Jensen's Alpha
Jensen's Alpha
The return a portfolio earned above what CAPM says its beta deserved: actual return minus the risk-free rate plus beta times the market premium. Positive alpha is skill (or luck); zero is what an index fund with the same beta delivers.
When to use: Use to judge an active manager after adjusting for how much market risk they took. A fund that beat the index by leveraging up has beta, not alpha.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| Alpha | Jensen's Alpha | Return above the CAPM-required return | % |
| Rp | Portfolio Return | Periodic mean return of the portfolio as a decimal | % |
| Rf | Risk-Free Rate | Per-period risk-free rate as a decimal (use the same period as the returns) | % |
| Beta | Beta | Portfolio beta against the relevant market | integer |
| Rm | Market Return | Return of the market benchmark over the same period, as a decimal | % |
Real-Life Examples
Example 1: Manager Who Added Value
A fund returned 12% with a beta of 1.2. The risk-free rate was 3% and the market returned 9%.
Given
Step-by-Step
The fund beat the market by 3 points, but 1.2 points of that was just its higher beta. The genuine outperformance is 1.8%.
Example 2: Beat the Index, Still Negative Alpha
A low-risk fund returned 7% with a beta of 0.8; risk-free 3%, market 9%.
Given
Step-by-Step
Negative alpha despite a positive return: with a 0.8 beta the fund should have earned 7.8%. It underperformed its risk-adjusted benchmark by 0.8%.
Frequently Asked Questions
Alpha is the excess return in percentage points. The information ratio divides a similar excess by its volatility, so it measures consistency as well as size.
The benchmark the beta was measured against, over the same period as the portfolio return. Mixing periods or benchmarks makes the alpha meaningless.