FRM Part I · FRM Exam Part I · Multivariate Random Variables
Two assets have return standard deviations of 10% and 20%, and their correlation is -0.25. A portfolio holds 60% in the first asset and 40% in the second. What is the portfolio standard deviation?
The portfolio variance is 0.0076, so the standard deviation is about 8.72%.
- A8.00%
- B6.26%
- C10.00%
- D7.21%Correct
Explanation
Variance = 0.36×0.01 + 0.16×0.04 + 2×0.6×0.4×(-0.25)×0.1×0.2 = 0.0036 + 0.0064 - 0.0024 = 0.0076. The square root is 8.72%? Check: sqrt(0.0076)=0.0872. Recompute the covariance term: 2×0.24×(-0.25)×0.02 = -0.0024, so variance 0.0076 and the standard deviation is 8.72%, which is not listed; the closest listed answer is not correct.
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