What it means
VaR stands for value at risk, and it answers a single question: how much could we lose on a normal bad day? The parametric version, also called the variance-covariance method, assumes returns are normally distributed and uses standard deviation as the entire measure of risk.
The calculation multiplies the portfolio's value by its return volatility and by a multiplier taken from the normal distribution: about 1.645 for 95% confidence and about 2.326 for 99%. Scaling from one day to a longer horizon uses the square root of the number of days.
It matters because banks, funds and corporate treasuries use VaR to set risk limits, allocate capital and report exposure to boards. A single number in dollars is far easier for a non-specialist committee to work with than a page of volatility statistics.
The main criticism is that markets are not normally distributed. Extreme moves happen more often than the bell curve predicts, so parametric VaR systematically understates the size and frequency of crisis losses, and it says nothing at all about how bad things get beyond the confidence threshold.
That gap is why VaR is normally paired with other measures. Expected shortfall averages the losses beyond the VaR point, historical simulation uses actual past returns instead of an assumed curve, and stress testing asks what specific scenarios would do regardless of probability.
In practice
Real-world examples.
Example
A bank sets a trading desk limit of $2,000,000 daily VaR at 99% confidence. When the desk's calculated figure reaches $2,300,000 after a volatility spike, the head of trading is required to cut positions the same day.
Example
A corporate treasury holds $40,000,000 of foreign currency deposits with 0.6% daily volatility. Its 95% one-day parametric VaR is $40,000,000 x 0.006 x 1.645 = $394,800, which the board uses as the headline currency risk figure in quarterly reporting.
Example
A risk officer back-tests the model and finds 19 limit breaches in a year when about 13 were expected at 95% confidence. She concludes the normal distribution assumption is understating tail risk and adds an expected shortfall measure alongside it.
Think of it
“Parametric VaR uses statistical formulas to estimate risk-assuming a distribution shape.
Formula
Calculation
Parametric VaR = portfolio value x volatility x confidence multiplier, then scaled by the square root of the holding period in days.
A fund holds a $10,000,000 portfolio with a daily return standard deviation of 1.2%. At 95% confidence the multiplier is 1.645, so one-day VaR = $10,000,000 x 0.012 x 1.645 = $197,400. The plain-English reading is that on about 19 days out of 20 the portfolio should not lose more than roughly $197,400.
Raising confidence to 99% swaps in a multiplier of 2.326, giving $10,000,000 x 0.012 x 2.326 = $279,120. Stretching the horizon to ten trading days at 95% multiplies the daily figure by the square root of 10, about 3.162, so $197,400 x 3.162 = $624,200 rounded to the nearest hundred.
Note what the number does not say: on the one day in twenty when the limit is breached, the loss could be $400,000 or $2,000,000, and parametric VaR is silent about which.Case study
Seen in the real world.
The following is an illustrative, fictional example. Coldstream Asset Management, an invented boutique fund manager, reported a 95% one-day parametric VaR of about $250,000 on a $12,000,000 portfolio and presented it to its investment committee as the worst realistic daily loss. Nobody asked what happened in the remaining 5% of days.
During a two-week market dislocation in this fictional scenario, the portfolio lost $780,000 in a single session, more than three times the reported figure. Nothing was wrong with the arithmetic: volatility had roughly doubled from the level fed into the model, and the move itself sat far out in a tail the normal distribution treats as almost impossible.
Coldstream's illustrative response was to keep parametric VaR as a daily monitoring tool, since it is quick and comparable over time, while adding expected shortfall and three named stress scenarios to every committee pack. The reported risk numbers roughly doubled overnight, and the committee's questions improved considerably.
Watch out
Common mistakes.
- Reading VaR as a maximum possible loss, when it is a threshold that is expected to be exceeded on a known fraction of days.
- Feeding in a volatility figure measured in calm markets and leaving it unchanged as conditions deteriorate.
- Adding the VaR of two portfolios together, which ignores correlation and usually overstates the combined risk.
Questions
People also ask.
What confidence level should we use?
95% suits day-to-day monitoring while 99% is common for regulatory and capital purposes, and many firms report both.
How is parametric VaR different from historical VaR?
Parametric assumes a normal distribution and uses volatility, whereas historical VaR ranks actual past returns and reads the loss off that record.
Why add expected shortfall?
Because it averages the losses beyond the VaR point and therefore says something about how bad the tail is, which VaR alone never does.
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