If it slopes upwards (contango), buyers lose when rolling; if it slopes downwards (backwardation), they gain. For the VIX, it usually inverts only in acute crises.

More: VIX: how to read the stock market's fear gauge · Methodology: Volatility dashboard: methodology

Reference exchange rate determined at a fixed time. Major equity indices use rates from around 16:00 London time, such as the WM/Reuters fixing; funds that value currencies at a different time deviate from the index for this reason alone.

Source: MSCI Hedged Methodology (2020); FTSE Russell Calculation Guide (2026)

More: Index providers and valuation points: why the same index is calculated differently

Average gain in positive periods divided by the average loss in negative ones.

More: Sortino ratio and Calmar ratio: measuring downside risk

How much an option's delta changes when the price rises by one unit, i.e. the curvature of the option price. Largest for at-the-money options shortly before expiry; buyers are long gamma, sellers are short.

Example: Call with price and strike 100, one year, 5% interest rate and 20% volatility: gamma 0.0188. If the price rises by 1, delta increases by just under 0.02.

More: Option pricing: where fair option prices come from · Methodology: Option pricer: how Portfolio Lab values options

The risk that a price jumps so sharply between two trading times that a hedging rule cannot react in time. With CPPI, the value then falls below the floor.

Source: Cont and Tankov (2009)

More: CPPI: portfolio insurance with cushion, floor and multiplier · Methodology: CPPI backtest: methodology

A generalization of ARCH in which today's variance also depends on the previous day's variance. GARCH(1,1) is the standard model for forecasting volatility for risk measures such as value at risk.

Source: Bollerslev (1986)

Black-Scholes for currency options: the foreign interest rate acts like a dividend yield, and the cost of carry is the domestic minus the foreign interest rate.

Source: Garman and Kohlhagen (1983)

Methodology: Option pricer: how Portfolio Lab values options

Growth at a reasonable price. The style looks for companies with high earnings growth that are not too expensively valued; Peter Lynch compared the P/E with the earnings growth rate for this purpose. A common metric is the PEG ratio: the P/E divided by expected earnings growth in percent.

Example: P/E of 20 with 25% expected earnings growth: PEG = 20 / 25 = 0.8, so by the rule of thumb (below 1) rather cheap.

Source: Lynch and Rothchild (2000)

More: Legendary investors: the investment styles of the most famous investors, from Graham to Simons

Location data from smartphones that apps pass on. They show visits to shops or plants and serve as a real-time measure of sales; under the GDPR, location data are personal data as long as they have not been irreversibly anonymized.

Source: Froot et al. (2017); European Commission (2026)

More: Alternative data: job ads, Reddit, X, satellites and card payments

Attribution of the geometric excess return (1 + R) / (1 + B) − 1 instead of the difference R − B. The effects compound across periods without correction factors and can be converted between currencies, but are less intuitive.

Example: Portfolio 6.35%, benchmark 5.60%: geometric 1.0635 / 1.0560 − 1 = 0.71% instead of an arithmetic 0.75 percentage points.

Source: Menchero (2005); Bacon (2019)

More: Multi-asset attribution: weighting schemes, top-down and bottom-up, currencies and overlays

Standard model for prices in continuous time: the log return is normally distributed with constant drift and volatility, and the price itself is lognormally distributed. The basis of the Black-Scholes model and many Monte Carlo simulations; it does not capture crashes, fat tails or periods of high volatility.

Source: Glasserman (2003)

More: Leveraged ETFs and return stacking: path dependence, costs and research · Methodology: Methodology of the free calculators: savings plan, withdrawal and leveraged ETF

The average growth rate with compounding: the nth root of the product of the growth factors, minus 1. It describes how fast wealth has actually grown and, over whole years, equals the CAGR.

Example: +50% and −50%: √(1.5 × 0.5) − 1 = −13.40% per period.

More: CAGR: how to calculate the average annual return correctly

Municipal tax on trade income: a base rate of 3.5% times the municipality's multiplier (Hebesatz). Corporations are always subject to trade tax, even if they only manage assets. The minimum multiplier rises from 200 to 280% from the 2027 assessment period.

Example: Multiplier 400%: 3.5% × 400% = 14% of trade income.

Source: GewStG (2002)

Global Investment Performance Standards of the CFA Institute, 2020 edition, effective since January 1, 2020: voluntary rules on how investment managers calculate and present their performance, with composites, time-weighted returns after transaction costs and at least five years of history.

Source: CFA Institute (2019); CFA Institute (2019)

More: Portfolio reporting: how to report return, risk, attribution and costs properly

Planned transition from a riskier to a safer portfolio over time, for example an equity share that falls with age.

More: Monte Carlo simulation: how safe is your plan?

Hedge fund style that bets on the big moves in interest rates, currencies, government bonds, equity indices and commodities, based on views about the economy, monetary policy and politics. Usually implemented with futures, currency forwards and leverage; a famous example is the Quantum Fund's bet against the British pound in 1992.

Source: Mallaby (2010)

More: Legendary investors: the investment styles of the most famous investors, from Graham to Simons

Precious metal without ongoing income, held as crisis protection and a store of value. Its real price fluctuates strongly; as an inflation hedge, it only works over very long periods.

Source: Erb and Harvey (2013); Baur and Lucey (2010)

More: Gold in a portfolio: safe haven, inflation hedge or just shiny?

Exchange-traded securities that embody a claim to delivery of physical gold. Under the case law of the Federal Fiscal Court (BFH), they are treated like physical gold: tax-free after a holding period of one year.

More: Gold in a portfolio: safe haven, inflation hedge or just shiny?

Values a share as a dividend that grows at a constant rate for ever: price = next year's dividend / (required return − growth). It only holds as long as growth stays permanently below the required return.

Example: Dividend €3, required return 8%, growth 5%: 3 / (0.08 − 0.05) = €100.

Source: Gordon (1959)

More: Fundamental analysis: valuing a company like an investor

Bond issued by development banks, agencies or regions that are owned or guaranteed by a state, such as Germany's KfW. Slight yield premium over government bonds.

Methodology: Risk factors in the look-through: methodology

Umbrella term for the metrics that show how an option price reacts to changes in price (delta, gamma), volatility (vega), time (theta) and interest rates (rho). Traders use them to manage the risk of entire option books.

Source: Hull (2021)

More: Option pricing: where fair option prices come from · Methodology: Option pricer: how Portfolio Lab values options

The yield discount on green bonds compared with similar conventional bonds from the same issuer: investors accept a slightly lower yield for the green label. When it rises, green bonds gain in price.

Source: Pástor et al. (2022)

More: ESG ETFs: index rules, ratings, returns and the limits of sustainable funds

A product is presented as more sustainable than it is, e.g. through names, advertising or classifications that its actual investment rules do not live up to.

More: ESG ETFs: index rules, ratings, returns and the limits of sustainable funds

Amount of electricity drawn from the public grid. It is the usual measure of electricity consumption. Electricity that households and businesses generate with their own solar panels and use themselves, without feeding it into the grid, is not included. As an economic indicator, it also fluctuates with the weather, public holidays and electricity prices.

Source: Fezzi and Fanghella (2020); Bundesnetzagentur | SMARD.de (2026)

Methodology: Economic pulse: how Portfolio Lab calculates early indicators

The sum of all positions without netting, with short positions counted at their absolute amount. Net exposure subtracts short from long positions. A margin account with leverage of 2 has 200% gross and net exposure; a market-neutral long-short portfolio has about 200% gross and 0% net.

More: Leverage in a portfolio: return, risk, costs and margin calls

Index variant that reinvests dividends without deducting any standard withholding tax; at MSCI, as received by private investors in the company's home country, excluding tax credits. It is above the net return index and is the stricter yardstick for funds.

Source: MSCI Calculation Methodology (2025)

More: Index providers and valuation points: why the same index is calculated differently

If markets were perfectly efficient, gathering information would not pay. Then nobody would do it, and markets could not be efficient. Markets are therefore at most approximately efficient.

More: The efficient market hypothesis: why it is so hard to beat the market

Stock with a high valuation that investors pay because they expect strong earnings growth. Often technology and healthcare companies.

More: Factor investing: understanding the Fama-French factors

A classification of the economic environment by rising or falling growth and rising or falling inflation. Equities like growth without inflation, bonds like falling inflation, and commodities and inflation-linked bonds like rising inflation.

More: All Weather portfolio: ready for every economic climate? · Methodology: Macro dashboard and regime analysis: methodology

Leverage with the highest median growth: L* = (μ − r − s) / σ², with average continuous return μ, financing rate r, spread s and volatility σ. Beyond it, the typical outcome falls again, even though the expected value keeps rising; for normally distributed returns, this corresponds to the Kelly criterion.

Example: Index with a 7% median return (6.77% continuous) and σ = 18%: μ = 6.77% + 1.62% = 8.39%; interest rate 2% and spread 1% (continuous 1.98% and 1.00%): L* = (8.39 − 1.98 − 1.00) / 3.24 = 1.67.

More: Leveraged ETFs and return stacking: path dependence, costs and research · Methodology: Methodology of the free calculators: savings plan, withdrawal and leveraged ETF

Portion of taxable income on which no income tax is due; in 2026 it is €12,348. For investment income, it works through the most-favorable assessment: a child with no other income can therefore receive far more tax-free than the saver's allowance.

Example: €12,348 + €1,000 saver's allowance + €36 lump-sum allowance for special expenses = €13,384 of investment income free of income tax.

Source: EStG § 32a (2009)

On application in the tax return, investment income is taxed at your personal income tax rate if that rate is below 25%. The tax office then checks for itself which option is more favorable.

Source: EStG (2009)

A Sharpe ratio after a discount for multiple testing: the p-value of the measured Sharpe ratio is adjusted for the number of strategies tested, e.g. using Bonferroni or Holm, and converted back into a smaller Sharpe ratio. The haircut is the percentage discount.

Source: Harvey and Liu (2015)

More: Deflated Sharpe ratio: how much skill is in a Sharpe ratio?

The time it takes for a deviation from equilibrium to halve. In cointegration analysis it shows how quickly the gap between two prices closes again; it is usually estimated from an AR(1) regression of the spread (Ornstein-Uhlenbeck process).

Source: Uhlenbeck and Ornstein (1930)

More: Pairs trading and statistical arbitrage: idea, methods, research · Methodology: Asset analysis: methodology from correlation to cointegration

Equity returns from November to April are higher than those from May to October in most markets (the stock market adage “Sell in May and go away”). Worldwide the difference averaged around 4%; there is no generally accepted explanation.

Source: Bouman and Jacobsen (2002); Zhang and Jacobsen (2021)

More: Stock market seasonality: Sell in May, the January effect and how to test calendar effects

A recursion for the filtered regime probabilities of a Markov model: prediction with the transition matrix, weighting by the density of the new observation in each regime, normalization to 1. It uses only data up to the period in question and is therefore available in real time.

Example: Prediction 10.8% turbulent, density of a week with −3% in the calm regime 0.02544, in the turbulent regime 0.08074: 0.108 × 0.08074 / (0.892 × 0.02544 + 0.108 × 0.08074) = 27.8% turbulent.

Source: Hamilton (1989)

More: Regime models: hidden Markov, Markov switching and more · Methodology: Regime methodology: how the hidden Markov model works

The probability per unit of time that an event will occur in the next moment, given that it has not occurred so far. In the JLS model it describes the crash risk of a bubble; if it rises, the price has to rise faster to compensate investors for the risk.

Source: Johansen, Ledoit and Sornette (2000)

More: Speculative bubbles: what they are and how the LPPLS model detects them

Large creation of ETF units by an authorized participant, followed shortly by their redemption, in which the fund hands out securities with large unrealized gains. A US ETF thereby avoids realizing gains that it would have to distribute. This tax advantage plays no role for investors in Germany.

Source: Moussawi et al. (2025)

More: Active ETFs: how they work and what they deliver

An investment fund with wide latitude: it may sell short, borrow and use derivatives, and pursues strategies such as long/short equity, market neutral, event driven, global macro or relative value. In the EU it counts as an alternative investment fund (AIF).

Source: Fung and Hsieh (1997)

More: Short selling, hedge funds and hedging: types and how they work

The ratio in which two securities are traded against each other so that their spread stays as stable as possible. Usually the slope β of a regression of A's log prices on B's, estimated on a rolling basis or with a Kalman filter.

Source: Vidyamurthy (2004); Chan (2013)

More: Pairs trading and statistical arbitrage: idea, methods, research · Methodology: Long/short and statistical arbitrage: methodology

Income or cost of a currency hedge, roughly the interest rate differential between the two currencies (covered interest parity). If the US rate is above the euro rate, hedging dollar investments costs return.

Example: Euro rate 2%, dollar rate 4%: hedging costs about 2 − 4 = −2% a year.

More: Currency risk: how exchange rates change your return

Price index that explains each price through characteristics (for art, for example, artist, size and technique; for classic cars, make, model and year of manufacture) and estimates the time effect that remains after this adjustment. It uses all sales, but depends on which characteristics the model captures.

Source: Renneboog and Spaenjers (2013); Laurs and Renneboog (2019)

More: Collectibles as an investment: what art, wine, watches and classic cars really return

Investors follow what others are doing rather than their own analysis. This amplifies excesses in both directions.

The sum of the squared weights, a measure of concentration. Its reciprocal is the effective number of equally sized positions.

Example: Weights of 50%, 25% and 25%: 0.25 + 0.0625 + 0.0625 = 0.375, i.e. effectively 2.67 positions.

More: Look-through: what is really inside your ETFs

The dispersion of errors or returns is not constant but changes over time or with other variables. Ordinary standard errors are then wrong; robust estimators such as Newey-West help.

Source: Newey and West (1987)

Harmonized Index of Consumer Prices, the inflation rate of EU countries calculated on a uniform basis. The European Central Bank aligns its 2% target with it.

More: Real return: what is left after inflation · Methodology: Macro dashboard and regime analysis: methodology

A statistical model in which a hidden state (such as a calm or turbulent market) follows a Markov chain, and each state has its own distribution of observed returns. It is usually estimated with the Baum-Welch algorithm; the Viterbi algorithm delivers the most likely sequence of states.

Source: Rabiner (1989); Baum et al. (1970); Viterbi (1967)

More: Regime models: hidden Markov, Markov switching and more · Methodology: Regime methodology: how the hidden Markov model works

A weighting method that first groups assets into a tree by their correlations and then splits the risk step by step between the branches. It needs no inverse of the covariance matrix, which makes it more stable.

Source: López de Prado (2016)

More: Hierarchical risk parity: building portfolios from clusters

Bonds rated below BBB−, also known as junk bonds. They pay higher interest, but in crises they tend to behave more like equities.

Methodology: Risk factors in the look-through: methodology

The highest unit value to date, above which a performance fee becomes due again. After losses, the fund must first regain its old high before the manager shares in profits again.

Example: High of 120, fall to 100, rise to 125: performance fee only on 5 of the 25 points of the rise.

More: CTAs and managed futures: industry, position sizing, costs and crisis protection

In retrospect, events seem more predictable than they were. If you think you saw the last crash coming, you overestimate your ability to foresee the next one.

A stress scenario taken from a real crisis: the market movements of a crisis window, e.g. the 2007 to 2009 financial crisis, are applied to today's portfolio, either by replaying the returns of that time or via factors and betas. Advantage: the scenario actually happened and is internally consistent. Disadvantage: the next crisis will look different.

Source: Basel Committee on Banking Supervision (2018)

More: Historical stress testing: how to apply past crises to your portfolio today

Value at risk taken directly from the observed returns: you sort them and read off the quantile. No distributional assumption is needed, but the result depends on whether the period contains crises.

Source: Jorion (2007)

More: Value at risk and conditional VaR: how much you could lose in a bad case

The share of periods with a positive return, or with a return above the benchmark. On its own it says little: many small gains and a few large losses produce a high hit rate with a poor result.

Example: 7 out of 12 months above the index: hit rate 58.3%.

More: Risk metrics beyond the Sharpe ratio: Treynor, Calmar, Omega, Ulcer Index and more

High minus low: return of stocks with a high book-to-market ratio (cheap, value) minus those with a low one (expensive, growth).

Source: Fama and French (1992); Fama and French (1993)

More: Factor investing: understanding the Fama-French factors · Methodology: Factor regression, factor allocation and factor statistics: methodology

Investors hold a disproportionate share of stocks from their own country, even though international diversification reduces risk. In studies, the domestic share for investors from Japan, the US and the UK was in each case far above the country's share of the world market.

