Portfolio & Risk

Jensen's Alpha

Excess return above the CAPM prediction

What is Jensen's Alpha?

Jensen's Alpha measures a portfolio manager's value-add above what the Capital Asset Pricing Model (CAPM) predicts, given the portfolio's market exposure (Beta). A positive Alpha means the manager outperformed what their Beta exposure would predict; negative Alpha means underperformance. Alpha of 2% means the portfolio returned 2 percentage points more than CAPM would predict given its market risk. It is the most common measure of manager skill in academic finance. However, Alpha is model-dependent: it relies on the accuracy of the CAPM benchmark. Multi-factor models (Fama-French, Carhart) use the same concept but attribute returns to additional risk factors.

Formula

Alpha = Portfolio Return − [Risk-Free Rate + Beta × (Market Return − Risk-Free Rate)]

CAPM Expected Return = Rf + Beta × (Rm − Rf)

Rf = risk-free rate

Rm = market (benchmark) return

Beta = portfolio's sensitivity to market moves

Calculator

Portfolio Return (%)Market Return (%)Risk-Free Rate (%)Portfolio Beta

How to Use

1
Enter portfolio return: The actual annualised return of the portfolio over the measurement period.
2
Enter market return and risk-free rate: S&P 500 return for the same period and the prevailing T-bill rate.
3
Enter portfolio beta: The beta of the portfolio relative to the S&P 500.
4
Read Alpha: Positive = outperformance beyond market risk. Negative = manager destroyed value vs passive investing.

Worked Example

Example: Active fund evaluation

Portfolio

16%

Market

12%

Beta

1.10

CAPM expected = 5% + 1.10 × (12% − 5%) = 5% + 7.7% = 12.7%. Alpha = 16% − 12.7% = +3.3%. The manager generated 3.3% above what CAPM predicts given the risk taken, strong evidence of skill (if sustained over multiple periods).