Value at Risk (VaR) Calculator

What a VaR threshold means

Value at Risk (VaR) is a model-based estimate of a portfolio loss threshold over a chosen horizon and confidence level. In the calculator, a 1-day VaR of $10,000 at 95% confidence is commonly read as: under the model assumptions, losses are expected to stay at or below $10,000 about 95% of the time, while roughly 5% of comparable periods may end worse than that. The figure is useful because it compresses the downside into a single number that can be compared across books and strategies.

That usefulness comes with an important caution. VaR is not a guarantee, and it is not the worst loss you could ever see. It is only a cutoff built from a distributional assumption and the inputs you provide. VaR is often used for internal limits, exposure comparisons, and risk reporting, but it should be paired with stress testing or tail-risk measures when the portfolio contains options, illiquid assets, or concentrated bets. In other words, VaR says where the model's normal zone ends; it does not tell you what happens after the line is crossed.

Inputs (what to enter)

Each field in this VaR calculator pushes the result in a different direction. Portfolio Value ($) scales dollar VaR directly, so a larger book produces a larger dollar loss threshold even if the return profile is unchanged. Daily Volatility (%) captures how rough the daily return distribution is; if volatility rises, the threshold rises too. Time Horizon (days) extends the window over which losses can accumulate. Under the standard rule used here, that multi-day effect grows with the square root of time, not in a straight line. Confidence Level chooses how deep into the loss tail the calculator looks, so a 99% setting produces a larger number than a 95% setting when everything else stays the same.

If you are deciding what value to enter for volatility, consistency matters more than any single source. Use a daily estimate that matches the asset mix and the measurement frequency of the portfolio itself. Do not paste in an annualized number unless you first convert it into a daily figure, and do not mix return data from one instrument with a portfolio that behaves very differently. The same caution applies to the horizon: a 1-day VaR is useful for short-term trading risk, while a 10-day or 20-day horizon can be more useful for policy, planning, or capital review.

VaR formula and time scaling

Under the parametric normal model, the calculator uses the following VaR formula:

VaR ($) = V × σ_d × √T × z

• V = portfolio value (in dollars)
• σ_d = daily volatility (as a decimal, so 1.2% → 0.012)
• T = time horizon in days
• z = z-score for the confidence level (standard normal quantile)

The square-root-of-time rule (√T) is the usual way to scale daily volatility to a multi-day horizon when daily returns are assumed independent and identically distributed. A useful shortcut is that percentage VaR does not depend on portfolio value at all; it is simply σ_d × √T × z. Dollar VaR then multiplies that percentage loss by the portfolio value. This is why two portfolios with the same return volatility profile can have the same percentage VaR but very different dollar VaR.

MathML version of the VaR formula

Typical z-scores are approximately 1.2816 for 90%, 1.6449 for 95%, and 2.3263 for 99%. Because the z-score rises as confidence rises, the 99% VaR will always be larger than the 95% VaR if the other inputs stay the same.

How to interpret the VaR result

VaR is best read as a threshold rather than a promise. If the calculator returns $X at 95% over T days, the model implies losses will be greater than $X about 5% of the time over that horizon. That is why VaR is often used for setting limits: it gives you a boundary that can be monitored, compared, and escalated when breached.

Just as important is what VaR does not tell you. It does not describe how bad losses can be once you are already in the tail beyond the cutoff. Two portfolios can have the same VaR but very different tail severity if one has options, illiquid positions, concentrated exposures, or jump risk. VaR also says nothing by itself about the path to the loss, the speed of liquidation, or the effect of stressed correlations. That is why practitioners often pair VaR with stress testing, scenario analysis, drawdown limits, and Expected Shortfall (CVaR), which estimates the average loss in the worst part of the distribution.

Worked VaR example

Scenario for this VaR calculator: Portfolio value = $100,000; daily volatility = 1.20%; horizon = 10 days; confidence = 95%.

1. Convert volatility to decimal: σ_d = 1.20% = 0.012
2. Time scaling: √T = √10 ≈ 3.1623
3. z-score (95%): z ≈ 1.6449
4. Compute: VaR = 100,000 × 0.012 × 3.1623 × 1.6449 ≈ $6,244

Interpretation: Under the calculator's model assumptions, there is a 95% chance the 10-day loss will be about $6,244 or less, and a 5% chance it will exceed that amount. Expressed as a share of the portfolio, the loss threshold is about 6.24%. The example shows the role of each input clearly: lower volatility pushes the answer down, a shorter horizon reduces the square-root-of-time term, and a higher confidence level increases the z-score and therefore increases VaR even when the portfolio value stays fixed.

VaR assumptions and limitations

The parametric method is fast and convenient, which is why it remains common, but that convenience depends on a chain of assumptions. The biggest assumption is that daily returns are approximately normal and that volatility can be summarized with a single standard deviation number. Real markets do not always cooperate. Heavy tails, volatility clustering, sudden correlation shifts, and liquidity shocks can all push realized losses beyond what a simple normal VaR would suggest.

• Normality and thin tails: Parametric VaR assumes returns are approximately normal. Real markets can have fat tails, meaning extreme losses may occur more often than the model implies.
• Volatility is treated as stable: Using one daily volatility estimate assumes risk conditions are reasonably steady. In practice, volatility often jumps during stress.
• Independence and √T scaling: The square-root-of-time rule assumes returns are independent and similarly distributed through time. Serial correlation, regime shifts, illiquidity, and changing volatility can make that scaling inaccurate.
• Mean return is often ignored: Over short horizons the mean is usually small relative to volatility, so many VaR implementations effectively assume zero drift. That is usually acceptable for short-term risk measurement, but it is still an assumption.
• Not a maximum loss: A 99% VaR still leaves 1% of outcomes worse than VaR, and those tail outcomes can be much larger.
• Portfolio structure matters: A single volatility input cannot capture nonlinear option payoffs, concentration risk, changing correlations, market impact, or forced selling conditions.

For that reason, VaR works best as one tool inside a wider risk framework. It is especially useful for rough sizing, day-to-day monitoring, and internal communication, but it should not be your only guide when exposure is concentrated, markets are stressed, or the portfolio contains instruments with nonlinear behavior. Disclaimer: this calculator provides an estimate for educational and planning purposes and is not financial advice.

Method used by this VaR calculator (Parametric / Variance-Covariance VaR)

This calculator uses parametric VaR, also called variance-covariance VaR. Compared with historical simulation or Monte Carlo simulation, it is lightweight and fast because it only needs a volatility estimate and a confidence-based z-score. That simplicity is an advantage when you need a quick benchmark, but it is also why the assumptions above matter so much. Historical simulation relies on realized return history, while Monte Carlo builds many possible paths from an assumed process. This page deliberately keeps the method transparent so you can see exactly where the output comes from.

Common VaR confidence levels

When VaR is useful in practice

VaR is most useful when you need a shared language for downside risk. A risk manager can compare desks with different holdings, a trader can see how a change in volatility moves the threshold, and an investor can translate a percentage uncertainty into a dollar number that is easier to discuss. Because the output is standardized, it can help with position sizing, limit checks, internal reporting, and conversations about whether the current exposure still fits the intended horizon.

The best use of VaR is as a starting point for better questions. If the number jumps, ask whether volatility rose, the book got larger, the horizon changed, or confidence was tightened. If the portfolio contains options, credit tail risk, thinly traded assets, or highly concentrated positions, follow up with scenario analysis and stress tests. VaR is a helpful dashboard gauge, but it is only one gauge.