Jensen's Alpha Calculator

Jensen's alpha (α) is a measure of risk-adjusted excess return based on the CAPM model. It measures the difference between a portfolio’s actual return (Rp) and the return that should have been generated by that portfolio according to CAPM for the same level of systematic risk (beta). Its unit is percentage points. The concept was introduced by Michael C. Jensen in 1968 to evaluate mutual fund performance.

The formula: α = Rp − [Rf + β × (Rm − Rf)]. Rp = actual portfolio return, Rf = risk-free rate (e.g. government bond yields), β = portfolio beta against the market, Rm = market return (benchmark). The bracketed part is the CAPM expected return — so alpha is actual return minus the CAPM expectation. Example: Rp = 12%, Rf = 3%, β = 1.2, Rm = 10% → CAPM expectation = 3 + 1.2 × (10 − 3) = 11.4%, so α = 12 − 11.4 = 0.6%.

Both measure excess return, but their reference and risk measures differ. Jensen's alpha compares actual return against the CAPM model’s expectation, and its risk is measured with beta (systematic risk). The information ratio compares portfolio return against the actual return of a benchmark, then divides by tracking error (the standard deviation of return differences). Simply put: alpha answers “did my return beat the CAPM prediction?”, while the information ratio answers “how consistently did I beat the benchmark per unit of tracking error?”. To compute the information ratio, use the information ratio calculator.

Sharpe ratio = (Rp − Rf) ÷ σp, using total risk (portfolio standard deviation, σp) as the denominator. Jensen's alpha uses beta — only systematic risk that cannot be diversified away. As a result, the Sharpe ratio penalizes portfolios that are not fully diversified (specific risk is counted too), while alpha ignores specific risk. Descriptively: the Sharpe ratio suits judging a portfolio as someone’s entire investment, while alpha suits judging the contribution of a manager or asset inside an already-diversified portfolio.

Mathematically: α > 0 means the portfolio’s actual return exceeds the CAPM expectation for that beta — the difference is unexplained by the model. α < 0 means actual return is below the CAPM expectation. α = 0 means actual return exactly equals the CAPM expectation. This is a descriptive reading of the figure, not a judgment: alpha does not declare a portfolio “good” or “bad”, does not determine buy/sell decisions, and does not account for fees, taxes, or the measurement period.

First, alpha is only as good as its CAPM model: CAPM assumes stable beta and expected returns linear in beta, which often fails in real data. Second, results are sensitive to the choice of benchmark (Rm) and risk-free rate (Rf) proxy — different benchmarks produce different alphas. Third, alpha is backward-looking: computed from historical returns, so it does not guarantee the same pattern continues. Fourth, this single-factor model ignores other factors (company size, valuation, momentum) that also explain returns.

No. This calculator is an educational tool for understanding Jensen's alpha and CAPM calculations. Its results are descriptive figures from the formula, not recommendations to buy, sell, hold, or choose any particular investment manager. Investment decisions involve risk tolerance, time horizon, fees, and taxes not covered here. For real decisions, consult a financial planner or licensed advisor.