Expected Shortfall Calculator

Measure the average loss in the tail beyond value at risk, the risk measure regulators prefer.

About Expected Shortfall Calculator

Expected shortfall averages the losses in the tail rather than marking its edge, so it is always larger than VaR. Unlike VaR it is a coherent risk measure, which is why Basel moved to it for market risk capital. VaR can be gamed by pushing risk just beyond the threshold; expected shortfall cannot, because it prices the whole tail.

Formula

Expected Shortfall

Expected shortfall = volatility × φ(z) ÷ (1 − confidence), with φ the normal density at z

φ(z): Standard normal density at the confidence threshold
expected shortfall: Average loss given that the VaR threshold has been breached

Worked example

With the default values below, Expected Shortfall Calculator returns Expected Shortfall of $30,799.53. Change any input above and every figure here is recalculated in your browser.

Inputs used

Portfolio valueminimum 0: 500,000
Annual volatilityaccepts 0–100 %: 15 %
Horizonaccepts 1–365 days: 10 days
Confidence levelaccepts 80–99.9 %: 95 %

Results

Expected Shortfall: $30,799.53
Expected Shortfall as Share of Portfolio: 6.160%
Value at Risk for Comparison: $24,580.05
Expected Shortfall Divided by Value at Risk: 1.253
Volatility Over the Horizon: 2.988%

Step by step

1Values used
2Expected Shortfall
3Expected Shortfall= 30,799.53
4Expected Shortfall as Share of Portfolio= 6.160
5Value at Risk for Comparison= 24,580.05
6Expected Shortfall Divided by Value at Risk= 1.253
7Volatility Over the Horizon= 2.988

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax or fees or charges into account.
Figures are rounded for display to 3 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
This is an estimate for general information and not professional financial, tax or legal advice. See the full disclaimer for the limits that apply to this kind of calculator.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is Expected Shortfall calculated?

Expected shortfall = volatility × φ(z) ÷ (1 − confidence), with φ the normal density at z Expected shortfall averages the losses in the tail rather than marking its edge, so it is always larger than VaR. Unlike VaR it is a coherent risk measure, which is why Basel moved to it for market risk capital.

Why does Expected Shortfall matter?

VaR can be gamed by pushing risk just beyond the threshold; expected shortfall cannot, because it prices the whole tail.

What values do I need to enter?

This calculator takes 4 inputs: Portfolio value, Annual volatility, Horizon, Confidence level. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.