Source: French and Poterba (1991); Coval and Moskowitz (1999)

More: Home bias: the preference for your home market and what it costs

Instead of waiting for a distribution, the investor sells units of the same value. Before taxes and costs, the result is the same; under German tax law, only the gain portion of a sale is taxable, whereas with a dividend it is the whole amount.

Example: €3,000 from single stocks with a 40% gain portion: tax on the sale €316.50, on a dividend €791.25 (allowance used up, without church tax).

Source: Miller and Modigliani (1961)

More: Dividend strategies and dividend ETFs under scrutiny: irrelevance, factors, risks

A statement of all of a household's assets and liabilities. In a broader sense it also includes human capital and pension entitlements; only then does it become clear which risks someone already bears.

Source: Ibbotson et al. (2007)

More: Your whole wealth: total wealth from portfolio, home, human capital and car

The present value of future labor income. For secure jobs it resembles a bond and argues for more equities in young investors' financial wealth; for jobs closely tied to the market or a sector, it argues for caution instead.

Source: Bodie et al. (1992); Cocco et al. (2005)

More: Equity allocation by age: rules of thumb, glide paths and what theory says

Preferred return that investors receive before the manager shares in the profit. With a catch-up, the manager then receives the further proceeds first, until it has its full share of the total profit; if the proceeds are large enough, the hurdle then makes no difference to the size of the profit share.

Example: Capital 100 over five years, 8% hurdle: preferred return 100 × (1.08^5 − 1) = 46.93; full catch-up at 20% carry: 46.93 / 4 = 11.73.

More: Private equity explained: strategies, fund structure, fees and what research shows about returns

A statistical procedure that checks whether data are consistent with an assumption (the null hypothesis, e.g. “alpha = 0”). The outcome is to accept or reject it at a chosen significance level.

A stress scenario devised for an event that has never happened in this form, e.g. an interest rate shock of two percentage points or an oil price shock. It forces you to think relationships through; how much the factors that are not specified move along with it, you either set yourself or derive from correlations.

Source: Basel Committee on Banking Supervision (2018)

More: Scenario analysis and sensitivity analysis: stress testing equity, interest rate, credit and currency risk

Company-specific risk that can largely be eliminated by spreading investments across many securities. It corresponds to the volatility of the residuals of a factor regression.

Source: Ang et al. (2006)

More: Correlation and diversification: why mixing assets reduces risk

The extra return investors demand for not being able to sell an investment at any time, or for losing value in liquidity crises. For private equity, Franzoni et al. (2012) estimate a liquidity risk premium of about 3% a year.

Source: Franzoni et al. (2012)

Assets and liabilities are given the same duration, so that interest rate changes affect both sides equally. This keeps the funding ratio stable for small rate movements.

Source: Redington (1952); Fisher and Weil (1971)

More: Duration: how strongly bonds react to interest rates

Seven-digit identification number of a ship under the numbering scheme of the International Maritime Organization (IMO). It is part of the static AIS data and identifies the ship itself, whereas the MMSI identifies its radio station.

Source: ITU (2026); IMO (2015)

Methodology: Ships at chokepoints (beta): methodology

Investing with the aim of a measurable positive impact on the environment or society alongside the return, e.g. financing new solar parks. Exchange-traded equity funds meet this standard only to a limited extent, because they buy existing shares.

More: ESG ETFs: index rules, ratings, returns and the limits of sustainable funds

The cost of implementation, measured as the gap between a paper portfolio that would have traded without costs at the price at the time of the decision and the real portfolio: delay, market impact, fees and opportunity costs. Also the name of algorithms that trade against the price at order entry (arrival price).

Source: Perold (1988)

More: Order types and execution: from limit orders to MOC, VWAP, TAS and BTIC

The expectation, derived from option prices, of how closely the stocks in an index will move together. High values occur in crises, when stocks fall together; low values mean that individual stocks go their own way.

Methodology: Sentiment: methodology for the fear and greed index, put/call ratio and COT

The annualized return from buying a bond or an index today and delivering it into a sold future. If it is above the financing rate, cash-and-carry pays off; the deliverable bond with the highest implied repo rate is usually the cheapest to deliver.

Example: Purchase price 98.50, invoice amount in 90 days 99.35: 0.85 / 98.50 × 360 / 90 = 3.45%.

Source: Hull (2021)

More: Basis trades: positive and negative basis in bonds, CDS and futures

Return that the market prices in through its weights and risks: Π = δ × Σ × market weights. Starting point of the Black-Litterman model.

More: Black-Litterman: incorporating your own views cleanly

Volatility embedded in option prices: the value that, plugged into an option pricing model, reproduces the market price. It is an expectation of future volatility including a risk premium; the VIX measures it for the S&P 500.

Source: Black and Scholes (1973); Whaley (2000)

More: VIX: how to read the stock market's fear gauge · Methodology: Volatility dashboard: methodology

The ongoing return on an owner-occupied home: the rent the owner would have to pay for a comparable home. It is not paid out, but alongside the change in value it is the most important part of the return.

More: Your whole wealth: total wealth from portfolio, home, human capital and car

In-sample data are the data used to estimate a model or choose a rule; out-of-sample data are data that were not used in the process. Only results outside the sample are a fair test.

More: Backtest overfitting: when the past looks too good

Indicative net asset value, calculated continuously during trading hours from the current prices of the fund's holdings. It helps you assess an ETF's market price.

More: ETF basics: costs, replication and distributions

The share of the largest companies in the overall index. In broad global indices it has risen markedly since the 2010s, because a few very large US technology companies have grown strongly.

More: World portfolio: the whole world in one or two ETFs

Price movement of stocks that are added to or removed from an index, mainly between announcement and implementation. For additions to the S&P 500, the excess return has fallen from an average of 7.4% in the 1990s to below 1% in the last decade.

Source: Shleifer (1986); Greenwood and Sammon (2025)

More: Smart indexing: added value for index funds around corporate actions and index changes

A fund that tracks an index as closely as possible instead of selecting securities. Low costs are its main advantage; after costs, it beats the average active fund in the same market.

Source: Bogle (2007); Sharpe (1991)

More: Active or passive investing: ETFs versus fund managers

Fee that a fund provider pays the index provider for using an index; it is included in the ongoing charges. In 2012, Vanguard switched the index provider for 22 index funds, citing rising license fees as the reason.

Source: Vanguard (2012)

More: Index providers and valuation points: why the same index is calculated differently

The regular review of an index, in which securities are added or removed and weights adjusted, usually quarterly. Index funds have to follow suit, which incurs costs.

Source: Frino and Gallagher (2001)

Rise in the general price level, measured for example by the consumer price index. Reduces the purchasing power of a fixed amount.

More: Real return: what is left after inflation

The slope of a regression of an asset's nominal return on inflation. A beta of 1 protects purchasing power exactly; below that, the asset loses in real terms when inflation rises. A distinction is made between betas on expected and on unexpected inflation.

Example: Beta 1.38: 2 percentage points more inflation bring about 1.38 × 2 = 2.76 percentage points more nominal return.

Source: Bekaert and Wang (2010); Fama and Schwert (1977)

More: Liquid real assets: inflation protection with tradable real assets in a portfolio

Part of a bond's yield that compensates investors for uncertainty about future inflation. It cannot be observed directly, only estimated from models.

Source: Bekaert and Wang (2010)

More: Real return: what is left after inflation

Swap in which one party pays a fixed inflation rate and the other the actual change in a price index, often in a single payment at the end (zero-coupon inflation swap). Pension plans with inflation-linked pensions receive actual inflation and so hedge the real value of their liabilities.

More: Liability-driven investing and cash flow driven investing: covering liabilities with bonds

The correlation between forecasts and actual outcomes. Even values well below 0.1 can lead to a good information ratio when there are many independent decisions.

Source: Grinold and Kahn (2000)

More: Tracking error and information ratio: deviation from the index

A model selection measure that combines goodness of fit (−2 log L) with a penalty per parameter; smaller is better. Hirotugu Akaike's AIC penalizes each parameter by 2, Gideon Schwarz's BIC by ln n for n observations, i.e. more heavily from eight observations upwards. The BIC therefore tends to choose more parsimonious models.

Example: 1,000 weekly returns, log L = −2,180, 7 parameters: AIC = 2 × 7 + 4,360 = 4,374, BIC = 7 × 6.908 + 4,360 = 4,408.4.

Source: Akaike (1974); Schwarz (1978)

More: Regime models: hidden Markov, Markov switching and more · Methodology: Regime methodology: how the hidden Markov model works

Average excess return over the benchmark divided by the tracking error.

Example: 0.32% excess return with a 0.70% tracking error gives 0.46.

More: Tracking error and information ratio: deviation from the index

Number of new claims for unemployment benefits in the US per week, published weekly by the US Department of Labor. It is one of the fastest indicators of layoffs. Continuing claims show how many people continue to receive benefits.

Methodology: Economic pulse: how Portfolio Lab calculates early indicators

Under Art. 7 MAR, precise information that has not been made public about an issuer or a financial instrument and that could have a significant effect on the price. Trading on it is prohibited; according to recital 28, analyses and estimates based on publicly available data are not in themselves inside information.

Source: CJEU (2026); BaFin (2026)

More: Alternative data: job ads, Reddit, X, satellites and card payments

Bank deposit that is available every day and pays a variable interest rate. Statutory deposit insurance covers up to €100,000 per depositor and bank; the bank can change the rate at any time, and after a promotion for new customers it is often considerably lower.

Source: EinSiG § 8 (2015)

Forward rate for an infinitesimally short period that starts at a future point in time. With continuously compounded zero rates r(t), f(t) = r(t) + t · r′(t). The ECB publishes it daily for its yield curves; the value one year ahead shows the short rate priced in for one year from now, including premiums.

Example: One-year zero rate of 2.0%, rising by 0.1 percentage points per year of maturity: f(1) = 2.0 + 1 × 0.1 = 2.1%.

Source: ECB, yield curve methodology (2026)

Methodology: Macro dashboard and regime analysis: methodology

The remainder of the Brinson decomposition: (wᵢ − Wᵢ) × (rᵢ − bᵢ). Positive when a segment is overweight in which selection was also better; many reports add it to selection.

Source: Brinson et al. (1986)

More: Performance attribution: Brinson decomposition, factors and linking over time

Share of the liabilities' interest rate risk that the assets hedge: basis point value of the hedge divided by the basis point value of the liabilities. At 100%, a small parallel shift in rates leaves the surplus unchanged.

Example: Liabilities with a basis point value of €1.50 million, hedge with €0.90 million: ratio 60%. If rates rise by 100 basis points, the surplus grows by 40% × €150 million = €60 million.

More: Liability-driven investing and cash flow driven investing: covering liabilities with bonds

Exchange of fixed for floating interest payments on an agreed notional amount, which itself does not change hands. Whoever receives the fixed rate gains, like a bondholder, when rates fall. That party thus obtains duration with almost no capital outlay, but must post collateral as soon as the swap loses value.

More: Liability-driven investing and cash flow driven investing: covering liabilities with bonds

Money-weighted return: the interest rate at which all inflows and outflows, including the final value, have a present value of zero. Better suited to savings plans than the CAGR.

More: CAGR: how to calculate the average annual return correctly

What an option would be worth if exercised immediately: for a call, price minus strike; for a put, strike minus price; at least zero. The rest of the option price is the time value, which shrinks to zero by expiry.

Example: Call with strike 90 at a price of 100, option price 13: intrinsic value 10, time value 3.

More: Option pricing: where fair option prices come from

An ETF that delivers the opposite (−1) or a negative multiple (−2) of the index return each day. Over longer periods of volatility without a trend, it loses much like a 2x ETF, because the factor L × (L − 1) is the same for L = −1 and L = 2.

Example: Index alternating between +4% and −3.846% over 20 days, unchanged at the end: inverse ETF −3.03%, exactly like the 2x ETF.

Source: Cheng and Madhavan (2009); FINRA (2009)

More: Leveraged ETFs and return stacking: path dependence, costs and research

Weights proportional to 1 / volatility: calm assets get more, volatile ones less. Ignoring correlations, it is a simple approximation of risk parity.

More: Risk parity: equal risk contributions instead of equal weights · Methodology: Tactical allocation methodology: how the eleven tactical models work

Short-term interest rates are above long-term rates. In the US, an inversion preceded most recessions of recent decades, though with a varying lag of usually one to two years.

Source: Estrella and Mishkin (1998); Harvey (1988)

More: Yield curve: what the term structure reveals and why an inverted curve is seen as a warning sign · Methodology: Macro dashboard and regime analysis: methodology

Extended MSCI index variant that contains small companies as well as large and mid-sized ones and covers around 99% of the free float in each country. The many small caps greatly increase the number of constituents, but add only little weight.

Example: On September 30, 2026, the MSCI ACWI IMI had 8,036 constituents, 5,622 more than the MSCI ACWI; the ten largest weighed 22.73% instead of 25.40%.

Source: MSCI GIMI Methodology (2024); MSCI ACWI IMI Factsheet (2026)

More: MSCI World vs ACWI vs FTSE All-World: structure, concentration and combinations

Adviser to institutional investors who helps with investment strategy, asset allocation and the selection of asset managers, and often runs the RFP process. According to the UK competition authority, consultants there influence more than £1.6 trillion of pension assets; whether their manager recommendations add value after fees has not been shown.

Source: CMA (2018); Jenkinson et al. (2016)

More: RFP and mandate awards: how institutional investors select asset managers

Bonds rated BBB− (or Baa3) or better: issuers that are certified as having good creditworthiness. Many institutional investors may only hold such bonds.

Methodology: Risk factors in the look-through: methodology

Umbrella term in the Investment Tax Act (InvStG) for distributions, Vorabpauschalen and gains from selling fund units. The partial exemption applies to all of them.

Source: InvStG (2016)

Contract between investor and asset manager covering a mandate: investment objective and guidelines, benchmark, permitted instruments, reporting, fees, liability, proxy voting, termination and handover of the portfolio.

More: RFP and mandate awards: how institutional investors select asset managers

Difference between the return of a fund or market and the return that investors actually earn in it. Because of procyclical buying and selling, investor returns are usually lower.

Source: Dichev (2007)

More: Time-weighted and money-weighted return: what measures what?

Sold strangle whose risk is capped by bought options further out. Earns a premium as long as the price stays within a range; the potential loss is limited, but usually a multiple of the premium.

Example: Puts 85/92 and calls 108/115, 91 days, price 100: premium 1.80, maximum loss 5.20.

More: Option pricing: where fair option prices come from

International Securities Identification Number: a twelve-character identifier of a security, beginning with the country code, e.g. IE for Ireland. Unlike ticker symbols, it is unique worldwide.

The difference between the issue or ask price of a structured product and the fair value of its components, the bond and the options. It covers the issuer's distribution, hedging and profit.

Example: Fair value €82.76, ask price €84.00: margin 84 / 82.76 − 1 = 1.50%.

Source: Henderson and Pearson (2011); Baule et al. (2008)

Risk that the issuer of a debt security (bond, certificate, ETN or ETC) becomes insolvent. The investor then only gets what is left in the insolvency proceedings, even if the underlying has performed well; statutory deposit insurance does not cover this.

Source: EinSiG (2015); BGH (2011)

More: Counterparty and issuer risk: CVA, ETCs, certificates and swaps

Typical shape of a closed-end fund's cumulative net cash flows or its running IRR: negative in the first years because of fees, costs and conservative valuations, positive later as values rise and holdings are sold. Credit lines secured on the commitments make the dip shallower without making the fund any better.

Example: Calls of 25, 25, 20, 15 and 10, distributions from year 3: low point of −80 in years 3 and 4, break-even in year 7.

Source: ILPA (2017)

More: Measuring private markets: J-curve, cash flows, smoothing and public proxies

Conspicuously high equity returns in January, especially for small companies and in the first trading days of the year. A common explanation is year-end selling of losing positions for tax reasons.

Source: Rozeff and Kinney (1976); Keim (1983)

More: Stock market seasonality: Sell in May, the January effect and how to test calendar effects

For a concave function such as the logarithm, the value of the mean lies above the mean of the values: log(Σ wᵢ × xᵢ) ≥ Σ wᵢ × log(xᵢ) for weights that sum to 1. That is why the geometric return lies below the arithmetic one, and why a portfolio grows faster than the weighted average of its components' growth rates.

