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NISM Certifications · NISM-Series-X-A: Investment Adviser (Level 1) · Operational Aspects of Investment Management

A portfolio manager's portfolio returned 14% in a year with a standard deviation of 10% and a beta of 1.2. The risk-free rate was 6% and the market return was 12%. What are the Sharpe ratio and the Treynor ratio (return per unit of beta, in percentage points) of the portfolio?

Sharpe ratio is 0.8 and Treynor ratio is 6.67. Both use the portfolio's excess return over the risk-free rate, which is 8 percentage points. Dividing by the standard deviation of 10 gives 0.8, and dividing by beta of 1.2 gives 6.67.

  1. ASharpe 0.8; Treynor 6.67Correct
  2. BSharpe 1.4; Treynor 11.67
  3. CSharpe 0.8; Treynor 11.67
  4. DSharpe 0.6; Treynor 6.67

Explanation

Excess return = 14 - 6 = 8%. Sharpe = 8/10 = 0.8. Treynor = 8/1.2 = 6.67. Sharpe 1.4 results from using 14 instead of excess return, and 0.6 uses the market premium of 6 instead of the portfolio's excess return.

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