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CMA Final · Strategic Financial Management · Portfolio Theory and Practice

Security M has expected return 14% and standard deviation 20%. Security N has expected return 8% and standard deviation 10%. Their correlation is -1. What weight in M gives a zero-risk portfolio?

With perfect negative correlation, risk is eliminated when the weight in M equals the standard deviation of N divided by the sum of both standard deviations: 10 divided by 30, or 33.33%. Then 33.33% of 20 equals 66.67% of 10, so the risks cancel exactly.

  1. A33.33%Correct
  2. B66.67%
  3. C50.00%
  4. D25.00%

Explanation

With correlation -1, the minimum variance weight in M is sN/(sM+sN) = 10/(20+10) = 33.33%. Check: risk = 0.3333x20 - 0.6667x10 = 6.67 - 6.67 = 0. The 66.67% option reverses the weights and leaves risk of 13.33 - 3.33 = 10%.

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