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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 expected return 8% and standard deviation 12%. An investor with 50,000 invests 80,000 in the market portfolio by borrowing 30,000 at the risk-free rate. What are the expected return and standard deviation of the investor's portfolio, as a proportion of the 50,000?

The expected return is 11.6% and the standard deviation is 19.2%. The investor's market weight is 1.6 and the risk-free weight is -0.6, so return is 12.8% minus 1.2%, and risk is 1.6 times the market's 12% volatility.

  1. AReturn 11.6%, standard deviation 19.2%Correct
  2. BReturn 9.6%, standard deviation 19.2%
  3. CReturn 11.6%, standard deviation 12.0%
  4. DReturn 9.6%, standard deviation 7.5%

Explanation

Weight in market = 80/50 = 1.6; risk-free weight = -0.6. Return = 1.6x8% + (-0.6)x2% = 12.8% - 1.2% = 11.6%. Standard deviation = 1.6x12% = 19.2%. Check via CML: 2% + 0.5x19.2% = 11.6%. The 9.6% option omits the borrowing cost adjustment incorrectly.

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