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NISM Certifications · NISM-Series-X-A: Investment Adviser (Level 1) · Introduction to Modern Portfolio Theory

Mr. Iyer holds a portfolio with an expected return of 14%, a standard deviation of 18% and a beta of 1.2. The risk-free rate is 6%. What is the Sharpe ratio of his portfolio?

The Sharpe ratio is 0.44. It is excess return over the risk-free rate divided by total risk measured by standard deviation: (14% minus 6%) divided by 18% equals about 0.44. Using beta in the denominator would give the Treynor ratio instead.

  1. A0.44Correct
  2. B0.67
  3. C0.78
  4. D1.00

Explanation

Sharpe ratio = (Rp - Rf)/standard deviation = (14-6)/18 = 8/18 = 0.444, i.e. 0.44. Dividing by beta (8/1.2 = 6.67) gives the Treynor measure, not Sharpe. Using 14/18 = 0.78 ignores the risk-free rate.

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