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FRM Part II · FRM Exam Part II · Parametric Approaches (II): Extreme Value

A risk analyst at a bank wants to model the joint behavior of extreme losses on an equity portfolio and a high-yield bond portfolio. She notes that under a multivariate normal model, extreme losses on the two portfolios become nearly independent far out in the tails, even when the overall correlation is high. Which feature of multivariate extreme value theory (EVT) most directly addresses this weakness?

Multivariate EVT models tail dependence directly, so extreme losses can co-occur more often than a multivariate normal model implies. The normal model has asymptotic tail independence and understates joint extremes, whereas EVT dependence functions describe how extremes cluster across assets or portfolios.

  1. AIt models tail dependence directly, allowing extremes to occur together more often than a normal model impliesCorrect
  2. BIt assumes the marginal distributions of both portfolios are identical and normal
  3. CIt replaces the correlation coefficient with the sample variance of each portfolio
  4. DIt requires each portfolio's losses to be independent over time

Explanation

Multivariate EVT captures the dependence structure of extreme observations, including tail dependence. The normal model has asymptotic tail independence, so it understates joint extremes. The other options misstate what multivariate EVT does.

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