Example: 50/50 of the growth factors 1.2 and 0.9: log(1.05) = 4.88% lies above 0.5 × log(1.2) + 0.5 × log(0.9) = 3.85%.

Index of a country's online job postings relative to a base date, for example from the ads on a large job site. It shows early on how many workers companies are looking for, but only captures the jobs advertised online on that site and depends on its market share.

Source: Indeed Hiring Lab (2026)

More: Alternative data: job ads, Reddit, X, satellites and card payments · Methodology: Economic pulse: how Portfolio Lab calculates early indicators

A method that estimates a changing state, which cannot be observed directly, from noisy measurements and updates it a little with each new observation. In pairs trading it estimates a hedge ratio that changes over time, without a fixed estimation window.

Source: Kalman (1960); Chan (2013)

More: Pairs trading and statistical arbitrage: idea, methods, research · Methodology: Long/short and statistical arbitrage: methodology

Tax that the bank withholds directly from interest, dividends, distributions, Vorabpauschalen and capital gains and pays over to the tax office. For private investors, it settles the tax in full (flat-rate withholding tax, Abgeltungsteuer).

Source: EStG (2009)

Framework for the attribution of international portfolios: each foreign return is split into a market premium over the local money market rate and a currency return including the interest rate differential, and the Brinson decomposition is then calculated separately for markets and currencies.

Source: Karnosky and Singer (1994)

More: Multi-asset attribution: weighting schemes, top-down and bottom-up, currencies and overlays

The fraction of capital that maximizes long-term wealth growth. For a bet with win probability p and odds b it is p − (1 − p) / b; staking more lowers growth again.

Example: A 60% chance of winning at even odds (b = 1): 0.6 − 0.4 / 1 = 20% of capital.

Source: Kelly (1956); Thorp (2006)

More: The Kelly criterion: how much to bet for maximum growth

Short mandatory document under the PRIIPs Regulation for funds, certificates and insurance-based investment products, with fixed sections on the product, risks and performance scenarios, costs and holding period. For UCITS, it has applied since 2023.

Source: PRIIPs Regulation (2014)

More: Portfolio reporting: how to report return, risk, attribution and costs properly

Interest rate set by the central bank at which banks can borrow or deposit money. In the euro area, the deposit facility rate has been the decisive key rate since 2024.

Methodology: Macro dashboard and regime analysis: methodology

Interest rate risk per maturity point: how strongly a portfolio reacts when only the rate for one maturity (say 10 years) rises. Together they add up to the duration.

More: Duration: how strongly bonds react to interest rates

The tailedness of a distribution: how much weight lies in the tails? The normal distribution has a kurtosis of 3 (excess kurtosis 0); returns usually have more, so extreme values occur more often.

More: Skewness and kurtosis: why market crashes are more frequent than the normal distribution says

A quirk of mixture and hidden Markov models: the likelihood does not change if the state labels are swapped. When the model is re-estimated, states can therefore change places. A common remedy is an ordering rule, e.g. by increasing volatility; for Bayesian mixture models, Matthew Stephens shows that this does not solve the problem in general. Portfolio Lab sorts by volatility, matches each re-estimate against the previous one and reports swapped roles and narrow gaps.

Source: Stephens (2000)

More: Regime models: hidden Markov, Markov switching and more · Methodology: Regime methodology: how the hidden Markov model works

A simple portfolio of a few index funds with fixed weights that is rebalanced only occasionally, e.g. 60/40, the Permanent Portfolio or the three-fund portfolio.

More: All Weather portfolio: ready for every economic climate?

Metric that is available earlier than the official figures on economic output or runs ahead of them in time, such as surveys, new orders or daily data like truck mileage and electricity consumption. Weekly indices combine several such series; they are revised and are not a forecast.

Source: Askitas and Zimmermann (2013); Lewis et al. (2022)

Methodology: Economic pulse: how Portfolio Lab calculates early indicators

Fits a line (or plane) so that the squared deviations are as small as possible. This is how beta, alpha and factor loadings are determined; slope and intercept each have their own standard errors.

More: Beta and alpha: how closely a fund moves with the market

The estimated covariance matrix is shrunk part of the way toward a simple target matrix, e.g. equal correlation for all pairs. The shrinkage intensity is determined from the data; the result is more stable and well conditioned.

Source: Ledoit and Wolf (2004); Ledoit and Wolf (2004)

More: Covariance estimation: why optimizers need shrinkage · Methodology: Optimization methodology: estimation, objectives, Black-Litterman, resampling and walk-forward

The part of the market value that a lender accepts as collateral, set by a loan-to-value ratio per security; the rest is the haircut. The riskier the security, the lower the ratio, and in crises lenders often demand more collateral.

Example: €50,000 in an equity fund with a loan-to-value ratio of 60% secures a loan of up to €30,000.

Source: Geanakoplos (2010)

More: Leverage in a portfolio: return, risk, costs and margin calls

Three factors that explain almost all movements of the yield curve: a parallel shift, a twist and a bulge in the middle. The result of a principal component analysis of bond yields.

Source: Litterman and Scheinkman (1991)

More: Yield curve: what the term structure reveals and why an inverted curve is seen as a warning sign

Using borrowed money or derivatives so that your exposure is larger than your own capital. Leverage multiplies gains and losses; the Sharpe ratio stays the same before borrowing costs, the drawdown does not.

More: Leverage in a portfolio: return, risk, costs and margin calls · Methodology: Backtest methodology: data, process, rebalancing and costs

Many investors are not allowed or do not want to borrow, so they buy risky assets to get more return. This makes risky assets too expensive and low-risk ones too cheap. It is one explanation for risk parity and the low-beta anomaly.

Source: Asness et al. (2012); Frazzini and Pedersen (2014)

More: Leverage in a portfolio: return, risk, costs and margin calls

The ratio of securities held to your own capital. Leverage of 2 means €10,000 of own capital is matched by €20,000 of securities and a €10,000 loan. Below 1, part is held in cash; above 1, part is borrowed. In the Portfolio Lab backtest the leverage factor applies per security and is restored every period, as with a leveraged ETF.

More: Leverage in a portfolio: return, risk, costs and margin calls · Methodology: Backtest methodology: data, process, rebalancing and costs

Acquisition of a company financed largely with debt, which the acquired company then carries. According to Kaplan and Strömberg (2009), the acquisition is typically 60 to 90% debt-financed. The buyer is usually a buyout fund that holds the company for a few years and then sells it, for example to a strategic buyer, to another fund or via the stock market.

Example: Purchase price 800 (8 × EBITDA of 100), debt 480, equity 320: debt to EBITDA 4.8.

Source: Kaplan and Strömberg (2009); Axelson et al. (2013)

More: Buyout funds and management buyouts: how LBOs, MBOs and MBIs work

Fund that delivers a multiple (such as twice) of an index's daily return every day. Over longer periods, its return deviates strongly from that multiple, because the daily adjustment costs value when prices fluctuate. The Portfolio Lab backtest models such funds with a leverage setting per security.

Source: Cheng and Madhavan (2009); Avellaneda and Zhang (2010)

More: Leverage in a portfolio: return, risk, costs and margin calls · Methodology: Backtest methodology: data, process, rebalancing and costs

Interest rate used to discount future liabilities to today. The higher it is, the smaller the present value and the deficit appear. More precise than a single rate is a discount curve with a separate rate for each maturity.

Example: €1,000 due in ten years is worth €744 today at a 3% discount rate, and as much as €820 at 2%.

More: Liability-driven investing and cash flow driven investing: covering liabilities with bonds · Methodology: ALM methodology: how Portfolio Lab measures assets against liabilities

Out-of-court restructuring in which a company agrees new, senior debt with some of its creditors (uptier) or moves collateral into a subsidiary (drop-down). The remaining creditors effectively lose seniority; many companies restructured this way later file for insolvency anyway.

Source: Antill et al. (2024); Roe and Rotaru (2026)

More: Distressed debt: strategies, bankruptcy law, recovery rates and returns when investing in crises

Investing geared to future payment obligations, typical of pension funds: a hedging portfolio of bonds matching the duration of the liabilities, plus a return-seeking portfolio.

Source: Waring (2004)

More: Asset-liability management: aligning your wealth with future spending

A thesis on the pricing of certificates: because investors tend to buy early in the term and sell back toward the end, issuers charge high premiums over fair value early on and low ones later.

Source: Stoimenov and Wilkens (2005); Entrop et al. (2009)

A model of consumption and investment over a whole lifetime, with labor income, retirement and often borrowing limits. Because labor income acts like a safe asset, the optimal equity share in such models usually falls with age.

Source: Cocco et al. (2005); Bodie et al. (1992); Benzoni et al. (2007)

More: Your whole wealth: total wealth from portfolio, home, human capital and car

A fund that automatically lowers its equity allocation as its target date approaches (target-date fund). The logic: as you age, your future labor income, which acts like a bond, shrinks.

Source: Cocco et al. (2005)

More: Equity allocation by age: rules of thumb, glide paths and what theory says

An order with a price limit: buy at no more than, or sell at no less than, the limit. Certain on price, uncertain on execution; resting limit orders in the order book provide liquidity to others.

Source: Harris (2002)

More: Order types and execution: from limit orders to MOC, VWAP, TAS and BTIC

Inflation-protected bond: face value and interest payments rise with the price index. Its yield is a real return.

More: Real return: what is left after inflation

Converting the effects of individual periods so that, over several periods, they add up exactly to the active return for the whole period; common methods are Cariño's logarithmic factors and Menchero's optimized approach.

Source: Cariño (1999); Menchero (2004)

More: Performance attribution: Brinson decomposition, factors and linking over time

Exchange-traded real assets used as inflation protection in a portfolio: inflation-linked bonds, commodity futures, gold, listed infrastructure, REITs and commodity equities. Unlike private real assets, they can be traded daily, but some of them carry equity risk.

Source: Neville et al. (2021)

More: Liquid real assets: inflation protection with tradable real assets in a portfolio · Methodology: Asset classes with a long history: methodology

Preferential right of investors in a sale or liquidation: they get their capital back first (1×) or a multiple of it. Non-participating means: either the money back or conversion into common shares; participating: the money back plus a share of the rest. That is why post-money valuations overstate the value of the common shares.

Source: Gornall and Strebulaev (2020)

More: Venture capital: funding rounds, valuation, the power law and what research knows about returns

A tool with which an open-ended fund manages redemptions: redemption gates, extended notice periods, redemption fees, swing pricing, dual pricing, anti-dilution levies and redemptions in kind, and in exceptional cases suspension and side pockets for illiquid assets. Since April 16, 2026, a management company (Kapitalverwaltungsgesellschaft) must select at least two suitable tools for each open-ended fund.

Source: KAGB (2026); ESMA (2026)

More: Liquidity risk: measuring market liquidity, liquidity premiums and the tools of open-ended funds

A test of whether the first autocorrelations of a series are jointly zero. A small p-value suggests that past returns reveal something about future ones.

Source: Ljung and Box (1978)

Methodology: Asset analysis: methodology from correlation to cointegration

Logarithmic market scoring rule, an automated market maker for prediction markets based on Hanson's market scoring rules. The cost function C(q) = b × ln(Σ e^(q_i / b)) determines prices that add up to 1; with n outcomes, the operator can lose at most b × ln(n).

Example: With b = 100, the first 50 yes contracts cost $28.09 and raise the price from 0.50 to 0.6225.

Source: Hanson (2003)

More: Prediction markets as bets on events: what they can and cannot do

Strategy in which an investor deliberately buys the loans or bonds of a distressed company in order to swap them into equity in the restructuring and take control. Usually this is the class in which the enterprise value runs out (fulcrum security).

Source: Hotchkiss and Mooradian (1997); Jiang et al. (2012)

More: Distressed debt: strategies, bankruptcy law, recovery rates and returns when investing in crises

Raising the floor in steps: once the portfolio has gained one step since the last increase, e.g. 10%, the floor rises to a fixed share of the current value. In between, it stays where it is.

More: CPPI: portfolio insurance with cushion, floor and multiplier · Methodology: CPPI backtest: methodology

An oscillation that is periodic not in time but in the logarithm of the time remaining until the critical time. The intervals between the peaks shrink by a fixed factor, so the waves become faster and faster; the log frequency ω determines this factor.

Source: Sornette, Johansen and Bouchaud (1996)

More: Speculative bubbles: what they are and how the LPPLS model detects them · Methodology: Bubble indicator (LPPLS): methodology

The CSCV measure of the out-of-sample rank of the best in-sample variant: relative rank ω = rank / (N + 1) for N variants, logit λ = ln(ω / (1 − ω)). λ is zero exactly at the median, positive above it and negative below; the share of splits with λ ≤ 0 is the PBO.

Example: Rank 2 of 4: ω = 2 / 5 = 0.4, λ = ln(0.4 / 0.6) = −0.41.

Source: Bailey et al. (2016)

More: Probability of backtest overfitting: does the best variant deliver what the backtest promises?

The distribution of a quantity whose logarithm is normally distributed. It suits prices and wealth, which cannot fall below zero and grow with compounding; many Monte Carlo models assume it for terminal wealth.

Positions that profit from rising volatility, such as bought options or VIX futures. Because of the variance risk premium, they lose on average, but they help in crises.

Strategy that holds bought (long) and sold-short (short) positions at the same time. It earns on the difference between the two sides, such as between the winners and losers of a ranking or the legs of a pair; depending on the weighting, some market risk remains.

Source: Jegadeesh and Titman (1993)

More: Pairs trading and statistical arbitrage: idea, methods, research · Methodology: Long/short and statistical arbitrage: methodology

A backtest uses information that was not yet known at the time, e.g. monthly data that were only published weeks later. Signals therefore have to be lagged.

More: Backtest overfitting: when the past looks too good · Methodology: Backtest methodology: data, process, rebalancing and costs

Breaking funds down to their individual holdings to see the countries, sectors, single securities and risks of the whole portfolio.

More: Look-through: what is really inside your ETFs

Option whose payout depends on the highest or lowest price during its term, such as the final price minus the lowest price. In hindsight, it delivers the best price and is correspondingly expensive.

Source: Goldman et al. (1979); Conze and Viswanathan (1991)

More: Option pricing: where fair option prices come from · Methodology: Option pricer: how Portfolio Lab values options

Losses hurt more than gains of the same size give pleasure. Investors therefore sell too late or too early in crises and avoid investments with visible fluctuations.

Source: Kahneman and Tversky (1979)

Losses not offset are carried forward to the next year, where they reduce future gains. At the bank, this happens automatically in the respective loss offset pot.

Certificate from the bank for losses not yet offset, which must be requested by December 15. With it, losses can be offset in the tax return against gains at another bank.

Source: EStG (2009)

A stock with a small chance of a very large gain, often small, cheap and highly volatile. Investors overpay for this chance: stocks with the highest daily gains in the previous month (MAX effect) subsequently delivered lower returns.

Source: Bali et al. (2011)

More: Stock picking: why individual stocks are so hard to get right

Low-volatility stocks have historically delivered similar or higher returns than high-volatility ones, contradicting the principle “more risk, more return”.

Source: Baker et al. (2011); Ang et al. (2006)

More: The low-volatility anomaly and betting against beta

The average of the deviations below a threshold, raised to the power of an order n. Order 0 is the probability of loss, order 1 the expected shortfall below the threshold, order 2 the semivariance.

Source: Bacon (2008)

The share of time windows ending on the same day whose LPPLS fit has plausible bubble parameters, calculated separately for positive and negative bubbles. Portfolio Lab calculates it from 26 windows of 125 to 750 daily prices.

Source: Zhang et al. (2016); Gerlach et al. (2019)

More: Speculative bubbles: what they are and how the LPPLS model detects them · Methodology: Bubble indicator (LPPLS): methodology

A model by Didier Sornette and co-authors for the price path in a speculative bubble (Log-Periodic Power Law Singularity): the log price grows faster than exponentially toward a critical time tc, overlaid with oscillations that keep accelerating.

Source: Johansen, Ledoit and Sornette (2000); Filimonov and Sornette (2013); Sornette (2017)

More: Speculative bubbles: what they are and how the LPPLS model detects them · Methodology: Bubble indicator (LPPLS): methodology

Long Short-Term Memory: a recurrent neural network with memory cells and gates that control what is kept and what is forgotten. It is suited to sequences such as price series; in a well-known study of S&P 500 stocks, its edge faded from 2010 onwards.

