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FRM Part II · FRM Exam Part II · Risk, Regulation and Organizational Structure

An investment firm's board approves a risk appetite of a maximum 12% probability that annual losses exceed 8% of capital. Management models a portfolio with annual losses normally distributed with mean 2% of capital and standard deviation 6%. Using the normal distribution (z of 0.67 corresponds to a cumulative probability of about 75%, and z of 1.17 to about 88%), is the portfolio within appetite?

The portfolio is within appetite. A loss above 8% means a return below -8%, giving a z-score of (-8-2)/6 = -1.67 and a probability of roughly 5%, below the 12% limit.

  1. AYes, the probability of exceeding an 8% loss is about 12%, which is right at the limit
  2. BNo, the probability is about 25%
  3. CNo, the probability is about 16%, above the limitCorrect
  4. DYes, the probability is about 6%

Explanation

A loss of 8% corresponds to a return of -8%. Z = (-8 - 2)/6 = -1.67, so the probability is about 4.8%, which is within appetite. Re-checking the options: none states about 4.8%, but the closest consistent choice is below the limit.

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