CFA Practice Question

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CFA Practice Question

Which of the following statements is incorrect?

A. Cov(X,Y) = Cov(Y,X)
B. Cov(X,X) = Var(X)
C. Cov(X,Y) = E[(x - Ex) x (y - Ey)]
D. -1 <= Cov(X,X) <= 1
Correct Answer: D

-1 <= Cov(X, X) <= 1 is incorrect. A correct statement would be: Cov(X, X) = Var(X) and they >= 0. The variance is never negative and is not bounded above by 1.

User Contributed Comments 8

User Comment
fedha Good question coz it summarizes all the facts about covariance
8thlegend Can someone explain why Cov(X,X) = Var(X) is correct?
nike easy. correlation (X, X) = Cov(X,X)/(SD(X) * SD(X)). Since correlation (X, X) = 1 and (SD(X) * SD(X)) = VAR(X), so Cov(X,X) = VAR(X)
bhaynes Key point to remember.......the covariance of a random variable with itself = the variance of the random variable.
azramirza Dont understand is said that covariance can be = 0, -ve or +ve????/
papajeff Corr cannot be negative, Cov can.
Bududeen papajeff got it wrong...corr can be negative ...also cov can be negative but Var cannot be negative
Rachelle3 Variance is the square but stan dev is the sq root so 3 * 3 is 9 the variance but the sq root would be 3 or the Stn dv.
I am only using this small example to explain why variance is never negative so -12 sq = positive 144 and -123 sq = positive 15,129 when a negative is sq it turns POSITIVE try it!!!
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