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

The risk-free rate is 3%, the market portfolio has an expected return of 9% and a standard deviation of 15%. An investor wants an efficient portfolio with a standard deviation of 20% using the risk-free asset and the market portfolio. What is its expected return?

The expected return is 11%. The CML slope is the market Sharpe ratio, (9% - 3%)/15% = 0.4. Adding 0.4 times the 20% standard deviation, or 8%, to the 3% risk-free rate gives 11%, implying leveraged borrowing at the risk-free rate.

  1. A11.0%Correct
  2. B12.0%
  3. C13.0%
  4. D10.0%

Explanation

CML slope = (9% - 3%)/15% = 0.4. Expected return = 3% + 0.4 × 20% = 11%. The 12% answer comes from using the market return wrongly as 9% plus a 3% premium on the extra risk; 13% results from ignoring the risk-free rate adjustment in slope.

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