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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 10% and Asset B has a volatility of 20%. Their correlation is 0.2. What weight in Asset A gives the minimum-variance fully invested portfolio, with no short sales assumed?

The minimum-variance weight in A is 85.7%. It equals (σB² − covariance) divided by (σA² + σB² − 2 × covariance), which is 0.036/0.042. The lower-volatility asset gets most of the weight, and the positive correlation shifts it somewhat further from the 80% obtained when correlation is ignored.

  1. A85.7%Correct
  2. B80.0%
  3. C66.7%
  4. D14.3%

Explanation

wA = (σB² − ρσAσB)/(σA² + σB² − 2ρσAσB) = (0.04 − 0.004)/(0.01 + 0.04 − 0.008) = 0.036/0.042 = 85.7%. The 80% option ignores correlation (0.04/0.05). The 14.3% option is the weight in B, not A.

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