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

A portfolio combines Asset X (standard deviation 12%) and Asset Y (standard deviation 8%) with a correlation of -1. What weight in X gives a risk-free portfolio?

The weight in X is 40%. With perfect negative correlation the standard deviation is the absolute difference of weighted standard deviations, which is zero when 12 times wx equals 8 times (1 minus wx). That gives wx equal to 8/20, or 40%.

  1. A40%Correct
  2. B50%
  3. C60%
  4. D33.3%
  5. 66.7%

Explanation

With correlation -1, portfolio sd = |wx*12 - (1-wx)*8|. Setting this to zero gives 12wx = 8 - 8wx, so wx = 8/20 = 40%. The 60% option reverses the weights, putting the larger weight on the more volatile asset.

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