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NISM Certifications · NISM-Series-V-A: Mutual Fund Distributors · Risk, Return and Performance of Funds

A fund has an annual return of 14%, the risk-free rate is 6%, and the fund's standard deviation is 16%. The fund's beta is 0.8. Which statement about its Sharpe and Treynor ratios is correct?

Sharpe ratio is 0.50 and Treynor ratio is 0.10. Both use the excess return of 8% over the risk-free rate; Sharpe divides it by the standard deviation of 16%, while Treynor divides it by the beta of 0.8, giving 0.08/0.8 = 0.10.

  1. ASharpe ratio is 0.50 and Treynor ratio is 0.10Correct
  2. BSharpe ratio is 0.50 and Treynor ratio is 10
  3. CSharpe ratio is 0.875 and Treynor ratio is 0.10
  4. DSharpe ratio is 0.50 and Treynor ratio is 0.175

Explanation

Excess return = 14 − 6 = 8%. Sharpe = 8/16 = 0.50 (uses standard deviation). Treynor = 8/0.8 = 10 percentage points, i.e. 0.10 in decimal terms (0.08/0.8). Option 0.875 divides 14 by 16, ignoring the risk-free rate. Option 0.175 divides 14 by 0.8, again ignoring it.

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