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CFA Level I · CFA Level I Exam · Portfolio Risk and Return: Part II

An investor can borrow at the same rate as the risk-free lending rate and invests 130% of her wealth in a risky portfolio with an expected return of 9% and standard deviation of 20%. The risk-free rate is 3%. Her portfolio's expected return and standard deviation are most likely closest to:

Borrowing 30% of wealth at 3% and investing 130% in the risky portfolio gives expected return of 3% plus 1.3 times the 6% premium, which is 10.8%. Risk scales with the weight, so standard deviation is 1.3 times 20%, or 26%.

  1. A10.8% and 20.0%
  2. B10.8% and 26.0%Correct
  3. C12.0% and 26.0%

Explanation

Weight in risk-free asset is −30%. Expected return = −0.3×3% + 1.3×9% = −0.9% + 11.7% = 10.8%. Standard deviation = 1.3×20% = 26%. Check: 3% + 1.3×6% = 10.8%.

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