Value at RiskVaR
Value at risk estimates a loss threshold for a given period and confidence level: a one-day 95% VaR of $10,000 means losses should exceed $10,000 on only about 5% of days, if the model is right. Conditional VaR (expected shortfall) is the average loss on those worst days.
Value at risk compresses portfolio risk into one number: how much you might lose on a bad day, at a chosen level of confidence. Banks and funds have used it for decades, and many trading platforms show it. It is useful, but it is also widely misunderstood: VaR says nothing about how bad the worst days can be. This entry explains what VaR measures, how it is calculated, its limits, and why expected shortfall is often used alongside it.
- Category
- Risk Management
- Reading time
- 4 min
- Also called
- Conditional value at risk, Expected shortfall, VaR model
- Updated
VaR in plain words
VaR estimates the worst expected loss on a portfolio from market moves over a given time horizon, at a chosen confidence level.1 A one-day 95% VaR of $10,000 means: on about 19 days out of 20, losses should stay below $10,000.
On the remaining days, losses can be larger — and VaR does not say by how much. Expected shortfall fills that gap: it is the average of the losses beyond the VaR level.1 See Drawdown.
How VaR is estimated, step by step
Choose horizon and confidence
For example one day at 95% or 99%.
Historical method
Rank past daily profit and loss; the 5th-percentile loss is the 95% VaR.
Parametric method
Assume a distribution: VaR ≈ position × volatility × a factor (about 1.65 for 95%, normal distribution). See Volatility.
Simulation method
Generate many possible scenarios and read off the loss percentile.
Add expected shortfall
Average the losses beyond the VaR level.
Backtest
Compare actual daily results with the VaR estimates to check the model.1 See Backtesting.
Worked examples
Example 1 — Parametric VaR
EstimateA $100,000 position with daily volatility of 1.2%.
| 1-day 95% VaR | $100,000 × 1.2% × 1.65 ≈ $1,980 |
On about 95% of days, the loss should be below roughly $2,000 — if returns behave like the model assumes.
Example 2 — Historical VaR
TailOver the last 200 days, the 10th-worst daily loss was $2,600.
| 1-day 95% VaR (historical) | ≈ $2,600 |
| Average of the 10 worst days | $4,100 (expected shortfall) |
Expected shortfall shows how bad the bad days actually were.
Example 3 — The model breaks
Tail eventA calm year gives a 1-day 99% VaR of $3,000. A sudden shock causes a $15,000 loss in one day.
| VaR | $3,000 |
| Actual loss | $15,000 |
VaR built on calm data underestimates risk when conditions change. Stress-test beyond the model.
VaR vs. expected shortfall
| Aspect | Value at risk | Expected shortfall |
|---|---|---|
| Answers | How bad is a bad day (threshold)? | How bad are the worst days (average)? |
| Tail beyond the threshold | Ignored | Included |
| Ease of use | Simple, widely reported | Harder to estimate |
| Typical use | Limits and reporting | Tail-risk assessment |
Where VaR is used
Risk limits
Capping how much risk a desk or account can carry.
Comparing portfolios
One number across different assets.
Leverage decisions
Seeing how leverage scales potential losses. See Leverage.
Stress testing
A starting point, followed by scenarios VaR cannot capture.
Advantages and disadvantages
Advantages
- Summarises risk in one money figure.
- Works across different assets and portfolios.
- Standard in professional risk management.
Disadvantages
- Says nothing about losses beyond the threshold.
- Depends heavily on the data period and model.
- Often underestimates risk before crises.
- Can give false comfort.
Going deeper
Read as far as you need. Each level builds on the one before it.
VaR is not a maximum
Beginner
A 95% VaR is exceeded on about one day in twenty by design. It is a threshold, not a worst case.
Scaling over time
Intermediate
A common approximation scales one-day VaR by the square root of the number of days. It assumes independent returns, which often fails in stressed markets.
Risk in finance
Advanced
Risk is the uncertainty about returns and the harm when results differ from expectations.2 VaR captures one part of it — typical bad days — so it is best combined with drawdown limits and stress scenarios.
Common mistakes
Treating VaR as the worst case
Losses beyond VaR happen regularly.
Using only calm-period data
Include stressed periods.
Ignoring correlation changes
Diversification can disappear in crises. See Correlation.
Never checking the model
Backtest VaR against actual results.
Check your understanding
Test yourself before moving on. Each answer comes with an explanation.
Key points to remember
- VaR estimates a loss threshold at a confidence level over a horizon.
- It is exceeded on a known share of days by design.
- It says nothing about how large those excess losses are.
- Expected shortfall averages the losses beyond VaR.
- Backtest and stress-test; do not rely on VaR alone.
Frequently asked questions
What does a 99% one-day VaR of $5,000 mean?
Is VaR useful for individual traders?
Why do regulators also use expected shortfall?
Further learning
- Volatility
The input to parametric VaR.
- Drawdown
A complementary measure of how bad it got.
- Correlation
Why diversification can fail in stress.
- Risk of Ruin
Survival over a sequence of losses.
Sources
This article is written in our own words. The sources below support the specific facts, rules and figures marked with a number in the text. Links open the original publisher’s page.
- Basel Committee on Banking Supervision (BIS). Market risk terminology (MAR10) (opens in a new tab) Checked .
- Investor.gov (SEC). Risk (glossary) (opens in a new tab) Checked .
Read more elsewhere
- Trading Metrics (our sister site): Value at Risk (VaR) (opens in a new tab)
Educational content, not financial advice. Examples use hypothetical prices and simplified costs; actual fees, margin rules and regulations vary by broker, market and country. Trading Metrics is our sister site, under the same ownership; we are not affiliated with any other publisher linked above. Last reviewed . Report an error or request a source credit.