CMA Final · Strategic Financial Management · Portfolio Theory and Practice
Two securities, A and B, have uncorrelated returns (correlation = 0). Standard deviations are 10% for A and 20% for B. Which proportion of funds invested in A gives the minimum-variance portfolio?
The minimum-variance portfolio puts 80% in A. With zero correlation, the weight in A equals variance of B divided by the sum of both variances: 400 divided by 500. The less risky security therefore receives the larger weight.
- A20%
- B50%
- C66.7%
- D80%Correct
Explanation
With zero correlation, wA = σB² / (σA² + σB²) = 400 / (100 + 400) = 80%. Check: variance = 0.64×100 + 0.04×400 = 80, which is below the variance of A alone (100). Option 66.7% wrongly uses standard deviations instead of variances.
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