Value at Risk Calculator (VaR)

Estimate the maximum expected loss on a portfolio using the parametric (variance-covariance) method. Enter portfolio value, annual volatility, confidence level, and time horizon to see the dollar amount at risk.

Quick Facts

Model
Parametric (variance-covariance) VaR
Assumes portfolio returns are normally distributed around a zero mean.
Formula
VaR = Value × Z × σ(daily) × √T
Z is the confidence multiplier, σ(daily) the daily volatility, T the horizon in trading days.
Common Z-scores
90% → 1.282 · 95% → 1.645 · 99% → 2.326
One-tailed z-scores from the standard normal distribution.

Your Results

Calculated
Value at Risk
-
Estimated max loss at chosen confidence
VaR as % of portfolio
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Loss relative to portfolio value
Daily volatility
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Annual volatility scaled to 1 trading day
Z-score used
-
Confidence-level multiplier

Ready

Enter portfolio value, annual volatility, confidence level, and time horizon, then press Calculate.

How the Value at Risk Calculator works

Value at Risk (VaR) answers a specific question: over a given time horizon, how much could this portfolio lose, at a given confidence level, under normal market conditions? This calculator uses the parametric (variance-covariance) method — the most widely taught VaR approach — which assumes portfolio returns follow a normal distribution around a mean of zero.

The formula

For a portfolio value V, an annual volatility (standard deviation of returns) σ, a one-tailed confidence multiplier Z, and a time horizon of T trading days, Value at Risk is:

VaR = V × Z × σ(daily) × √T, where σ(daily) = σ(annual) / √252

The 252 in the denominator is the standard number of trading days in a year, used to scale annual volatility down to a daily figure. The square root of T then scales that 1-day figure up to the chosen holding period, based on the assumption that daily returns are independent and identically distributed.

Worked example

Take a $100,000 portfolio with 20% annual volatility, a 95% confidence level, and a 1-day horizon. Daily volatility is 20% / √252 ≈ 1.26%. The Z-score for 95% confidence is 1.645. VaR = $100,000 × 1.645 × 0.0126 ≈ $2,073. In plain terms: there is roughly a 5% chance this portfolio loses more than about $2,073 in a single trading day, assuming normally distributed returns.

What moves VaR the most

  • Volatility: VaR scales directly with σ — doubling the annual volatility input doubles the dollar VaR.
  • Confidence level: moving from 90% to 99% confidence raises the Z-score from 1.282 to 2.326, nearly doubling the estimated loss for the same portfolio.
  • Time horizon: VaR scales with the square root of time, not linearly — a 10-day VaR is about √10 ≈ 3.16 times the 1-day VaR, not 10 times.
  • Portfolio value: VaR scales linearly with portfolio size, since it is expressed in dollars of that portfolio.

Limitations of parametric VaR

Parametric VaR is fast and transparent, but it assumes returns are normally distributed with constant volatility. Real market returns typically have fatter tails than a normal distribution, so this method can understate the frequency and size of extreme losses, especially during market stress. It also does not describe how bad a loss could be once the VaR threshold is breached — that is the role of Expected Shortfall (Conditional VaR), which averages the losses in the worst-case tail beyond VaR. Historical simulation and Monte Carlo simulation are common alternative methods that do not assume a normal distribution.

Frequently Asked Questions

How is Value at Risk calculated?
This calculator uses the parametric (variance-covariance) method: VaR = Portfolio Value × Z-score × Daily Volatility × √(Time Horizon in days). The daily volatility is the annual volatility divided by the square root of 252 trading days, and the Z-score is the one-tailed normal-distribution multiplier for the chosen confidence level (1.282 for 90%, 1.645 for 95%, 2.326 for 99%).
What confidence level should I use?
95% is the most common choice for internal risk reporting, meaning there is a 5% chance losses exceed the calculated VaR over the chosen horizon. 99% is stricter and often used for regulatory capital requirements. A lower confidence level (90%) produces a smaller, less conservative VaR estimate.
Why does VaR scale with the square root of time?
Under the assumption that daily returns are independent and identically distributed, variance grows linearly with time, so standard deviation (volatility) grows with the square root of time. Multiplying the 1-day VaR by the square root of the number of days extends the estimate to a longer holding period.
What are the limitations of parametric VaR?
Parametric VaR assumes returns are normally distributed with a constant volatility, which tends to understate the risk of large, sudden losses because real market returns have fatter tails than a normal distribution. It also does not by itself describe how large losses could be beyond the VaR threshold — that is what Expected Shortfall (Conditional VaR) is used for. Historical simulation and Monte Carlo methods are common alternatives that do not assume normality.

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