How CVaR, or expected shortfall, measures losses beyond VaR

Value at risk tells you a loss limit, but not what happens beyond it. Conditional value at risk, also called CVaR or expected shortfall, fills that gap. This page explains what it means, how it differs from VaR and why banks now use it.

Quick answer

Expected shortfall, also known as conditional value at risk (CVaR), is the average loss a portfolio is expected to suffer on its worst days, beyond the VaR cut-off. For example, if one-day 95 percent VaR is Rs 30,000, the expected shortfall is the average of all losses on the worst 5 percent of days. It gives a fuller picture of extreme losses than VaR alone.

Key takeaways

• Expected shortfall is the average loss in the worst cases.
• It is also called CVaR or conditional value at risk.
• It looks beyond the VaR cut-off into tail losses.
• Basel rules use it at 97.5 percent for bank trading books.
• It is always equal to or larger than VaR at the same level.

What is expected shortfall?

VaR draws a line and says losses should stay below it most of the time. This measure asks the next question: on the days when losses cross that line, how bad are they on average? It averages the losses in the 'tail', the worst part of the range.

Because it looks at all the worst outcomes, not just the cut-off point, it gives a better sense of how much a portfolio could lose in a crisis.

A simple example

Say a portfolio has 100 days of history. The 95 percent VaR is the loss on the sixth-worst day, say Rs 30,000. Now look at the five worst days: losses of Rs 35,000, Rs 40,000, Rs 50,000, Rs 70,000 and Rs 1,05,000.

The average of these five losses is Rs 60,000. That is the expected shortfall at 95 percent. It is double the VaR in this example, which shows how VaR alone can hide the size of bad days.

Why do regulators prefer it?

During the 2008 crisis, many banks faced losses far larger than their VaR numbers suggested. After that, the Basel Committee on Banking Supervision reviewed its rules for market risk.

Under the revised framework, known as the Fundamental Review of the Trading Book, banks using internal models measure trading risk with expected shortfall at a 97.5 percent confidence level instead of VaR at 99 percent. The aim is to capture tail risk better.

Strengths and limits

A big strength is that it responds to how severe extreme losses are. Researchers also consider it a more consistent measure, because combining two portfolios never makes it look worse than the sum of their parts, which is not always true for VaR.

Its limit is that it needs more data about rare events, which are by nature few. Estimates can be unstable, and like VaR, it depends on the model and data used. It works best alongside stress testing.

The key point to remember

Expected shortfall looks at the average of the worst losses, not just where they begin. For anyone studying risk, it is a useful step beyond VaR, especially for understanding tail risk.

Frequently Asked Questions