VaRp is the tail value at risk at level p. Which description is correct?

• A. The maximum possible loss
• B. The percentile where p% below that value
• C. The mean of the distribution
• D. The standard deviation

Answer: (B)

Value at risk at level p is the p-th percentile of the loss distribution. It’s the loss threshold such that there is probability p that the loss will be at or below that value. In other words, p% of outcomes fall at or below VaR_p. This is why it’s the best description: VaR tells you the maximum loss you shouldn’t expect to exceed with probability p, not the absolute maximum, the mean, or the spread of losses. (Note: when losses exceed this threshold, the average of those excess losses is described by the expected shortfall or tail value at risk, not VaR.)