Glossary: terms starting with M

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.

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 of the EU Market Abuse Regulation (MAR), 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; in Germany, it is a criminal offense under Section 119 of the Securities Trading Act (WpHG) if it affects the price.

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

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 like Treasury bills. Serves as the risk-free rate in the backtest: in US dollars the Treasury bill yield, in euros the €STR.

Fund that invests in very short-dated, safe securities and overnight deposits. Its return follows the money market rate; in the euro area, 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)