# Portfolio Volatility and VaR Calculator

> Free value at risk calculator. Enter portfolio value, daily volatility, confidence level and horizon to estimate VaR and expected shortfall in dollars.

Source: https://learn.tradelabsai.com/tools/var-calculator/  
Track: Calculators · Level: Beginner · Updated: 2026-10-03  
Publisher: TradeLabs AI (https://tradelabsai.com). Education, not financial advice.  
Cite as: TradeLabs Learn, "Portfolio Volatility and VaR Calculator", https://learn.tradelabsai.com/tools/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

*Interactive calculator: use it at https://learn.tradelabsai.com/tools/var-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)](https://learn.tradelabsai.com/portfolio/value-at-risk/) and [Expected Shortfall (CVaR)](https://learn.tradelabsai.com/portfolio/expected-shortfall/).

**Example: A $1 million portfolio**
A $1,000,000 portfolio has daily volatility of 1.2%. The one day 95% VaR is 1.645 times 1.2% times $1,000,000, about $19,740. The one day 95% expected shortfall is about $24,750: on the worst 5% of days, the average loss is about a quarter larger than VaR. Over 10 days, 95% VaR scales by the square root of 10 to about $62,400. A daily volatility of 1.2% corresponds to roughly 19% annual volatility, similar to a stock index in normal times. See [Variance and Standard Deviation](https://learn.tradelabsai.com/math/variance-and-standard-deviation/).

## Estimating daily volatility

| Source | How |
|---|---|
| Your own returns | Standard deviation of daily returns. See [Sharpe and Sortino Calculator](https://learn.tradelabsai.com/tools/sharpe-and-sortino-calculator/) |
| Annual volatility | Divide by the square root of 252 for stocks (365 for crypto) |
| Implied volatility | Use options implied volatility for a forward looking estimate. See [Implied Volatility (IV)](https://learn.tradelabsai.com/volatility/implied-volatility/) |
| ATR | Average true range divided by price gives a rough daily range. See [ATR (Average True Range)](https://learn.tradelabsai.com/indicators/atr/) |

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

## Normal versus real world tails

| Daily move | Normal model frequency | Real equity markets |
|---|---|---|
| 3 standard deviations | About once in 3 years | Several times a year in volatile periods |
| 5 standard deviations | About once in thousands of years | Has happened repeatedly in modern history |

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](https://learn.tradelabsai.com/math/fat-tails/) and [Stress Testing and Scenario Analysis](https://learn.tradelabsai.com/portfolio/stress-testing/).

## 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](https://learn.tradelabsai.com/portfolio/risk-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](https://learn.tradelabsai.com/tools/bond-calculator/).

## Continue learning

- Next lesson: [Bond Price, Duration and DV01 Calculator](https://learn.tradelabsai.com/tools/bond-calculator/)
- Previous lesson: [Correlation and Beta Calculator](https://learn.tradelabsai.com/tools/correlation-and-beta-calculator/)
- Related: [Correlation and Beta Calculator](https://learn.tradelabsai.com/tools/correlation-and-beta-calculator/): Free correlation and beta calculator. Paste two lists of returns to get correlation, beta, alpha per period and R squared for a stock, fund or strategy.
- Related: [Value at Risk (VaR)](https://learn.tradelabsai.com/portfolio/value-at-risk/): Value at risk estimates the loss a portfolio should not exceed with a given confidence over a set period. Learn the three methods, an example and the limits.
- Related: [Expected Shortfall (CVaR)](https://learn.tradelabsai.com/portfolio/expected-shortfall/): Expected shortfall, or CVaR, is the average loss on the worst days beyond the VaR threshold. Learn the formula, a worked example and why regulators adopted it.
- Related: [Stress Testing and Scenario Analysis](https://learn.tradelabsai.com/portfolio/stress-testing/): Stress testing asks how a portfolio would fare in extreme but plausible events. Learn historical and hypothetical scenarios and reverse stress tests.
- Related: [Fat Tails](https://learn.tradelabsai.com/math/fat-tails/): Fat tails mean extreme market moves happen far more often than the normal curve predicts. Learn the evidence, the causes, how to measure them and how to manage them.
- Related: [Risk, Position, Loss and Drawdown Limits](https://learn.tradelabsai.com/portfolio/risk-limits/): Risk limits turn a risk policy into hard rules on position size, exposure, daily loss and drawdown. Learn how to set them, enforce them and avoid mistakes.