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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 5%, and the market portfolio has an expected return of 11% with a standard deviation of 20%. An investor wants an expected return of 14% using only the risk-free asset and the market portfolio. What standard deviation will the investor's portfolio have?

The standard deviation is 30%. The CML slope is (11% - 5%)/20% = 0.3, so a 14% return requires risk of (14% - 5%)/0.3 = 30%. This means holding 1.5 times the market portfolio, financed by borrowing at the risk-free rate.

  1. A20%
  2. B25%
  3. C30%Correct
  4. D35%

Explanation

CML slope = (11% - 5%)/20% = 0.3. Required risk = (14% - 5%)/0.3 = 30%. Check: market weight = 9/6 = 1.5, and 1.5x20% = 30%, financed by borrowing at the risk-free rate.

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