Jensen's Alpha
Jensen's alpha: alpha = Rp - [Rf + beta(Rm - Rf)].
Measure a portfolio's excess return above the CAPM prediction for its level of market risk.
The Formula
Jensen's alpha measures the excess return of a portfolio above what the Capital Asset Pricing Model (CAPM) predicts for its level of market risk. Developed by economist Michael C. Jensen in his landmark 1968 paper on mutual fund performance, it provides a single number that answers the question: "Did this portfolio manager generate returns through skill, or simply by taking on market risk?" A positive alpha means the manager outperformed expectations; a negative alpha means the manager underperformed.
The term in brackets — Rf + βp(Rm − Rf) — is exactly the CAPM expected return. It represents the return an investor should expect from a passively managed portfolio with the same beta. Rf is the risk-free rate, βp is the portfolio's beta (sensitivity to market movements), and Rm is the actual return of the market benchmark (typically the S&P 500 or a relevant index). The market risk premium (Rm − Rf) multiplied by beta gives the additional return expected for bearing systematic risk.
Alpha is the difference between what the portfolio actually returned (Rp) and what it was expected to return given its risk exposure. A portfolio with beta 1.2 in a market that returned 10% (with 4% risk-free rate) would be expected to return 11.2% under CAPM. If it actually returned 13%, its alpha is +1.8% — meaning the manager added 1.8% of value beyond what the market risk exposure alone explains.
In practice, generating consistently positive alpha is extremely difficult. Academic research, including Jensen's own 1968 study of 115 mutual funds, found that most actively managed funds have negative or near-zero alpha after fees. Alpha is used to justify active management fees: if a manager cannot consistently deliver positive alpha, investors may be better served by low-cost index funds that target zero alpha by design.
Variables
| Symbol | Meaning | Unit |
|---|---|---|
| α | Jensen's alpha — excess return above CAPM expectation | % |
| Rp | Portfolio return — actual annualized return achieved | % |
| Rf | Risk-free rate — return on government bonds or Treasury bills | % |
| βp | Portfolio beta — sensitivity to market return | dimensionless |
| Rm | Market return — benchmark index return for the period | % |
Example 1
A fund returned 14% over the year. The market returned 11%, the risk-free rate is 3%, and the fund has a beta of 1.1. What is the fund's Jensen's alpha?
CAPM expected return = 3% + 1.1 × (11% − 3%) = 3% + 1.1 × 8% = 3% + 8.8% = 11.8%
α = 14% − 11.8% = +2.2%
Jensen's alpha = +2.2% — the manager outperformed CAPM expectations by 2.2 percentage points
Example 2
A hedge fund returned 9% when the market returned 12% and the risk-free rate was 4%. The fund has beta = 0.6. Did the manager add value?
CAPM expected return = 4% + 0.6 × (12% − 4%) = 4% + 4.8% = 8.8%
α = 9% − 8.8% = +0.2%
Jensen's alpha = +0.2% — a very small positive alpha. The low-beta fund barely beat its CAPM benchmark
When to Use It
Jensen's alpha is used when evaluating portfolio manager performance:
- Assessing whether an active fund manager adds value beyond passive market exposure
- Comparing multiple fund managers operating at different beta levels on a risk-adjusted basis
- Justifying (or challenging) active management fees relative to passive index alternatives
- Performance attribution analysis to isolate skill from market exposure in fund returns
- Academic finance research on market efficiency and the value of active stock picking
- Institutional investment due diligence and manager selection processes