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

Which statement about Value at Risk (VaR) at the 95% level over one year is correct?

95% VaR is the loss level exceeded with only 5% probability, the 95th percentile of losses. It is not the maximum loss, not the expected loss beyond that point (which is tail VaR), not equal to the standard deviation, and it is not coherent generally since it can fail subadditivity.

  1. AIt is the expected loss given that the loss exceeds the 95th percentile
  2. BIt is the loss level that is exceeded with probability 5%Correct
  3. CIt is the maximum possible loss over the year
  4. DIt is a coherent risk measure for all distributions
  5. It equals the standard deviation of losses

Explanation

95% VaR is the 95th percentile of the loss distribution, so losses exceed it with probability 5%. Option A describes tail VaR (expected shortfall). VaR is not the maximum loss and is not coherent in general because it can fail subadditivity.

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