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

Two risky portfolios are available along with a risk-free rate of 2%. Portfolio X has an expected return of 10% and a standard deviation of 16%. Portfolio Y has an expected return of 8% and a standard deviation of 10%. An investor wants the highest expected return at a target standard deviation of 20%, using only the risk-free asset and one of the risky portfolios. The expected return of the best choice is closest to:

The best choice earns about 14%. Portfolio Y has the higher Sharpe ratio, 0.60 versus 0.50 for X, so its CAL dominates. At a 20% standard deviation, the return is 2% plus 0.60 times 20%, which equals 14%, achieved by leveraging Y.

  1. A10.0%
  2. B12.5%
  3. C14.0%Correct

Explanation

Sharpe ratio of X = 8/16 = 0.50; of Y = 6/10 = 0.60. Y has the steeper CAL, so it is the better choice. At 20% risk the return is 2% + 0.60 × 20% = 14%. Using X would give 2% + 0.50 × 20% = 12%. The 12.5% option does not correspond to a valid answer, and 10% is X's unlevered return.

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