Value at Risk Calculator (VaR)

How to use the Value at Risk calculator

What this calculator does

This calculator estimates parametric Value at Risk, a loss threshold for a portfolio over a chosen time horizon and confidence level. It applies a normal-distribution z-score and the square-root-of-time rule to a one-day standard deviation, then offsets that risk amount by the expected return for the whole horizon. The result is a compact planning estimate, not a prediction of the worst possible loss. It does not model fat tails, jumps, changing correlations, liquidity constraints, nonlinear derivatives, or losses beyond the VaR threshold.

When to use it

Use this estimate to compare the risk of two portfolios on a consistent basis, set an internal risk limit, test how a longer holding period changes the loss threshold, or create a quick briefing for a risk review. It is most defensible when the volatility estimate is recent, the horizon convention is consistent, and the portfolio behaves approximately like the distribution assumed by the model.

How to calculate

1. The calculator opens with a complete demonstration: a $1,000,000 portfolio, 0.6% daily standard deviation, 10% expected horizon return, 182.5 days, and 95% confidence. Its example XLSX is immediately available.
2. Replace each sample value with assumptions that use the same definitions and time basis. Results update live; no Calculate button is needed.
3. Read the headline Value at Risk first, then compare VaR as % of portfolio, Volatility buffer, Expected return amount, and VaR floor value.
4. Select Download Excel to create a fresh workbook from the current validated controls. Reset clears the demonstration and results; Download Excel remains unavailable until a complete valid set is entered again.

Input guide

Portfolio value is a required positive U.S.-dollar amount. Enter plain digits with an optional decimal point, such as 1000000; commas and a leading dollar sign are also accepted in standard U.S. grouping. A larger value scales every dollar output proportionally. Do not enter accounting parentheses or ambiguous decimal-comma notation.

Standard deviation is the required one-day return volatility in percent, such as 0.6 for 0.6%. It must be greater than zero and no more than 100%. Raising it increases the confidence-adjusted volatility buffer and usually increases VaR. A common mistake is entering 0.006 when the field expects percent units; that would mean 0.006%, not 0.6%.

Expected return is the required expected return over the entire selected timeframe, entered as a percent. It may be negative, zero, or positive; for example, 10 means 10%. A higher expected return offsets modeled downside, while a negative expectation increases the loss threshold. Do not annualize this value unless the chosen timeframe is one year.

Timeframe is a required positive number of calendar days, such as 182.5. The volatility term grows with the square root of days, not linearly. Longer horizons therefore increase modeled volatility, although the expected return input is not automatically rescaled. Keep the expected return and timeframe on the same horizon.

Confidence level is required and selected from 90%, 95%, 97.5%, or 99%. The corresponding one-tailed z-score is applied automatically. Higher confidence produces a more conservative threshold. For background on this statistical convention, see the original RiskMetrics technical document.

Output guide

Value at Risk is the estimated positive dollar loss threshold. A value of $33,324.49 at 95% confidence means the model places the portfolio's loss threshold at about that amount over the selected horizon under its assumptions; it does not mean losses cannot be larger. VaR as % of portfolio expresses the same threshold as a percentage, which helps compare differently sized portfolios. Zero indicates that the entered expected return fully offsets the model's confidence-adjusted volatility term.

Volatility buffer is portfolio value multiplied by the z-score, daily standard deviation, and square root of days. Expected return amount is portfolio value multiplied by the entered horizon return. VaR floor value subtracts the VaR amount from portfolio value and should be read as the modeled threshold portfolio value, not a guaranteed minimum. The breakdown table repeats the expected return rate and amount, confidence-adjusted volatility rate and amount, and final VaR rate and amount so the subtraction is auditable.

Worked example

With the startup inputs, the 95% one-tailed z-score is about 1.64485. The confidence-adjusted volatility rate is 1.64485 × √182.5 × 0.6% = 13.3324%. Multiplying by $1,000,000 gives a volatility buffer of $133,324.49. The expected return amount is 10% × $1,000,000 = $100,000.00. The positive difference is $33,324.49, so the first-open Value at Risk is $33,324.49, or 3.33% of the portfolio, and the VaR floor value is $966,675.51.