Value at Risk (VaR) and Expected Shortfall (CVaR)
Risk metrics estimating potential losses: Value at Risk estimates the maximum expected loss over a period at a given confidence level, while Expected Shortfall estimates the average loss beyond that threshold.
Value at Risk, or VaR, estimates the maximum loss a portfolio is expected to experience over a given time period, at a specified confidence level — for example, a one-day 95% VaR of $10,000 means there's estimated to be only a 5% chance of losing more than $10,000 in a single day, based on the model and historical data used to calculate it. Expected Shortfall, also called Conditional Value at Risk (CVaR), addresses a key limitation of VaR by estimating the average loss specifically in the scenarios where losses do exceed the VaR threshold, rather than stopping at the threshold itself.
VaR's key limitation is that it says nothing about how severe a loss could be once the threshold is actually breached — two assets could have the identical VaR figure while one has a far more catastrophic worst-case tail beyond that threshold than the other, which is exactly the gap Expected Shortfall is designed to address. Both metrics depend heavily on the underlying historical data and statistical assumptions used to calculate them, and both can understate genuine tail risk during unprecedented market conditions that differ meaningfully from the historical data the model was built on, a limitation particularly relevant to crypto markets' comparatively short history and historically fat-tailed volatility.
Examples
- A portfolio with a one-day 95% VaR of $10,000 is estimated to have only a 5% chance of losing more than that amount in a single day, based on the underlying model's assumptions.
- Expected Shortfall addresses VaR's key blind spot by estimating how severe losses are likely to be specifically in the scenarios where the VaR threshold is actually breached.