NASAA Series 66 Uniform Combined State Law ExaminationEconomic Factors and Business InformationHard
A fund manager is assessing the risk-adjusted returns of different portfolios. Portfolio A has an average return of 12% and a standard deviation of 8%. Portfolio B has an average return of 10% and a standard deviation of 5%. The risk-free rate is 3%. Which portfolio has a higher Sharpe Ratio, and what does it imply?
- APortfolio A, implying lower total risk.
- BPortfolio B, implying higher return with lower risk.
- CPortfolio A, implying higher absolute return.
- DPortfolio B, implying better return per unit of risk.
Show answer & explanationAnswer & explanation
Correct answer: D. Portfolio B, implying better return per unit of risk.
The Sharpe Ratio is calculated as (Portfolio Return - Risk-Free Rate) / Standard Deviation. For Portfolio A: (12% - 3%) / 8% = 9% / 8% = 1.125. For Portfolio B: (10% - 3%) / 5% = 7% / 5% = 1.4. Portfolio B has a higher Sharpe Ratio (1.4 vs 1.125), indicating that it provides a better return for each unit of risk taken.
Why the other options are wrong
- A. Portfolio A has a higher standard deviation (8%) than Portfolio B (5%), indicating higher total risk, not lower.
- B. Portfolio B has lower risk (lower standard deviation), but its return is also lower. The Sharpe Ratio helps determine which combination is superior on a risk-adjusted basis; it's not simply 'higher return with lower risk' but rather 'better return *per unit of risk*'.
- C. Portfolio A has higher absolute return but not necessarily higher risk-adjusted return. The Sharpe Ratio measures risk-adjusted return.
Sharpe Ratio
A measure of risk-adjusted return, indicating the average return earned in excess of the risk-free rate per unit of total risk (standard deviation).
- Formula: (Portfolio Return - Risk-Free Rate) / Standard Deviation.
- Higher ratio implies better risk-adjusted performance.
- Used to compare portfolios with different risk levels.
Memory trick: Sharpe: Subtract Risk-Free, Divide by Shake.