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NISM Certifications · NISM-Series-X-A: Investment Adviser (Level 1) · Portfolio Performance Measurement and Evaluation

Portfolio A has a return of 15%, beta of 1.5 and standard deviation of 20%. The risk-free rate is 6%. Portfolio B has a return of 12%, beta of 0.8 and standard deviation of 10%. Which statement is correct?

Portfolio B has both the higher Sharpe and the higher Treynor ratio. B's Sharpe is 0.60 against A's 0.45, and B's Treynor is 7.5 against A's 6.0. Each unit of risk, whether total or market risk, earned more excess return in B.

  1. AB has a higher Sharpe ratio, while A has a higher Treynor ratio
  2. BA has a higher Sharpe ratio and a higher Treynor ratio
  3. CB has a higher Sharpe ratio and a higher Treynor ratioCorrect
  4. DA has a higher Sharpe ratio, while B has a higher Treynor ratio

Explanation

Sharpe A = 9/20 = 0.45; Sharpe B = 6/10 = 0.60. Treynor A = 9/1.5 = 6.0; Treynor B = 6/0.8 = 7.5. B is higher on both measures, so B is better on both total risk and systematic risk basis.

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