FRM Part I · FRM Exam Part I · Measuring Return, Volatility, and Correlation
Random variables X and Y have Var(X) = 16, Var(Y) = 9, and Cov(X,Y) = -6. What is Var(X - Y)?
Var(X - Y) equals 37. Using Var(X) + Var(Y) - 2Cov(X,Y) gives 16 + 9 + 12 = 37, because the negative covariance becomes a positive addition when subtracting Y. Adding the covariance with the wrong sign would give 13 instead.
- A13
- B25
- C37Correct
- D1
Explanation
Var(X-Y) = Var(X) + Var(Y) - 2Cov(X,Y) = 16 + 9 - 2(-6) = 37. Option 13 comes from adding the covariance term with the wrong sign (as in Var(X+Y) = 25 - 12 = 13). Option 25 ignores covariance.
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