Factor-Adjusted Alpha Evaluation

A long-short equity strategy returns 14% a year with a Sharpe of 1.3, and the pitch calls it "stock selection alpha." Run the same return series through a four-factor regression and the story changes: 11 of those 14 points come from an unhedged tilt toward small, cheap, high-momentum names — a tilt any index provider will sell for a few basis points. The remaining 3 points, the actual alpha, aren't even statistically distinguishable from zero at this sample length. The strategy wasn't dishonest. Nobody had checked what it was actually exposed to.

The regression

Regress the strategy's excess returns on a set of known factor returns — market, size, value, momentum, whatever set is standard for the asset class:

$$r_t - r_f = \alpha + \beta_{\text{mkt}}(r_{\text{mkt},t} - r_f) + \beta_{\text{smb}}\,\text{SMB}_t + \beta_{\text{hml}}\,\text{HML}_t + \beta_{\text{mom}}\,\text{MOM}_t + \varepsilon_t.$$

In words: today's return is a weighted combination of how much the market moved, how much small stocks beat large ones, how much cheap stocks beat expensive ones, and how much recent winners beat recent losers — plus a leftover, $\alpha$, that none of those factors explain. The betas are the exposures; $\alpha$ is what's left to actually be proud of, and only if it's large enough relative to its own standard error to not be noise.

Worked example

Three years of monthly returns, strategy averages 14% annualised excess return. Fit the regression above:

Term	Estimated exposure	Contribution to 14%
Market beta	0.15	1.2 pts
Size (SMB)	0.55	4.4 pts
Value (HML)	0.40	3.9 pts
Momentum (MOM)	0.35	2.8 pts
Alpha (intercept)	—	1.7 pts

Sum of factor contributions is 12.3 of the 14 points; the regression's intercept, the genuine alpha, is 1.7% a year with a standard error of 1.9% — a t-statistic under 1, nowhere near conventionally significant. What looked like "stock selection alpha" of 14% is mostly four cheap, replicable tilts and a residual that could plausibly be zero. An allocator paying a 2-and-20 fee for this strategy is paying active-management prices for beta they could buy through an ETF for a few basis points.

Drag the points and watch the fitted line and residuals move together — the intercept of that line is exactly the role $\alpha$ plays here: whatever the line doesn't explain about each point is the residual, and the strategy's alpha is the analogous leftover once every factor's contribution has been subtracted out.

Choosing the factor set matters as much as running the regression

The intercept from a factor regression is only as trustworthy as the factors included in it, and there is no universally correct set. A market-only regression will call almost any tilted equity strategy "alpha," because it has nothing else to attribute the return to. A five-factor regression is stricter but can also over-correct: if a strategy's real edge happens to correlate with a factor that's in the model for unrelated reasons — say, a low-turnover quality strategy regressed against a momentum factor it only weakly resembles — some genuine skill gets misattributed to beta it doesn't actually carry. The practical fix is to report the alpha under more than one reasonable factor set (a simple three-factor model and a richer one that includes anything the strategy could plausibly be exposed to) and treat disagreement between the two as a flag to investigate rather than a nuisance to average away.

Betas estimated over one static window can also drift. A strategy that trades sector rotation, for instance, might carry a strongly positive value beta in one regime and a near-zero one in another; a single full-sample regression averages the two and produces an alpha estimate that was never true at any single point in time. A rolling regression, refit every quarter or every year, shows whether the exposures are stable — and whether the alpha itself is a persistent residual or is really an artefact of the beta estimate being stale at one end of the sample.

Factor-adjusted alpha evaluation only works if the factor definitions and betas are stable enough to trust — a strategy whose exposures drift month to month needs a rolling regression, not a single static one, or the reported alpha will just be absorbing whatever the fixed-window factor loadings missed. See Fama-MacBeth Regression for the cross-sectional version of this same idea, and Fundamental vs Statistical Factor Models for how the factor set itself gets built.