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

A risk analyst fits a generalized extreme value (GEV) distribution to the monthly maximum daily losses of a trading portfolio. The estimated tail index ξ is 0.30. Which statement correctly describes the implied behavior of the loss distribution?

A positive tail index of 0.30 indicates the Fréchet type of GEV distribution. Its tail decays as a power law, so it is heavy and unbounded. Gumbel corresponds to a zero tail index and Weibull to a negative one, which would imply thinner or bounded tails.

  1. AThe tail is thin and bounded, which corresponds to the Weibull type
  2. BThe tail follows a power law with heavy tails, which corresponds to the Fréchet typeCorrect
  3. CThe tail declines exponentially, which corresponds to the Gumbel type
  4. DThe tail is bounded above, so extreme losses cannot exceed a finite maximum

Explanation

In the GEV framework, ξ > 0 corresponds to the Fréchet case, where the tail decays as a power law and is heavy. Financial return losses typically fall into this category. Gumbel arises when ξ = 0 and Weibull when ξ < 0.

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