What it means
Value at Risk, written VaR by most practitioners, answers a deliberately narrow question. Over a stated time horizon, such as one day or ten days, what loss would be exceeded only a small percentage of the time, such as 5% or 1%?
The idea became popular in banks during the 1990s and is still widely used in internal limits and regulatory reporting. The result is a dollar figure that boards, regulators and risk committees can compare across desks and businesses.
A treasury team might report that its one-day 95% VaR is $200,000, meaning that on 19 days out of 20 it expects to lose less than that. The remaining one day in twenty is expected to be worse, which is the point of the confidence level.
There are three common ways to compute it. The parametric method assumes returns follow a bell-shaped curve and uses the average and spread of past returns, historical simulation replays real past price moves against today's positions, and Monte Carlo simulation (running thousands of random scenarios) builds a distribution from a model.
The nuance that matters most is what VaR does not say. It gives the threshold that is crossed rarely, but it says nothing about how bad the loss is when it is crossed, and in a crisis the losses beyond the threshold can be many times larger.
For that reason risk teams pair it with stress tests and with expected shortfall, which averages the losses in the worst cases. Treat VaR as a speedometer, not a guarantee of safety.
In practice
Real-world examples.
Example
A hedge fund with $50 million of shares calculates a one-day 99% VaR of $1.1 million each morning. The risk officer compares it with the limit of $1.5 million and signs off on the day's positions. If the figure approached the limit, traders would be asked to trim positions or add hedges before the market opened the next day.
Example
A multinational treasurer holds foreign currency receivables worth $20 million. The team calculates how much the exchange rate could move against them over a week at 95% confidence. The result helps decide how much of the exposure to hedge with forward contracts and how much to leave open.
Example
A small pension scheme with bonds and shares reports its monthly VaR to trustees. The trustees see that a larger share allocation would roughly double the figure. They use it to decide whether the extra risk is acceptable given the scheme's funding level and the time before benefits fall due.
Formula
Calculation
Parametric VaR = Portfolio value x Z-score x Daily volatility x Square root of number of days
A fund holds a $1,000,000 portfolio. Its returns have a daily volatility (standard deviation) of 1%, and for 95% confidence the Z-score is 1.645. One-day VaR = 1,000,000 x 1.645 x 0.01 = $16,450. For a four-day horizon, multiply by the square root of 4, which is 2, so four-day VaR = 16,450 x 2 = $32,900. The fund therefore expects to lose less than $32,900 over four days on 95% of occasions.Case study
Seen in the real world.
This illustrative story involves a fictional trading firm, Ardmore Capital, with a $200 million book. Its risk report showed a one-day 99% VaR of $2 million for months, and the head of trading took comfort from how stable the number was. The figure was built on a calm two-year window of history.
When markets turned violent, the firm lost $9 million in a single day, far beyond the reported VaR. The report had not been wrong in a technical sense, because a 1% day was always possible. It had been misread as a worst case, when it was only the edge of normal conditions.
After the event the fictional firm added stress scenarios based on historical crises and set position limits using both VaR and expected shortfall. It also lengthened the data window so that quieter and more violent periods both fed the model.
Watch out
Common mistakes.
- Treating VaR as the maximum possible loss. It is the loss level exceeded on a small fraction of days, and actual losses beyond it can be much larger.
- Using a calm history window and trusting the result in a crisis. If the data period contains no stress, the model will understate the risk.
- Adding VaR figures from different desks to get a total. Diversification means the combined VaR is normally lower than the sum, and the calculation must be done on the whole portfolio.
Questions
People also ask.
Is VOR the same as VaR?
Yes, VOR is an uncommon alternative spelling of the same measure, and the market standard abbreviation is VaR.
What confidence level should I choose?
Common choices are 95% and 99%, with the higher level giving a larger loss figure that is exceeded less often.
Why scale by the square root of time?
Under the usual assumption that daily moves are independent, volatility grows with the square root of the number of days rather than in a straight line.
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