What it means
VaR always has three components: a time horizon, a confidence level and a currency amount. Change any one of them and the number changes, which is why quoting a VaR without stating the horizon and confidence level is meaningless.
Banks, funds and corporate treasuries use VaR because it compresses thousands of positions into a comparable figure. Regulators use it to set capital requirements, and risk committees use it to allocate risk budgets across desks and strategies.
There are three usual ways to calculate it. The parametric method assumes returns follow a normal distribution, historical simulation replays actual past returns against today's portfolio, and Monte Carlo simulation generates thousands of randomised scenarios.
The critical nuance is what VaR does not tell you. It gives the threshold of the worst 5% of outcomes but says nothing about how bad things get beyond that threshold, which is why the related measure expected shortfall is now often reported alongside it.
VaR also relies on the past resembling the future, and correlations that held for years can break in a crisis. Sensible risk teams therefore pair VaR with stress tests that ask what happens under specific severe scenarios rather than statistical averages.
In practice
Real-world examples.
Example
A corporate treasurer at an exporter with $40,000,000 of foreign currency receivables reports a one-day 95% VaR of $310,000 to the audit committee. The committee sets a limit of $250,000, so the treasurer hedges part of the exposure with forward contracts to bring the number down.
Example
A hedge fund risk officer notices the fund's 99% one-day VaR has doubled in a fortnight without any new positions being added. Market volatility has risen sharply, and she instructs the portfolio managers to cut position sizes to keep the risk budget intact.
Example
An insurance company's investment board compares two external managers with similar returns. One runs a portfolio with a 95% monthly VaR of 2.1% of assets and the other 5.4%, so the board concludes the second manager is taking far more risk for the same result.
Think of it
“VaR is the abbreviation for Value at Risk-expected maximum loss.
Formula
Calculation
The parametric, or variance-covariance, version is:
VaR = Portfolio value x Volatility for the period x Confidence multiplier
The confidence multiplier is 1.645 for 95% confidence and 2.326 for 99% confidence.
A trading desk holds a portfolio worth $10,000,000 with an estimated daily volatility of 1.2%, and the risk committee wants the one-day 95% figure.
Daily standard deviation in dollars = $10,000,000 x 0.012 = $120,000
One-day 95% VaR = $120,000 x 1.645 = $197,400
So on a typical day the desk expects to lose less than $197,400, and to exceed that loss roughly one trading day in twenty, which is about 12 or 13 days a year. To convert to a ten-day horizon, multiply by the square root of 10, which is about 3.16, giving roughly $624,000.Case study
Seen in the real world.
This is an illustrative, fictional example used to show the idea in practice. Calderbrook Asset Management, an invented mid-sized fund manager, ran a $300,000,000 multi-asset fund and reported a one-day 95% VaR of $2,100,000, which was 0.7% of assets and comfortably inside its internal limit.
During a two-week market shock the fund lost more than the VaR figure on six separate days, and one day produced a loss of $9,400,000. The model had not been wrong in the narrow sense, since it only ever described normal days, but the committee had been reading it as a worst case.
Calderbrook responded by adding expected shortfall reporting, which estimated the average loss on the bad 5% of days rather than just the threshold, and by running quarterly stress tests based on specific severe scenarios. The VaR number stayed in the report, but it was no longer the only number the committee looked at.
Watch out
Common mistakes.
- Reading VaR as a maximum possible loss. It is a threshold that is expected to be breached regularly, and losses beyond it can be several times larger.
- Comparing VaR figures with different horizons or confidence levels. A 99% ten-day number and a 95% one-day number are not remotely the same measure and cannot be placed side by side.
- Adding the VaR of two portfolios together. Because positions are not perfectly correlated, combined VaR is normally lower than the sum of the parts, and treating it additively overstates risk.
Questions
People also ask.
How often should the loss exceed a 95% one-day VaR?
About one trading day in twenty, so roughly 12 or 13 times a year; far more breaches than that suggests the model needs recalibrating.
Is VaR still used after past crises exposed its limits?
Yes, widely, but it is now normally reported with expected shortfall and stress test results rather than standing alone.
Which calculation method is best?
Historical simulation is simplest to explain and makes no assumption about the shape of returns, parametric is quickest, and Monte Carlo copes best with options and other non-linear positions.
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