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

A risk manager fits a GEV distribution to the maxima of weekly losses on an equity portfolio and estimates a tail index parameter xi of 0.30. Which conclusion is most appropriate?

A positive tail index of 0.30 indicates a Frechet-type heavy tail, consistent with fat-tailed financial returns. Gumbel corresponds to a zero index with thin tails, and Weibull corresponds to a negative index with a finite upper bound on losses.

  1. AThe tail is heavy and follows a Frechet-type distribution, consistent with fat-tailed returnsCorrect
  2. BThe tail is thin and follows a Gumbel-type distribution, like the normal
  3. CThe distribution has a finite upper bound on losses, as in a Weibull-type distribution
  4. DThe data are inconsistent with EVT because xi must be negative for financial losses

Explanation

A positive xi indicates the Frechet case, with a power-law decaying heavy tail, typical of financial returns. Xi equal to zero is Gumbel (thin tails like the normal), and xi below zero is Weibull with a finite upper endpoint. Financial losses typically have positive xi, so option D is false.

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