Jensen's Alpha Calculator
Measure risk-adjusted excess return. Compare your portfolio or fund return to the CAPM expected return and see if you beat the market.
e.g. 10-year Treasury yield
Benchmark (e.g. S&P 500) return
Underperformed benchmark
E(R) = Rf + β(Rm − Rf)
Interpretation
Alpha = Actual return − Expected return. Positive alpha means the portfolio or fund beat the risk-adjusted benchmark; negative alpha means it underperformed.
Your portfolio returned 0.00%; CAPM expected 0.00%. Excess return (alpha) = 0.00%.
What is Jensen's Alpha?
Jensen's Alpha (or Jensen's measure) is the difference between a portfolio's or fund's actual return and its expected return under the Capital Asset Pricing Model (CAPM). It measures risk-adjusted excess return: how much you gained or lost relative to what you "should" have earned given the risk (beta) you took.
Formula
Alpha (α) = Rp − [Rf + β(Rm − Rf)], where Rp is portfolio return, Rf is the risk-free rate, β is beta, and Rm is market return. The term in brackets is the CAPM expected return. So alpha = actual return − expected return.
How to Use This Calculator
- Portfolio / Fund Return: Enter the actual return of your portfolio or fund (e.g. 12%).
- Risk-Free Rate: Use a proxy like the 10-year Treasury yield (e.g. 2%).
- Beta: Enter the beta of the portfolio or fund vs. the market (e.g. 1.2).
- Market Return: Enter the return of the benchmark (e.g. S&P 500 at 10%).
- Read Alpha: Positive alpha = outperformance; negative alpha = underperformance vs. CAPM.
Why Alpha Matters
- Skill vs. luck: Alpha isolates excess return after accounting for market risk (beta), so it's often used to judge manager skill.
- Fund comparison: Compare funds or strategies on a risk-adjusted basis instead of raw returns.
- Benchmarking: See whether your portfolio beat the "fair" return implied by CAPM.
Frequently Asked Questions
What is Jensen's Alpha?
Jensen's Alpha is the difference between a portfolio's or fund's actual return and its expected return under the Capital Asset Pricing Model (CAPM). It measures risk-adjusted excess return: how much you gained or lost relative to what you 'should' have earned given the beta (market risk) you took.
How do you calculate Jensen's Alpha?
Alpha = Rp − [Rf + β(Rm − Rf)], where Rp is portfolio return, Rf is the risk-free rate, β is beta, and Rm is market return. The term in brackets is the CAPM expected return. So Jensen's Alpha = actual return − CAPM expected return.
What does a positive or negative Jensen's Alpha mean?
A positive alpha means the portfolio or fund outperformed the risk-adjusted benchmark (beat CAPM). A negative alpha means it underperformed. Alpha is often used to judge manager skill: consistent positive alpha suggests skill; negative alpha suggests underperformance after accounting for risk.
How is Jensen's Alpha different from Sharpe ratio?
Jensen's Alpha measures excess return relative to CAPM (beta-adjusted). The Sharpe ratio measures excess return per unit of total volatility (standard deviation). Alpha focuses on market risk (beta); Sharpe focuses on total risk. Both are risk-adjusted performance metrics but use different risk definitions.
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