An equity portfolio manager achieves a portfolio return (Rp) of 16.0% with a portfolio Beta of 1.20 and a return standard deviation of 5.0%. The broad market return (Rm) is 12.0%, and the risk-free rate (Rf) is 6.0%. What are the portfolio's Jensen's Alpha, Sharpe Ratio, and Treynor Ratio?

[ A ]Jensen's Alpha = 2.80% (16.0% - [6% + 1.2 * (12% - 6%)]); Sharpe Ratio = 2.00 ((16% - 6%) / 5%); Treynor Ratio = 8.33% ((16% - 6%) / 1.20)[ CORRECT ]

[ B ]Jensen's Alpha = 4.00%; Sharpe Ratio = 3.20; Treynor Ratio = 13.33%

[ C ]Jensen's Alpha = 0.00%; Sharpe Ratio = 1.00; Treynor Ratio = 5.00%

[ D ]Jensen's Alpha = -2.80%; Sharpe Ratio = 0.50; Treynor Ratio = 2.00%

Takeaway

Option A is correct: Jensen's Alpha = 2.80% (16.0% - [6% + 1.2 * (12% - 6%)]); Sharpe Ratio = 2.00 ((16% - 6%) / 5%); Treynor Ratio = 8.33% ((16% - 6%) / 1.20)

Derivation

Step-by-step calculations: (1) CAPM Expected Return = Rf + Beta * (Rm - Rf) = 6.0% + 1.20 * (12.0% - 6.0%) = 6.0% + 7.20% = 13.20%. Jensen's Alpha = Actual Return - Expected Return = 16.0% - 13.20% = 2.80% (positive alpha reflects superior stock selection). (2) Sharpe Ratio = (Rp - Rf) / Standard Deviation = (16.0% - 6.0%) / 5.0% = 10.0% / 5.0% = 2.00. (3) Treynor Ratio = (Rp - Rf) / Beta = (16.0% - 6.0%) / 1.20 = 10.0% / 1.20 = 8.333% (or 0.0833). This question tests all three major risk-adjusted performance metrics simultaneously. The primary error is using unadjusted market return instead of CAPM expected return.

Why the others fail

B — Jensen's Alpha = 4.00%; Sharpe Ratio = 3.20; Treynor Ratio = 13.33%

Alpha of 4.00% simply subtracts market return (16 - 12) without adjusting for portfolio Beta risk, and miscomputes Sharpe and Treynor ratios.

C — Jensen's Alpha = 0.00%; Sharpe Ratio = 1.00; Treynor Ratio = 5.00%

Zero Alpha incorrectly assumes the fund exactly matched CAPM expectations, contradicting the calculated 2.80% outperformance.

D — Jensen's Alpha = -2.80%; Sharpe Ratio = 0.50; Treynor Ratio = 2.00%

Negative Alpha and inverted ratio outputs result from incorrect mathematical operations in the risk premium numerators.