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FRM Part I · FRM Exam Part I · Modern Portfolio Theory (MPT) and the Capital Asset Pricing Model (CAPM)

A portfolio is 60% invested in the market portfolio and 40% in the risk-free asset. The risk-free rate is 2%, the market's expected return is 10%, and the market's standard deviation is 20%. What are the portfolio's expected return and standard deviation?

The portfolio has an expected return of 6.8% and a standard deviation of 12%. Return is the weighted average, 0.6 times 10% plus 0.4 times 2%. Risk is only the market weight times market volatility, 0.6 times 20%, because the risk-free asset contributes no volatility.

  1. A6.8% and 12%Correct
  2. B8.0% and 12%
  3. C6.8% and 20%
  4. D8.0% and 8%

Explanation

Expected return = 0.6 x 10% + 0.4 x 2% = 6.8%. Risk-free asset has zero volatility and zero correlation, so standard deviation = 0.6 x 20% = 12%. Option 8.0% mistakenly uses beta-type weights that ignore the risk-free component.

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