Alpha Calculator
Jensen's Alpha Calculator
Calculate Jensen's alpha to determine whether your portfolio is generating returns above or below what the Capital Asset Pricing Model (Capital Asset Pricing Model (CAPM)) predicts for its level of systematic risk. Positive alpha indicates skilled management; negative alpha suggests underperformance.
Inputs
Results
INSTRUCTIONS
How to Use This Calculator
1. Portfolio Return
Enter the actual annualized return your portfolio achieved during the measurement period.
2. Market Parameters
Enter the risk-free rate (Treasury bill yield) and the market return (such as S&P 500 return) for the same period.
3. Portfolio Beta
Enter the beta of your portfolio relative to the market benchmark. Beta measures systematic risk exposure.
4. Read the Alpha
Positive alpha means the portfolio beat CAPM expectations. Negative alpha means it fell short of risk-adjusted benchmarks.
EDUCATION
Understanding Jensen's Alpha
Jensen's alpha, developed by Michael Jensen in 1968, measures the abnormal return of a portfolio relative to the theoretical expected return predicted by the Capital Asset Pricing Model (CAPM). The formula is: α = Rp - [Rf + β(Rm - Rf)], where Rp is the actual portfolio return, Rf is the risk-free rate, β is the portfolio beta, and Rm is the market return. The term in brackets represents the expected return given the portfolio's level of systematic risk.
A positive alpha indicates that the portfolio manager has added value through security selection, market timing, or other active management techniques. A negative alpha suggests the manager underperformed relative to what could have been achieved with a passive index strategy at the same risk level. An alpha of zero means the manager exactly matched the risk-adjusted expectation, earning precisely the return predicted by CAPM for the level of beta exposure.
For example, if a portfolio returned 14% with a beta of 1.1, while the market returned 10% and the risk-free rate was 4%, the expected return per CAPM would be 4% + 1.1 x (10% - 4%) = 10.6%. The Jensen's alpha is 14% - 10.6% = 3.4%, indicating significant value added by the manager. Alpha is widely used in the fund management industry to evaluate portfolio manager skill, often alongside the Sharpe and Treynor ratios for a complete picture of performance.
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