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

A portfolio's return was 16%, the risk-free rate was 6%, and the portfolio's standard deviation was 20%. The benchmark market portfolio had a return of 13% and a standard deviation of 10%. Which statement is correct about the Sharpe ratios?

The portfolio's Sharpe ratio is 0.50 and the market's is 0.70, so the market is better on a risk-adjusted basis. Sharpe ratio divides excess return over the risk-free rate by standard deviation, and the market earns more excess return per unit of total risk.

  1. APortfolio has 0.50 and market has 0.70, so the market is better on a risk-adjusted basisCorrect
  2. BPortfolio has 0.50 and market has 0.70, so the portfolio is better on a risk-adjusted basis
  3. CPortfolio has 0.80 and market has 0.65, so the portfolio is better
  4. DPortfolio has 0.80 and market has 0.70, so the market is better

Explanation

Portfolio Sharpe = (16-6)/20 = 0.50. Market Sharpe = (13-6)/10 = 0.70. The market has the higher Sharpe ratio, so it delivered better return per unit of total risk despite the lower absolute return.

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