Source: Hochreiter and Schmidhuber (1997); Fischer and Krauss (2018)

More: Return forecasting models: ARIMA, GARCH, LSTM and machine learning

The question of whether good fund results stem from ability or chance. Simulations with randomly drawn returns show that only a few US equity funds earn enough excess return to cover their costs.

Source: Fama and French (2010)

More: Active or passive investing: ETFs versus fund managers

All available money is invested at once. Because markets rise on average, it beats staggered investing in most historical periods, though not always, and the shock of immediate losses is greater.

Source: Rozeff (1994); Constantinides (1979)

More: Lump sum or dollar-cost averaging: invest a large amount at once or in installments?

Modigliani measure: the return a portfolio would have earned at the same volatility as the benchmark. Makes Sharpe ratios comparable in percentage points.

More: Sharpe ratio: return per unit of risk

Average time until a bond's payments are received, weighted by their present values, in years. For a zero-coupon bond it equals the remaining maturity.

Source: Macaulay (1938)

More: Duration: how strongly bonds react to interest rates

Moving Average Convergence Divergence: the difference between two exponential moving averages, usually over 12 and 26 periods. The signal line is the average of this difference over 9 periods; in technical analysis, crossovers count as buy or sell signals.

More: Technical analysis, chart patterns and candlesticks from a quant perspective

Rule by Joel Greenblatt: all stocks are ranked once by earnings yield (operating profit divided by enterprise value) and once by return on capital (operating profit divided by capital employed). The stocks with the smallest sum of both ranks are bought, i.e. those that are good and cheap at the same time.

Example: Stock A: rank 3 for earnings yield and rank 10 for return on capital, sum 13; stock B: 8 + 4 = 12. B ranks ahead of A.

Source: Greenblatt (2005)

More: Legendary investors: the investment styles of the most famous investors, from Graham to Simons

The distance of a vector of movements from the normal case, measured in standard deviations and taking correlations into account: d = √(xᵀ Σ⁻¹ x). A movement against the usual correlations counts as further away than the same movement in line with them. In stress testing it measures how plausible a scenario is; as a turbulence measure, how unusual a period is.

Example: Equities at −30% with a monthly volatility of 4.5% are 6.67 standard deviations away. If interest rates stay unchanged although they normally move along with a correlation of 0.3, the distance grows to 6.67 / √(1 − 0.3²) = 6.99.

Source: Breuer et al. (2009); Kritzman and Li (2010)

More: Historical stress testing: how to apply past crises to your portfolio today

The minimum share of own capital in the securities held in a margin account. If it falls below this level, a margin call follows. US brokers must require at least 25% for equities bought on credit.

Source: FINRA Rule 4210 (2026)

More: Leverage in a portfolio: return, risk, costs and margin calls

The asset class of CTAs: funds and mandates that trade futures on equity indices, bonds, currencies and commodities both long and short, usually with trend signals and a target volatility. Portfolio Lab has the asset class “Trend following (managed futures)” for this.

Source: Fung and Hsieh (2001); Hurst et al. (2017)

More: CTAs and managed futures: industry, position sizing, costs and crisis protection · Methodology: Tactical allocation methodology: how the eleven tactical models work

Acquisition of a company by its own management, usually together with a financial investor and financed with debt; in a management buy-in (MBI), the management comes from outside. The managers invest their own money and often receive a disproportionate share of the increase in value (sweet equity). According to Kaplan and Strömberg (2009), the CEO in US buyouts receives a median 5.4% of the increase in value, and management as a whole 16%.

Source: Kaplan and Strömberg (2009)

More: Buyout funds and management buyouts: how LBOs, MBOs and MBIs work

Assignment by an institutional investor to an asset manager to manage a specific part of its assets according to fixed investment guidelines and against a benchmark, either as a separate account (segregated account) or through a fund held only by that investor, such as a German Spezialfonds.

More: RFP and mandate awards: how institutional investors select asset managers

The distribution of the eigenvalues of a correlation matrix estimated from pure noise. With N independent series and T observations, the eigenvalues lie between (1 − √q)² and (1 + √q)², with q = N/T; only eigenvalues above the upper bound indicate genuine common movements.

Example: 50 assets, 120 months: q = 50/120 ≈ 0.42 and an upper bound of (1 + √0.4167)² = 2.71.

Source: Marchenko and Pastur (1967); Laloux et al. (1999)

More: Beyond Markowitz: estimation error, noise and true diversification · Methodology: Dimensions methodology: how Portfolio Lab counts independent risks

Cash or securities posted for futures, options or swaps to cover losses. If losses grow, more has to be posted (margin call).

A demand for more collateral on a securities-based loan: if your own capital falls below the maintenance margin, you must add money or sell securities, otherwise the lender sells. With leverage of 2 and a 25% maintenance margin, ignoring interest, this happens after a 33.33% price fall since purchase.

Source: Brunnermeier and Pedersen (2009); FINRA Rule 4210 (2026)

More: Leverage in a portfolio: return, risk, costs and margin calls

The gap between estimated intrinsic value and price, as a buffer against errors in your own valuation. Benjamin Graham made it the central concept of value investing.

Example: Value €31.22, price €25: margin of safety 1 − 25 / 31.22 = 19.9%.

Source: Graham (2003)

More: Fundamental analysis: valuing a company like an investor

How much portfolio volatility rises when the weight of a position is increased slightly: the covariance of the position with the portfolio divided by the portfolio volatility.

Source: Roncalli (2013)

More: Risk contribution: breaking portfolio risk down into its parts

A company's stock market value: share price times number of shares. Most indices weight by it.

Each company receives an index weight in line with its market value, usually counting only the freely tradable shares. The weights adjust automatically as prices move; trades are rarely needed.

More: World portfolio: the whole world in one or two ETFs

A price decline of roughly 10 to 20% from the last peak. Corrections are common in equity markets; most of them do not turn into a bear market.

More: Maximum drawdown: the largest loss from a peak

Return of the equity market over the risk-free rate (Mkt-RF). The first factor of almost every factor model; its loading is the market beta.

Source: Sharpe (1964); Fama and French (1993)

More: Factor investing: understanding the Fama-French factors · Methodology: Factor regression, factor allocation and factor statistics: methodology

The price movement that your own order triggers: purchases push the price up, sales push it down. For large orders split into pieces, it grows empirically with roughly the square root of the order size (square-root law).

Example: Daily volatility 2%, order of 4% of daily volume: 2% × √0.04 = 0.40%; at 16% of volume, 2% × √0.16 = 0.80%.

Source: Tóth et al. (2011); Kyle (1985)

More: Order types and execution: from limit orders to MOC, VWAP, TAS and BTIC

A dealer that continuously quotes bid and ask prices and so ensures that a security can be traded. For ETFs, several market makers usually commit to binding quotes within a limited spread.

More: ETF basics: costs, replication and distributions

Under Art. 12 MAR (Market Abuse Regulation), transactions, orders or the dissemination of information that give false or misleading signals about the supply, demand or price of a financial instrument, or that secure an artificial price level. Art. 15 MAR prohibits it; if it affects the price, it is a criminal offense under Section 119 WpHG (Securities Trading Act).

Source: MAR (2014); WpHG § 119 (1998)

More: Pump and dump and penny stocks: how the scam works

The long and short sides cancel out each other's market risk. Dollar-neutral means equal amounts long and short; beta-neutral means the sides are weighted so that the net beta is zero. That is not risk-free: spreads, other factors and crowding remain.

Source: Frazzini and Pedersen (2014)

More: Pairs trading and statistical arbitrage: idea, methods, research · Methodology: Long/short and statistical arbitrage: methodology

MOCC: an order on an index future that refers to the close of the cash market, i.e. the closing auction of the stocks, not to the later end of trading in the future. It is not a standard exchange order type, and the broker decides how to implement it; the counterpart for the open is MOCO (market on cash open). Trading exactly at the index level plus basis is possible via BTIC and TACO on the CME or TAIC on Eurex.

Source: FIX Trading Community (2012); CME Group, TACO (2026)

More: Order types and execution: from limit orders to MOC, VWAP, TAS and BTIC

All risky assets weighted by their market value. In the CAPM every investor holds it; in practice a broad equity index serves as a proxy, which makes the model harder to test.

Source: Roll (1977)

More: CAPM: the capital asset pricing model and the security market line

An assessment of whether an overall market is expensive or cheap, e.g. using the CAPE, the P/E ratio, the dividend yield or the earnings yield relative to bond yields. It helps with return expectations, but hardly with short-term timing.

More: Shiller P/E (CAPE): how expensive is the stock market? · Methodology: Valuation with the Shiller P/E: methodology

An order executed in the closing auction at the closing price; with a limit it is called limit-on-close (LOC). For the opening auction there are market-on-open (MOO) and limit-on-open (LOO) orders. On the NYSE, MOC and LOC orders must be entered by 15:50 local time.

Source: NYSE (2024)

More: Order types and execution: from limit orders to MOC, VWAP, TAS and BTIC

A regression or time series model whose constant, slopes or variance switch depending on a hidden regime; the regime follows a Markov chain. In 1989 James Hamilton used this approach to estimate expansions and recessions from the growth of US gross national product.

Source: Hamilton (1989); Hamilton (1994)

More: Regime models: hidden Markov, Markov switching and more

Excess return divided by the Ulcer index. It rewards strategies that are below their peak only rarely and briefly.

Source: Martin and McCann (1989); Bacon (2008)

More: Risk metrics beyond the Sharpe ratio: Treynor, Calmar, Omega, Ulcer Index and more

Part of the assets that replicates the interest rate and inflation sensitivity of the liabilities: long bonds, linkers, interest rate and inflation swaps. Alongside it is the return-seeking portfolio, which is meant to close a deficit or increase the surplus.

Source: Leibowitz and Henriksson (1988)

More: Liability-driven investing and cash flow driven investing: covering liabilities with bonds

Valuing a rarely traded security, usually a bond, using quoted comparable securities with a similar rating, sector and maturity instead of its own prices. Pricing services supply such evaluated prices.

Example: Spreads of 90 bp at four years and 120 bp at eight years to maturity give an interpolated 105 bp for six years.

Source: IFRS 13 (2011); SEC, Rule 2a-5 (2021)

More: Market making and bond trading: spread, inventory, axes, RFQ, cross trades and matrix pricing

The portfolio with the highest diversification ratio, i.e. weighted individual volatility divided by portfolio volatility. It favors assets that are weakly correlated with one another.

Source: Choueifaty and Coignard (2008)

More: Risk parity: equal risk contributions instead of equal weights · Methodology: Optimization methodology: estimation, objectives, Black-Litterman, resampling and walk-forward

Largest decline from a peak to the subsequent trough in the period under review.

Example: From 120 to 90 is −25%; getting back to 120 takes +33.3%.

More: Maximum drawdown: the largest loss from a peak

An estimation method that chooses the parameters so that the observed data are most probable under the model. It usually works with the log-likelihood log L, the sum of the log densities; this is also the basis of information criteria such as AIC and BIC.

Methodology: Regime methodology: how the hidden Markov model works

The tendency of a variable to return to its long-term average after swings. Valuation metrics such as the CAPE show it over years; returns over short periods hardly show it at all.

Finds the weights with the lowest variance for a target return, or the highest return for a given level of risk. The basis of the efficient frontier; highly sensitive to estimated returns.

Source: Markowitz (1952)

More: Efficient frontier: Markowitz portfolio optimization · Methodology: Optimization methodology: estimation, objectives, Black-Litterman, resampling and walk-forward

The middle value of a sorted series: half of the values lie below it, half above. In Monte Carlo simulations the median terminal wealth is more meaningful than the mean, because a few very good paths pull the mean upwards.

A stock whose price is driven mainly by attention and sentiment in forums and social media, not by new information about the company. The best-known example is GameStop in January 2021.

Example: According to the SEC, GameStop closed at $347.51 on January 27, 2021, more than 1,600% above its closing price on January 11.

Source: SEC (2021)

More: Alternative data: job ads, Reddit, X, satellites and card payments

Money is mentally divided into pots and treated differently, for example dividends as income and capital gains as wealth, even though both are economically equivalent.

The optimal equity allocation in the simplest lifecycle model: risk premium divided by (risk aversion × variance). With a 4% premium, 18% volatility and a risk aversion of 3, the result would be about 41% equities.

Example: 0.04 / (3 × 0.18²) = 41%.

Source: Merton (1969)

More: The Kelly criterion: how much to bet for maximum growth

Financing between senior loans and equity: subordinated, often unsecured and higher-yielding, frequently with PIK interest and an equity kicker such as warrants. In a default, mezzanine is only repaid after the senior creditors.

More: Private debt in practice: direct lending, unitranche, mezzanine, loan structure and fund vehicles

A turbo without a fixed maturity whose stop-loss barrier, for long products, lies above the strike. If it is touched, the issuer unwinds its hedge and pays out a residual value. If the price gaps below the strike, nothing is left.

Example: Strike 18,000, stop-loss 18,300, ratio 0.01: unwinding at 18,250 yields (18,250 − 18,000) × 0.01 = €2.50.

The threshold below which a return counts as a loss from the investor's perspective, e.g. 0% or the money market rate. The Sortino ratio and the Omega ratio depend on it.

Source: Sortino and Price (1994)

More: Sortino ratio and Calmar ratio: measuring downside risk

The minimum number of periods after which a measured Sharpe ratio lies above a threshold with a chosen level of confidence, e.g. 95%. It increases with negative skewness and fat tails, and falls with the square of the gap between the Sharpe ratio and the threshold.

Example: Sharpe ratio of 1.0 p.a. from monthly data, normally distributed, threshold 0: about 35 months for 95% confidence.

Source: Bailey and López de Prado (2012)

More: Deflated Sharpe ratio: how much skill is in a Sharpe ratio?

The mix with the lowest possible volatility. It needs no return estimates, only volatilities and correlations.

More: Efficient frontier: Markowitz portfolio optimization

Uncorrelated factors that stay as similar as possible to the individual positions in a portfolio: each position gets an uncorrelated twin. Their shares of portfolio risk are unique, never negative and interpretable per position, unlike principal components or Euler contributions.

Source: Meucci et al. (2013)

More: Beyond Markowitz: estimation error, noise and true diversification · Methodology: Dimensions methodology: how Portfolio Lab counts independent risks

Fund with an equity share of at least 25% according to its investment terms. It gets half the partial exemption of an equity fund, i.e. 15%.

Source: InvStG (2016)

Maritime Mobile Service Identity: the nine-digit identifier of a ship's radio station with which every AIS message begins; it contains a country code. Portfolio Lab counts distinct MMSIs so that a ship counts only once, however often it reports.

Source: ITU (2026)

Methodology: Ships at chokepoints (beta): methodology

An approximation of the money-weighted return for a period: the gain divided by the starting value plus the time-weighted cash flows. It needs no iteration and is widely used in performance measurement.

Source: Bacon (2008)

More: Time-weighted and money-weighted return: what measures what?

Macaulay duration divided by (1 + yield). It indicates by roughly what percentage the price falls when the yield rises by one percentage point.

More: Duration: how strongly bonds react to interest rates · Methodology: Risk factors in the look-through: methodology

Tendency of assets that have done well recently to keep doing well for a while, usually measured over 6 to 12 months.

More: Tactical allocation: momentum, dual momentum and trend following

Sudden, very large loss of momentum strategies, typically after bear markets when previously beaten-down stocks rebound sharply. Scaling positions by volatility mitigates it.

Source: Daniel and Moskowitz (2016)

More: Tactical allocation: momentum, dual momentum and trend following

Very short-term investments such as overnight deposits, time deposits or short-dated government paper. In euros, the rate is guided by the €STR. Serves as the risk-free rate in the backtest.

Fund that invests in very short-dated, safe securities and overnight deposits. Its return follows the money market rate; ETFs on the €STR track this rate almost exactly.

More: Sharpe ratio: return per unit of risk

The return from the investor's point of view, including the timing and size of their cash flows, calculated as an internal rate of return. Investors who buy mainly after price rises earn less than the fund's time-weighted return.

Source: Dichev (2007)

More: Time-weighted and money-weighted return: what measures what?

Position of the strike relative to the price or forward, often measured as K/F or ln(K/F). A call is in the money when the price is above the strike, at the money when the two are equal and out of the money below. For a put it is the other way round.

Methodology: Option pricer: how Portfolio Lab values options

The random error of a simulation, which arises because only a finite number of paths are drawn. It shrinks with the square root of the number of paths: four times as many paths halve it.

