what is the difference between var and expected shortfall

VaR is a threshold and expected shortfall is an average beyond it. A 95% VaR of ₹20,000 says a loss bigger than ₹20,000 is expected about one day in twenty, but it says nothing about the size of those losses; the expected shortfall takes exactly those worst 5% of days and averages their losses, giving a number like ₹26,000. So VaR answers "how often", and expected shortfall answers "how bad when it happens". They use the same confidence level and horizon, but ES always reaches into the tail that VaR ignores.

why is expected shortfall better than var

Expected shortfall is better because it describes the tail that VaR leaves blind. VaR can be identical for two portfolios that have wildly different catastrophic-loss profiles — one that loses a little beyond the threshold and one that can lose everything — because VaR stops at the threshold. Expected shortfall distinguishes them by averaging the actual tail losses. It also behaves better mathematically (it is a coherent risk measure that rewards diversification), which is why global banking regulation under Basel has shifted from VaR to expected shortfall for market risk.

how do you calculate expected shortfall

For the parametric (normal) case, expected shortfall equals the portfolio value times the horizon volatility times the normal density at the confidence multiplier divided by one minus the confidence — which always comes out larger than the corresponding VaR. In practice it is more often computed from historical or simulated returns: take all the returns worse than the VaR threshold and simply average them. Whatever the method, the principle is the same: isolate the tail beyond VaR and average the losses inside it, rather than reading off a single cut-off point.

What is expected shortfall (CVaR) and why it beats VaR

The Value at Risk lesson ended on a warning: VaR tells you how often a bad loss occurs but never how bad it gets. Expected shortfall — also called conditional VaR — is the answer to that missing question. It is the metric that looks past the threshold and averages the losses in the tail, and it is why regulators have quietly moved on from VaR.

The average of the worst days

Take the worst slice of days — the 5% beyond a 95% VaR — and average their losses. That average is the expected shortfall. Where VaR stops at the edge of the tail and reports the cut-off, expected shortfall steps inside and asks what the losses there actually look like. Because it averages losses that are all worse than the VaR, it is always the larger number, and the size of the gap tells you how heavy the tail is.

Loading interactive demo…

Set the portfolio, volatility and confidence, and compare the VaR with the expected shortfall — watch how much larger the ES is, and how the gap widens as you push the confidence deeper into the tail.

Worked example

VaR versus ES on the same portfolio

₹10 lakh, 20% vol, 1 day

95% VaRThe threshold≈ ₹20,700

95% expected shortfallAverage loss beyond it≈ ₹26,000

99% VaRDeeper threshold≈ ₹29,300

99% expected shortfallAverage of the worst 1%≈ ₹33,600

The pointIt counts the tail VaR skipsES > VaR always

The 95% VaR says "you should not lose more than about ₹20,700 on a normal day"; the expected shortfall says "but on the days you do, expect to lose about ₹26,000 on average". The second number is the one that tells you whether a bad day is survivable — which is exactly why it is the more useful of the two for real risk management.

Check yourself

Two portfolios both have a one-day 95% VaR of ₹20,000. Portfolio A’s expected shortfall is ₹24,000; Portfolio B’s is ₹60,000. What does this tell you?

Simple bhasha mein

Bura din kitna bura

VaR sirf batata hai ki bura din kitni baar aayega — expected shortfall (CVaR) batata hai ki us din nuksaan kitna bada hoga. ES un sabse bure dinon ka average nuksaan hai jo VaR ki line paar karte hain, isliye hamesha VaR se bada. Do portfolio ka VaR same ho sakta hai par ek ka ES ₹24k aur doosre ka ₹60k — yahi asli tail risk hai jo VaR chhupa deta hai. Isiliye Basel ne VaR se ES pe switch kiya.

What to remember

Expected shortfall (CVaR) is the average loss on the days VaR is breached.
VaR gives the threshold; ES averages the losses beyond it — so ES is always larger.
It distinguishes portfolios with identical VaR but different tail severity.
It is a coherent risk measure, which is why Basel shifted market risk from VaR to ES.
Parametric ES still assumes a distribution, so pair it with real crash stress tests.

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Up nextSkewness and kurtosis: why returns aren’t a bell curve Previous: Value at Risk: the loss you should not exceed on a normal day

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Common questions

Short, direct answers to what people ask about this topic.

what is expected shortfall: Expected shortfall, also called conditional Value at Risk or CVaR, is the average loss a portfolio suffers on the days its Value at Risk is breached. Where VaR gives only a threshold — the loss you should not exceed on a normal day — expected shortfall goes further and averages all the losses that lie beyond that threshold, answering the question of how bad the bad days actually are. It is always at least as large as the VaR at the same confidence, and the gap between the two is a measure of how fat the loss tail is.
what is the difference between var and expected shortfall: VaR is a threshold and expected shortfall is an average beyond it. A 95% VaR of ₹20,000 says a loss bigger than ₹20,000 is expected about one day in twenty, but it says nothing about the size of those losses; the expected shortfall takes exactly those worst 5% of days and averages their losses, giving a number like ₹26,000. So VaR answers "how often", and expected shortfall answers "how bad when it happens". They use the same confidence level and horizon, but ES always reaches into the tail that VaR ignores.
why is expected shortfall better than var: Expected shortfall is better because it describes the tail that VaR leaves blind. VaR can be identical for two portfolios that have wildly different catastrophic-loss profiles — one that loses a little beyond the threshold and one that can lose everything — because VaR stops at the threshold. Expected shortfall distinguishes them by averaging the actual tail losses. It also behaves better mathematically (it is a coherent risk measure that rewards diversification), which is why global banking regulation under Basel has shifted from VaR to expected shortfall for market risk.
how do you calculate expected shortfall: For the parametric (normal) case, expected shortfall equals the portfolio value times the horizon volatility times the normal density at the confidence multiplier divided by one minus the confidence — which always comes out larger than the corresponding VaR. In practice it is more often computed from historical or simulated returns: take all the returns worse than the VaR threshold and simply average them. Whatever the method, the principle is the same: isolate the tail beyond VaR and average the losses inside it, rather than reading off a single cut-off point.

Expected shortfall: how bad the bad days really are

The average of the worst days

Common questions