Value at Risk (VaR) Calculator
What Value at Risk (VaR) means
Value at Risk (VaR) is a statistical estimate of how much you could lose over a chosen time horizon at a chosen confidence level. A 1‑day VaR of $10,000 at 95% confidence is commonly read as: “Based on the model assumptions, there is a 95% chance the loss over one day will be no more than $10,000, and a 5% chance it will be more than $10,000.”
VaR is widely used for setting risk limits, comparing portfolio risk across strategies, and communicating downside in a single dollar figure. It is not a guarantee and it is not the worst‑case loss.
Method used by this calculator (Parametric / Variance–Covariance VaR)
This calculator uses parametric VaR (also called variance–covariance VaR). It assumes returns are approximately normally distributed and uses volatility plus a standard normal z-score to translate “confidence level” into a loss threshold.
Compared with historical simulation or Monte Carlo simulation, the parametric approach is fast and needs only a volatility estimate, but its accuracy depends on the assumptions listed later.
Inputs (what to enter)
- Portfolio Value ($): current market value of the portfolio (or position) you want to measure.
- Daily Volatility (%): the standard deviation of daily returns, expressed as a percentage (e.g., 1.2 for 1.2%).
- Time Horizon (days): the number of trading days you want to measure (e.g., 1, 5, 10).
- Confidence Level: commonly 90%, 95%, or 99%.
Formulas (including time scaling)
Under the parametric normal model, VaR is calculated as:
VaR ($) = V × σd × √T × z
- V = portfolio value (in dollars)
- σd = daily volatility (as a decimal, so 1.2% → 0.012)
- T = time horizon in days
- z = z‑score for the confidence level (standard normal quantile)
The square‑root‑of‑time rule (√T) is the usual way to scale daily volatility to a multi‑day horizon when daily returns are assumed independent and identically distributed.
MathML version
Typical z‑scores (approx.): 90% → 1.2816, 95% → 1.6449, 99% → 2.3263.
How to interpret the result
VaR is best read as a threshold rather than a promise:
- If the calculator returns $X at 95% over T days, the model implies losses will be greater than $X about 5% of the time over that horizon.
- VaR does not tell you how bad losses can be beyond the threshold. Two portfolios can have the same VaR but very different tail risk.
If you want a tail‑severity measure, practitioners often pair VaR with Expected Shortfall (CVaR), which estimates the average loss in the worst q% of cases.
Worked example
Scenario: Portfolio value = $100,000; daily volatility = 1.20%; horizon = 10 days; confidence = 95%.
- Convert volatility to decimal: σd = 1.20% = 0.012
- Time scaling: √T = √10 ≈ 3.1623
- z‑score (95%): z ≈ 1.6449
- Compute: VaR = 100,000 × 0.012 × 3.1623 × 1.6449 ≈ $6,244
Interpretation: Under the model assumptions, there is a 95% chance the 10‑day loss will be about $6,244 or less, and a 5% chance it will exceed that amount. This does not rule out larger losses (especially during market stress).
Quick comparison table (confidence levels)
| Confidence level | Tail probability | Typical z‑score | Plain‑language meaning |
|---|---|---|---|
| 90% | 10% | ≈ 1.282 | Loss should be below VaR in ~9 out of 10 periods (model‑based). |
| 95% | 5% | ≈ 1.645 | Loss should be below VaR in ~19 out of 20 periods (model‑based). |
| 99% | 1% | ≈ 2.326 | Loss should be below VaR in ~99 out of 100 periods (model‑based). |
Assumptions & limitations (important)
- Normality / thin tails: Parametric VaR assumes returns are approximately normal. Real markets often have fat tails, meaning extreme losses can happen more frequently than the model suggests.
- Volatility is constant: Using a single daily volatility implies risk is stable. In practice, volatility clusters and can rise sharply in stress periods.
- Independence and √T scaling: The square‑root‑of‑time rule assumes returns are i.i.d. Serial correlation, changing volatility, and illiquidity can break this scaling.
- Mean return often ignored: Over short horizons the mean is typically small versus volatility, so many VaR implementations assume zero mean. If you include drift, VaR shifts slightly.
- Not a maximum loss: A 99% VaR still allows 1% of outcomes worse than VaR, and those tail losses can be much larger.
- Portfolio composition matters: A single volatility input cannot capture nonlinear payoffs (options), regime changes, concentration risk, or liquidity/market impact during forced selling.
Disclaimer: This calculator provides an estimate for educational and planning purposes and is not financial advice.