CFA Level IPortfolio ManagementEasy
A portfolio earned an annual return of 12% with a standard deviation of 18%. The risk-free rate is 3%. What is the portfolio's Sharpe ratio?
- A0.17
- B0.83
- C0.50
- D0.67
Show answer & explanationAnswer & explanation
Correct answer: C. 0.50
Sharpe ratio = (Portfolio return − Risk-free rate) / Portfolio standard deviation = (12% − 3%) / 18% = 9%/18% = 0.50.
Why the other options are wrong
- A. Incorrectly divides the risk-free rate by the standard deviation instead of the excess return.
- B. Results from dividing total return by risk-free rate rather than by standard deviation.
- D. Uses total return (12%) divided by standard deviation without subtracting the risk-free rate incorrectly scaled.
Sharpe Ratio
A measure of risk-adjusted return that divides excess return over the risk-free rate by total portfolio risk (standard deviation).
- Formula: (Rp − Rf) / σp
- Uses total risk, appropriate for non-diversified or total portfolios
- Higher Sharpe ratio indicates better risk-adjusted performance
Memory trick: Sharpe shares excess return among total risk takers