NASAA Series 65, Uniform Investment Adviser Law ExaminationClient Investment Recommendations and StrategiesHard
A client is evaluating two investment funds, Fund X and Fund Y. Fund X has an average annual return of 12%, a standard deviation of 15%, and a beta of 1.1. Fund Y has an average annual return of 10%, a standard deviation of 10%, and a beta of 0.9. The risk-free rate is 3%, and the market return is 8%. Based on the Treynor Ratio, which fund offers superior risk-adjusted performance?
- ABoth funds have equal risk-adjusted performance.
- BThe Treynor Ratio is not applicable for this comparison.
- CFund Y
- DFund X
Show answer & explanationAnswer & explanation
Correct answer: D. Fund X
The Treynor Ratio measures risk-adjusted return using systematic risk (beta). Formula: (Portfolio Return - Risk-Free Rate) / Beta. For Fund X: (12% - 3%) / 1.1 = 9% / 1.1 = 8.18%. For Fund Y: (10% - 3%) / 0.9 = 7% / 0.9 = 7.78%. Since Fund X has a higher Treynor Ratio (8.18% > 7.78%), it offers superior risk-adjusted performance.
Why the other options are wrong
- A. The ratios are different, so performance is not equal.
- B. The Treynor Ratio is applicable here as we have returns, risk-free rate, and beta for both funds.
- C. Fund Y has a lower Treynor Ratio.
Treynor Ratio
A risk-adjusted performance measure that calculates the excess return per unit of systematic risk (beta) in a portfolio.
- Formula: (Portfolio Return - Risk-Free Rate) / Beta.
- Higher ratio indicates better risk-adjusted performance.
- Focuses only on systematic risk.
Memory trick: Treynor: Excess return over beta.