About the Jensen's Alpha Calculator
Jensen’s alpha measures how much a portfolio or fund beat (or lagged) the return it should have earned for the market risk it took. It compares the actual return with the return predicted by the capital asset pricing model (CAPM) — the risk-free rate plus beta times the market’s excess return. A positive alpha means the manager added value beyond what the portfolio’s beta explains.
This calculator is for investors reviewing an actively managed fund, advisers reporting risk-adjusted performance, and finance students checking homework. Alongside alpha it reports the CAPM expected return, the Treynor ratio (excess return per unit of beta), the market’s own Treynor ratio for comparison, and the Sharpe ratio if you enter the portfolio’s standard deviation.
Use returns over the same period for the portfolio, the benchmark and the risk-free rate (usually annualised), and a beta estimated against that benchmark. Alpha from one short period is noisy; a consistent alpha over many years is far more meaningful.
With the default inputs, the jensen's alpha is 1.4%. Change any value above to recalculate instantly.
How to use the jensen's alpha calculator
- 1Enter the portfolio’s return for the period (annualised if longer than a year).
- 2Enter the risk-free rate and the benchmark’s return for the same period.
- 3Enter the portfolio’s beta against that benchmark.
- 4Optionally add the portfolio’s standard deviation for the Sharpe ratio.
- 5Read alpha: positive means outperformance after adjusting for market risk.
Formula and method
The CAPM says a portfolio with beta β should earn the risk-free rate plus β times the market risk premium (Rm − Rf). Jensen’s alpha is the actual return minus that required return, expressed in percentage points. Michael Jensen introduced the measure in 1968 to evaluate mutual fund managers.
The Treynor ratio divides the portfolio’s excess return by beta, so it measures reward per unit of systematic (market) risk; the market’s own Treynor ratio equals the market risk premium, because the market’s beta is 1. The Sharpe ratio divides excess return by total volatility instead. A portfolio has positive alpha exactly when its Treynor ratio exceeds the market’s (for positive beta).
- α
- Jensen's alpha (percentage points)
- Rp
- Portfolio return
- Rf
- Risk-free rate
- Rm
- Benchmark (market) return
- β
- Portfolio beta relative to the benchmark
- σp
- Standard deviation of portfolio returns
Worked examples
Fund returns 12% with beta 1.1 vs a 10% market
CAPM requires 4% + 1.1 × (10% − 4%) = 10.6%. The fund earned 12%, so alpha is +1.4 percentage points. Its Treynor ratio of 8 ÷ 1.1 = 7.27 beats the market’s 6.
Defensive fund that lagged
With beta 0.8 the fund should have earned 4.5% + 0.8 × 4.5% = 8.1%. It returned 7%, an alpha of −1.1 points, even though its lower beta means it took less market risk.
Aggressive growth portfolio
A beta of 1.5 calls for 3% + 1.5 × 8% = 15%. Returning 18% gives an alpha of 3 points and a Treynor ratio of 10 versus the market’s 8.
Frequently asked questions
What is a good Jensen's alpha?+
Any positive alpha means the portfolio beat its risk-adjusted benchmark over the period. Because alpha from short periods is noisy and fees reduce it, a consistently positive alpha over five years or more is the meaningful signal.
What is the difference between alpha and the Treynor ratio?+
Alpha is the extra return in percentage points relative to the CAPM prediction. The Treynor ratio is excess return per unit of beta. For a positive beta, alpha is positive exactly when the portfolio’s Treynor ratio is higher than the market’s.
Treynor vs Sharpe ratio: which should I use?+
Treynor uses beta, so it suits a portfolio that is one part of a diversified whole. Sharpe uses total volatility, so it suits a portfolio that is your entire investment. A concentrated fund can look good on Treynor but poor on Sharpe.
Where do I find a fund’s beta?+
Fund fact sheets and financial websites publish beta, usually calculated from 36 to 60 months of returns against a stated index. You can also estimate it yourself with the beta calculator from your own return history.
Is alpha the same as excess return over the benchmark?+
No. Simple excess return just subtracts the benchmark return. Jensen’s alpha adjusts for beta, so a fund with beta 1.5 must beat the benchmark by more in a rising market before it shows positive alpha.
Results are estimates for educational purposes and are not financial advice. Rates, fees and terms vary — confirm with your lender or a licensed advisor before making decisions.