FRM Exam Part II · Hedge Fund Investment Strategies

Hedge Fund Performance, Biases and Factor Models

Q: What is the difference between survivorship bias and backfill bias?

Survivorship bias comes from dead funds disappearing from the database, leaving only successful survivors. Backfill bias comes from a new fund adding its earlier history, often after good results. Both push average reported returns up.

Q: Why does return smoothing matter for risk managers?

Smoothed returns hide true volatility, correlation and beta, so the fund appears safer than it is. The Sharpe ratio looks better and diversification benefits look larger. Unsmoothing the returns gives a more honest risk estimate.

Q: What is the Fung-Hsieh seven-factor model?

It is a regression model of hedge fund returns on seven factors: equity market, size spread, bond market, credit spread and three trend-following factors for bonds, currencies and commodities. The trend-following factors are option-like lookback straddles. Alpha is the intercept after these exposures.

Q: How do I measure hedge fund alpha and beta?

Regress fund returns on a set of risk factors. The slopes are the betas, which show exposure to each factor. The intercept is alpha. Use factors that capture option-like payoffs, or alpha may be overstated.

Updated 11 October 2026 · Fact-checked

Hedge fund databases rely on voluntary reporting, so index returns are usually overstated by survivorship, backfill and selection biases. Smoothed returns understate volatility and beta. Factor models such as Fung-Hsieh separate beta (including option-like trend-following exposures) from alpha, which is the intercept left after factor exposures.

Understand Hedge Fund Performance, Biases and Factor Models

Hedge funds are not required to publish returns. They report to commercial databases and index providers by choice. That single fact creates most of the problems in this topic: the data you see is not a clean sample of all funds.

Three biases matter. Survivorship bias arises when funds that closed or stopped reporting drop out of the database, so only survivors remain and average returns look better. Backfill (instant history) bias arises when a fund joins a database and its earlier, usually good, returns are added. Funds tend to start reporting after a strong run. Selection bias arises because managers choose whether to report. Good performers may report to attract capital. Some strong funds close to new money and stop reporting. The direction of this bias is less certain than the other two.

There is also an issue of return smoothing. Funds holding illiquid assets use stale or model-based prices. Reported returns then show positive autocorrelation: this month's return is partly last month's. Smoothing lowers measured standard deviation, lowers measured correlation and beta to markets, and inflates the Sharpe ratio. Risk looks smaller than it is. Unsmoothing methods (such as the Getmansky-Lo-Makarov approach) try to recover the true returns.

To split performance into skill and market exposure, use a multi-factor model. Return = alpha + Σ(beta × factor return) + error. Hedge funds hold option-like positions, so linear equity-beta models fit badly. The Fung-Hsieh seven-factor model adds three trend-following factors (bond, currency and commodity lookback straddles), plus equity market, size spread, bond market and credit spread factors. Trend followers show payoffs like a long straddle: they gain in large moves either way. Merger arbitrage and many credit strategies look like short put options: steady small gains and occasional large losses.

A high alpha from a model with missing factors is not skill. It is often an unmodelled option-like risk premium.

Key formulas to remember

Multi-factor return model: R(fund) = α + β₁F₁ + β₂F₂ + … + βₖFₖ + ε; α is the intercept (return not explained by factors). Betas are estimated by regression. Alpha is only as good as the factor set.
Survivorship bias: Bias = average return of surviving funds − average return of all funds (including dead funds); Positive in sign: databases that drop dead funds overstate performance.
Smoothed return (MA model): R(observed, t) = θ₀R(t) + θ₁R(t−1) + θ₂R(t−2), with θ₀ + θ₁ + θ₂ = 1; Weights sum to 1, so the mean is unchanged but variance is reduced. Smaller θ₀ means more smoothing.
Effect of smoothing on volatility: σ(observed) < σ(true) when θs are positive; Observed beta and correlation to markets are also biased down. Sharpe ratio is biased up.
Annualising with autocorrelation: σ(annual) ≠ σ(monthly) × √12 when returns are autocorrelated; With positive autocorrelation, the √12 rule understates true annual volatility.
Fung-Hsieh seven factors: Equity market, size spread, bond market, credit spread, bond trend-following, currency trend-following, commodity trend-following; The three trend-following factors are lookback straddles, which capture option-like payoffs.

How to solve Hedge Fund Performance, Biases and Factor Models questions

Use this sequence for any question on hedge fund data, biases or factor models.

