FRM Part I · FRM Exam Part I · Sample Moments
Which statement about the coskewness S(X,X,Y) is correct?
A positive S(X,X,Y) means that large deviations of X, up or down, tend to coincide with Y being above its mean. The squared X deviation removes direction. It is not the correlation, zero does not imply independence, and it is not bounded by ±1.
- AA positive value means that large deviations of X in either direction tend to occur together with Y above its mean.Correct
- BIt equals the correlation between X and Y.
- CA value of zero proves that X and Y are independent.
- DIt is bounded between -1 and 1.
Explanation
S(X,X,Y) is based on E[(X-μx)²(Y-μy)]. Squaring the X deviation removes its sign, so a positive value means big X moves in either direction coincide with Y above its mean. It is not correlation, it can be zero for dependent variables, and it is not confined to [-1, 1].
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