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FRM Part I · FRM Exam Part I · Modern Portfolio Theory (MPT) and the Capital Asset Pricing Model (CAPM)

Asset A has a standard deviation of 20% and Asset B has a standard deviation of 10%. A portfolio holds 50% in each, and the correlation between them is 0.2. What is the portfolio standard deviation?

The portfolio standard deviation is about 12.0%, computed from a variance of 0.0145. This was not an exact match to the options, so the question is flawed.

  1. A10.5%
  2. B12.4%Correct
  3. C13.0%
  4. D15.0%

Explanation

Variance = 0.25(0.04) + 0.25(0.01) + 2(0.5)(0.5)(0.2)(0.2)(0.1) = 0.01 + 0.0025 + 0.002 = 0.0145. The square root is 12.04%, which rounds to about 12.0%, so check: sqrt(0.0145)=0.12042. The nearest option is 12.4%? Recompute: 2x0.25x0.2x0.2x0.1 = 0.002, correct, giving 12.04%.

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