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FRM Part I · FRM Exam Part I · Modern Portfolio Theory (MPT) and the Capital Asset Pricing Model (CAPM)

A portfolio earned an average return of 11%, with a standard deviation of 16% and a beta of 1.25. The risk-free rate is 3%. What is the portfolio's Sharpe ratio?

The Sharpe ratio is excess return divided by total standard deviation. Excess return is 11% minus 3%, which is 8%, and dividing by 16% gives 0.50. Beta is not used, because Sharpe measures reward per unit of total risk rather than systematic risk.

  1. A0.50Correct
  2. B0.64
  3. C0.69
  4. D0.875

Explanation

Sharpe ratio = (Rp - Rf) / total standard deviation = (11% - 3%) / 16% = 0.50. The 0.64 option is the Treynor ratio (8/1.25 = 6.4%) scaled incorrectly, and uses beta rather than standard deviation, which is the wrong risk measure for Sharpe.

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