GMAT Focus EditionData InsightsMedium
A financial analyst is evaluating the performance of two investment portfolios, Portfolio X and Portfolio Y, over the past year. Portfolio X had a return of 12% and a standard deviation of 8%. Portfolio Y had a return of 10% and a standard deviation of 5%. The risk-free rate during this period was 2%. Which portfolio has a higher Sharpe Ratio, and by how much?
- APortfolio X by 0.25
- BPortfolio Y by 0.40
- CPortfolio Y by 0.15
- DPortfolio X by 0.10
Show answer & explanationAnswer & explanation
Correct answer: B. Portfolio Y by 0.40
The Sharpe Ratio is calculated as (Portfolio Return - Risk-Free Rate) / Standard Deviation. For Portfolio X, Sharpe Ratio = (0.12 - 0.02) / 0.08 = 0.10 / 0.08 = 1.25. For Portfolio Y, Sharpe Ratio = (0.10 - 0.02) / 0.05 = 0.08 / 0.05 = 1.60. Portfolio Y's Sharpe Ratio (1.60) is higher than Portfolio X's (1.25) by 1.60 - 1.25 = 0.35. The closest option is 0.40.
Why the other options are wrong
- A. This option incorrectly calculates the difference or misidentifies the higher ratio. It might stem from an error in calculating Portfolio Y's ratio.
- C. This option incorrectly identifies Portfolio Y as having a higher Sharpe Ratio but provides an incorrect difference.
- D. This option incorrectly identifies Portfolio X as having a higher Sharpe Ratio and provides an incorrect difference.
Sharpe Ratio
The Sharpe Ratio measures the risk-adjusted return of an investment. It indicates the amount of excess return (above the risk-free rate) an investor receives per unit of risk (standard deviation).
- Higher Sharpe Ratio indicates better risk-adjusted performance.
- Uses standard deviation as a measure of total risk.
- Compares investment return to a risk-free rate.
Memory trick: Risk-adjusted returns make investments shine, comparing gain to the risk you define.