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 $\mathrm{ES}=\mu -\sigma \frac{\phi \left(z\right)}{1-\alpha }$, where $\mu$ is the mean return, $\sigma$ is the volatility, $z$ is the critical value, $\phi$ is the standard normal density, and $\alpha$ 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.

Beyond the Normal Approximation

Real markets do not always follow neat bell curves. Periods of high volatility or dramatic price swings produce heavy tails that the normal model fails to capture. In practice, analysts often use historical simulation or Monte Carlo methods to estimate expected shortfall without making strict distributional assumptions. These approaches sample thousands of scenarios from past data or model-based random draws, tally the worst outcomes, and compute the average. If your portfolio contains options or other nonlinear instruments, exploring these techniques can reveal hidden risks that a simple normal approximation might miss.

Putting ES in Context

Expected shortfall complements other risk measures like value at risk, drawdown, and stress tests. While VaR tells you the threshold that only a small percentage of outcomes exceed, ES describes how severe those extreme losses could be. Portfolio managers compare ES across strategies to determine which positions have outsized tail exposure. Regulators may also require banks to report ES to ensure adequate capital buffers. By monitoring this metric alongside more traditional volatility measures, you gain a clearer picture of potential downside, especially during turbulent market conditions.

Example Scenario

Suppose your portfolio has a mean daily return of 0.05% and a volatility of 1.2%. At a 99% confidence level, the ES jumps noticeably compared to the 95% example—roughly 3.1% in this case. Such numbers highlight how a tighter confidence band captures rarer events with steeper losses. You can adjust the mean, volatility, and confidence level above to explore how these factors interact, helping you plan for worst-case scenarios.