NASAA Series 65, Uniform Investment Adviser Law ExaminationClient Investment Recommendations and StrategiesHard
A client is evaluating two investment options: Fund A, which has an average annual return of 8% with a standard deviation of 12%, and Fund B, which has an average annual return of 10% with a standard deviation of 18%. The risk-free rate is 3%. Which fund has a better risk-adjusted return as measured by the Sharpe Ratio?
- AFund B, with a Sharpe Ratio of 0.67
- BFund B, with a Sharpe Ratio of 0.39
- CFund A, with a Sharpe Ratio of 0.67
- DFund A, with a Sharpe Ratio of 0.42
Show answer & explanationAnswer & explanation
Correct answer: D. Fund A, with a Sharpe Ratio of 0.42
The Sharpe Ratio is calculated as (Portfolio Return - Risk-Free Rate) / Standard Deviation. For Fund A: (0.08 - 0.03) / 0.12 = 0.05 / 0.12 = 0.4167 ≈ 0.42. For Fund B: (0.10 - 0.03) / 0.18 = 0.07 / 0.18 = 0.3889 ≈ 0.39. Fund A has a higher Sharpe Ratio (0.42) than Fund B (0.39), indicating a better risk-adjusted return.
Why the other options are wrong
- A. This calculation for Fund B is incorrect, and Fund B does not have a better Sharpe Ratio.
- B. This is the correct Sharpe Ratio for Fund B, but it is lower than Fund A's.
- C. This calculation for Fund A is incorrect.
Sharpe Ratio
A measure of risk-adjusted return, indicating the amount of excess return (or risk premium) per unit of total risk (standard deviation) in an investment.
- Formula: (Portfolio Return - Risk-Free Rate) / Standard Deviation.
- Higher Sharpe Ratio indicates better risk-adjusted performance.
- Used to compare the performance of different investment portfolios.
Memory trick: Risk-adjusted is about 'BALANCE': Better Alpha, Lower Beta, Adjusted for volatility, Net gain.