What Is Expected Shortfall?

Expected shortfall (ES), sometimes called conditional value at risk (CVaR), measures the average loss of an investment in the worst-case tail of the return distribution. While value at risk (VaR) tells you the loss threshold that will not be exceeded with a given probability, ES goes further—it averages all losses beyond the VaR cutoff, offering a fuller picture of potential downside. Portfolio managers use ES to understand extreme risk in turbulent markets.

Using a Normal Distribution Approximation

For simplicity, this calculator assumes daily portfolio returns follow a normal distribution with specified mean and standard deviation. Under that assumption, we first compute the z-score associated with the chosen confidence level. The formula for ES under normality is , where $\mathrm{\backslash mu}$ is the mean return, $\mathrm{\backslash sigma}$ is the volatility, $z$ is the critical value, $\mathrm{\backslash phi}$ is the standard normal density, and $\mathrm{\backslash alpha}$ equals the confidence level divided by 100.

Why It Matters

Traditional VaR can give a false sense of security because it ignores losses that exceed the threshold. During market crashes or liquidity crises, those tail losses can be catastrophic. Expected shortfall captures this risk and has gained favor in regulatory frameworks like Basel accords for banks. Investors comparing strategies often examine ES to gauge which portfolio has less extreme downside potential.

Limitations

The normal distribution assumption simplifies the calculation but may not reflect reality—financial returns often exhibit fat tails and skew. When using this tool, understand that the true expected shortfall could differ if returns are not normally distributed. More advanced approaches rely on historical simulation or Monte Carlo methods to model complex return patterns.

Example Calculation

Imagine a portfolio with a mean daily return of 0.1% and volatility of 1%. At a 95% confidence level, the z-score is approximately 1.645. Plugging these numbers into the equation above yields an expected shortfall of about 2.06%, representing the average loss on the worst 5% of days.