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IAI Actuarial Core Principles · Economic Modelling · Mean-variance portfolio theory

Asset A has standard deviation 20% and asset B has standard deviation 30%. Their returns are uncorrelated. What is the standard deviation of the minimum-variance portfolio of A and B (short selling allowed), to the nearest 0.1%?

The minimum-variance standard deviation is about 16.7%. With zero correlation the variance equals sA squared times sB squared divided by their sum, which is 0.0036 divided by 0.13, giving about 0.0277, and the square root is roughly 16.6 to 16.7 percent, below either asset's own risk.

  1. A16.7%
  2. B20.0%
  3. C14.4%Correct
  4. D18.0%
  5. 25.0%

Explanation

With zero correlation, weight in A = sB^2/(sA^2+sB^2) = 0.09/0.13 = 0.6923. Variance = 0.6923^2*0.04 + 0.3077^2*0.09 = 0.019172+0.008521 = 0.027692 (equivalently 0.04*0.09/0.13). Square root = 16.64%... check: 0.0036/0.13 = 0.027692, sqrt = 0.1664. So the answer is 16.6%, nearest option 16.7%.

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