1Identify what the question is really about: a data bias, return smoothing, or factor exposure.
2If it is a bias, ask who is missing or added: dead funds (survivorship), early history (backfill), or self-chosen reporters (selection).
3State the direction of the effect on average return. Survivorship and backfill overstate returns. Selection bias is ambiguous.
4If returns are smoothed, state the effects: positive autocorrelation, lower volatility, lower beta and correlation, higher Sharpe ratio.
5If it is a factor model, read alpha as the intercept and betas as exposures. Check the factors included before judging alpha.
6For option-like exposure, link the strategy to a payoff: trend followers are long straddles, merger arbitrage resembles a short put.
7Do any arithmetic carefully (differences in returns, weights, annualising), then choose the option that matches both the number and the interpretation.

Quickest way: Bias-and-direction shortcut

When to use it: Use when the question asks which bias applies or what happens to reported results, with no heavy calculation.

Dead funds removed: survivorship, returns too high.
Past returns added when a fund joins: backfill, returns too high.
Managers choose to report: selection, direction uncertain.
Stale or model prices: smoothing, risk too low, Sharpe too high, positive autocorrelation.
Large alpha with few factors: suspect omitted option-like risk.
Trend following means long straddle. Selling insurance-like premiums means short put.

Common mistakes in Hedge Fund Performance, Biases and Factor Models

Saying survivorship and backfill bias are the same thing.
Both inflate returns, so they feel identical.
Fix: Survivorship is about funds that leave. Backfill is about history added when a fund enters.
Claiming smoothing raises volatility.
Students link autocorrelation with persistence and assume more risk.
Fix: Smoothing lowers measured volatility and raises the Sharpe ratio. True risk is hidden, not reduced.
Treating alpha from a regression as pure skill.
Alpha is the intercept, so it looks like skill by definition.
Fix: Alpha is what the chosen factors leave unexplained. Missing option-like factors can create false alpha.
Stating that selection bias always overstates returns.
It is grouped with the other two biases.
Fix: Say its direction is ambiguous: strong funds may report to attract capital, or stop reporting when closed to investors.
Annualising monthly volatility with √12 for a smoothed fund and treating it as exact.
The square-root-of-time rule is habit.
Fix: It needs uncorrelated returns. With positive autocorrelation it understates annual volatility.

Worked examples

Example 1

A database shows an average annual return of 9.0% for funds that are still reporting. Including funds that closed during the period, the average is 7.2%. A second effect: a fund that joined the database in 2020 had 2018-2019 returns added afterwards. Name the two biases and compute the survivorship bias.

Show the solution

Funds that closed and dropped out make the sample survivors only: survivorship bias.
Bias = 9.0% − 7.2% = 1.8% per year.
Adding earlier returns when a fund joins, usually after good performance, is backfill (instant history) bias.
Both overstate the average return of the hedge fund index.

Answer: Survivorship bias of 1.8% per year; the added history is backfill bias. Both overstate returns.

Example 2

A fund holds illiquid assets. Its true monthly returns have a standard deviation of 4%. Reported returns follow R(observed) = 0.6R(t) + 0.4R(t−1), and true returns are uncorrelated month to month. What is the reported monthly standard deviation, and what happens to its Sharpe ratio?

Show the solution

Variance of observed = (0.6² + 0.4²) × variance of true, because true returns are uncorrelated.
0.6² + 0.4² = 0.36 + 0.16 = 0.52.
Variance of true = 0.04² = 0.0016, so observed variance = 0.52 × 0.0016 = 0.000832.
Observed standard deviation = √0.000832 ≈ 0.0288, or about 2.9%.
The weights sum to 1, so the mean return is unchanged.
Same mean, lower volatility: the Sharpe ratio is overstated.

Answer: Reported monthly standard deviation is about 2.9% against a true 4%. The Sharpe ratio is overstated.

Exam tips

Memorise the direction of each bias: survivorship and backfill overstate returns, selection is ambiguous.
For smoothing, list all four effects: positive autocorrelation, lower volatility, lower beta or correlation, higher Sharpe ratio.
If a question asks about a high alpha, check whether option-like factors are missing before accepting skill.
Link strategies to payoffs: trend following to long straddles, merger arbitrage to short puts.
Read options carefully. Several answers may sound plausible, so match the exact bias definition.

Practice questions from Hedge Fund Investment Strategies