ジェンセンのアルファ計算：リスク調整収益

Jensen’s alpha measures whether a portfolio earned more or less than CAPM said it should, given its beta. Michael Jensen introduced the intercept in a time-series regression of excess portfolio returns on excess market returns. In a single-period classroom version, alpha is just realized return minus the CAPM required return. The Jensen’s alpha calculator uses alpha = portfolio return − [risk-free rate + beta × (market return − risk-free rate)]. CAPM expected return is that bracketed term. Portfolio excess return is portfolio return minus the risk-free rate, and market risk premium is market return minus the risk-free rate. Enter all returns as percents. A 12.5% portfolio return, 2% risk-free rate, 8% market return, and beta of 1.2 produce a 9.20% CAPM return and a 3.30% alpha. A 6% portfolio return, 3% risk-free rate, 9% market, and beta 0.8 produce a 7.80% CAPM return and a −1.80% alpha. Positive alpha means the portfolio beat its CAPM benchmark over the window you measured. It does not prove skill. A lucky year, stale prices, a mismatched market index, or beta estimated on a different sample can all create a non-zero intercept. Negative alpha means the portfolio lagged the security-market line; high fees often show up here. Keep the return window consistent: do not mix an annual portfolio return with a monthly T-bill yield. Beta should be estimated against the same market proxy you enter as market return. The calculator does not annualize, does not adjust for residual risk, and does not run a t-test on alpha. Use it to unpack a performance number into the CAPM pieces, then judge whether the beta and the benchmark actually describe the portfolio. Multi-factor models add size, value, momentum, or profitability slopes that CAPM ignores, so a CAPM alpha can disappear once those factors are included. Record the return window, the market index, and the beta sample whenever you present Jensen’s alpha as a performance statistic.