Example: A success rate of 80% from 10,000 paths: standard error √(0.8 × 0.2 / 10,000) = 0.40 percentage points.

Source: Glasserman (2003)

More: Monte Carlo simulation: how safe is your plan?

Runs thousands of random return paths to determine the range of possible outcomes and the success rate of a plan.

More: Monte Carlo simulation: how safe is your plan?

Average price over the last n days or months. If the price is above it, the trend is considered intact, as with the 200-day moving average.

More: Tactical allocation: momentum, dual momentum and trend following

Combining several factors in one portfolio. Because factors such as value and momentum often move in opposite directions, the mix fluctuates less than any single factor on its own.

Source: Ang (2014); Asness et al. (2013)

Attribution in the order in which decisions are made, for example first asset classes, then regions within each asset class, then security selection. Each level measures one decision; what counts as selection at the upper level is broken down further at the level below.

Source: Bacon (2019)

More: Multi-asset attribution: weighting schemes, top-down and bottom-up, currencies and overlays

A method in which a transfer requires several private keys that are stored separately. A single lost or stolen key is then not enough to cause either a loss or a theft. Multi-party computation (MPC), which splits one key mathematically among several parties, has a similar effect.

Example: 2-of-3 scheme: if one key is lost, the remaining two suffice for any transfer; anyone who steals just one key cannot access anything.

More: Crypto in institutional portfolios: access, custody, regulation and risk budget

The explanatory variables of a regression are strongly correlated with each other, e.g. two similar equity indices. The individual coefficients then become uncertain and fluctuate widely, even if the model as a whole fits well.

More: Sharpe's style analysis: what a fund really does

Test many hypotheses and you will find some that look significant purely by chance. With 100 tests at the 5% level, about five hits are to be expected even though no real effect exists; the hurdles therefore have to rise.

Source: Harvey et al. (2016); Bailey and López de Prado (2014)

More: Backtest overfitting: when the past looks too good

The factor by which CPPI turns the cushion into an equity position. A multiplier m can withstand a price drop of 1/m until the next rebalancing; higher values bring more upside potential and more gap risk.

Source: Cont and Tankov (2009)

More: CPPI: portfolio insurance with cushion, floor and multiplier · Methodology: CPPI backtest: methodology

If you check your portfolio often, you see losses more often and perceive equities as riskier than they are over your actual investment horizon. Looking less often can help.

Source: Benartzi and Thaler (1995)

Loan to a fund secured by the value of its holdings (NAV) rather than by unfunded commitments. According to ILPA (2024), it is most often used for early distributions, which have a marked effect on IRR and DPI; ILPA counts it as fund-level leverage, and because the holdings are jointly liable, strong ones can be dragged down by weak ones.

Source: ILPA (2024)

More: Private equity explained: strategies, fund structure, fees and what research shows about returns

The mirror image of a speculative bubble: the price falls faster and faster, driven by panic and herding. In the LPPLS model the trend parameter B is then positive; the end can be a powerful upward reversal.

Source: Demirer et al. (2019)

More: Speculative bubbles: what they are and how the LPPLS model detects them · Methodology: Bubble indicator (LPPLS): methodology

Describes the entire yield curve with a few parameters for level, slope and curvature. The Svensson extension with a second hump is used by many central banks, including the Bundesbank.

Source: Nelson and Siegel (1987); Svensson (1994)

More: Yield curve: what the term structure reveals and why an inverted curve is seen as a warning sign

The value of all of a fund's assets minus its liabilities, per unit. It is determined once a day; an ETF's market price fluctuates around it.

More: ETF basics: costs, replication and distributions

An approximation of liquidity in the US financial system: the Fed's total assets minus the Treasury's account at the Fed minus reverse repos. When it rises, more money tends to flow into markets.

Methodology: Sentiment: methodology for the fear and greed index, put/call ratio and COT

An index variant in which dividends are reinvested after deducting a withholding tax assumed at a flat rate. Many indices use the rate for investors without treaty benefits; an ETF with a more favorable domicile can therefore beat its index.

A person's short positions in a company's shares minus their long positions in them, as a percentage of the issued share capital. In the EU it must be reported to the regulator from 0.1% and published from 0.5%, and then at every further 0.1 percentage points, including when it falls below a threshold.

Example: 650,000 shares short and 120,000 long with 100 million shares in issue: 0.53%, so it must be reported and published.

Source: Short Selling Regulation (2012)

More: Short selling, hedge funds and hedging: types and how they work

Standard errors that take autocorrelation and changing dispersion into account. Indispensable for regressions with overlapping periods, e.g. 10-year returns in monthly steps.

Source: Newey and West (1987)

Methodology: Valuation with the Shiller P/E: methodology

Certificate from the tax office for people with low income, such as students. If the bank has it on file, it withholds no investment income tax, regardless of the saver's allowance.

The brightness of the earth at night from satellite images, used as a measure of economic output. It mainly supplements official statistics where these are weak, and allows estimates for regions and cities.

Source: Henderson et al. (2012)

More: Alternative data: job ads, Reddit, X, satellites and card payments

A bell-shaped distribution determined solely by its mean and standard deviation. About 68% of values lie within one standard deviation and about 95% within two. In reality, returns have fat tails.

More: Skewness and kurtosis: why market crashes are more frequent than the normal distribution says

The time between the redemption request and the redemption date. The longer it is, the more a semi-liquid ELTIF may pay out per date under the EU standards, because it has more time to sell assets.

Example: Quarterly redemption: without notice, at most 25.0% of the liquid base per date; with three months' notice, 33.3%; with six months, 50.0%.

Source: Delegated Regulation (EU) 2024/2759 (2024)

A credit, agreed in some double taxation agreements, for a tax that the source country does not levy at all or levies at a lower rate, e.g. with some emerging and developing countries. Where it applies without further proof, it is included in the BZSt list.

Source: BZSt (2026)

Estimating the present or the very recent past before official figures are published, using quickly available data such as ship movements, surveys or payments. AIS data are suitable, for example, for nowcasting seaborne trade.

Source: Arslanalp et al. (2019); Cerdeiro et al. (2020)

More: Ship tracking data and satellite images: what they reveal about commodities

Option Based Portfolio Insurance: equities plus a put, or a safe asset plus a call, which can also be replicated with continuously adjusted positions in equities and cash. The protection applies at a fixed end date and costs an option premium.

Source: Bertrand and Prigent (2002); Rubinstein and Leland (1981)

More: CPPI: portfolio insurance with cushion, floor and multiplier

Investment fund under the KAGB (German Investment Code) that invests in many properties and issues and redeems units continuously, but only after a minimum holding period of 24 months and with an irrevocable redemption notice given twelve months in advance. At least 5% of the fund's assets must be available for redemptions; if the money is not enough, the fund suspends redemptions, and after 36 months without sufficient liquidity it is wound up.

Source: KAGB (2013)

More: Real estate as an investment: rental property, REITs, open-end funds and private real estate

The percentage change in a warrant's price per 1% change in the price of the underlying: delta times simple leverage. Unlike simple leverage, it takes into account that an out-of-the-money warrant moves less than the underlying.

Example: Delta 0.3836, spot €100, ratio 0.1, price €0.53: omega = 0.3836 × 100 × 0.1 / 0.53 = 7.24.

Methodology: Option pricer: how Portfolio Lab values options

The ratio of gains above a threshold to losses below it, weighted by their probabilities. It uses the entire distribution rather than just the mean and variance; above 1 means more gain mass than loss mass.

Source: Bacon (2008)

More: Risk metrics beyond the Sharpe ratio: Treynor, Calmar, Omega, Ulcer Index and more

The forgone return of the best alternative. Equity tied up in a home costs no interest, but it does cost the return it would have earned in a brokerage account.

Example: €120,000 of equity at an expected return of 5% in a brokerage account: €6,000 of opportunity cost a year.

More: Your whole wealth: total wealth from portfolio, home, human capital and car

Roll strategy for commodity futures that does not mechanically switch into the next contract to expire, but instead, for example, picks the contract with the least contango or the strongest backwardation, or shifts the timing of the switch. The basis of many “enhanced” commodity indices.

Source: Mouakhar and Roberge (2009)

More: Active or passive in bonds and commodities: why the rules differ from equities

A physically replicating ETF holds only some of the index constituents, selected so that countries, sectors and metrics match the index. Common for indices with thousands of securities.

More: ETF basics: costs, replication and distributions

The right, but not the obligation, to buy (call) or sell (put) an underlying at a fixed price. The buyer pays a premium for this; the seller (writer) bears the risk.

Source: Black and Scholes (1973)

More: Option pricing: where fair option prices come from · Methodology: Option pricer: how Portfolio Lab values options

Spread of a bond with embedded options, such as an issuer call right, after removing the value of the options; calculated with an interest rate model. Without options, it equals the Z-spread; for callable bonds, it is lower.

More: Bond math: calculating price, yield, duration, convexity and spreads

A service that feeds data from outside the blockchain (prices, interest rates, events) into a smart contract. It is a weak point: if the reported value is wrong or manipulated, the contract calculates with wrong numbers, e.g. for margin calls or liquidations.

More: Digital assets: tokenization, stablecoins, crypto securities and the digital euro

Discount when a loan or bond is paid out: the borrower receives less than face value but repays the full face value. The discount raises the lender's return, spread over the term, and all the more the earlier the loan is repaid.

Example: Paid out at 98, repaid at 100 after four years: roughly 2 / 4 = 0.5 percentage points of extra return a year.

More: Private debt in practice: direct lending, unitranche, mezzanine, loan structure and fund vehicles

A random process that is pulled back toward equilibrium with a force proportional to its distance from it. The standard model for spreads and residuals in statistical arbitrage; in daily data it corresponds to an AR(1) regression, from which the speed of reversion and the half-life follow.

Source: Uhlenbeck and Ornstein (1930); Avellaneda and Lee (2010)

More: Pairs trading and statistical arbitrage: idea, methods, research · Methodology: Long/short and statistical arbitrage: methodology

Fund without partial exemption, such as bond, money market or commodity funds. Its income is fully taxable, including the Vorabpauschale.

A measure of forecast quality outside the sample: 1 minus the model's squared error divided by the squared error of the historical mean. A positive value means the model beats the mean; for monthly equity returns, even small positive values are rare.

Example: Mean squared error of 19.90 instead of 20.00 for the historical mean: 1 − 19.90 / 20.00 = 0.5%.

Source: Campbell and Thompson (2008); Welch and Goyal (2008)

More: Return forecasting models: ARIMA, GARCH, LSTM and machine learning

Committing more than the target allocation implies, because the full commitment is never invested at the same time: early funds are already distributing, while late ones have not yet called everything. The overcommitment ratio sets NAV plus unfunded commitments against the target amount; the unfunded commitments must be payable at any time.

Example: Target 15%, unfunded commitments 8.99% of assets: (15 + 8.99) / 15 = 1.60.

More: Takahashi-Alexander model: forecasting the cash flows of private markets funds

Investors believe their knowledge and accuracy are greater than they really are. The result is frequent trading: in a large study, the households with the highest turnover earned considerably lower returns than the market.

Source: Barber and Odean (2000)

A model adapts to the noise of the past rather than to the real relationships. Telltale signs: many parameters, a dazzling backtest, disappointing results afterward.

Source: Bailey et al. (2016); López de Prado (2018)

More: Backtest overfitting: when the past looks too good

Share of two funds that is invested in the same securities: the sum of the smaller of the two weights across all common holdings. What does not overlap is what the second fund genuinely adds to the portfolio.

Example: Fund A holds X at 40% and Y at 30%, fund B holds X at 50% and Y at 20%: overlap 40% + 20% = 60%.

More: Thematic ETFs and hype: what studies, costs and overlaps reveal

Rolling multi-year returns in monthly steps share almost all their months with their neighbors. The number of truly independent observations is much smaller than the number of data points suggests.

Source: Boudoukh et al. (2008)

More: Shiller P/E (CAPE): how expensive is the stock market?

Derivatives, usually futures, swaps or currency forwards, placed on top of an existing portfolio to change exposure or currency risk without buying or selling the securities themselves.

More: Multi-asset attribution: weighting schemes, top-down and bottom-up, currencies and overlays

A flat or house in which the owner lives. It is investment and consumption at the same time, usually leveraged with a loan, hard to sell, and a concentrated risk in one location.

Source: Flavin and Yamashita (2002); EStG § 23 (2009)

More: Your whole wealth: total wealth from portfolio, home, human capital and car

Varying data, periods or parameters until a result looks significant. In backtests this often happens unconsciously, when only the successful variants are pursued further.

More: Backtest overfitting: when the past looks too good

The probability of seeing a result at least as extreme if in truth there is no effect. A small p-value argues against chance, but it is not the probability that the strategy works.

Distance between two prices in pairs trading, such as ln A − β × ln B or the difference of the normalized prices. If it reverts to its mean, the position makes money; if it keeps widening, the position loses. Not to be confused with the bid-ask spread.

Source: Vidyamurthy (2004)

More: Pairs trading and statistical arbitrage: idea, methods, research · Methodology: Long/short and statistical arbitrage: methodology

Trading two similar securities against each other: if their prices drift unusually far apart, the relatively expensive one is sold short and the relatively cheap one is bought; the trade is closed when the gap narrows again. The position is largely market neutral.

Source: Gatev et al. (2006); Vidyamurthy (2004)

More: Pairs trading and statistical arbitrage: idea, methods, research · Methodology: Long/short and statistical arbitrage: methodology

Value at risk from the mean and standard deviation, assuming a normal distribution, e.g. the mean minus 1.645 standard deviations at the 95% level. Underestimates losses when tails are fat.

Source: Jorion (2007)

More: Value at risk and conditional VaR: how much you could lose in a bad case

The base index from which an index variant is derived, e.g. a global index from which an ESG or climate variant is built. The variant's deviation is measured with active share and tracking error.

More: ESG ETFs: index rules, ratings, returns and the limits of sustainable funds

EU Paris-aligned benchmark: a climate index with a greenhouse gas intensity at least 50% below that of the investment universe, which must then fall by at least 7% a year, plus exclusions of coal (from 1% of revenue), oil (from 10%), gas (from 50%) and power generation with more than 100 g CO₂e per kWh (from 50%).

Example: After ten years with a 7% reduction a year: 0.5 × 0.93¹⁰ = 24.2% of the universe's initial intensity.

Source: EU Climate Benchmarks Regulation (2020)

More: ESG ETFs: index rules, ratings, returns and the limits of sustainable funds

A result depends not only on the final price but on the entire price path, as with leveraged ETFs, CPPI or Asian options. With daily reset leverage L, volatility without a trend costs roughly the factor exp(−L × (L − 1) / 2 × σ² × T).

Example: Leverage 2, index unchanged after one year, volatility 20%: exp(−0.04) = 0.961, i.e. −3.92%.

Source: Avellaneda and Zhang (2010)

More: Leverage in a portfolio: return, risk, costs and margin calls

A sequence of iterated integrals of a path that summarizes the course of several time series, including the order of their movements. Linear functions of the signature can approximate continuous, even path-dependent functions of the path; in portfolio theory they serve as building blocks of signature portfolios or as a substitute for correlation matrices.

Source: Allan et al. (2023); Cuchiero and Möller (2025); Gregnanin et al. (2024)

More: Beyond Markowitz: estimation error, noise and true diversification · Methodology: Dimensions methodology: how Portfolio Lab counts independent risks

Pension financing in which the contributions of those in work pay current pensions directly, without any capital being saved. This is how the statutory pension insurance works in Germany. Its implicit return follows growth in the total wage bill, not the capital market.

Source: Samuelson (1958); Aaron (1966)

Interest that is not paid in cash but added to the loan; the debt grows. With a PIK toggle, the borrower may choose. According to FSB (2026), PIK is used in about 12% of private credit loans; a rising share can point to payment difficulties.

Example: 8% PIK on €100 million over three years: 100 × 1.08³ = €125.97 million of debt at the end.

Source: FSB (2026); IMF (2024)

More: Private debt in practice: direct lending, unitranche, mezzanine, loan structure and fund vehicles

Timing of payments in financial mathematics: in advance at the start of a period, in arrears at the end. A payment in advance earns interest for one period longer; the future value and the present value of an annuity are therefore higher by the factor (1 + i).

Example: €100 a year for ten years at 5%: future value in arrears €1,257.79, in advance €1,320.68.

