Jensen's Alpha

If a fund returned 14% last year, was the manager good? You can't answer without knowing how much market risk they took. A fund that swings 50% more than the market should return more than the market when times are good — that's just leverage on beta, not skill. Jensen's alpha strips this out. It compares a portfolio's actual return to the return The Capital Asset Pricing Model (CAPM) predicts for its level of market risk, and calls the leftover alpha.

$$\alpha = R_p - \big[\,R_f + \beta_p\,(R_m - R_f)\,\big].$$

The bracket is the CAPM benchmark. $R_f$ is the risk-free rate, $R_m$ is the market return, so $R_m - R_f$ is the market's excess return (its risk premium), and $\beta_p$ scales that premium up or down by how much market risk the portfolio takes. The bracket is therefore "the fair return for this much beta." Subtract it from the actual return $R_p$, and what's left, $\alpha$, is the return the manager added (positive) or destroyed (negative) beyond what the market handed them.

Worked example

Set the risk-free rate at 2% and the market return at 10%, so the market's excess return is $10 - 2 = 8\%$. Three funds report their year:

Fund	Beta	CAPM-expected return	Actual return	Alpha
A	1.2	$2 + 1.2\times 8 = 11.6\%$	14.0%	+2.4%
B	0.8	$2 + 0.8\times 8 = 8.4\%$	9.0%	+0.6%
C	1.5	$2 + 1.5\times 8 = 14.0\%$	13.0%	−1.0%

Look at Fund C. It posted a healthy-looking 13%, beating both A and B on raw return. But it did so by taking a lot of market risk (beta 1.5), and CAPM says a beta-1.5 portfolio should have made 14% in a year the market rose 10%. C fell short of its own risk-adjusted bar, so its alpha is negative. Fund A, despite a lower raw return, is the real standout: +2.4% of genuine outperformance. Raw return ranked them C > A > B; alpha ranks them A > B > C. That reordering is the whole value of the measure.

Alpha versus its cousins

Jensen's alpha, the Treynor Ratio, and the Information Ratio all live on the same CAPM picture but answer different questions:

• Jensen's alpha is a distance — a return number, the vertical gap above the security market line. It doesn't divide by risk, so a big-beta fund and a small-beta fund with the same alpha aren't equally impressive per unit of risk.
• Treynor turns that into a slope per unit of beta, letting you rank funds of different market risk.
• Information ratio divides alpha by its tracking error, telling you how reliably the alpha was earned.

Where it misleads

• It's only as good as the model. A single-factor CAPM alpha can evaporate the moment you control for size, value, or momentum. A "skilled" manager may just be tilted toward well-known factors (see The Fama-French Factor Models and Factor Investing) — that's alpha to CAPM but not to a richer model.
• Small samples hide luck. One good year of alpha means little. What matters is whether the regression intercept is statistically different from zero, which needs a long, stable track record and a decent t-statistic.
• Beta drifts. If the portfolio's beta changes over the measurement window, a single static beta mis-states the benchmark and contaminates the alpha.