Value at Risk (VaR) Calculator
Introduction
Value at Risk, usually shortened to VaR, is one of the most common ways to summarize portfolio downside in a single number. Instead of describing every possible return, VaR asks a practical question: how large could a loss plausibly be over a chosen period, at a chosen confidence level, under the model assumptions? This calculator uses the classic parametric or variance-covariance approach. That means it starts with your portfolio value, your estimate of daily volatility, the number of days you want to examine, and a confidence level such as 90%, 95%, or 99%.
The result is shown both as a dollar amount and as a percentage of the portfolio. That combination is useful because dollar VaR is easy to communicate, while percentage impact helps you compare positions of different sizes. VaR is popular because it is simple to report and simple to compare across desks or strategies. At the same time, it is easy to misuse if you forget what it actually says. This page is designed to help with both parts: first, the calculator gives you the number; then the explanation below shows what the number means, what each input does, and where the method can break down.
How to use this VaR calculator
Using the calculator is straightforward, but it helps to know what the inputs represent before you type anything. Start with the portfolio value, which is the current market value of the holdings or position you want to measure. Then enter daily volatility as a percentage. If your daily standard deviation of returns is 1.2%, you should enter 1.2, not 0.012. Next, choose the time horizon in trading days. A one-day horizon is common for short-term risk control, while 5-day or 10-day horizons are often used for reporting or planning. Finally, pick the confidence level. A higher confidence level produces a higher VaR because it pushes the threshold deeper into the loss tail.
Once you press Calculate VaR, the tool estimates the loss threshold implied by the parametric normal model. Read the output as a model-based cutoff, not as a promise. If the calculator returns $6,244 at 95% over 10 days, the intended reading is that losses should stay below about $6,244 in roughly 95 out of 100 comparable 10-day periods, assuming the volatility estimate and normal-distribution framework are reasonable. In other words, the number separates “usual enough to fit inside the confidence band” from “rare enough to fall beyond it.”
- Enter current portfolio value in dollars.
- Enter daily volatility as a percentage.
- Enter the time horizon in whole trading days.
- Select a confidence level.
- Click the button and read the result as a threshold, not a maximum loss.
What Value at Risk (VaR) means
Value at Risk (VaR) is a statistical estimate of how much you could lose over a chosen time horizon at a chosen confidence level. A 1-day VaR of $10,000 at 95% confidence is commonly read as: “Based on the model assumptions, there is a 95% chance the loss over one day will be no more than $10,000, and a 5% chance it will be more than $10,000.”
That sentence is useful because it compresses risk into language a portfolio manager, client, or risk committee can compare across positions. Still, the wording matters. VaR does not say a 5% loss occurs exactly one day in twenty, and it does not say the remaining 5% is only a little worse. It is a threshold estimate built from a model. VaR is widely used for setting risk limits, comparing portfolio risk across strategies, and communicating downside in a single dollar figure. It is not a guarantee and it is not the worst-case loss.
Inputs (what to enter)
Each input affects the result in a different way. Portfolio Value ($) scales the answer directly: double the position size and, all else equal, you double the dollar VaR. Daily Volatility (%) measures how much returns typically move from day to day. This is often estimated from historical data, a risk model, or implied volatility proxies. Time Horizon (days) tells the calculator how long risk has time to accumulate. Under the standard scaling rule used here, multi-day volatility grows with the square root of time rather than linearly. Confidence Level chooses how far into the tail you want the threshold to sit.
If you are unsure what number to use for volatility, a practical approach is to stay consistent with your data frequency and portfolio definition. Daily volatility for an equity portfolio should come from daily returns on that same portfolio or a close proxy, not from annualized volatility pasted into the daily input field. Similarly, the horizon should reflect the question you are asking. Traders often focus on short horizons, while longer horizons may be used for scenario planning, policy limits, or liquidity-aware review.
Formulas (including time scaling)
Under the parametric normal model, VaR is calculated as:
VaR ($) = V × σd × √T × z
- V = portfolio value (in dollars)
- σd = 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 σd × √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
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 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 example
Scenario: Portfolio value = $100,000; daily volatility = 1.20%; horizon = 10 days; confidence = 95%.
- Convert volatility to decimal: σd = 1.20% = 0.012
- Time scaling: √T = √10 ≈ 3.1623
- z-score (95%): z ≈ 1.6449
- Compute: VaR = 100,000 × 0.012 × 3.1623 × 1.6449 ≈ $6,244
Interpretation: Under the 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, that is about 6.24%. Notice how each ingredient contributes: if volatility were lower, the number would fall; if the horizon were shorter, the √T term would shrink; if confidence were raised to 99%, the z-score would rise and the VaR would increase even if the portfolio itself did not change.
Assumptions and limitations
The parametric method is fast and convenient, which is why it remains common, but its convenience comes from assumptions. The biggest assumption is that returns are approximately normal and that volatility is adequately summarized by a single standard deviation number. Real markets often do not behave that cleanly. Heavy tails, volatility clustering, changing correlations, and liquidity shocks can all make realized losses exceed model-based expectations more often than 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 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.
Quick comparison table (confidence levels)
| Confidence level | Tail probability | Typical z-score | Plain-language meaning |
|---|---|---|---|
| 90% | 10% | ≈ 1.282 | Loss should stay below VaR in about 9 out of 10 periods under the model. |
| 95% | 5% | ≈ 1.645 | Loss should stay below VaR in about 19 out of 20 periods under the model. |
| 99% | 1% | ≈ 2.326 | Loss should stay below VaR in about 99 out of 100 periods under the model. |
When VaR is useful in practice
VaR is most helpful when you need a common language for downside risk. A risk manager can compare desks with very different holdings, a trader can see how changing volatility alters the limit picture, and an investor can translate percentage uncertainty into a dollar loss threshold that feels concrete. Because the output is standardized, VaR can also help with position sizing, budget discussions, internal reporting, and conversations about whether current exposure is appropriate for the horizon being considered.
That said, the best habit is to use VaR as a starting point for better questions. If the number suddenly rises, ask whether volatility increased, exposure increased, or the chosen horizon or confidence changed. If the portfolio contains options, credit tail risk, thinly traded assets, or concentrated bets, follow up with stress tests and scenario analysis. VaR is a useful dashboard gauge, but the road still matters.
Mini-game: Tail-Risk Desk
This optional arcade-style mini-game turns the VaR idea into a fast sorting challenge. Each incoming scenario card shows a portfolio value, daily volatility, time horizon, and confidence level. Your job is to place the desk selector over the correct VaR band before the scenario reaches the decision line. Most of the run uses portfolio-impact bands, so you are effectively estimating σ × √T × z. During stress shifts, the floor switches to dollar VaR bands, which means portfolio value suddenly matters too. It is a quick way to build intuition for why higher volatility, longer horizons, higher confidence, and larger books produce bigger risk numbers.