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IAI Actuarial Core Principles · Economic Modelling · Measures of investment risk

An investment manager wants a single risk measure that tells the board the loss that will be exceeded only with a small stated probability over a fixed horizon, without describing how severe losses beyond that point could be. Which measure does this describe?

Value at Risk at a chosen confidence level is the answer. It is the loss quantile exceeded with only a small stated probability over the horizon, and it ignores how large losses are beyond that point, unlike expected shortfall, which averages the tail.

  1. AValue at Risk at a chosen confidence levelCorrect
  2. BTail Value at Risk (expected shortfall) at the same level
  3. CVariance of returns
  4. DSemi-variance of returns below the mean
  5. Shortfall probability relative to a zero-return target

Explanation

Value at Risk is the quantile of the loss distribution at a chosen confidence level and horizon. It says nothing about the size of losses beyond that quantile. Tail Value at Risk averages those tail losses, so it does describe severity beyond the cut-off.

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