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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 4%. The market portfolio has expected return 10% and standard deviation 20%. Portfolio P has expected return 11% and standard deviation 25%, and a correlation with the market of 0.9. An investor can lend and borrow at the risk-free rate. Which conclusion is correct?

Portfolio P is inefficient. Its Sharpe ratio is (11% - 4%)/25% = 0.28, below the market's 0.30. Leveraging the market to 25% volatility would earn 11.5%, more than P's 11%, so P lies below the Capital Market Line.

  1. AP's Sharpe ratio is 0.28, below the market's 0.30, so P is inefficient relative to the CMLCorrect
  2. BP's Sharpe ratio is 0.28, above the market's 0.30, so P lies above the CML
  3. CP's Sharpe ratio equals 0.30, so P lies on the CML
  4. DP's Sharpe ratio is 0.44, so P lies above the CML

Explanation

Market Sharpe = (10-4)/20 = 0.30. P Sharpe = (11-4)/25 = 0.28. Since 0.28 < 0.30, P plots below the CML and is dominated: market plus risk-free at 25% volatility yields 4% + 0.3×25% = 11.5%. Option 2 misstates the inequality; option 4 divides by 16%.

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