Value at Risk (VaR) Calculator

This Value at Risk calculator estimates a portfolio loss threshold over a chosen number of days and tail probability. It is designed for a quick parametric VaR scenario, not a full institutional risk system. You enter portfolio value, daily standard deviation, expected return over the selected timeframe, timeframe in days, and a 10%, 5%, or 1% VaR tail. The result includes a dollar loss amount, an implied loss rate, the z-score used, the volatility move, the expected period return, and the portfolio value after the VaR loss. Informational, not investment advice.

The calculation uses a normal-distribution shortcut often associated with RiskMetrics-style calculations. It multiplies the selected z-score by the square root of the timeframe and by daily standard deviation expressed as a decimal. It then subtracts expected return over the whole timeframe. If that result is negative, the loss rate is floored at zero. Finally, it multiplies the loss rate by portfolio value.

How to use this calculator

Enter the portfolio value in dollars. This can be an account balance, fund value, trading book, or model portfolio. Enter daily standard deviation as a percentage of daily returns. For example, enter 0.6 for 0.6% daily standard deviation. The calculator does not annualize from annual volatility; it assumes the input is already daily and scales it by the square root of days.

Enter expected return over timeframe as the return you expect for the whole selected horizon, not a daily return. If your timeframe is 182.5 days and your expected return for that half-year is 10%, enter 10. Then enter timeframe in days and choose the VaR tail probability. The available choices are 10% VaR, 5% VaR, and 1% VaR. Smaller tail probabilities use larger z-scores and usually produce more conservative loss estimates.

Use VaR together with other risk and return measures. Compare drawdown with the maximum drawdown calculator, total performance with the holding period return calculator, and annualized performance with the annualized rate of return calculator. For compounding scenarios after a loss, use the compound interest calculator.

Formula

The selected z-scores are 1.2816 for 10% VaR, 1.6449 for 5% VaR, and 2.3263 for 1% VaR. The calculator calculates:

$\text{volatility move} = \text{z-score} \times \sqrt{\text{timeframe days}} \times \frac{\text{daily standard deviation}}{100}$

The expected return input is converted to a decimal:

$\text{expected period return} = \frac{\text{expected return}}{100}$

Then the loss rate is floored at zero:

$\text{loss rate} = \max\left(0,\text{volatility move} - \text{expected period return}\right)$

Finally:

$\text{Value at Risk} = \text{portfolio value} \times \text{loss rate}$

$\text{portfolio after VaR loss} = \text{portfolio value} - \text{Value at Risk}$

This is a one-sided normal approximation. It does not model fat tails, jumps, changing volatility, liquidity constraints, or position-specific nonlinear payoffs.

Checking the primary result

The default inputs are a $1,000,000 portfolio, 0.6% daily standard deviation, 10% expected return over the timeframe, 182.5 days, and 5% VaR. The 5% tail uses a z-score of 1.6449.

Daily standard deviation as a decimal is:

$0.6\% \div 100 = 0.006$

The volatility move is:

$1.6449 \times \sqrt{182.5} \times 0.006 = 0.13332825$

As a percentage, the calculator displays 13.33%. The expected period return is:

$10\% \div 100 = 0.10$

The implied loss rate is:

$\max\left(0,0.13332825 - 0.10\right) = 0.03332825$

That is 3.33%. The dollar Value at Risk is:

$\$1{,}000{,}000 \times 0.03332825 = \$33{,}328.25$

The portfolio after the VaR loss is:

$\$1{,}000{,}000 - \$33{,}328.25 = \$966{,}671.75$

So the calculator reports $33,328.25 as 5% VaR over 182.5 days, with a 3.33% implied loss rate, 1.6449 z-score, 13.33% volatility move, 10.00% expected period return, and $966,671.75 after the modeled loss.

How VaR is used

VaR is popular because it translates risk into one currency amount over one horizon. A risk manager can say, under this model, losses are expected to exceed a certain dollar amount only a selected percentage of the time. That makes VaR useful for comparing portfolios, setting risk limits, sizing positions, communicating downside exposure, and monitoring changes in volatility.

The chosen horizon and confidence level are part of the result. A 1-day 5% VaR is not comparable with a 30-day 1% VaR unless the difference is clearly stated. The model assumptions are also part of the result. This calculator assumes normally distributed returns and square-root-of-time volatility scaling. Those assumptions can be reasonable for simple screening, but they often understate crisis losses, concentrated positions, and nonlinear instruments.

Use VaR as a threshold estimate, not as a worst-case number. If the model says 5% VaR is $33,328, it means losses above that amount are in the modeled tail. It does not say whether a tail loss might be $34,000, $100,000, or more. Expected shortfall, stress tests, historical scenarios, and liquidity analysis can add context beyond this single threshold.

Limitations and tips

• Enter daily volatility, not annual volatility.
• Keep the expected return input aligned with the full timeframe.
• Compare VaR results only when horizon, tail probability, and model method match.
• Use zero expected return for a conservative quick screen if you do not have a defensible forecast.
• Remember that normal VaR can understate extreme market moves and correlation breakdowns.
• Treat the output as one risk lens, not a buy, sell, or hold recommendation.

Sources

• MSCI, 1996 RiskMetrics Technical Document — reference for RiskMetrics-style market risk measurement.
• Corporate Finance Institute, Value at Risk — VaR definition and interpretation.
• Wikipedia, Value at risk — reference overview of VaR methods and limitations.