Comparison, in Risk & Portfolio Construction
VaR vs CVaR (Expected Shortfall)
Both summarize portfolio loss at a confidence level such as 95% or 99%, and both are built from the same loss distribution. The difference is where on the tail they look. VaR is a quantile: the loss you will not exceed with the stated probability. CVaR averages everything beyond that quantile, so it answers the question VaR refuses to: given that today is a bad day, how bad is it on average. For thin tails the two nearly agree; for fat tails CVaR is materially larger and the gap is the part of the risk VaR hides. This matrix sets them side by side.
6 criteria. Published May 26, 2026. By AI Fin Hub Research.
The loss threshold at a chosen confidence level: with 95% VaR of one million, losses exceed one million on roughly one day in twenty. A single quantile of the loss distribution.
Pros
- Universally reported and easy to communicate as a single threshold number
- Backed by decades of literature, with well-known backtests such as Kupiec and Christoffersen
- Cheap to estimate by historical, parametric, or Monte Carlo methods
- Intuitive as a regulatory and limit-setting threshold that desks and risk teams already speak
Cons
- Says nothing about the size of losses beyond the threshold, so it is blind to tail severity
- Not subadditive in general, meaning a diversified book can show higher VaR than its parts, violating coherence
- Can be gamed by strategies that sell deep tail risk, which look calm until the rare loss lands
- Sensitive to the estimation method and to the assumed distribution at high confidence levels
A headline risk threshold, regulatory and internal limits, and quick communication when the tail shape is well understood
The average loss conditional on being past the VaR threshold. Where VaR marks the edge of the tail, CVaR averages the whole tail beyond it.
Pros
- Captures tail severity directly, distinguishing a soft tail from a catastrophic one at the same VaR
- Coherent: subadditive, so diversification never increases it, which makes it sound for allocation and limits
- Harder to game with tail-risk-selling strategies because the rare large loss enters the average
- Now the Basel market-risk standard, replacing VaR at the 97.5% level for capital
Cons
- Needs more data or stronger distributional assumptions to estimate the deep tail reliably
- Higher estimation variance than VaR because it depends on the sparse, extreme observations
- Less universally quoted historically, so it is harder to benchmark against legacy VaR numbers
- Backtesting Expected Shortfall is harder than backtesting VaR and remains an active research area
Fat-tailed books, capital allocation, and any decision where the cost of the worst losses, not just their frequency, drives the choice
Decision table
See the tradeoffs side by side
| Criterion | Value at Risk (VaR) | Conditional VaR (CVaR / Expected Shortfall) |
|---|---|---|
| What it measures | Loss threshold at a confidence level | Average loss beyond that threshold |
| Sees tail severity | No, ignores everything past the quantile | Yes, averages the whole tail |
| Coherent risk measure | No, can violate subadditivity | Yes, subadditive by construction |
| Estimation difficulty | Lower, single quantile | Higher, depends on sparse tail data |
| Backtesting | Mature: Kupiec, Christoffersen | Harder, active research |
| Regulatory status (Basel) | Legacy market-risk metric | Current standard at 97.5% |
Verdict
Report both, and treat the gap between them as information. VaR is the threshold everyone recognizes and the natural unit for a hard loss limit. CVaR is the number that tells you whether the tail past that limit is a flesh wound or a fatality, and it is the measure to use for capital and for comparing books, because it is coherent and rewards genuine diversification. If you can keep only one for risk allocation, keep CVaR. If you must satisfy a legacy limit framework, keep VaR but never read it as a statement about how bad the worst days are.
Run the numbers next
- Playgrounds VaR Backtest — Kupiec & Christoffersen
Paste P&L + VaR series and run Kupiec POF, Christoffersen independence, and joint conditional-coverage tests. Likelihood-ratio χ² p-values.
- Calculators Returns Distribution Analyzer
Paste a returns CSV. Histogram, normal QQ plot, skewness, excess kurtosis, Jarque-Bera test, tail-weight index. See why Sharpe alone misleads.
- Calculators Risk-Adjusted Returns Calculator
Paste a returns CSV. Sharpe, Sortino, Calmar, Omega, alpha, beta, tracking error, information ratio, max drawdown, and tail moments — plus.
Questions people ask next
Is CVaR always larger than VaR?
At the same confidence level, yes, CVaR is greater than or equal to VaR by construction, because it averages losses that are all at least as large as the VaR threshold. The two are equal only in the degenerate case where the loss is constant beyond the threshold. The size of the gap reflects tail thickness: a small gap means a thin tail, a large gap means heavy losses lurk just past the VaR cutoff.
Why is VaR not a coherent risk measure?
Coherence requires subadditivity, meaning the risk of a combined portfolio should never exceed the sum of the parts. VaR can violate this for non-elliptical or fat-tailed distributions, so merging two positions can raise total VaR even though diversification should lower risk. CVaR is subadditive by construction, which is one reason Basel moved its capital standard from VaR to Expected Shortfall.
Which confidence level should I use?
Common choices are 95% and 99% for VaR; Basel's market-risk framework uses CVaR at 97.5%, which roughly matches 99% VaR for normal distributions while remaining more tail-aware for fat-tailed ones. State the level explicitly and the estimation method, since both materially change the number, especially deep in the tail where data is sparse.
Sources
- Coherent Measures of Risk , Artzner, Delbaen, Eber, Heath, Mathematical Finance (1999)
- Minimum Capital Requirements for Market Risk , Basel Committee on Banking Supervision (2019)
Keep the topic connected
- Learn Value at Risk (VaR)
Value at Risk: the loss threshold you'll exceed with probability α. Why historical VaR is brittle and what it doesn't tell you about the tail.
- Learn Expected Shortfall (CVaR)
Expected shortfall: the average loss given a VaR breach. Why regulators are migrating from VaR and what ES catches that VaR misses.
- Learn Volatility
Volatility as the standard deviation of returns: realized vs implied, the annualization gotcha, and why volatility-of-volatility matters.
- Learn Drawdown
Drawdown explained: peak-to-trough decline, why max drawdown alone is misleading, and the recovery math that actually matters.