FRM Part I · FRM Exam Part I · Random Variables
Two assets have returns A and B with Var(A)=0.04, Var(B)=0.09 and correlation 0.5. A portfolio holds 60% in A and 40% in B. What is the portfolio variance?
Portfolio variance is 0.0432. It is the sum of 0.36×0.04, 0.16×0.09 and the covariance term 2×0.6×0.4×0.5×0.2×0.3, each equal to 0.0144. Leaving out the covariance term would understate the risk.
- A0.0400
- B0.0292
- C0.0432Correct
- D0.0245
Explanation
sd A=0.2, sd B=0.3. Var = 0.36(0.04)+0.16(0.09)+2(0.6)(0.4)(0.5)(0.2)(0.3) = 0.0144+0.0144+0.0144 = 0.0432. Omitting the covariance term gives 0.0288, and 0.0292 is not from a valid calculation.
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