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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 volatility of 20% and Asset B has a volatility of 30%. A portfolio holds 60% in A and 40% in B, and the correlation between the two assets is 0.5. What is the portfolio volatility?

Portfolio variance is 0.0432, found by adding the two squared-weight variance terms and twice the weighted covariance term, each equal to 0.0144. The square root gives 20.78%. This is below the 24% weighted average because the correlation of 0.5 is less than 1, so diversification reduces risk.

  1. A20.78%Correct
  2. B24.00%
  3. C16.97%
  4. D18.97%

Explanation

Variance = 0.6^2(0.04) + 0.4^2(0.09) + 2(0.6)(0.4)(0.5)(0.2)(0.3) = 0.0144 + 0.0144 + 0.0144 = 0.0432, so volatility = 20.78%. The 24% option is the weighted average of volatilities, which holds only when correlation is 1. The 18.97% option leaves out the factor of 2 on the covariance term.

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