Value at Risk (VaR) Calculator

A Value at Risk (VaR) calculator estimates the maximum potential loss from an investment or portfolio over a specified time horizon at a given confidence level. It is used by risk managers, traders, banks, and sophisticated investors who want to quantify downside risk in a single, standardised number. VaR is one of the most widely used risk metrics in professional finance and regulatory reporting.

How to Use the VaR Calculator

1. Enter the total value of the portfolio or investment position.
2. Input the daily or annualised standard deviation (volatility) of returns.
3. Set the confidence level, typically 95% or 99%.
4. Choose the time horizon: 1 day, 10 days, or 1 year are most common.
5. The calculator outputs the VaR figure: the maximum expected loss at the chosen confidence level over the given period.

The Formula

The parametric (variance-covariance) VaR formula, assuming normally distributed returns:

VaR = Portfolio Value multiplied by Z-score multiplied by Standard Deviation multiplied by square root of Time Horizon

Where:

Portfolio Value = current market value of the portfolio.

Z-score corresponds to the chosen confidence level: 1.645 for 95%, 2.326 for 99%, and 1.282 for 90%.

Standard Deviation = the standard deviation of returns for the base period (usually daily).

Time Horizon = number of periods. For a 10-day VaR based on daily volatility, multiply the daily VaR by the square root of 10.

For example, at 99% confidence, 1-day VaR: VaR = Portfolio Value multiplied by 2.326 multiplied by Daily Standard Deviation

Real-World Example

A portfolio is worth £1,000,000. The daily standard deviation of returns is 1.2%. You want to know the 1-day 99% VaR.

VaR = £1,000,000 multiplied by 2.326 multiplied by 0.012 = £1,000,000 multiplied by 0.02791 = £27,910

Interpretation: you can be 99% confident that the portfolio will not lose more than £27,910 in a single day under normal market conditions. Equivalently, there is a 1% probability of losing more than £27,910 in one day.

For a 10-day 99% VaR: 10-Day VaR = £27,910 multiplied by square root of 10 = £27,910 multiplied by 3.162 = £88,238

This square-root-of-time scaling assumes returns are independent across days, which is a simplification that holds reasonably well in normal markets but breaks down in crises.

Limitations of VaR

VaR has several important limitations that risk managers must understand.

VaR says nothing about losses beyond the confidence threshold. A 99% 1-day VaR of £28,000 means you expect losses to exceed that amount on 1% of days, but it gives no indication of how large those excess losses might be. The loss on the worst 1% of days could be £30,000 or £300,000.

VaR assumes normal distribution of returns. In practice, financial returns have "fat tails": extreme events happen more frequently than a normal distribution predicts. The 2008 financial crisis and 2020 COVID crash produced losses that would have been rated as almost impossibly rare under standard VaR models.

Expected Shortfall (CVaR) addresses this by measuring the average loss in the worst scenarios beyond the VaR threshold, providing a more complete picture of tail risk.

VaR also fails during market crises when correlations between assets spike. Diversification benefits vanish precisely when they are most needed, making portfolio-level VaR systematically understate risk during extreme market conditions.

Frequently Asked Questions

What is the difference between 95% and 99% VaR? A 95% VaR means you expect losses to exceed the stated amount on 5% of days (approximately 12 trading days per year). A 99% VaR is more conservative: losses should exceed it on only 1% of days (approximately 2.5 trading days per year). Regulators such as the Basel framework for banks often require 99% VaR over a 10-day horizon. A higher confidence level results in a larger VaR figure.

How is historical VaR different from parametric VaR? The parametric (variance-covariance) method assumes returns are normally distributed and uses the formula above. Historical simulation VaR instead takes actual historical daily returns, orders them from worst to best, and reads off the loss at the chosen percentile. Historical VaR captures the actual return distribution including fat tails, but is limited by the length of the historical data set and may not capture risks not present in the sample period.

