NISM Certifications · NISM-Series-X-A: Investment Adviser (Level 1) · Introduction to Modern Portfolio Theory
A portfolio manager's portfolio earned 15% in a year with a standard deviation of 10% and a beta of 1.2. The risk-free rate was 6%. What are the Sharpe ratio and the Treynor ratio (as a percentage return per unit of beta) respectively?
The Sharpe ratio is 0.9 and the Treynor ratio is 7.5. Excess return over the risk-free rate is 9%; dividing by the standard deviation of 10% gives 0.9, and dividing by the beta of 1.2 gives 7.5.
- A0.9 and 7.5Correct
- B1.5 and 12.5
- C0.9 and 12.5
- D0.6 and 7.5
Explanation
Excess return = 15% - 6% = 9%. Sharpe = 9/10 = 0.9 using standard deviation. Treynor = 9/1.2 = 7.5 using beta. Swapping the denominators or using the total return of 15 gives the other options (15/10 = 1.5; 15/1.2 = 12.5).
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