Jensen's Alpha

Jensen's Alpha

Jensen's alpha (α) measures a portfolio's (or asset's) risk-adjusted outperformance relative to what CAPM predicts. It was introduced by Michael Jensen in 1968 to evaluate mutual fund managers.

$\alpha_i = R_i - [r_f + \beta_i (R_m - r_f)]$

where:

• R_i = actual return of the asset/portfolio
• r_f = risk-free rate
• β_i = asset's beta
• R_m = actual market return

Interpretation

• α > 0: the manager (or asset) generated returns above what CAPM predicts — positive skill or mispricing
• α = 0: performance perfectly in line with systematic risk
• α < 0: underperformance relative to CAPM prediction

Note

Jensen's alpha uses realized market and asset returns (not just expected), making it useful for performance attribution after the fact.

Your Task

Implement jensens_alpha(actual_return, rf, beta, market_return) that computes Jensen's alpha.