How is parametric VaR calculated?

VaR % = z-score × volatility × √(horizon in periods), then multiplied by portfolio value for a currency figure. The z-score comes from the normal distribution at the chosen confidence level (1.6449 at 95%, 2.3263 at 99%).

Why does VaR grow with the square root of time?

Under the model's assumption that returns are independent from period to period, variance adds linearly across periods, so standard deviation (and VaR) scales with the square root of the number of periods, not the number itself.

What confidence level should I use?

95% and 99% are the industry standards; 99% is more common for regulatory and worst-case risk reporting since it captures a larger slice of the tail.

What are the limitations of parametric VaR?

It assumes normally distributed returns, which understates real-world tail risk — markets have fatter tails than a normal distribution predicts, so actual losses beyond the VaR threshold can exceed what the model implies.

How is this different from historical or Monte Carlo VaR?

Historical VaR resamples actual past returns and Monte Carlo VaR simulates many random paths; both can capture non-normal behaviour that this parametric (variance-covariance) method assumes away in exchange for a single closed-form calculation.

Risk & Money Management

Value at Risk (VaR) Calculator

Calculate parametric (variance-covariance) Value at Risk from portfolio value, volatility, confidence level and time horizon — the loss not expected to be exceeded.

Value at Risk (VaR) is the loss a portfolio is not expected to exceed over a given time horizon at a chosen confidence level, such as 95% or 99%.

Value at Risk

$3,289.80

VaR %: 3.29%
z-score: 1.6449

Parametric (variance-covariance) VaR assumes normally distributed returns — real tails are usually fatter than this model implies.

Worked example

A $100,000 portfolio has a 2% daily volatility. A trader wants the 1-day Value at Risk at 95% confidence.

z-score (95%): 1.6449
VaR %: 1.6449 × 2% × √1 = 3.29%
VaR amount: $100,000 × 3.29% = $3,289.80

There is roughly a 95% chance the portfolio's 1-day loss stays below $3,289.80. Stretching to 99% confidence over a 10-day horizon grows the same portfolio's VaR to $14,712.81 — VaR scales with the confidence z-score and the square root of time.

How this is calculated

Parametric VaR assumes returns are normally distributed and scales a confidence-level z-score by volatility and the square root of time:

VaR % = z-score × volatility × √(horizon in periods); VaR amount = portfolio value × VaR %

The z-score comes from the standard normal distribution: 1.6449 at 95% confidence, 2.3263 at 99%, and so on — higher confidence needs a larger z-score because it has to cover more of the distribution's tail.

The square-root-of-time scaling assumes returns from period to period are independent, so variance (not volatility) adds up linearly across periods. That is why a 10-day VaR is √10 ≈ 3.16 times the 1-day figure, not 10 times it.

When to use this calculator

Use this to put a single number on portfolio risk: given a volatility estimate, confidence level and time horizon, it answers 'how much could I plausibly lose?' in a way that's comparable across very different portfolios.

It is a standard tool for setting risk limits — a desk or fund with a stated VaR limit uses this exact calculation to check whether current volatility and position size keep it within that limit.

Run it at more than one confidence level and horizon side by side: the 95%/1-day and 99%/10-day figures tell a fuller story than either alone, since real drawdowns often exceed a single VaR snapshot.

Common mistakes

Treating VaR as the worst-case loss — by construction it is the loss not expected to be exceeded at the chosen confidence level; the remaining 1% or 5% of outcomes can be worse, sometimes far worse.
Mixing volatility periods and horizons — volatility must be measured over the same period the horizon is expressed in (daily volatility with a horizon in days), or the square-root-of-time scaling is wrong.
Using a short, calm sample to estimate volatility — parametric VaR is only as good as the volatility input, and quiet-period estimates understate risk heading into turbulent markets.

Frequently asked questions

What is Value at Risk?: VaR is the loss a portfolio is not expected to exceed, over a given time horizon, at a chosen confidence level — e.g. '95% confidence the 1-day loss stays below $3,290'.
How is parametric VaR calculated?: VaR % = z-score × volatility × √(horizon in periods), then multiplied by portfolio value for a currency figure. The z-score comes from the normal distribution at the chosen confidence level (1.6449 at 95%, 2.3263 at 99%).
Why does VaR grow with the square root of time?: Under the model's assumption that returns are independent from period to period, variance adds linearly across periods, so standard deviation (and VaR) scales with the square root of the number of periods, not the number itself.
What confidence level should I use?: 95% and 99% are the industry standards; 99% is more common for regulatory and worst-case risk reporting since it captures a larger slice of the tail.
What are the limitations of parametric VaR?: It assumes normally distributed returns, which understates real-world tail risk — markets have fatter tails than a normal distribution predicts, so actual losses beyond the VaR threshold can exceed what the model implies.
How is this different from historical or Monte Carlo VaR?: Historical VaR resamples actual past returns and Monte Carlo VaR simulates many random paths; both can capture non-normal behaviour that this parametric (variance-covariance) method assumes away in exchange for a single closed-form calculation.