Glossary: terms starting with B

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 dollars 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 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

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 $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