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NISM Certifications · NISM-Series-V-A: Mutual Fund Distributors · Mutual Fund Scheme Performance

Over a period, a scheme earned 14% with a standard deviation of 10% and a beta of 1.25. The risk-free rate was 6%. What is its Sharpe ratio, and which ratio would use the same numerator but beta in the denominator?

The Sharpe ratio is 0.80, being the excess return of 8% over the risk-free rate divided by the standard deviation of 10%. The Treynor ratio uses the same excess return divided by beta, giving 8 divided by 1.25, which equals 6.4.

  1. A0.80; Treynor ratio, which equals 6.4Correct
  2. B1.40; Treynor ratio, which equals 11.2
  3. C0.80; Jensen's alpha, which equals 6.4
  4. D1.40; Treynor ratio, which equals 6.4

Explanation

Excess return = 14 - 6 = 8. Sharpe = 8/10 = 0.80. Treynor = 8/1.25 = 6.4, using beta as the risk measure. Options with 1.40 wrongly use the 14% return without deducting the risk-free rate. Jensen's alpha is a return difference versus CAPM, not excess return divided by beta.

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