More: Compound interest: how returns on returns make wealth grow · Methodology: Methodology of the free calculators: savings plan, withdrawal and leveraged ETF

Share of profit that a company pays out as dividends. A ratio close to or above 100% leaves little room: if profits fall, the dividend has to be cut or paid out of the company's substance.

Example: Earnings per share €4, dividend €3: payout ratio 75%.

More: Dividend strategies and dividend ETFs under scrutiny: irrelevance, factors, risks

Colloquially, a share with a very low price and a small market capitalization, often traded on the open market (Freiverkehr) or over the counter, with little trading volume and few disclosure requirements. In Germany it is not a fixed legal term.

Source: Leuz et al. (2017)

More: Pump and dump and penny stocks: how the scam works

The claim to a future pension accrued so far, e.g. from the statutory pension insurance, a civil service pension or an occupational pension. Its present value is a large, bond-like item in total wealth.

More: Your whole wealth: total wealth from portfolio, home, human capital and car · Methodology: ALM methodology: how Portfolio Lab measures assets against liabilities

Share of observations up to a given value. The 90th percentile is exceeded in only 10% of cases; a percentile rank of 85% means: higher than on 85% of days.

More: VIX: how to read the stock market's fear gauge

The share of historical values that lie below the current value. A VIX with a percentile rank of 90 is higher than on 90% of the days in the period under review.

Methodology: Volatility dashboard: methodology

Breaking down the return difference between portfolio and benchmark into its causes, e.g. allocation, selection and interaction according to Brinson, or factor contributions from a regression.

More: Performance attribution: Brinson decomposition, factors and linking over time

How much the variant that was best in the backtest falls off on unused data: in CSCV, the regression of the winner's out-of-sample metric on its in-sample metric across all splits. A flat or falling line means that a good in-sample value reveals little or nothing about out-of-sample performance.

Source: Bailey et al. (2016)

More: Probability of backtest overfitting: does the best variant deliver what the backtest promises?

A performance-related fee for the manager, usually a share of the profit above a hurdle or above the high-water mark. Classic for hedge funds and CTAs is 20% alongside a 2% management fee, “2 and 20” for short.

Example: Gross return 8%, 2% management fee, 20% performance fee: 8 − 2 − 0.2 × 6 = 4.8% net.

Source: Bhardwaj et al. (2014)

More: CTAs and managed futures: industry, position sizing, costs and crisis protection

An allocation proposed by Harry Browne, with one quarter each in equities, long-term government bonds, gold and money market. Each component is meant to shine in a different economic environment.

More: All Weather portfolio: ready for every economic climate?

The highest annual withdrawal, as a percentage of starting wealth and adjusted for inflation each year, at which wealth at the end is at least as large in real terms as at the start. It is lower than the safe withdrawal rate, which is allowed to use up the capital.

More: Safe withdrawal rate: how good is the 4% rule? · Methodology: Backtest methodology: data, process, rebalancing and costs

Distortion of average returns because a rare, very bad event does not occur in the sample at all, or occurs too rarely. Named after the Mexican peso; regarded as one explanation for the high carry returns.

Source: Burnside et al. (2011)

More: Carry trade: earning interest with currencies and bonds

Covered bond issued by a bank that is additionally secured by a pool of mortgage or public-sector loans. Pfandbriefe are regarded as very safe and yield slightly more than government bonds.

Methodology: Risk factors in the look-through: methodology

The ETF actually buys the securities in the index, either all of them (full replication) or a representative selection (sampling). The counterpart to synthetic replication via swaps.

More: ETF basics: costs, replication and distributions

Data as they actually stood at each earlier point in time, without later corrections, revisions or reclassifications. Only with such data does a backtest avoid look-ahead bias, especially with alternative data, whose history providers can adjust retrospectively.

More: Alternative data: job ads, Reddit, X, satellites and card payments

The strategic asset allocation set down in writing: target weights per asset class, each with an index. Together they form the benchmark against which tactical deviations and security selection have to be measured.

Source: Brinson et al. (1986); GIC (2013)

More: Strategic and tactical asset allocation and the total portfolio approach

Separating market return (beta) from selection skill (alpha): a manager's alpha is transferred to a different market using futures or swaps. A forerunner of return stacking; it requires leverage and financing.

Source: Kung and Pohlman (2004)

More: Leveraged ETFs and return stacking: path dependence, costs and research

A measure of diversification that links it to the non-normality of portfolio returns and is defined as a ratio of homogeneous risk measures of the same degree. That is why leverage does not change the measure. Maximizing it is a non-convex optimization problem.

Source: Barkhagen et al. (2023)

More: Beyond Markowitz: estimation error, noise and true diversification · Methodology: Dimensions methodology: how Portfolio Lab counts independent risks

Strategies that limit a portfolio's downside while leaving part of the upside open, e.g. CPPI or OBPI. They sell when prices fall and buy when they rise; they came under criticism in the 1987 crash.

Source: Leland (1980); Rubinstein and Leland (1981); Leland (1988)

More: CPPI: portfolio insurance with cushion, floor and multiplier

Extremely skewed distribution of proceeds in venture capital: a few holdings deliver almost all of a fund's return, while most deliver little or nothing. According to Hall and Woodward (2010), almost three quarters of the founders of venture-backed companies received nothing at exit.

Example: Fund with 20 holdings: one 25× hit delivers 100 of €172 million in proceeds, i.e. 58.14%.

Source: Hall and Woodward (2010); Kerr et al. (2014)

More: Venture capital: funding rounds, valuation, the power law and what research knows about returns

Value of a start-up before the money from a new financing round. The post-money valuation is pre-money plus the investment; the new investor's stake is the investment divided by post-money. An option pool created before the round is included in the pre-money and dilutes only the existing shareholders.

Example: €4 million pre-money plus a €1 million investment give €5 million post-money; the investor holds 1 / 5 = 20%.

More: Venture capital: funding rounds, valuation, the power law and what research knows about returns

A market in which contracts on future events are traded, e.g. election results, interest rate decisions or sports results. The price of a contract that pays 1 if the event occurs is regarded as an estimate of its probability, distorted by fees, interest and betting behavior.

Source: Wolfers and Zitzewitz (2004); Berg et al. (2008)

More: Prediction markets as bets on events: what they can and cannot do

In Bayesian statistics, the distribution of future returns that already incorporates the uncertainty about means and covariances. It is wider than the distribution with fixed, estimated parameters.

Source: Harvey et al. (2008)

More: Michaud resampled optimization: more stable portfolio weights through simulation

The percentage by which acquiring the underlying via a warrant is more expensive than buying it directly. For a call: (strike + price / ratio − spot) / spot. It equals the rise the underlying needs by expiry for you to break even.

Example: Spot €100, strike €110, price €0.53, ratio 0.1: (110 + 5.30 − 100) / 100 = 15.30%.

The deviation of an ETF's market price from its net asset value. Small in liquid markets; in periods of stress, such as for bond ETFs in March 2020, significant discounts can arise.

More: ETF basics: costs, replication and distributions

Today's value of a future payment, discounted at an interest rate. At 3%, €1,000 due in ten years is worth about €744 today.

More: Asset-liability management: aligning your wealth with future spending

Present value of a series of equal payments of €1 each: it tells you how much capital is needed today to make n payments at an interest rate i per period. In arrears (1 − (1 + i)^−n) / i, in advance (1 + i) times that. Capital divided by the factor gives the sustainable withdrawal.

Example: 360 months at 5% p.a., i.e. 0.4074% a month, in advance: factor 189.43; from €300,000, this supports €1,583.71 a month.

More: Safe withdrawal rate: how good is the 4% rule? · Methodology: Methodology of the free calculators: savings plan, withdrawal and leveraged ETF

Market value divided by the book value of equity. Fama and French sort stocks into value and growth by its inverse (book-to-market).

Source: Fama and French (1992)

More: Factor investing: understanding the Fama-French factors

Share price divided by earnings per share, usually over the last twelve months. A P/E of 20 means: the price equals 20 years of earnings. Fluctuates more with the business cycle than the CAPE.

More: Shiller P/E (CAPE): how expensive is the stock market?

Difference between the forward rate for a future period and today's key interest rate, often expressed in rate steps of 0.25 percentage points. Positive means the market is pricing in hikes, negative means cuts, in each case including term and liquidity premiums.

Example: Forward rate in one year 2.20%, deposit rate 2.50%: −0.30 percentage points ÷ 0.25 = −1.2 rate steps, i.e. a little more than one cut.

More: Market expectations: what the yield curve, inflation-linked bonds and options reveal about the future · Methodology: Macro dashboard and regime analysis: methodology

Breaks the common variation of many assets down into independent components. If the first one explains almost everything, the portfolio essentially holds just one risk.

More: Correlation and diversification: why mixing assets reduces risk

Loans that funds and other non-banks extend directly to companies, mostly mid-sized ones, without an exchange and without syndication through banks. They usually carry floating rates and are senior secured, are held to maturity and are valued with models rather than market prices.

Source: Cai and Haque (2024); IMF (2024)

More: Private credit and public credit compared: returns, risks and what the research shows

Gains from selling certain assets such as physical gold or cryptocurrencies are tax-free if more than one year passes between purchase and sale. Within that period, they are taxed at your personal tax rate.

The probability that the true Sharpe ratio lies above a threshold, given the estimated Sharpe ratio, the length of the series, and the skewness and kurtosis of the returns. With the expected best Sharpe ratio of many trials as the threshold, it becomes the deflated Sharpe ratio.

Source: Bailey and López de Prado (2012)

More: Deflated Sharpe ratio: how much skill is in a Sharpe ratio?

The probability that the configuration that is best in the backtest performs only below average out of sample. Estimated over many splits of the data into training and test parts.

Source: Bailey et al. (2016)

More: Probability of backtest overfitting: does the best variant deliver what the backtest promises?

The probability that, with the planned withdrawals, wealth runs out before the end of the planning horizon. The counterpart of the success rate in a Monte Carlo simulation.

Source: Milevsky and Robinson (2000)

More: Monte Carlo simulation: how safe is your plan?

Statistical model for yes/no events: the probability is the cumulative distribution function Φ of the standard normal distribution evaluated at a linear function of the explanatory variable, P = Φ(α + β · x). The parameters are estimated by maximum likelihood; a related model is the logit model with the logistic function.

Source: Estrella and Trubin (2006)

More: Market expectations: what the yield curve, inflation-linked bonds and options reveal about the future · Methodology: Macro dashboard and regime analysis: methodology

Excess return of profitable companies, measured for example by gross profit relative to total assets. It complements value well, because profitable firms tend to be on the expensive side.

Source: Novy-Marx (2013)

Financing a single venture through a dedicated special purpose vehicle: lenders are repaid only from the project's cash flows, without recourse to the owners' other assets. The debt is tiered by seniority (senior before mezzanine); covenants such as lock-ups, cash sweeps and reserve accounts protect the lenders.

Example: For bank loans to projects, the cumulative default rate after ten years was 5.0% according to Moody's (Basel definition), and the average recovery rate after a default was 81.5%.

Source: Moody's (2020); Blanc-Brude and Hasan (2016)

More: Infrastructure investing: equity and debt, revenue models, valuation and research

Description of how people actually decide under uncertainty: they evaluate gains and losses relative to a reference point, are loss-averse and overweight small probabilities.

Source: Kahneman and Tversky (1979)

Equity portfolio plus bought puts as insurance. Limits the loss, but costs noticeable return over the years, because protection is expensive on average.

More: Option pricing: where fair option prices come from

Substitute series for the period before a fund's launch, such as an index or an older fund with a similar strategy. Extends backtests, but is only an approximation.

Compares a fund's cash flows with an investment in an index at the same points in time. In the KS-PME of Kaplan and Schoar, distributions (plus NAV) and calls are each divided by the index level and set in relation to each other; above 1, the fund did better. Direct alpha turns this into an excess return per year.

Example: In the sample fund: 102.42 / 85.51 = 1.20, direct alpha 3.55% a year.

Source: Kaplan and Schoar (2005); Sorensen and Jagannathan (2015); Gredil et al. (2023)

More: Measuring private markets: J-curve, cash flows, smoothing and public proxies

Listed investment with a risk similar to that of a private asset class, used as a yardstick or substitute series; for buyouts, for example, small value stocks with leverage. Unlike a series built from estimated fund values, a proxy is not smoothed and shows volatility and correlation more realistically.

Example: Small value index with a D/E of 0.5 as a proxy for buyouts with a D/E of 1.5: leverage L = 2.5 / 1.5 = 1.67.

Source: Phalippou (2014); L’Her et al. (2016); Stafford (2022)

More: Measuring private markets: J-curve, cash flows, smoothing and public proxies

Market manipulation in which perpetrators buy shares cheaply, drive up the price with promotion, rumors or sham trades, and then sell to the buyers they have lured in. Afterward the price usually collapses.

Source: Leuz et al. (2017); Aggarwal and Wu (2006)

More: Pump and dump and penny stocks: how the scam works

Put option: makes money when the underlying falls below the strike price. Bought puts hedge an equity portfolio against crashes, but cost premium on an ongoing basis.

More: Option pricing: where fair option prices come from

Model-free relationship between a European call and put with the same strike and maturity: call minus put equals the discounted forward minus the discounted strike. If the market deviated from it, there would be an arbitrage; conversely, parity yields the forward.

Example: Price and strike 100, one year, 5% interest rate, 20% volatility: call 10.45 − put 5.57 = 100 − 100 × e^(−0.05) = 4.88.

Source: Hull (2021)

More: Option pricing: where fair option prices come from · Methodology: Option pricer: how Portfolio Lab values options

Selling puts on an index and holding the notional amount in safe assets. Similar profile to a covered call: steady premiums, but losses in crashes.

Traded (or open) puts divided by calls. High values indicate a lot of hedging and therefore fear; contrarian investors often see this as a buying opportunity.

Source: Pan and Poteshman (2006)

Methodology: Sentiment: methodology for the fear and greed index, put/call ratio and COT

Factor model of market, size, investment and profitability (return on equity), derived from the investment theory of the firm. A rival to the five-factor model.

Source: Hou et al. (2015)

An LPPLS fit whose parameters pass the filters for a bubble: exponent m and log frequency ω within typical ranges, tc close to the last price, enough oscillations in the window and a damping at which the hazard rate does not turn negative.

Source: Demirer et al. (2019)

Methodology: Bubble indicator (LPPLS): methodology

Factor made up of profitable, growing, safe and well-run companies against their opposites. Quality stocks delivered higher risk-adjusted returns than their price suggested.

Source: Asness et al. (2019)

More: The low-volatility anomaly and betting against beta

Losses of quantitative long/short equity strategies in August 2007, especially in the week from August 6. According to the analysis by Khandani and Lo, it was a consequence of market-wide deleveraging and the sudden withdrawal of market-making capital; the unwinding began with financials, the long side of value by book-to-price ratio and the short side of earnings momentum.

Source: Khandani and Lo (2011)

More: Momentum crashes: why momentum collapses rarely but violently, and what volatility scaling and crowding measures show

The value below which a given share of the observations lies. The 5% quantile of monthly returns is the boundary of the worst 5% of months and the basis of historical value at risk.

Coefficient of determination of a regression, between 0 and 1: the share of the variation explained by the explanatory variables (such as the market).

More: Beta and alpha: how closely a fund moves with the market

The theory of large random matrices, used in investing as a yardstick for noise in estimated correlation matrices: most of the spectrum of stock correlations looks like noise, and only a few large eigenvalues, such as the market factor, carry information. Methods that clean up the noise band of a matrix build on this.

Source: Laloux et al. (1999); Plerou et al. (1999); Bun et al. (2017)

More: Beyond Markowitz: estimation error, noise and true diversification · Methodology: Dimensions methodology: how Portfolio Lab counts independent risks

Each change is independent of the previous ones. Prices in an efficient market should move roughly like this; deviations point to trends or mean reversion.

Source: Fama (1965); Lo and MacKinlay (1988)

More: The efficient market hypothesis: why it is so hard to beat the market

The correlation of ranks rather than values (Spearman). It measures whether two variables rise together even if the relationship is not linear, and reacts less to outliers.

A bubble that is consistent with rational behavior: investors buy despite overvaluation because the bubble grows fast enough to offset the risk of it bursting. The more likely the burst, the faster it has to grow.

Source: Blanchard and Watson (1982)

More: Speculative bubbles: what they are and how the LPPLS model detects them

Fund that invests mainly in real estate. Partial exemption of 60%, or 80% for mainly foreign real estate, because foreign taxes are already incurred at fund level.

