What it means
Every VaR number needs three ingredients: a time horizon, a confidence level and a currency amount. Change any one of them and the number changes, so quoting VaR without stating the horizon and confidence level is meaningless.
There are three common ways to calculate it. The parametric method assumes returns follow a normal distribution and works from volatility, historical simulation replays actual past returns against the current portfolio, and Monte Carlo simulation generates thousands of random scenarios.
Banks, asset managers and corporate treasuries use VaR to set position limits, allocate capital between desks and report risk to boards in a single comparable figure. Its appeal is precisely that it compresses a complicated portfolio into one number that a non-specialist can discuss.
That compression is also the danger. VaR tells you the threshold beyond which losses become unlikely, not the size of those losses, and portfolios containing options or illiquid assets can show a comfortable VaR while hiding severe tail exposure.
Practitioners therefore pair it with conditional value at risk, sometimes called expected shortfall, which averages the losses that occur beyond the VaR threshold. They also run stress tests against specific scenarios, because history-based models struggle badly with events they have never seen.
In practice
Real-world examples.
Example
An investment bank sets a daily VaR limit of $5,000,000 for its currency desk. When a large position pushes the calculated figure to $6,300,000, the risk system flags the breach automatically and the desk must reduce exposure before the next trading session.
Example
A pension scheme reports a one-year 95% VaR of $42,000,000 on a $600,000,000 portfolio to its trustees. The board uses that figure to decide whether the scheme's growth allocation is compatible with its funding position.
Example
A commodity trading company calculates VaR on its unhedged fuel inventory and finds a ten-day 99% figure of $8,400,000. The board judges this too large relative to annual profit and instructs the treasury team to hedge roughly half the position with futures.
Think of it
“VaR is the most you expect to lose-maximum likely loss at a given confidence level.
Formula
Calculation
Parametric VaR = Portfolio Value x z-score x Standard Deviation of Returns
Multi-day VaR = One-day VaR x the square root of the number of days
A trading book is worth $10,000,000 with a daily return standard deviation of 1.2%. Management wants a one-day figure at 95% confidence, where the one-tailed z-score is 1.645.
One-day VaR = $10,000,000 x 1.645 x 0.012
One-day VaR = $10,000,000 x 0.01974 = $197,400
So on a typical day the book should lose less than $197,400, with roughly one trading day in twenty expected to exceed it. Over about 250 trading days a year, that implies around 12 or 13 breaches, which is normal rather than a sign the model is broken.
Scaling to a ten-day horizon, the square root of 10 is approximately 3.162:
Ten-day VaR = $197,400 x 3.162 = $624,200 (rounded)
At 99% confidence the z-score rises to 2.326, so the one-day figure becomes:
One-day 99% VaR = $10,000,000 x 2.326 x 0.012 = $279,120Case study
Seen in the real world.
Halcyon Asset Management is a fictional firm used purely to illustrate how VaR can mislead. Its multi-strategy fund reported a steady one-day 95% VaR of about $3,000,000 on $250,000,000 of assets, and the risk committee treated the stability of that number as reassuring.
The fund had been quietly selling out-of-the-money options for premium income. Those positions produced small consistent gains and barely moved the VaR figure, because on 95 days out of 100 the options simply expired worthless and the historical data contained no severe move.
When a sharp market dislocation arrived, the fund lost roughly $41,000,000 in three days, more than thirteen times the daily VaR. The illustrative lesson Halcyon's committee drew was to report expected shortfall alongside VaR and to run explicit stress scenarios, because a model built on ordinary days had told them nothing useful about extraordinary ones.
Watch out
Common mistakes.
- Reading VaR as the maximum possible loss, when it is only a threshold that losses are expected to stay below most of the time.
- Quoting a VaR number without its horizon and confidence level, which makes the figure impossible to interpret or compare.
- Relying on a model built from calm historical data, which systematically understates risk for portfolios holding options, illiquid assets or heavily correlated positions.
Questions
People also ask.
What does a 99% one-day VaR of $500,000 actually mean?
On roughly 99 trading days out of 100 the portfolio should lose less than $500,000, with no statement about the size of losses on the remaining day.
How does expected shortfall improve on VaR?
It averages the losses that occur beyond the VaR threshold, so it describes the severity of bad outcomes rather than only their likelihood.
Should a small business use VaR?
Rarely, because it is designed for portfolios of traded instruments, and a simple sensitivity or scenario analysis is usually a better fit for operating risk.
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