Glossary: terms starting with L

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

Large AI model trained on text (large language model, LLM). In quant research it rates headlines; in backtests its prior knowledge of the outcome or of well-known companies can distort the results.

Source: Lopez-Lira and Tang (2026); Glasserman and Lin (2023)

Race among fast traders to hit stale quotes before they are canceled. In FTSE 100 stocks, about one race per minute per stock, typically 5 to 10 microseconds long, together about 20% of trading volume.

Source: Aquilina et al. (2022); Budish et al. (2015)

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 fund management company in the EU 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 that cannot be offset are carried forward to the next year, where they reduce future gains.

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?