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CFA Level I · CFA Level I Exam · The Return and Risk of a Financial Portfolio

The risk-free rate is 2%. A risky portfolio has an expected return of 10% and a standard deviation of 20%. An investor wants a complete portfolio with a standard deviation of 15% using this risky portfolio and the risk-free asset. The expected return of the complete portfolio is closest to:

The expected return is about 8.0%. Since standard deviation scales linearly with the risky weight, the investor holds 15/20 = 75% in the risky portfolio. The return is 2% plus 75% of the 8% risk premium, which gives 8.0%.

  1. A6.0%
  2. B8.0%Correct
  3. C9.5%

Explanation

Weight in risky portfolio = 15%/20% = 0.75. E(R) = 2% + 0.75(10% - 2%) = 2% + 6% = 8.0%. Check: 0.25(2%) + 0.75(10%) = 0.5% + 7.5% = 8.0%. The 6.0% answer omits the risk-free rate from the calculation (0.75 x 8%).

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