A benchmark comparison is not the same as alpha

Choose the question before choosing the benchmark

A benchmark expresses the alternative against which a strategy is being judged. A broad capitalization-weighted index may be appropriate for a market allocation question, while an eligible-universe benchmark can better isolate a stock-selection rule. Neither automatically identifies skill. A strategy may outperform a broad index because it holds smaller companies, takes more market exposure or concentrates in a favorable sector.

French's five-factor documentation describes market, size, value, profitability and investment research factors. These are useful explanatory references, not interchangeable investable products or a complete description of every equity strategy. Momentum, industry exposure and other relevant variables may remain outside a chosen specification. State which model is used, why it is relevant, and what it omits.

Reconcile one illustrative period

Suppose a fictional portfolio earns a 3% excess return over the selected risk-free rate. The market excess return is 2%, the value factor returns 1%, and assumed exposures are 1.1 to market and 0.3 to value. Their combined contribution is 2.2% plus 0.3%, or 2.5%. The unexplained remainder for that period is 0.5%.

The portfolio also exceeds the market excess return by one percentage point. That active difference is not the same as the 0.5% residual after the two assumed exposures. Neither number is an estimated alpha from this one observation. A regression intercept requires a time series, an explicit model and uncertainty assessment; the assumed coefficients here were not fitted to real data.

Make inputs economically comparable

Align dates, currency, total-return treatment and risk-free convention. Comparing a dividend-inclusive portfolio with a price-only index creates a mechanical advantage. Comparing a net strategy with a gross reference answers a different question from comparing both gross. For a long-short portfolio, define financing and capital clearly before applying a familiar long-only excess-return equation.

Use exposures known or estimated under the stated research design. A full-sample regression may be informative as retrospective attribution, but it is not evidence that those betas were forecastable at the time. Rolling estimates can reveal changing exposures while introducing estimation noise. Report the window and available history, and avoid interpreting every unstable coefficient as a genuine change in economic behavior.

Residuals need explanation, not celebration

An unexplained return can reflect omitted factors, nonlinear exposures, stale prices, timing differences or chance. Inspect residual patterns and concentration before labeling the intercept skill. Dependence across time and overlapping holdings affect standard errors; a large number of daily observations does not necessarily provide an equally large number of independent bets. Report uncertainty and sample length alongside any fitted coefficient.

Keep benchmark selection fixed for the main test and show predeclared alternatives as sensitivities. Choosing whichever benchmark makes the strategy look strongest is another research trial. Attribution is useful for understanding what a portfolio did, but it cannot independently validate data provenance or execution. The table provides a fictional arithmetic decomposition only, with no actual factor regression, alpha estimate or claim of persistent outperformance.

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Sources & reproduction

Primary references support the definitions and method. Numerical examples are illustrative unless a source record is explicitly identified.

• Kenneth French: Description of Fama/French Five Factors

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