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 12%, with a standard deviation of 20% 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 volatility. Excess return is 12% minus 3%, or 9%, and dividing by the 20% standard deviation gives 0.45. Using beta in the denominator would give Treynor, and ignoring the risk-free rate would give 0.60.
- A0.45Correct
- B0.60
- C0.72
- D0.09
Explanation
Sharpe ratio = (Rp - Rf)/sigma = (12% - 3%)/20% = 0.09/0.20 = 0.45. The option 0.072 style error of dividing by beta gives the Treynor ratio (0.072), not Sharpe. Using 12%/20% = 0.60 ignores the risk-free rate.
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