SIDC Module 12 Portfolio management and performance evaluation question: Fund P returned

SIDC Module 12Portfolio management and performance evaluation

The risk-free rate is 4%. Fund P returned 13% with a standard deviation of 25% and a beta of 0.8. Fund Q returned 11% with a standard deviation of 16% and a beta of 1.0. Which statement is correct?

A P ranks higher on the Sharpe ratio; Q ranks higher on the Treynor ratio
B Q ranks higher on both the Sharpe ratio and the Treynor ratio
C P ranks higher on both the Sharpe ratio and the Treynor ratio
D Q ranks higher on the Sharpe ratio; P ranks higher on the Treynor ratio

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Answer: D. Q ranks higher on the Sharpe ratio; P ranks higher on the Treynor ratio

Sharpe = (Rp − Rf) ÷ σp: P = 9 ÷ 25 = 0.36; Q = 7 ÷ 16 = 0.44, so Q leads. Treynor = (Rp − Rf) ÷ βp: P = 9 ÷ 0.8 = 11.25%; Q = 7 ÷ 1.0 = 7.00%, so P leads. The rankings conflict because P carries a lot of firm-specific risk: its total risk is high relative to its beta. Sharpe penalises that diversifiable risk, Treynor ignores it. Neither fund wins on both, and reversing the rankings swaps the two denominators. 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

Assuming the measures must agree. They diverge when a portfolio is poorly diversified.

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