Alpha

The standard construction begins with a required return. Take the risk-free rate, add the portfolio's beta multiplied by the market risk premium, and you have the return the asset pricing model says an investor should demand for bearing that quantity of systematic risk. Alpha is the realised portfolio return minus that required return. Everything hinges on beta: a fund with a beta of 1.4 in a market that rose ten percentage points above cash is expected to deliver fourteen points above cash, and only returns beyond that threshold count.

Geometrically, alpha is vertical distance from the security market line. A portfolio plotting above the line earned more than its systematic risk warranted; one plotting below destroyed value. Because the measure is stated per unit of nothing-it is an absolute return figure, not a ratio-alpha can be compared across portfolios only when their risk exposures have already been properly priced out.

In practice alpha is not computed from a single period but estimated. Regress the portfolio's excess returns over the risk-free rate on the market's excess returns across many periods; the slope is beta and the intercept is alpha. This makes alpha a statistical estimate carrying a standard error, which is why a positive point estimate proves very little on its own. With monthly data and typical equity volatility, several years of history are often needed before an intercept becomes statistically distinguishable from zero.

Two consequences follow. First, short track records are close to uninformative about skill. Second, the estimate is sensitive to the sample window: a manager whose alpha is strongly positive over one cycle frequently shows nothing over the next. Persistence tests, not single-period figures, are the evidence that matters.

Alpha exists only relative to a model of required return, so the model's completeness determines the answer. A small-cap value manager measured against a broad market index will often show a positive intercept that is simply compensation for size and value exposure. Re-estimate the regression with size, value, momentum, profitability or quality factors on the right-hand side and the intercept typically shrinks toward zero. What was called skill becomes a factor tilt that an investor can now buy cheaply through systematic products.

This is why institutional evaluation pairs alpha with the information ratio, which scales active return by tracking error and answers a different question: how efficiently was benchmark-relative risk deployed. It also underpins portable alpha strategies, where an active bet is separated from its market exposure and transported onto a chosen beta using derivatives.

Expect to compute Jensen's alpha from a portfolio return, a risk-free rate, a beta and a market return, and to rank portfolios by it while recognising that ranking by alpha alone ignores unsystematic risk. Know the companion measures and what distinguishes them: the Sharpe ratio uses total risk in the denominator, the Treynor ratio uses beta, M-squared restates performance as a risk-adjusted return in percentage terms, and the information ratio uses tracking error against a benchmark rather than the risk-free asset.

You should also be able to reason about implications. Under strong assumptions of market efficiency, expected alpha net of costs is approximately zero in aggregate because active positions are a zero-sum game before fees and negative-sum after them. Alpha is therefore best treated as an evidentiary claim requiring a stated benchmark, an estimation window and a fee basis.