Portfolio Volatility and VaR Calculator

Value at risk (VaR) estimates the loss a portfolio should not exceed on most days, at a chosen confidence level. A one day 95% VaR of $20,000 means losses should be smaller than $20,000 on about 19 days out of 20. Expected shortfall goes further, estimating the average loss on the days that do exceed VaR. This calculator uses the parametric method, which assumes normally distributed returns, to give quick estimates from a portfolio's value and volatility. Real markets have fatter tails, so treat the results as a lower bound on risk.

Calculator#

How it works#

Horizon volatility = Daily volatility × √(Days)
VaR = z × Horizon volatility × Portfolio value
Expected shortfall = (φ(z) / (1 - Confidence)) × Horizon volatility × Portfolio value

Here z is the normal distribution's critical value (1.645 for 95%, 2.326 for 99%) and φ is the normal density. The square root of time rule assumes independent daily returns and an unchanged portfolio. The expected return is assumed to be zero over short horizons. See Value at Risk (VaR) and Expected Shortfall (CVaR).

Estimating daily volatility#

Annual volatility of 20% equals about 1.26% daily for stocks.

Normal versus real world tails#

Because of fat tails, parametric VaR understates the size and frequency of extreme losses. Historical simulation and stress tests capture tails better. See Fat Tails and Stress Testing and Scenario Analysis.

Using VaR sensibly#

1. Use it as a daily risk gauge, not a worst case.
2. Set limits in VaR or expected shortfall terms. See Risk, Position, Loss and Drawdown Limits.
3. Pair it with stress tests for crisis scenarios.
4. Recalculate when volatility changes; risk rises in turbulent markets.
5. Backtest: count how often actual losses exceed VaR.

VaR for individual traders#

For a personal account, a simple version is enough: estimate your account's daily volatility from recent daily changes in equity, then use this calculator to see a typical bad day at 95% confidence. If that number would upset you or force you to change plans, your positions are larger than your tolerance. Remember that the worst days will be larger than VaR, so also look at your largest historical daily losses.

Frequently asked questions#

How do I calculate VaR?#

With the parametric method, multiply the portfolio value by the daily volatility, the square root of the horizon in days and the z score for your confidence level.

What is the difference between VaR and expected shortfall?#

VaR is the loss threshold at a confidence level; expected shortfall is the average loss on days beyond that threshold.

Is parametric VaR accurate?#

It is a useful quick estimate, but because it assumes normal returns, it usually understates extreme losses.

Next, price bonds and measure their rate risk with the Bond Price, Duration and DV01 Calculator.