CMA Final · Strategic Financial Management · Portfolio Theory and Practice
Security P has a standard deviation of 20% and Security Q has a standard deviation of 10%. The correlation between them is -1. What proportion of the portfolio should be invested in P to build a zero-risk portfolio?
The weight in P should be 33.33%. With perfect negative correlation, risk is eliminated when each security's weighted standard deviation is equal, so wP = σQ/(σP+σQ) = 10/30. The remaining 66.67% in Q gives offsetting risk of 6.67% each, which cancels out.
- A25%
- B33.33%Correct
- C50%
- D66.67%
Explanation
With correlation -1, zero risk needs weight in P = σQ/(σP+σQ) = 10/(20+10) = 33.33%. Check: 0.3333×20 = 6.67 and 0.6667×10 = 6.67, so the risks cancel. Choosing 66.67% inverts the weights, leaving risk of 0.6667×20 - 0.3333×10 = 10%.
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