How to calculate Value at Risk
Parametric VaR (loss) = z × σ × √h − μ × h
z: 1.282 (90%), 1.645 (95%), 1.960 (97.5%), 2.326 (99%)
Historical VaR = −(the (1 − confidence) quantile of observed returns)
VaR amount = VaR % × Portfolio value
Worked example
- Portfolio $100,000, mean daily return 0.05%, daily volatility 1.2%, 95% confidence.
- VaR = 1.645 × 1.2% − 0.05% = 1.924%.
- In money: $1,924. On roughly 1 day in 20 the loss should exceed this.
- For a 10-day horizon: 1.645 × 1.2% × √10 − 10 × 0.05% ≈ 5.74%, or about $5,740.
How to interpret Value at Risk
VaR is a threshold, not a worst case. A 95% one-day VaR of $1,924 says nothing about how bad the other 5% of days can be — that's why risk managers pair it with Expected Shortfall, which averages the losses beyond VaR.
Limitations and common mistakes
- The parametric method assumes normal returns and underestimates fat-tail risk.
- Historical VaR only knows the past it was fed; quiet sample periods give low VaR right before volatile ones.
- √time scaling assumes independent days, which breaks down in trending crises.