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

The risk-free rate is 2%. An investor's utility is U = E(R) − 0.5 × A × σ², with A = 4 and returns in decimals. The investor chooses between a risk-free asset and a risky portfolio with E(R) = 10% and σ = 20%. The optimal weight in the risky portfolio is closest to:

The optimal weight is about 50%. Maximizing utility gives w = (10% − 2%) divided by (4 × 0.20²), which is 0.08/0.16 = 0.50. Utility is 4% at 50%, higher than 3.5% at 75% and 2% at 100%.

  1. A50%
  2. B75%
  3. C100%Correct

Explanation

Optimal weight = (E(R) − Rf)/(A σ²) = 0.08/(4 × 0.04) = 0.08/0.16 = 0.50. Check: utility at w=0.5 is 0.02+0.5×0.08 −2×0.01=0.04... compute: return 6%, variance 0.01, penalty 0.02, utility 4%; at w=1: 10% − 8% = 2%; at 0.75: 8% − 2×0.0225=3.5%. So 50% is best. The key is therefore 50%, option A.

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