Glossary term
VaR (classroom)
Definition
A percentile from a toy simulation — here, starting equity minus the 5th percentile of simulated endings. Not a maximum loss and not next year’s result.
How it works
Value at risk is a percentile of outcomes. The classroom version is computed from the toy simulation: take the starting equity, find the 5th percentile of the simulated ending values, and subtract. VaR = start − p5. A 95% VaR says that in this sample, outcomes were worse than this on about 5% of the simulated paths.
That is all it says. The figure marks the edge of the bad tail but is silent about how far beyond the edge the tail goes. It is also only as informative as the assumptions behind the simulation: the drift, the volatility and the horizon were typed in, and a different set moves the percentile.
Worked example
Take a hypothetical $100,000 start, 6% assumed drift, 15% assumed volatility and a one-year horizon. Under geometric Brownian motion the 5th percentile ending value is about $100,000 × exp(0.04875 − 1.645 × 0.15) = $100,000 × exp(−0.198) ≈ $82,000. VaR is therefore about $100,000 − $82,000 = $18,000.
Raise the assumed volatility to 25% and the same arithmetic gives a 5th percentile near $68,200, so VaR rises to roughly $31,800. Nothing about any real holding changed; two typed-in numbers did. The figure is a description of the toy, not a forecast.
Hypothetical, for education only. Not a recommendation and not a prediction.
Common mistake
The mistake is reading VaR as a maximum loss, or as a promise that the next year will fall inside it. By construction about one path in twenty ends below the line, and the line says nothing about how far below. A VaR figure quoted without a statement of what happens beyond it stops just before the interesting part. It is not next year's result either, since it describes simulated paths.