FRM Part I · FRM Exam Part I · Multivariate Random Variables
Which feature distinguishes a multivariate Student's t distribution from a multivariate normal distribution with the same correlation matrix?
The multivariate t exhibits tail dependence, so extreme joint moves occur more often than under a multivariate normal with the same correlation matrix. Zero correlation in the t does not imply independence, which is a key difference.
- AUncorrelated components are always independent
- BExtreme joint losses occur more frequently because of tail dependenceCorrect
- CEach marginal distribution is uniform
- DConditional means are nonlinear in the conditioning variable
Explanation
The multivariate t has fat tails and positive tail dependence, so joint extreme moves are more likely than under the normal with the same correlations. Uncorrelated t components are not independent, unlike the normal case.
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