Value at Risk (VaR)
Explanation
Value at Risk answers a specific question: What is the worst I can expect to lose over a given period, with a given probability? A 95% daily VaR of $5,000 means that on 95 out of 100 trading days, the portfolio should not lose more than $5,000.
VaR became the standard risk measure in banking after JPMorgan published its RiskMetrics methodology in 1994. It is now required by bank regulators (Basel III) and used by virtually every institutional investor.
Three methods exist for calculating VaR: historical simulation (replaying past returns), variance-covariance (assuming normal distribution), and Monte Carlo simulation (generating thousands of random scenarios). Each has trade-offs between accuracy and computational cost.
Formula
| Variable | Meaning |
|---|---|
| VaR₉₅ | Value at Risk at 95% confidence (parametric method) |
| μ | Expected return over the period |
| 1.645 | Z-score for 95% confidence (one-tailed) |
| σ | Standard deviation of returns over the period |
Example
A $100,000 portfolio has daily expected return of 0.04% and daily standard deviation of 1.2%.
On 95% of trading days, the portfolio is expected to lose no more than $1,934. On the remaining 5% of days (roughly 12-13 days per year), losses could exceed this amount.
How Stoquity Uses This
Stoquity calculates 95% VaR for every portfolio and displays it on the risk dashboard. The Drawdown Governor uses VaR as one trigger: if realized daily loss approaches the VaR threshold repeatedly, the governor reduces position sizes to bring risk back within charter limits.
Common Mistakes
- VaR says nothing about how bad losses can get beyond the confidence threshold—that is what Conditional VaR (CVaR) addresses
- A 95% VaR does not mean the remaining 5% is catastrophic; it is simply unquantified by VaR alone
- VaR assumes relatively stable market conditions and can badly underestimate risk during regime changes