What is the simplest way to remember VaR and CVaR formulas across distributions?

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AcadiFi · Accepted Answer

The general structure is simpler than the formula list. VaR is a quantile of the loss distribution. If the loss distribution has cumulative distribution function F, then VaR at confidence level alpha is the value where the distribution reaches that tail probability. CVaR, or expected shortfall, is the average loss beyond that VaR threshold under the chosen convention.

Suppose Crestview Risk Analytics models one-day losses with a continuous distribution. The 99 percent VaR is the loss level L such that 99 percent of outcomes are no worse than L. The 99 percent CVaR asks for the average of the losses in the worst 1 percent region. Distribution-specific formulas are just different ways to compute those two ideas for normal, t, skewed, or other distributions.

This is why memorizing a table without understanding the structure is fragile. If the distribution changes, the quantile function and tail conditional expectation change, but the conceptual roles do not. FRM candidates should anchor on "VaR equals cutoff" and "CVaR equals average beyond cutoff." Once that is clear, formulas become implementation details rather than isolated facts. On the exam, also state the horizon, confidence level, data source, modeling assumption, and validation step, because those choices usually explain why two reasonable VaR answers differ materially. Practice more in our FRM question bank.

What is the simplest way to remember VaR and CVaR formulas across distributions?

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