Glossary: terms starting with F

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)

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

Knowledge and skills for making good money decisions. Usually measured with three basic questions on compound interest, inflation and diversification; in the 2021 Bundesbank survey, about 62% of households answered all three correctly.

Source: Lusardi and Mitchell (2014); Bucher-Koenen et al. (2023)

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

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 a non-US investor certifies residence outside the US. If the broker has it on file, the US withholds tax on dividends at the treaty rate instead of 30%, e.g. 15% for residents of Germany, whose 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

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.

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 European 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

Payment between buyers and sellers of a perpetual future, usually every eight hours. If the future trades above spot, buyers pay sellers, otherwise the reverse. The basis of the cash-and-carry trade in crypto markets.

Example: 0.01% per eight hours: 3 × 365 × 0.01% = 10.95% a year.

Source: He et al. (2022); Schmeling et al. (2026)

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