CMA Final · Strategic Financial Management · Portfolio Theory and Practice
Two securities have standard deviations of 8% and 12%, and their correlation is -1. What proportion invested in the 8% security gives a zero-risk portfolio?
The proportion to put in the 8% security is 60%. With perfect negative correlation, the weight in the first security is the second security's standard deviation divided by the sum of both, 12/20 = 0.6. Then 0.6 x 8 equals 0.4 x 12, so the risk cancels out.
- A40%
- B50%
- C60%Correct
- D66.7%
Explanation
With correlation of -1, the zero-variance weight in the first security is w1 = s2/(s1+s2) = 12/(8+12) = 0.60. Check: 0.6 x 8 = 4.8 and 0.4 x 12 = 4.8, so the risks offset exactly. The 40% option reverses the weights.
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