Hong Life CalculatorsUnderstanding the Jensen's alpha calculator — concept and principle
Jensen's alpha measures whether a portfolio or fund earned more or less than it should have for the market risk it took. Investors and analysts use it to judge active managers: did the manager add value beyond simply holding market exposure?
How it is calculated
α = Rp − [Rf + β × (Rm − Rf)]
- Rp: the portfolio's actual return for the period.
- Rf: the risk-free rate for the same period, such as a Treasury bill yield.
- Rm: the return of the benchmark market index.
- β: the portfolio's beta, its sensitivity to market moves.
- The bracket is the CAPM expected return. Alpha is the gap between actual and expected.
- The calculator also shows the Treynor ratio, (Rp − Rf) ÷ β, excess return per unit of market risk.
The principle
The Capital Asset Pricing Model says investors are paid only for market risk, which cannot be removed by diversifying. A portfolio with beta 1.1 should earn the risk-free rate plus 1.1 times the market's excess return. Michael Jensen proposed in 1968 that anything left over after that expected return reflects skill (or luck). A positive alpha means the portfolio beat its risk-adjusted benchmark; a negative alpha means it lagged.
Worked example
Default inputs: Rp = 12%, Rf = 4%, Rm = 9%, β = 1.1.
- Market risk premium = 9% − 4% = 5%.
- Return from market exposure = 1.1 × 5% = 5.5%.
- CAPM expected return = 4% + 5.5% = 9.5%.
- Alpha = 12% − 9.5% = 2.5%, so the verdict is "Beat its risk-adjusted benchmark".
- Treynor ratio = (12 − 4) ÷ 1.1 ≈ 7.27.
| Portfolio return for the period (%) | Jensen’s alpha |
|---|---|
| 3 | -6.5% |
| 6 | -3.5% |
| 9 | -0.5% |
| 12 | 2.5% |
| 15 | 5.5% |
| 18 | 8.5% |
| 24 | 14.5% |
How to read the result
An alpha near zero means the return is explained by market exposure alone. A positive alpha that persists over many periods is more convincing than one good year. Compare alphas only when they use the same benchmark, period and return frequency. Alpha before fees and after fees can differ a lot; investors receive the after-fee return.
Common mistakes
- Mixing annual and monthly figures in the same calculation.
- Using a benchmark that does not match the portfolio, such as the S&P 500 for a small-cap fund.
- Trusting a beta estimated from too few data points.
- Reading one period's alpha as proof of skill.
Frequently asked questions
What is a good Jensen's alpha?
Any consistently positive alpha after fees is notable, because most active funds struggle to beat their benchmarks over long periods.
How is Jensen's alpha different from simple outperformance?
Simple outperformance ignores risk. Alpha adjusts for beta, so a high-beta fund must beat the market by more in rising markets.
Can alpha be negative even if the fund made money?
Yes. If the fund earned less than CAPM expected for its beta, alpha is negative even with a positive return.
Where do I find beta?
Fund fact sheets and financial data sites publish beta, usually from 36 to 60 monthly returns against a stated index.
Sources: Jensen, M. C. (1968). The Performance of Mutual Funds in the Period 1945–1964. Journal of Finance, 23(2), 389–416. · Sharpe, W. F. (1964). Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk. Journal of Finance, 19(3).