Value at Risk (VaR) Explained With Examples

Value at Risk answers one question: on a normal bad day, how much could this portfolio lose? It turns volatility into a dollar figure with a stated confidence level, which makes it easy to compare positions and set limits.

It is also easy to misread. VaR is the size of an ordinary bad day, not the worst day.

The formula

The parametric (variance-covariance) method assumes returns are normally distributed:

VaR = portfolio value × volatility × z-score

The z-score comes from the confidence level: 1.6449 for 95%, 2.3263 for 99%.

A $100,000 portfolio with 2% daily volatility:

$100,000 × 0.02 × 1.6449 = $3,289.80

Read it as: on about 19 days out of 20, the loss should be smaller than $3,290. On the remaining day, it will be larger, and VaR says nothing about how much larger.

Confidence level changes the number a lot

Same portfolio, same volatility:

There is no correct level. 95% is common for day-to-day monitoring; 99% is the usual choice for setting hard limits. Pick one and stick to it, so the numbers stay comparable over time.

Longer horizons scale with the square root of time

If daily returns are independent, volatility over several days grows with the square root of the number of days, not the number itself:

VaR over n days = 1-day VaR × √n

At 95%, ten trading days gives $3,289.80 × √10 = $10,403.26, about 3.2 times the one-day figure, not ten times. This is the standard way to turn a daily number into a two-week one.

What VaR does not tell you

• The size of the bad day. VaR is a threshold. A 1-in-20 day might lose $3,300 or $15,000; the model is silent past the line.
• Fat tails. Real market returns have more extreme days than a normal distribution predicts. Crashes, gaps and news events land outside the model far more often than "1 in 100" suggests.
• Correlation in a crisis. Positions that usually move independently tend to fall together when markets panic, so a diversified portfolio's VaR understates its stress loss.
• Leverage and liquidity. VaR assumes you can hold or exit at market prices. A forced liquidation at a margin call does not wait for the distribution to behave.

Using it in practice

• Set a daily loss limit near your 95% VaR. If a normal bad day already breaches your limit, the position is too large for the limit.
• Watch it change, not just its level. Rising VaR with no new positions means volatility is climbing. That is often the signal to cut size before the drawdown arrives.
• Pair it with a drawdown plan. VaR covers a single day; a run of bad days compounds. Know how much gain a given drawdown needs to recover, and stop before the hole gets deep.