SIDC Module 12 Portfolio management and performance evaluation question: risk-adjusted return minus the market return

SIDC Module 12Portfolio management and performance evaluation

A portfolio returned 12% with a standard deviation of 25%. The market returned 10% with a standard deviation of 20%, and the risk-free rate was 4%. What is the portfolio's M², measured as its risk-adjusted return minus the market return?

A -3.6%
B 0.4%
C 2.0%
D 4.0%

Show the answer and explanation

Answer: B. 0.4%

M² scales the portfolio to the market's volatility. Sharpe ratio = (12% − 4%) ÷ 25% = 0.32. Risk-adjusted return = 4% + 0.32 × 20% = 10.4%. M² = 10.4% − 10% = 0.4%. The raw difference, 12% − 10% = 2.0%, ignores that the portfolio was riskier than the market. Scaling the wrong way, 4% + 8% × 25/20 = 14%, gives 4.0%. Forgetting to add back the risk-free rate gives 6.4% − 10% = −3.6%. Source: SIDC M12 Study Outline Topic 7.4 Evaluation of Investment Performance; Bodie, Kane and Marcus, Investments, chapter 'Portfolio Performance Evaluation'; CFA Institute, Portfolio Risk and Return: Part II (2026 Level I) (as at October 2026).

Common mistake

Comparing raw returns, or scaling the excess return by σp ÷ σm instead of σm ÷ σp.

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