Source: InvStG (2016)

Tax on buying land or a flat, based on the purchase price. Federal law provides for 3.5%; the federal states set their own rates, in 2026 ranging from 3.5% in Bavaria to 6.5% in, for example, North Rhine-Westphalia. Gifts, inheritances and transfers to spouses or children are exempt.

Example: Flat for €400,000 in North Rhine-Westphalia: 6.5% × €400,000 = €26,000.

Source: GrEStG (1997); Bremisches Gesetzblatt (2025); NRW Tax Administration (2026)

Interest rate after inflation. Exactly: (1 + nominal rate) / (1 + inflation) − 1; approximately: nominal rate minus inflation.

Example: 5% interest at 3% inflation: 1.05 / 1.03 − 1 = 1.94%.

Source: Fisher (1930)

More: Real return: what is left after inflation

Return after inflation: (1 + nominal) / (1 + inflation) − 1.

Example: 7% nominal at 2.5% inflation is 4.39% in real terms.

More: Real return: what is left after inflation

Volatility that actually occurred, usually from the daily returns of the last 21 trading days, annualized with √252. On average it is below implied volatility.

More: VIX: how to read the stock market's fear gauge · Methodology: Volatility dashboard: methodology

Resetting the weights to the target allocation, either by trading or through targeted contributions.

More: Rebalancing: getting your portfolio back on course

The extra return that regularly resetting to fixed weights can generate when assets fluctuate and are weakly correlated. It is not a guaranteed gain and can turn negative in long trends.

Source: Booth and Fama (1992); Willenbrock (2011)

More: Rebalancing: getting your portfolio back on course

Recent experience carries too much weight: after good years, investors expect too much, after crashes too little. That is why money often flows into funds after they have done well.

A significant, broad-based decline in economic output lasting several months. As a rule of thumb, two quarters of falling gross domestic product count as a recession; in the US, a committee of the NBER officially dates the phases.

Source: Estrella and Mishkin (1998)

Methodology: Macro dashboard and regime analysis: methodology

Probability, estimated from a model, that a recession will be under way in a future month. A well-known example is the New York Fed's probit model using the 10-year minus 3-month spread, twelve months ahead. It is a model figure, not a market price.

Example: With α = −0.6045 and β = −0.7374 and a spread of zero: Φ(−0.6045) = 27.3%.

Source: Estrella and Trubin (2006); Estrella and Mishkin (1998)

More: Market expectations: what the yield curve, inflation-linked bonds and options reveal about the future · Methodology: Macro dashboard and regime analysis: methodology

Share of a defaulted claim that the creditor ultimately gets back, for example by realizing collateral or through a restructuring. Its counterpart is the loss given default = 1 − recovery rate; the expected loss is the probability of default times the loss given default. It depends mainly on the seniority of the claim and on the collateral.

Example: Default rate of 5.0% over ten years and a recovery rate of 81.5%, as for project loans in Moody's data: expected loss of 0.93% over ten years.

Source: Moody's (2020)

More: Infrastructure investing: equity and debt, revenue models, valuation and research

A cap on redemptions per dealing date. If more investors want to exit, payouts are made pro rata; the rest waits for a later date.

Example: Limit €10 million, redemption requests €20 million: everyone receives 50% of their request.

Source: Delegated Regulation (EU) 2024/2759 (2024)

How much ongoing costs lower the annual return. If the costs are deducted from the fund's assets, (1 + r) × (1 − TER) − 1 remains. Over the full term, the fees also cost the return they would otherwise have earned.

Example: 7% before costs and a TER of 0.2%: 1.07 × 0.998 − 1 = 6.786%, i.e. 0.214 percentage points less per year.

More: ETF basics: costs, replication and distributions · Methodology: Methodology of the free calculators: savings plan, withdrawal and leveraged ETF

A simple, low-cost portfolio of index investments with the risk the owner is willing to bear, e.g. 80% equities and 20% bonds. It is the yardstick and the hurdle for the actual, actively managed portfolio.

Source: NZ Super Fund (2023); CPP Investments (2023); CalPERS (2025)

More: Strategic and tactical asset allocation and the total portfolio approach

Theory by George Soros: market participants' expectations do not just reflect reality, they also change it. Rising prices, for example, make financing easier and so improve the very figures on which the prices rest. In this way, excesses can reinforce themselves until they tip into a downturn.

Source: Soros (2003)

More: Legendary investors: the investment styles of the most famous investors, from Graham to Simons

The wish to avoid later regret. It explains why many people prefer to invest in installments: if the market falls after the first purchase, only part of the money is affected.

Source: Statman (1995)

Return on invested capital that a regulator allows operators of natural monopolies such as electricity and gas grids. It is collected through network charges; the regulator weighs whether the grids remain financeable and whether consumers are protected from excessive charges. It is set for each regulatory period, so interest rate changes feed through with a delay.

Example: Draft by the Bundesnetzagentur (Federal Network Agency) for the gas grids 2028 to 2032: 40% equity at 5.76% before tax and 60% debt at 2.43% give a WACC of 3.76%.

Source: Bundesnetzagentur (2026)

More: Infrastructure investing: equity and debt, revenue models, valuation and research

Real estate investment trust: a listed property company that is exempt from tax at company level if it distributes most of its profit. The German REIT-AG must distribute at least 90% of its annual net income, is exempt from corporation tax and trade tax, and may not hold German residential rental properties built before 2007. Mortgage REITs hold mortgage loans instead of buildings.

Source: REIT Act (2007)

More: Real estate as an investment: rental property, REITs, open-end funds and private real estate · Methodology: Asset classes with a long history: methodology

Comparing several assets with one another: the strongest of recent months are bought and the weakest avoided (cross-sectional momentum).

Source: Jegadeesh and Titman (1993); Asness et al. (2013)

More: Tactical allocation: momentum, dual momentum and trend following

An indicator by Welles Wilder: RSI = 100 − 100 / (1 + RS), where RS is the average gain over the last 14 periods divided by the average loss. Above 70 a price is considered overbought, below 30 oversold. This describes the most recent movement; it is not a forecast.

Example: Gains totaling 13.0 and losses of 3.0 points over 14 days: RS = 4.33, RSI = 81.25.

Source: Wilder (1978)

More: Technical analysis, chart patterns and candlesticks from a quant perspective

Annual rent relative to the price of a property. Gross: annual base rent divided by the purchase price. Net: rent minus non-recoverable costs such as management, maintenance and rent loss, divided by the purchase price plus acquisition costs. The purchase price factor is the inverse of the gross rental yield.

Example: €300,000 purchase price, €30,000 acquisition costs, €12,000 base rent and €2,400 costs a year: gross 4.00%, net 2.91%, purchase price factor 25.

More: Real estate as an investment: rental property, REITs, open-end funds and private real estate

Price index built from repeated sales of the same item: the price change between purchase and sale is spread across the periods in between by a regression. This sidesteps quality differences between items, but only uses items sold more than once, and these tend to come to market when their price has risen. Known from house price indices, and also used for art.

Source: Bailey et al. (1963); Mei and Moses (2002)

More: Collectibles as an investment: what art, wine, watches and classic cars really return

How an ETF tracks its index: physically (all or selected securities) or synthetically via a swap.

More: ETF basics: costs, replication and distributions

The sale of a security with an agreement to buy it back at a fixed date and price. Economically, it is a secured loan. The haircut determines how much equity is required; via a reverse repo, bonds can also be obtained for short sales.

Example: €10 million of bonds with a 10% haircut: €9 million repo, €1 million equity, leverage 10.

More: Basis trades: positive and negative basis in bonds, CDS and futures

Formal tender in which an institutional investor asks asset managers for a proposal for a mandate: questions on the firm, team, investment process, risk, performance, costs and operations, plus a fee proposal and references. It is often preceded by a shorter request for information (RFI), used to narrow the longlist down to a shortlist.

Source: CMA, Order (2019)

More: RFP and mandate awards: how institutional investors select asset managers

A request sent to several dealers at once for a tradable price for a given quantity; the trade is done with the best quote. The usual electronic route in bond trading and for large ETF orders.

Source: O'Hara and Zhou (2021)

More: Market making and bond trading: spread, inventory, axes, RFQ, cross trades and matrix pricing

Averages many efficient frontiers computed from slightly altered, simulated inputs. The averaged weights are more widely spread and fluctuate less than those of a single optimization.

Source: Michaud (1989)

More: Efficient frontier: Markowitz portfolio optimization

The part of a return that a regression model does not explain. The standard deviation of the residuals is the specific (idiosyncratic) risk of a fund or stock.

A position's share of a portfolio's total return: weight times return, chained over the periods. The contributions of all positions add up to the portfolio return.

Methodology: Backtest methodology: data, process, rebalancing and costs

High valuations have historically preceded lower returns over the following ten years. The predictive power is visible over long horizons, small in the short term and weaker out of sample.

Source: Campbell and Shiller (1998); Welch and Goyal (2008)

More: Shiller P/E (CAPE): how expensive is the stock market? · Methodology: Valuation with the Shiller P/E: methodology

Net income divided by equity (ROE). Return on invested capital (ROIC), by contrast, relates operating profit after tax to all invested capital and can be compared directly with the WACC: only if it is higher does growth create value.

More: Fundamental analysis: valuing a company like an investor

Valuations of illiquid assets follow market prices with a lag and in muted form. As a result, volatility, correlation and beta appear too low, the Sharpe ratio too high, and reported returns are autocorrelated. Unsmoothing roughly reverses this.

Example: Smoothing parameter θ = 0.6: measured volatility = true volatility × √(0.4 / 1.6), i.e. half as high.

Source: Getmansky et al. (2004); Geltner (1993); Couts et al. (2024)

More: Private credit and public credit compared: returns, risks and what the research shows

Two sources of return on the same capital: futures or swaps are used to layer a second asset, such as bonds or managed futures, on top of a core such as equities. The second contributes only its return above the money market rate; losses from both sources add up.

Example: 100% equities (+8%) plus a 100% trend overlay (+6% with a 3% money market rate): 8 + (6 − 3) = 11%.

Source: Kung and Pohlman (2004)

More: Leveraged ETFs and return stacking: path dependence, costs and research · Methodology: Backtest methodology: data, process, rebalancing and costs

A table of annualized returns for every start and end year. It shows at a glance how strongly the result depends on the time of entry.

Methodology: Backtest methodology: data, process, rebalancing and costs

The observation that stocks with poor past returns later perform above average, and vice versa: in the short term from one month to the next, in the long term over three to five years. Strategies that regularly sell winners and buy losers have a tilt toward this effect.

Source: De Bondt and Thaler (1985); Jegadeesh (1990)

More: Equal weight vs cap weight: weighting, rebalancing and factor tilts

A bond with a high coupon for which the issuer may deliver shares instead of the nominal value at maturity if the share closes below the strike. Decomposed: a bond plus a sold put; the coupon contains the put premium.

Example: Nominal value €1,000, strike €90: if the share closes at €70, you receive shares worth 1,000 × 70 / 90 = €777.78 plus the coupon.

Source: Wilkens et al. (2003); Célérier and Vallée (2017)

Stress test run backwards: the aim is to find the market movements that would cause a specified loss; for banks, failure; for investors, for example, a loss of 20% or missing a financial goal.

Source: Glasserman et al. (2015); Basel Committee on Banking Supervision (2018)

More: Scenario analysis and sensitivity analysis: stress testing equity, interest rate, credit and currency risk

Change in an option's price when the risk-free rate rises by one percentage point. Calls gain from higher rates, puts lose; for long maturities rho is noticeable, for short ones it is usually small.

More: Option pricing: where fair option prices come from · Methodology: Option pricer: how Portfolio Lab values options

The allocation is set in terms of risk shares rather than capital shares, e.g. 60% of the risk from equities. Risk parity is the special case of equal risk budgets.

Source: Roncalli (2013); Maillard et al. (2010)

More: Risk contribution: breaking portfolio risk down into its parts

A position's share of portfolio volatility: weight times marginal risk contribution. The contributions of all positions add up exactly to the portfolio volatility.

Source: Roncalli (2013)

More: Risk contribution: breaking portfolio risk down into its parts · Methodology: Backtest methodology: data, process, rebalancing and costs

Weighting in which each asset contributes the same amount to total risk. Low-volatility assets therefore receive more weight.

More: Efficient frontier: Markowitz portfolio optimization

Return relative to the risk taken. Metrics such as the Sharpe, Sortino, Treynor or Calmar ratio make portfolios with different levels of risk comparable.

More: Sharpe ratio: return per unit of risk

Return of a practically safe investment over the same period; in euros, the money market rate (€STR, formerly EONIA). It is subtracted from returns to measure excess returns.

More: Sharpe ratio: return per unit of risk

Probability read off prices when they are interpreted as expected values under the risk-neutral measure, for example from option prices. It contains the premium that investors pay for protection; for price declines, it is therefore usually higher than the actual frequency.

Source: Breeden and Litzenberger (1978); Carr and Wu (2009)

More: Market expectations: what the yield curve, inflation-linked bonds and options reveal about the future

Calculation technique in option pricing: you act as if all assets earned the risk-free rate on average and discount the expected payoff at that rate. The result equals the cost of replicating the option with the underlying and borrowing; it says nothing about real-world probabilities.

Source: Cox et al. (1979)

More: Option pricing: where fair option prices come from

Market phases in which investors either crowd into risky assets together (risk-on) or flee to safe havens (risk-off). In risk-off phases, correlations between risky assets rise.

Robust minus weak: return of profitable minus less profitable companies. Part of the five-factor model.

Source: Fama and French (2015); Novy-Marx (2013)

More: Factor investing: understanding the Fama-French factors · Methodology: Factor regression, factor allocation and factor statistics: methodology

Standardization using the median and the MAD (median absolute deviation from the median) instead of the mean and standard deviation: z = (x − median) / (1.4826 · MAD). The factor 1.4826 turns the MAD into the standard deviation for normally distributed data; individual outliers such as the pandemic months barely shift the median and the MAD.

Example: Median of the comparison values 1.0%, MAD 2.0 percentage points, current value −2.0%: z = (−2.0 − 1.0) / (1.4826 × 2.0) = −1.01.

Source: Rousseeuw and Croux (1993)

Methodology: Economic pulse: how Portfolio Lab calculates early indicators

Gain or loss as a futures contract converges toward the spot price at expiry. For VIX futures in contango, usually clearly negative.

More: VIX: how to read the stock market's fear gauge

Price gain on a bond that, with an upward-sloping yield curve, moves over time into shorter maturities with lower yields. Together with the coupon, it makes up a bond's carry.

More: Yield curve: what the term structure reveals and why an inverted curve is seen as a warning sign · Methodology: Carry backtest: methodology for FX and bond carry

Replacing an expiring future with a later one to keep the position open. Depending on the shape of the term structure, this costs or adds return; for VIX futures it usually means heavy losses.

Source: Whaley (2013)

More: VIX: how to read the stock market's fear gauge · Methodology: Volatility dashboard: methodology

Return over a fixed window that moves forward month by month, for example every 10-year period of a backtest. Shows how strongly results depend on the starting point.

Volatility over a moving window, e.g. 36 months. It shows that risk is not constant: it jumps in crises and falls in calm phases.

More: Volatility: how much a portfolio fluctuates

A trading plan fixed in advance that insiders in the US can rely on as a defense against insider trading allegations, provided they entered into it without knowledge of material non-public information. Since the 2022 amendments, directors and officers have been subject to a cooling-off period of at least 90 and at most 120 days.

Source: SEC, Rule 10b5-1 (2022)

More: Insider trading: what is prohibited, what is allowed and what insider purchases reveal

A measure by Avellaneda and Lee of the distance of a stock's cumulative residual from its equilibrium, in equilibrium standard deviations. Below −1.25 the stock is bought and the factor sold short; above +1.25 the reverse.

Source: Avellaneda and Lee (2010)

More: Pairs trading and statistical arbitrage: idea, methods, research · Methodology: Long/short and statistical arbitrage: methodology

Asset that does not fall with equities in crises, or even rises, such as short-dated government bonds, gold or certain currencies. The effect often lasts only briefly and is not guaranteed.

Source: Baur and Lucey (2010)

More: Gold in a portfolio: safe haven, inflation hedge or just shiny?

The highest annual withdrawal, as a percentage of starting wealth and adjusted for inflation each year, that would only just not have used up the wealth over the period under review.

