NASAA Series 65, Uniform Investment Adviser Law ExaminationClient Investment Recommendations and StrategiesMedium
A client is evaluating two investment options for their retirement portfolio: Fund A has an expected return of 8% with a standard deviation of 12%, and Fund B has an expected return of 10% with a standard deviation of 18%. The risk-free rate is 3%. Which fund has a better coefficient of variation?
- AFund A, with a coefficient of variation of 1.50.
- BFund B, with a coefficient of variation of 1.80.
- CFund B, with a coefficient of variation of 0.56.
- DFund A, with a coefficient of variation of 0.67.
Show answer & explanationAnswer & explanation
Correct answer: A. Fund A, with a coefficient of variation of 1.50.
The coefficient of variation (CV) is calculated as Standard Deviation / Expected Return. For Fund A: 12% / 8% = 1.50. For Fund B: 18% / 10% = 1.80. A lower CV indicates better risk-adjusted return, making Fund A better.
Why the other options are wrong
- B. Incorrect, Fund B's CV is 0.18 / 0.10 = 1.80. This is higher than Fund A's, meaning it's worse.
- C. Incorrect calculation. 10% / 18% = 0.56. The formula is Standard Deviation / Expected Return.
- D. Incorrect calculation. 8% / 12% = 0.67. The formula is Standard Deviation / Expected Return.
Coefficient of Variation (CV)
A statistical measure of the dispersion of data points around the mean, used in finance to compare the relative variability of different investment options.
- Calculated as Standard Deviation / Expected Return.
- Measures risk per unit of return.
- A lower CV indicates a more favorable risk-adjusted return.
Memory trick: CV: Compare Volatility, value returns.