What is Expected Shortfall and why did regulators switch to it?
VaR asks where is the line? Expected Shortfall asks how bad is it once you're past the line? It is the direct answer to the silence you found in the last lesson, and it is remarkably simple to compute.
You'll meet it under several names — Expected Shortfall (ES), Conditional VaR (CVaR), average VaR, or expected tail loss. Same idea.
The definition
Expected Shortfall at 95% = the average loss on the days when the loss exceeds the 95% VaR.
Not the threshold. The mean of everything past the threshold. Where VaR reports the entrance to the tail, ES reports the tail's centre of gravity.
Computing it from a sorted list
You already did the hard part. In your 500-day window sorted worst to best, the 25 worst days are the 5% tail:
- VaR is the 25th worst day: −2.0%
- ES is the average of all 25 of those days
Suppose those 25 days average −3.1%. Then on a $10 million portfolio:
- 95% VaR = $200,000
- 95% Expected Shortfall = $310,000
ES is always at least as large as VaR at the same confidence level, and usually meaningfully larger. The ratio between them describes the shape of your tail. A ratio near 1.2 says the tail slopes gently; a ratio of 2 or more says it drops away.
Back to the two portfolios
Portfolio A and Portfolio B both had a 95% VaR of $200,000. Their Expected Shortfalls:
- A (diversified equities): ES ≈ $290,000
- B (sold options): ES ≈ $2,400,000
The measure that could not distinguish them now distinguishes them by roughly a factor of eight. That is the entire case for ES in one line.
Why regulators moved
After the 2008 crisis the Basel Committee reviewed how banks measure trading-book risk. The result — the Fundamental Review of the Trading Book, finalised in 2016 and revised in 2019 — replaced the long-standing 99% VaR capital measure with 97.5% Expected Shortfall.
Two motivations, both worth understanding:
It captures tail severity. The crisis demonstrated that the size of extreme losses, not just their frequency, is what breaks institutions.
It is coherent. Unlike VaR, Expected Shortfall is mathematically sub-additive: combining two portfolios can never produce an ES larger than the sum of the parts. Diversification can never look harmful under ES. That property makes ES safe to aggregate across desks — something VaR never reliably was.
A neat detail: under a normal distribution, 97.5% ES ≈ 2.34 standard deviations and 99% VaR ≈ 2.33 — almost identical. The switch was deliberately calibrated to be near-neutral for well-behaved portfolios. The two measures only separate when the distribution isn't normal — which is exactly the case regulators were worried about.
What ES still does not fix
ES is an average of the tail, so it needs tail observations to average. With 500 days and a 95% cutoff you're averaging 25 numbers; at 99% you're averaging five. Estimating ES is statistically harder than estimating VaR, and it is far noisier for rare confidence levels. It is also just as dependent on the chosen window: a calm two years produce a comfortable ES.
Better question, same data problem. ES improves the map; it doesn't turn the map into the territory.
Try it now
- Five years of a broad index and five years of a small-cap basket are below. On the first, isolate the worst 5% of sessions — roughly one in twenty — Measure them, and average them. That is your 95% Expected Shortfall.
- Divide that average by the threshold itself — the mildest of the sessions you included. That single ratio is a compact description of how heavy this index's tail was in this window.
- Do both on the second chart over the identical dates. Compare the two ratios and describe the difference in one neutral sentence. If the small-cap ratio is the larger, its tail is not merely deeper, it is differently shaped.