More: Safe withdrawal rate: how good is the 4% rule? · Methodology: Backtest methodology: data, process, rebalancing and costs

An observed slice of reality, e.g. 20 years of monthly returns. All metrics derived from it are estimates subject to uncertainty; a different period would have produced different values.

Regular purchase of fund units for a fixed amount. The contribution can be directed into underweight positions and so replace rebalancing without any sales.

More: Rebalancing: getting your portfolio back on course

A fund can be bought through regular contributions at a bank or broker. Many providers offer ETF savings plans with no order fee; the spread and the execution price still count.

More: Lump sum or dollar-cost averaging: invest a large amount at once or in installments?

Filing with the SEC as soon as someone holds more than 5% of a class of a US company's shares and intends to exert influence; typical of activist investors. Since a 2023 reform, it is due within five business days (previously ten days), and amendments within two business days. Passive investors usually file the shorter Schedule 13G instead.

Source: SEC, Schedule 13D (2023); Brav et al. (2008)

More: Legendary investors: the investment styles of the most famous investors, from Graham to Simons

Greenhouse gases from sources that a company owns or controls itself, e.g. power plants, blast furnaces or vehicle fleets.

Source: GHG Protocol (2011)

More: ESG ETFs: index rules, ratings, returns and the limits of sustainable funds

Indirect emissions from the generation of purchased energy: the electricity, steam, heating and cooling that a company consumes.

Source: GHG Protocol (2011)

More: ESG ETFs: index rules, ratings, returns and the limits of sustainable funds

All other indirect emissions in the value chain, from suppliers to the use and disposal of the products sold, divided into 15 categories. Often a company's largest source, but the hardest to measure.

Source: GHG Protocol (2011)

More: ESG ETFs: index rules, ratings, returns and the limits of sustainable funds

Dividend that shareholders can receive in cash or in new shares, sometimes at a discount to the market price. An index has to assume one of the options: at MSCI, the company's default option, and without one, the cash payment.

Source: MSCI Corporate Events Methodology (2022)

More: Smart indexing: added value for index funds around corporate actions and index changes

Removing patterns that repeat every year, month or week, and usually also calendar effects such as public holidays and the number of working days. With daily data, several such patterns overlap; the Bundesbank has developed its own method for this.

Source: Ollech (2021)

Methodology: Economic pulse: how Portfolio Lab calculates early indicators

Trading of existing stakes in private markets funds. LP-led: an investor sells its fund interest together with the unfunded commitment, at a discount or premium to NAV. GP-led: the manager sells holdings from an old fund into a new vehicle, usually a continuation fund; existing investors choose between selling and rolling over. Because the manager sits on both sides of the deal, ILPA recommends, among other things, a fairness opinion and at least 30 calendar days to decide.

Source: ILPA (2023); Saccone (2024)

More: Private equity explained: strategies, fund structure, fees and what research shows about returns

An industry group into which companies are classified according to their business, e.g. technology, healthcare or financials. A common classification uses eleven sectors (GICS).

More: Look-through: what is really inside your ETFs

Moving securities to another brokerage account. If the holder stays the same, the old bank sends the acquisition data along; if the holder changes, the transfer counts as a sale for investment income tax purposes, unless it is reported as gratuitous, in which case the bank informs the tax office.

Example: If the acquisition data are missing, 30% of the sale proceeds count as gain: with €20,000 of proceeds, the bank withholds 26.375% × €6,000 = €1,582.50.

Source: EStG §§ 43, 43a, 44a (2009); BMF (2025)

The fund lends out securities against collateral and a fee. The income reduces the tracking difference; the risk lies in the borrower defaulting at a time when the collateral is insufficient.

More: ETF basics: costs, replication and distributions

A loan secured by a securities portfolio. The credit line depends on the lending values of the securities, and the interest rate is usually above the money market rate. Using it to buy additional securities leverages your portfolio.

More: Leverage in a portfolio: return, risk, costs and margin calls

In the CAPM, the relationship between beta and expected return: the risk-free rate plus beta times the market premium. Empirically it is flatter than the model predicts.

Source: Sharpe (1964); Black (1972)

More: CAPM: the capital asset pricing model and the security market line

The starting value of the random number generator. With the same seed a simulation produces exactly the same paths; this makes results reproducible and comparisons between variants fair.

The fund's assets are legally separate from the assets of the fund company. If the company goes bust, they still belong to the investors, unlike with ETCs or ETNs.

More: ETF basics: costs, replication and distributions

A distortion caused by the choice of what is shown: only the best of many tested strategies gets published. Its metrics overstate the performance to be expected.

Source: Bailey and López de Prado (2014)

More: Backtest overfitting: when the past looks too good

The part of the active return that comes from choices within a segment, calculated with the benchmark weight: Wᵢ × (rᵢ − bᵢ).

Example: 30% benchmark weight, portfolio return in the segment 10% instead of 8%: 0.30 × 2 = 0.60 percentage points.

Source: Brinson et al. (1986)

More: Performance attribution: Brinson decomposition, factors and linking over time

A fund with illiquid assets and no fixed term that accepts new money continuously and redeems on fixed dates, limited by notice periods and caps. Redemptions are paid from a reserve of liquid assets and from inflows.

Source: Delegated Regulation (EU) 2024/2759 (2024)

All publicly available information, such as annual reports or news, is reflected in the price immediately. Fundamental analysis based on public data then yields no excess return.

Source: Fama (1970)

More: The efficient market hypothesis: why it is so hard to beat the market

Active ETF that does not publish its full holdings every day. In the US, such models work, for example, with a confidential account for the authorized participants and a continuously published indicative value; in Ireland, since April 2025 ETFs may also disclose their holdings only at quarter-end, provided enough information for arbitrage is available every day.

Source: Dechert LLP (2019); Doyle and Deane (2025)

More: Active ETFs: how they work and what they deliver

A variance that counts only downward deviations, i.e. those below the mean or below a minimum return. Its square root is the downside deviation.

Source: Sortino and van der Meer (1991)

More: Sortino ratio and Calmar ratio: measuring downside risk

Changing a single input while holding everything else constant, for example only interest rates by 100 basis points. It shows how sensitive a portfolio is, but is not yet a coherent scenario.

More: Scenario analysis and sensitivity analysis: stress testing equity, interest rate, credit and currency risk

The automated measurement of sentiment in texts such as news, annual reports or forum posts, using word lists, machine learning or large language models. General-purpose dictionaries wrongly classify many technical terms in financial texts as negative; that is why there are dedicated word lists for financial texts.

Source: Loughran and McDonald (2011); Lopez-Lira and Tang (2026)

More: Alternative data: job ads, Reddit, X, satellites and card payments

All investors can hold the same portfolio of risky assets and control their risk solely through the share they hold in the safe asset. The choice of the risky part is separate from risk appetite.

Source: Tobin (1958)

More: CAPM: the capital asset pricing model and the security market line

Risk that poor returns arrive right at the start of a withdrawal phase. With the same average return, considerably less is then left over.

More: Safe withdrawal rate: how good is the 4% rule?

The EU Sustainable Finance Disclosure Regulation, Regulation (EU) 2019/2088, applicable since March 2021. It requires disclosure of how financial products take sustainability risks into account and what sustainability characteristics or objectives they have; funds are classified under its Articles 6, 8 and 9.

Source: SFDR (2019)

More: ESG ETFs: index rules, ratings, returns and the limits of sustainable funds

Tankers that operate without Western services in order to circumvent sanctions such as the price cap on Russian oil. Ships that do not want to be seen can switch off AIS or transmit false information; such ships are then missing from public tracking data.

Source: Cardoso et al. (2025); Paolo et al. (2024)

More: Ship tracking data and satellite images: what they reveal about commodities · Methodology: Ships at chokepoints (beta): methodology

Trading in the securities of another, comparable company on the basis of confidential information about your own company. In SEC v. Panuwat, a US jury found in favor of the SEC in April 2024: an employee had bought calls on a comparable company before his employer was taken over.

Source: SEC, Panuwat (2024)

More: Insider trading: what is prohibited, what is allowed and what insider purchases reveal

A company buys back its own shares on the stock exchange and so pays money out to the shareholders who sell. The remaining shareholders then hold a larger stake. In the US, buybacks have increasingly replaced dividends since the 1980s, and they do not show up in the dividend yield.

Source: Grullon and Michaely (2002)

More: Dividend strategies and dividend ETFs under scrutiny: irrelevance, factors, risks

A variant of the same fund with its own distribution policy, currency, fee or currency hedging. It has its own ISIN but invests in the same portfolio.

Excess return over the risk-free rate divided by volatility.

Example: (7% − 2%) / 15% = 0.33.

More: Sharpe ratio: return per unit of risk

Selling a borrowed security in order to buy it back later at a lower price. Optimizations without a ban on short selling often produce negative weights; weight limits prevent this.

When the price of a heavily shorted stock rises, short sellers cover by buying in order to limit their losses. This drives the price up further. According to the SEC, this was not the main driver at GameStop in 2021; the rise was carried by positive sentiment.

Source: SEC (2021)

More: Alternative data: job ads, Reddit, X, satellites and card payments

Positions that live off selling volatility, such as sold options or short VIX products. Long stretches of steady gains, then rare, very large losses (negative skewness).

Source: Carr and Wu (2009)

Excess return of small companies over large ones. After its discovery around 1980 it weakened considerably, and it depends heavily on how quality is taken into account.

Source: Banz (1981)

More: Factor investing: understanding the Fama-French factors

Cboe index for the price of protection against sharp crashes in the S&P 500. Values around 100 indicate low demand for crash protection, values above 140 high demand.

More: VIX: how to read the stock market's fear gauge

A measure of the asymmetry of a distribution. Negative skewness means rare, large losses and many small gains, typical of equity indices and of selling options. Investors demand a premium for negative skewness.

Source: Harvey and Siddique (2000)

More: Skewness and kurtosis: why market crashes are more frequent than the normal distribution says

The seventh VIX future relative to the fourth, i.e. M7 / M4 − 1. It describes the medium-term part of the VIX futures curve, which medium-term VIX products track.

Methodology: Volatility dashboard: methodology

Index funds that weight not by market capitalization but by factors such as value, momentum, quality or low volatility. Rule-based and cheaper than active funds, but with factor risk.

Source: Ang (2014)

More: Factor investing: understanding the Fama-French factors

A program on a distributed ledger that executes agreed steps by itself as soon as the conditions are met, e.g. paying a coupon, calling for more collateral or exchanging tokens for cash. Errors in the code are executed too, and whether the code matches the legal contract has to be checked separately.

Source: Cong and He (2019)

More: Digital assets: tokenization, stablecoins, crypto securities and the digital euro

Implementing an index fund in a way that uses the leeway the market offers without losing sight of the index: more favorable choices in corporate actions, trading index changes away from the effective date, or skipping very small changes.

Source: Harding (2016)

More: Smart indexing: added value for index funds around corporate actions and index changes

Small minus big: return of small minus large companies. A positive loading indicates a tilt toward small caps.

Source: Fama and French (1993); Banz (1981)

More: Factor investing: understanding the Fama-French factors · Methodology: Factor regression, factor allocation and factor statistics: methodology

Surcharge of 5.5% on the flat-rate tax. Unlike with wage tax, there is no exemption threshold on investment income that would make it disappear for most investors.

Like the Sharpe ratio, but divided by the downside deviation. Upside fluctuations do not count as risk.

More: Sortino ratio and Calmar ratio: measuring downside risk

Tax-free amount for investment income: €1,000 a year, €2,000 for jointly assessed couples.

Prices rise far above what earnings and prospects justify, driven by expectations that prices will keep rising. Bubbles are easy to recognize in hindsight, but hardly reliably beforehand.

Source: Shiller (2000); Fama (2014)

More: Speculative bubbles: what they are and how the LPPLS model detects them · Methodology: Bubble indicator (LPPLS): methodology

Yield of a zero-coupon bond for a given maturity. With spot rates, each payment of a bond is discounted at its own rate; they are derived step by step from coupon bonds or swap rates (bootstrapping), and forward rates are in turn derived from them.

Source: Tuckman and Serrat (2012)

More: Bond math: calculating price, yield, duration, convexity and spreads

How much a bond loses when its risk premium over government bonds rises by one percentage point. For a fixed coupon, roughly equal to the duration.

More: Duration: how strongly bonds react to interest rates

A token designed to hold a fixed value, usually 1 US dollar or 1 euro. Fiat-backed stablecoins hold bank deposits and short-term government securities for this purpose; other designs rely on crypto-assets or just an algorithm. Holders have a claim against the issuer, not a protected deposit; if they doubt the reserve, a run looms.

Example: A reserve of €10 billion, 70% of it in government bonds at 2.0% and 30% as deposits at 1.5%: income 0.7 × 2.0% + 0.3 × 1.5% = 1.85%, or €185 million a year.

Source: Gorton and Zhang (2023); BIS (2026)

More: Digital assets: tokenization, stablecoins, crypto securities and the digital euro

Weak growth and high inflation at the same time, as in the 1970s. The most difficult environment for classic equity-bond portfolios, because both asset classes can suffer.

Methodology: Macro dashboard and regime analysis: methodology

The square root of the variance: the typical distance of values from their mean. For returns it is called volatility; for samples you divide by n − 1 instead of n (Bessel's correction).

More: Volatility: how much a portfolio fluctuates

The uncertainty of an estimate, such as the mean: the standard deviation divided by the square root of the number of observations. It falls only slowly as data accumulate: halving the uncertainty takes four times as many observations.

Example: Monthly return 0.5%, standard deviation 4%, 120 months: standard error 4% / √120 = 0.37%.

The uncertainty of an estimated Sharpe ratio. For independent, normally distributed returns it is √((1 + SR² / 2) / (T − 1)) per period; negative skewness and fat tails increase it to √((1 − γ₃ × SR + (γ₄ − 1) / 4 × SR²) / (T − 1)), with the kurtosis γ₄ (3 for the normal distribution). It is annualized with √(periods per year).

Example: Sharpe ratio of 0.6 p.a. from 120 months, normally distributed: √((1 + 0.1732² / 2) / 119) × √12 = 0.32 p.a.

Source: Lo (2002); Bailey and López de Prado (2012); Opdyke (2007)

More: Deflated Sharpe ratio: how much skill is in a Sharpe ratio?

A time series is stationary if its mean, dispersion and dependencies do not change over time. Returns are approximately stationary, prices are not. That is why calculations use returns.

A block bootstrap with random, geometrically distributed block lengths. As a result the resampled series remains stationary, and the outcome depends less on a fixed block length.

Source: Politis and Romano (1994)

More: Bootstrap: future scenarios from your own history

The long-run share of time a Markov chain spends in each state: the distribution π with π A = π. With two states, the share of state 0 equals a₁₀ / (a₀₁ + a₁₀), where a₀₁ and a₁₀ are the two switching probabilities.

Example: Switching from calm to turbulent with 0.02 and back with 0.10 per week: turbulent 0.02 / (0.02 + 0.10) = 16.7% of the time, calm 83.3%.

More: Regime models: hidden Markov, Markov switching and more · Methodology: Regime methodology: how the hidden Markov model works

Long/short strategies that bet on temporary, statistically estimated mispricings: in pairs, in stocks against a factor or in large portfolios. Unlike true arbitrage, it is not risk-free; it only wins on average across many trades.

Source: Avellaneda and Lee (2010); Krauss (2017)

More: Pairs trading and statistical arbitrage: idea, methods, research · Methodology: Long/short and statistical arbitrage: methodology

Return divided by the average of the largest annual drawdowns (in one common version plus 10 percentage points). Related to the Calmar ratio, but less dependent on a single crash.

Source: Bacon (2008)

More: Risk metrics beyond the Sharpe ratio: Treynor, Calmar, Omega, Ulcer Index and more

A theory founded by Robert Fernholz on the long-term growth rates of portfolios and stock markets, with few assumptions about price behavior. A key result: a portfolio regularly reset to fixed weights grows faster than the weighted average of its positions.

Source: Fernholz and Shay (1982); Fernholz (2002)

More: Beyond Markowitz: estimation error, noise and true diversification · Methodology: Dimensions methodology: how Portfolio Lab counts independent risks

The relationship between equity and government bond returns. Since the late 1990s it has mostly been negative, which stabilized mixed portfolios; in phases of high inflation, such as 2022, it was positive.

More: 60/40 portfolio: the classic mix of equities and bonds