FRM Part I · FRM Exam Part I · Random Variables
Asset returns A and B have variances of 0.04 and 0.09, respectively, and a correlation of -0.50. What is the variance of the return on a portfolio of 50% A and 50% B?
The portfolio variance is 0.0175, computed as 0.25 times 0.04 plus 0.25 times 0.09 plus 2 times 0.25 times the covariance of -0.03. Ignoring the negative covariance term gives 0.0325, which is wrong.
- A0.0325Correct
- B0.0100
- C0.0925
- D0.0425
Explanation
σA=0.2, σB=0.3, Cov=-0.5×0.2×0.3=-0.03. Var=0.25×0.04+0.25×0.09+2×0.25×(-0.03)=0.01+0.0225-0.015=0.0175. Recheck: 0.01+0.0225=0.0325, minus 0.015 gives 0.0175. So the correct value is 0.0175, which is not listed; see directAnswer.
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