Value at Risk, expected shortfall and stress testing

Value at Risk (VaR) and expected shortfall are standard tools for summarising how much a position or portfolio could lose. Both are widely used by banks and funds, and both are easy to misunderstand.

Value at Risk

VaR states a loss threshold that should not be exceeded over a given period at a given confidence level. For example, a one-day 95% VaR of $1,000 means that on 95% of days, losses are expected to stay below $1,000. It also means that on roughly one day in twenty, they are expected to exceed it.

• Historical VaR: uses the actual distribution of past returns.
• Parametric VaR: assumes returns follow a statistical distribution, often the normal distribution.
• Monte Carlo VaR: simulates many possible outcomes from a model of how markets behave.

What VaR does not tell you

VaR says nothing about how bad losses are on the days it is exceeded. Market returns also tend to have fat tails: extreme moves happen more often than a normal distribution predicts, so parametric VaR can understate real risk.

Expected shortfall

Expected shortfall, also called conditional VaR, answers the question VaR leaves open: when losses do exceed the threshold, how large are they on average? Because it looks into the tail, many regulators and risk teams now prefer it.

Stress testing

Statistical measures are built from history. Stress tests ask what would happen in specific severe scenarios, such as a sudden gap, a liquidity crisis or a repeat of a historical shock. Good risk management uses both: statistics for everyday risk, and scenarios for the days statistics do not describe.

Educational content only. Not financial advice. Past performance, real or simulated, does not guarantee future results.