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FRM Part II · FRM Exam Part II · Correlation Basics: Definitions, Applications, and Terminology

A risk manager holds two assets whose joint returns are modelled with a Student-t copula with low degrees of freedom, and the same marginal distributions and the same linear correlation of 0.30 are also modelled under a Gaussian copula. Compared with the Gaussian copula, which conclusion is most appropriate about joint extreme losses?

The t copula gives a higher joint tail probability. It has positive tail dependence, whereas the Gaussian copula has none asymptotically. Identical Pearson correlation therefore does not mean identical dependence, and the t copula implies more simultaneous extreme losses.

  1. AThe t copula gives the same joint tail probability because the correlation is identical
  2. BThe t copula gives a lower joint tail probability because it has fatter marginal tails
  3. CThe t copula gives a higher joint tail probability because it exhibits tail dependenceCorrect
  4. DThe two differ only in the center of the distribution, not in the tails

Explanation

The Gaussian copula has zero asymptotic tail dependence, while the t copula with finite degrees of freedom has positive tail dependence even at modest correlation. With the same Pearson correlation, the t copula therefore implies a higher probability of simultaneous extreme losses. This shows correlation alone does not describe the full dependence structure.

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