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

An investor has a risk-aversion coefficient A = 5 and compares two portfolios using U = E(R) − 0.5Aσ². Portfolio X has E(R) = 12% and σ = 18%. Portfolio Y has E(R) = 8% and σ = 10%. The investor is most likely to:

Portfolio Y is preferred. Utility of X is 0.12 − 2.5 × 0.0324 = 0.039, while utility of Y is 0.08 − 2.5 × 0.01 = 0.055. The higher risk penalty on X outweighs its 4% return advantage for this investor.

  1. Aprefer Portfolio Y, because its utility is higher than that of Portfolio XCorrect
  2. Bprefer Portfolio X, because its utility is higher than that of Portfolio Y
  3. Cbe indifferent, because the two utilities are equal

Explanation

U(X) = 0.12 − 2.5 × 0.0324 = 0.12 − 0.081 = 0.039. U(Y) = 0.08 − 2.5 × 0.01 = 0.08 − 0.025 = 0.055. Y has the higher utility, so it is preferred despite its lower expected return.

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