Financial Calculators

Value at Risk (VaR) calculator

Parametric (variance–covariance) VaR for a single position over one period, given expected return, volatility, and a confidence Z-score.

Value at Risk (VaR) Calculator

Table of contents

◦Value at Risk (VaR)
◦Formula
◦How to use
◦Worked example
◦FAQ

Value at Risk (VaR)

Value at Risk is a single number that summarizes the worst expected loss on a position over a given time horizon at a stated confidence level. A one-day 95% VaR of class="jsx-43013d48d08af43a site-content "0,000 means: under normal market conditions, there is a 95% chance the loss over the next day will be less than class="jsx-43013d48d08af43a site-content "0,000.

This calculator uses the parametric (variance–covariance) method, which assumes returns are normally distributed.

Formula

VaR = V₀ × (z·σ − μ)

Where:

  • V₀ — portfolio value
  • μ — expected return for the period (as a decimal)
  • σ — standard deviation of returns for the period (as a decimal)
  • z — Z-score for the confidence level

Common Z-scores: 1.645 for 95% confidence, 1.96 for 97.5%, 2.326 for 99%.

How to use

  1. Enter the portfolio value in dollars.
  2. Enter the expected return for the period (often 0 for short horizons).
  3. Enter the standard deviation of returns for the same period.
  4. Enter the Z-score for your confidence level.

The dollar VaR appears instantly.

Worked example

Portfolio class="jsx-43013d48d08af43a site-content ",000,000 · expected daily return 0% · daily σ 1.5% · 99% confidence (z = 2.326)

VaR = 1,000,000 × (2.326 × 0.015 − 0) = $34,890

There's a 1% chance of losing more than $34,890 in a single day.

FAQ

Where do I get the standard deviation?

Compute it from your portfolio's recent daily returns (typically a 1–2 year rolling window). Spreadsheets have a STDEV function. For a quick estimate, use the historical volatility of the S&P 500 (~1% daily).

Why parametric and not historical or Monte Carlo?

Parametric VaR is fastest to compute and works well when returns are roughly normal. Historical VaR makes no distributional assumption but requires a long return series. Monte Carlo handles non-normal distributions and complex positions but is computationally heavy. Use parametric for a quick first-cut estimate.

Is VaR enough on its own?

No. VaR says nothing about losses beyond the confidence threshold. For tail-risk awareness, also compute Expected Shortfall (the average loss given that VaR is exceeded).