CMA Final · Strategic Financial Management · Portfolio Theory and Practice
Two-asset portfolio: Asset X has a standard deviation of 8% and Asset Y has a standard deviation of 12%. The correlation is -1. What proportion invested in X gives a zero-risk portfolio?
With perfect negative correlation, the weight in X for zero risk equals sigma Y divided by the sum of both standard deviations, which is 12 divided by 20, or 60%. Then the weighted risks of 4.8% each offset exactly.
- A40%
- B50%
- C60%Correct
- D66.7%
Explanation
With correlation -1, the minimum-variance weight in X is sigmaY/(sigmaX + sigmaY) = 12/(8+12) = 0.60. Check: 0.6 x 8 = 4.8 and 0.4 x 12 = 4.8, so the risks offset fully. The 40% option reverses the weights.
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