NISM Certifications · NISM-Series-XXI-A: Portfolio Management Services (PMS) Distributors · Investments
A portfolio has a return of 14%, a standard deviation of 10% and a beta of 1.2. The risk-free rate is 6%. What is its Sharpe ratio and Treynor ratio (Treynor expressed in percentage points per unit of beta, approximately)?
Sharpe ratio is 0.80 and Treynor ratio is about 6.67. Both use the excess return over the risk-free rate, which is 8%. Dividing by standard deviation of 10% gives Sharpe, and dividing by beta of 1.2 gives Treynor.
- ASharpe 0.80; Treynor 6.67Correct
- BSharpe 1.40; Treynor 11.67
- CSharpe 0.80; Treynor 11.67
- DSharpe 0.60; Treynor 6.67
Explanation
Excess return = 14 - 6 = 8. Sharpe = 8/10 = 0.80. Treynor = 8/1.2 = 6.67. Using the total return of 14 instead of excess return gives 1.40 and 11.67, a wrong-base error.
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