Calculate Jensen's Alpha, Treynor Ratio, Sharpe Ratio, and Information Ratio to evaluate risk-adjusted portfolio performance against the CAPM benchmark.
Jensen's Alpha measures a portfolio manager's ability to generate returns above what the Capital Asset Pricing Model (CAPM) would predict for the portfolio's level of systematic risk (beta). A positive alpha indicates the manager generated excess return through skill — stock selection, market timing, or both.
The CAPM says your expected return should equal the risk-free rate plus beta times the market risk premium. Any return above (or below) this is alpha. A fund with 14% return, 1.3 beta, 10% market return, and 5% risk-free rate has a CAPM expectation of 11.5% — the 2.5% excess is Jensen's Alpha.
This calculator computes alpha alongside four complementary metrics: the Treynor Ratio (excess return per beta), Sharpe Ratio (excess return per unit of total volatility), Information Ratio (active return per tracking error), and M² (Modigliani risk-adjusted return). Together, they give a complete picture of whether a portfolio manager is truly adding value.
Raw returns are meaningless without risk adjustment. A 14% return with 1.3 beta tells a completely different story than 14% with 0.8 beta. Jensen's Alpha and related metrics separate luck and leverage from genuine investment skill. Keep these notes focused on your operational context. Tie the context to the calculator’s intended domain. Use this clarification to avoid ambiguous interpretation.
α = R_p − [R_f + β × (R_m − R_f)] Treynor = (R_p − R_f) / β Sharpe = (R_p − R_f) / σ_p Information Ratio = (R_p − R_m) / Tracking Error M² = R_f + Sharpe × σ_m
Result: Jensen's Alpha = +2.50%
CAPM expected return = 5% + 1.3×(10%−5%) = 11.5%. The portfolio earned 14%, so alpha is 14% − 11.5% = +2.5%. The manager generated 2.5% excess return above the risk-adjusted benchmark.
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Consistently positive alpha (above 0%) is good. Alpha above 2% annually is exceptional and rare over long periods.
Yes — negative alpha means the portfolio underperformed what CAPM predicted for its risk level. The manager destroyed value.
Excess return is simply portfolio return minus benchmark return. Alpha adjusts for risk — a high-beta fund should earn higher returns, so excess return alone doesn't prove skill.
Treynor measures return per unit of beta. Alpha is the absolute excess return above CAPM. A positive alpha implies a Treynor ratio above the market's.
Short-period alpha (1 year) is unreliable. Persistent positive alpha over 5+ years with a strong Information Ratio is more meaningful.
Only if you use net-of-fee returns. Always compare alpha after fees to get a true picture of manager value-add.