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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 10% and a volatility of 16%. An investor with 50,000 invests 30,000 in the market portfolio and the remainder in the risk-free asset. What is the portfolio's expected return and standard deviation?

Expected return is 6.8% and standard deviation is 9.6%. With 60% in the market and 40% risk-free, return is 0.4 x 2% + 0.6 x 10% = 6.8%, while risk scales only with the market weight: 0.6 x 16% = 9.6%.

  1. AExpected return 6.8%, standard deviation 9.6%Correct
  2. BExpected return 6.8%, standard deviation 16.0%
  3. CExpected return 8.0%, standard deviation 9.6%
  4. DExpected return 10.0%, standard deviation 9.6%

Explanation

Weight in market = 30,000/50,000 = 0.6. Return = 0.4 x 2% + 0.6 x 10% = 6.8%. Standard deviation = 0.6 x 16% = 9.6% since the risk-free asset has zero volatility and zero correlation. Check on the CML: 2% + 0.5 x 9.6% = 6.8%.

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