Skip to content

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

A risk analyst fits a GEV distribution to maximum weekly losses of an equity portfolio and estimates a shape (tail) parameter ξ of 0.30. Which conclusion is most appropriate?

A positive shape parameter of 0.30 indicates the Frechet domain, meaning a heavy tail with power-law decay. Gumbel corresponds to a zero shape and thin exponential-type tails, while a negative shape implies a bounded upper endpoint. Positive values are typical of financial loss data.

  1. AThe tail is thin, with all moments finite, like the normal distribution
  2. BThe loss distribution has a finite upper bound
  3. CThe tail is heavy, in the Frechet domain, with power-law decayCorrect
  4. DThe tail is exactly exponential, as in the Gumbel case

Explanation

A positive ξ corresponds to the Frechet case, with a heavy power-law tail where high-order moments may not exist. ξ = 0 gives Gumbel (exponential-type tail) and ξ < 0 gives Weibull with a finite upper endpoint. Financial returns commonly show positive ξ.

Did you get it right without looking?

One question tells you little. A timed set on Parametric Approaches (II): Extreme Value shows your real accuracy, how long you take and where you lose marks.

Practise Parametric Approaches (II): Extreme ValueFree diagnostic mock

More Parametric Approaches (II): Extreme Value questions