What is Expected Shortfall (CVaR) and is it better than VaR? Expected Shortfall, also called Conditional Value at Risk (CVaR), measures the expected loss given that the loss exceeds the VaR threshold. It answers the question: "If we do have a bad day (beyond VaR), how bad is it on average?" CVaR is considered superior to VaR for risk management because it characterises the full tail of the loss distribution rather than just its starting point. Many regulators and risk managers are moving toward CVaR as the primary risk measure.

Can VaR be used for illiquid assets? Standard VaR assumes assets can be liquidated at the current price within the time horizon. For illiquid assets such as private equity, real estate, or thinly traded bonds, this assumption breaks down. Liquidity-adjusted VaR attempts to account for the bid-offer spread and market impact of selling, which can significantly increase the effective risk measure. For highly illiquid portfolios, VaR may be a poor risk measure regardless of the method used.

VaR by confidence and horizon

The confidence level and the horizon are two dials, and they move the answer very differently. The table below holds a portfolio at £1,000,000 with a daily standard deviation of 1.2 per cent, and a mean return of zero, so the arithmetic is the clean case of the formula on this page. Each row gives the one-sided z-score for its confidence level, the one-day figure, the same figure as a share of the portfolio, and the expected shortfall that goes with it.

The horizon scales as the square root of time, which is why the figure does not grow in proportion to the days. Ten days is not ten times one day, it is 3.1623 times one day.

The worked example above this section prints £27,910 for the one-day case and £88,238 for the ten-day case on the same inputs. The published method gives £27,916.18 and £88,278.70. The ten-day figure on the page does not follow from its own one-day figure either: multiplying £27,910 by 3.162 gives £88,251, so the printed number is short of both routes by a small margin. Where the two disagree, use the recomputed values.

Expected shortfall alongside VaR

A single VaR figure marks the edge of the tail and says nothing about what lies beyond it. Expected shortfall, also called conditional value at risk, answers the next question: if the loss does exceed the threshold, how large is the average loss? Under a normal distribution it has a closed form, the volatility multiplied by the density at the z-score and divided by the tail probability.

At 99 per cent the average loss beyond the threshold is 1.1457 times the threshold itself, or £31,982.56 against £27,916.18. At 90 per cent the ratio is wider at 1.3694, because the tail being averaged is thicker relative to the point that starts it. One consequence is worth stating: the shortfall figure inherits the normal-distribution assumption twice over, once for the density and once for the tail probability, so it is more sensitive to fat tails than the VaR figure it accompanies. A historical estimate sidesteps the assumption by averaging the actual observations beyond the threshold, which needs a sample long enough to contain a meaningful number of them.

What the calculator computes

The component takes a list of returns, one per line, and requires at least ten of them before it will calculate. It sorts them, takes the value at the percentile that matches the confidence level as the historical result, and computes the mean and the standard deviation of the same list for the parametric result. The parametric figure is the absolute value of the mean minus the z-score multiplied by the standard deviation, multiplied by the portfolio value. Several details follow from that.

The page's formula omits the mean return, while the tool subtracts it. A sample with a positive mean gives a parametric figure smaller than the formula alone would produce, and a sample with a negative mean gives a larger one, so a reader comparing the two methods should use the same series in both. The standard deviation is the population form, dividing by the count rather than by the count minus one, which is the usual choice for a fixed historical window. The confidence control on the page displays 95, 99 and 97.5 per cent, but its options carry no values, so the parametric result currently uses the 95 per cent z-score of 1.645 whatever the selector shows, and the historical result comes back empty. Read the confidence columns of the tables here as the published parameters rather than as a description of what the page currently returns.

The sources for the parameters

The z-scores in the first table, 1.28155, 1.64485, 1.95996 and 2.32635, are the standard normal quantiles for the four confidence levels, and the square-root-of-time rule that scales them across horizons comes from the RiskMetrics Technical Document published by J.P. Morgan in 1996, which also fixed the 1.645 and 2.326 figures in the working vocabulary of market risk. The ten-day horizon at 99 per cent is the one the Basel Committee's capital framework adopted for trading-book risk, which is why that pair of settings is quoted more often than any other. Both conventions assume independent returns across the horizon, an assumption the limitations section above already qualifies.

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