FRM Part I · FRM Exam Part I · Multivariate Random Variables
A portfolio holds 60% in asset A and 40% in asset B. Volatilities are 20% for A and 30% for B. The correlation is 0.25. What is the portfolio volatility, to the nearest 0.1%?
Portfolio variance is 0.0144 + 0.0144 + 0.0072 = 0.0360, so volatility is about 19.0%. That figure is not exactly listed, so this item is flawed.
- A18.0%
- B19.2%Correct
- C20.0%
- D21.0%
Explanation
Variance = 0.6²(0.04) + 0.4²(0.09) + 2(0.6)(0.4)(0.25)(0.2)(0.3) = 0.0144 + 0.0144 + 0.0072 = 0.0360. Square root = 0.1897, i.e. 19.0%. Check: 0.1897 rounds to 19.0%, not 19.2%, so the key is mismatched with the listed options.
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