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Value at Risk Calculator

Compute the Value at Risk (VaR) of a portfolio using parametric or historical simulation methods with custom inputs.

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days
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Value at Risk (VaR)

$3,290.00

There is a 5% chance the portfolio loses more than 3.29% ($3,290.00) over 1 day(s).

VaR percentage

3.29%

95% confidence threshold

Remaining value

$96,710.00

Portfolio above VaR loss

Scaled volatility

2.00%

1-day horizon

Z-score

1.645

Normal quantile

Portfolio loss exposure

Portfolio$100,000.00
  • Value at Risk$3,290.003.29%
  • Remaining Portfolio$96,710.0096.71%

VaR calculation steps

Parametric variance-covariance or historical simulation breakdown

  1. Scale daily statistics to the holding period

    σT=σdT,μT=μd×T\sigma_T = \sigma_d \sqrt{T},\qquad \mu_T = \mu_d \times T

    Daily volatility 2.00% scales to 2.00% over 1 day(s). Expected return scales from 0.00% to 0.00%.

  2. Apply the parametric VaR formula

    VaR%=−(μT−z×σT)\mathrm{VaR\%} = -(\mu_T - z \times \sigma_T)

    With z = 1.645 at 95% confidence, VaR% = -(0.00% - 1.645 × 2.00%) = 3.290%.

  3. Convert VaR percentage to dollar loss

    VaR$=P×VaR%100\mathrm{VaR}_{\$} = P \times \frac{\mathrm{VaR\%}}{100}

    Portfolio value $100,000.00 × 3.290% = $3,290.00 maximum expected loss at the 95% confidence level.

Report tool

What is Value at Risk (VaR)?

Value at Risk (VaR) estimates the maximum expected portfolio loss over a chosen time horizon at a specified confidence level. Banks, asset managers, and risk committees use VaR to set capital buffers, monitor trading desks, and compare strategies under a common loss metric. Basel market-risk frameworks reference VaR-style models for regulatory capital.

VaR answers a practical question: how much could I lose on a normal bad day? Pair VaR with return diagnostics from the Sharpe ratio calculator, systematic exposure from the portfolio beta calculator, and worst peak-to-trough loss from the maximum drawdown calculator for a fuller risk picture.

Parametric (variance-covariance) VaR

The parametric method assumes returns are normally distributed. You supply daily expected return and volatility, scale them to the holding period, and apply the confidence-level z-score from the standard normal distribution.

VaR%=−(μT−z×σT),σT=σdT,μT=μd×T\mathrm{VaR\%} = -(\mu_T - z \times \sigma_T),\qquad \sigma_T = \sigma_d \sqrt{T},\qquad \mu_T = \mu_d \times T

Common one-tailed z-scores are 1.282 for 90% confidence, 1.645 for 95%, and 2.326 for 99%. Dollar VaR equals portfolio value multiplied by VaR percentage divided by 100.

Worked example: parametric VaR

A $100,000 portfolio with 2% daily volatility, 0% expected daily return, 95% confidence, and a 1-day horizon produces:

  1. Scaled volatility: 2% × √1 = 2%
  2. VaR%: -(0% - 1.645 × 2%) = 3.29%
  3. Dollar VaR: $100,000 × 3.29% = $3,290

Interpretation: on 95% of trading days, losses should not exceed $3,290. On the worst 5% of days, losses may be larger.

Historical simulation VaR

Historical simulation avoids normality assumptions. You feed a series of realized daily returns, sort them from worst to best, and read the loss at the desired tail percentile. The horizon VaR scales by the square root of time, consistent with parametric scaling.

VaR%T=−Percentile(r,100−c)×T\mathrm{VaR\%}_T = -\mathrm{Percentile}(r, 100 - c) \times \sqrt{T}

Historical VaR captures fat tails and skew when your sample is long enough. A minimum of five return observations is required, but practitioners typically use hundreds of daily returns for stability.

Interpreting confidence levels and horizons

A 95% one-day VaR does not cap losses at that number. It means losses exceed VaR on roughly 5% of days. Extending the horizon from 1 day to 10 days increases VaR by roughly √10 under the square-root-of-time rule, assuming independent daily returns.

VaR is a forward-looking statistical estimate, not a guarantee. Stress testing, scenario analysis, and conditional VaR (expected shortfall) complement VaR when tail risk matters. For position sizing based on stop-loss distance, see the position size calculator.

Frequently asked questions

What does 95% VaR mean in plain language?
A 95% one-day VaR of $3,290 means that on 95 out of 100 trading days, the portfolio should not lose more than $3,290. On the remaining 5 days, losses may exceed that threshold.
When should I use parametric vs historical VaR?
Use parametric VaR when returns are approximately normal and you have reliable volatility estimates. Use historical simulation when return distributions are skewed, have fat tails, or when you want the model to reflect actual past market behavior.
Why scale volatility by the square root of time?
Under the assumption that daily returns are independent with constant variance, portfolio variance grows linearly with time. Standard deviation therefore grows with the square root of the number of days.
Does VaR include positive expected return?
Yes. The parametric formula subtracts the scaled expected return. A positive expected return reduces VaR because the distribution shifts right. A negative expected return increases VaR.
What are the main limitations of VaR?
VaR does not describe how bad losses can be beyond the threshold. It can underestimate tail risk during crises. Correlation breakdowns, liquidity shocks, and regime changes can make historical or parametric VaR too optimistic.
How is VaR used in portfolio risk management?
Institutions set position limits, allocate risk capital, and compare desk performance using VaR. Retail investors use VaR to sanity-check whether daily volatility on a concentrated portfolio fits their loss tolerance.

Resources and references

The formulas and methods in this calculator were checked against these independent sources.