NISM Certifications · NISM-Series-XXI-A: Portfolio Management Services (PMS) Distributors · Investments
A PMS portfolio earned 14% in a year, the risk-free rate is 6%, and the portfolio's standard deviation is 16%. Its beta is 1.25. What are its Sharpe ratio and Treynor ratio (Treynor expressed in percentage points per unit of beta)?
Sharpe ratio is 0.50 and Treynor ratio is 6.4. Both use the excess return over the risk-free rate, which is 8 percentage points. Dividing by standard deviation of 16 gives Sharpe, and dividing by beta of 1.25 gives Treynor.
- ASharpe 0.50; Treynor 6.4Correct
- BSharpe 0.875; Treynor 11.2
- CSharpe 0.50; Treynor 11.2
- DSharpe 0.875; Treynor 6.4
Explanation
Excess return = 14 - 6 = 8. Sharpe = 8/16 = 0.50. Treynor = 8/1.25 = 6.4. Using 14/16 = 0.875 and 14/1.25 = 11.2 ignores the risk-free rate deduction, which is the key error in the other options.
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