Glossary: terms starting with H

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.

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 foreign interest rate is above the US rate, hedging foreign investments costs return.

Example: Foreign rate 4%, dollar rate 2%: 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

HFT: algorithmic trading with infrastructure for minimal delay, such as co-location, orders without human intervention and very many messages; in the EU on average at least two messages per second in one instrument or four across all instruments on a trading venue.

Source: MiFID II, Art. 4 (2014); Delegated Regulation (EU) 2017/565, Art. 19 (2017)

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

Bank deposit that is available every day and pays a variable interest rate. Deposit insurance protects it up to a statutory limit 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)

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; for tax purposes, however, 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: if you sell, only the gain is taxable; as a dividend, the whole amount is.

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