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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 2%, the market portfolio has an expected return of 8% and a standard deviation of 12%. An investor puts 60% of her wealth in the market portfolio and 40% in the risk-free asset. What are the portfolio's expected return and standard deviation?

Expected return is 5.6% and standard deviation is 7.2%. The return is the weighted average, 0.4×2% + 0.6×8%. Because the risk-free asset has no variance, portfolio volatility is just 60% of the market's 12%. The point lies on the CML.

  1. A5.6% and 7.2%Correct
  2. B5.6% and 12.0%
  3. C6.4% and 7.2%
  4. D4.8% and 7.2%

Explanation

Expected return = 0.4×2% + 0.6×8% = 0.8% + 4.8% = 5.6%. Standard deviation = 0.6×12% = 7.2%, since the risk-free asset has zero volatility and zero correlation. Check: 2% + 0.5×7.2% = 5.6%, consistent with the CML slope of 0.5.

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