What does the VaR result mean?
VaR answers a specific question: How large a loss would be exceeded at a stated frequency over a stated period, if the model’s assumptions hold? For example, a one-day 95% VaR of US$1,645 means the model estimates a 5% chance that the position loses more than US$1,645 in one day. It does not mean the maximum possible loss is US$1,645.
Always read the dollar figure together with its horizon and confidence level. “95% VaR” alone is incomplete: a one-day estimate and a ten-day estimate answer different questions.
How the calculator works
This calculator uses the parametric, or variance-covariance, method. It assumes returns are approximately normally distributed and estimates a one-sided loss threshold:
VaR (US$) = z × daily volatility × √(days) × position value (US$)
| Input | Meaning | Unit |
|---|---|---|
| Position value | Current market value of the stock position | US$ |
| Volatility | Standard deviation of returns, entered as daily or annualized volatility | % |
| Confidence level | Sets the standard-normal multiplier, z | 95% or 99% |
| Horizon | Period over which the loss is measured | Trading days |
At 95% confidence, z ≈ 1.645. At 99% confidence, z ≈ 2.326. The higher confidence level produces a larger loss threshold for the same position, volatility and horizon.
The result can also be expressed as a share of the position: VaR (%) = z × daily volatility × √(days) × 100%, provided volatility is entered in decimal form in the formula. For example, 2% daily volatility is 0.02, not 2.
Converting annualized volatility to daily volatility
If your input is annualized volatility, convert it before applying the VaR formula:
Daily volatility = annualized volatility ÷ √252
The 252 represents a conventional approximation for the number of trading days in a year. Thus, 20% annualized volatility is approximately 20% ÷ √252 = 1.26% daily volatility. Do not enter an annualized percentage as a daily percentage: doing so would substantially overstate this formula’s result.
The horizon uses trading days, not calendar days. Under the calculator’s square-root-of-time assumption, a four-trading-day volatility estimate is twice the one-day estimate because √4 = 2. Real-world risk need not scale this way.
Worked example
Suppose, hypothetically, a stock position is worth US$50,000, its estimated daily volatility is 2%, and you choose a five-trading-day horizon at 95% confidence.
VaR = 1.645 × 0.02 × √5 × US$50,000 ≈ US$3,678
That is approximately 7.36% of the position’s value. Under the model, losses greater than about US$3,678 would occur on approximately 5% of comparable five-trading-day periods. It is an estimate, not an observed loss or a cap on losses.
If only the confidence level changes to 99%, the calculation becomes 2.326 × 0.02 × √5 × US$50,000 ≈ US$5,201. These two figures describe different thresholds for the same hypothetical position; neither predicts what will happen during a particular five-day period.
What this estimate leaves out
Parametric VaR is useful as a consistent way to compare modeled loss thresholds, but its assumptions matter:
- Fat tails: Extreme stock returns can occur more often than a normal distribution suggests. A normal-model VaR may therefore understate tail risk.
- Price gaps: Earnings announcements, other news or a market closure can lead to a jump between available prices. A stock need not move gradually through the VaR threshold.
- Changing volatility: Historical volatility may not represent volatility over the chosen future horizon, especially when market conditions change.
- Time scaling: The √(days) rule is a model assumption. Volatility clustering and changing conditions can make longer-horizon estimates inaccurate.
- Trading costs: This formula measures a modeled change in position value. It does not add the bid-ask spread, market impact, commissions or any other cost of closing a position.
- Direction and drift: The formula uses the position’s value and volatility; it does not model a directional return forecast or expected return.
VaR also cannot tell you the average loss after its threshold is breached. For that, a related measure is expected shortfall, sometimes called conditional VaR. At 95% confidence, expected shortfall estimates the average loss in the worst 5% of modeled outcomes. It, too, depends on the model and the quality of its inputs.
Using VaR in pre-trade analysis
A standalone VaR figure describes one modeled risk dimension, not whether an order should be placed or how readily it might execute. Before placing an order, other questions include how large the order is relative to daily trading volume, what spread and market impact it might face, and how the position affects portfolio concentration.
PreTrAIde offers a free value-at-risk calculator without sign-up. Its separate pre-trade analysis also estimates one-day 95% VaR alongside liquidity, volatility, execution and basket-level measures. Its GO, NO-GO and MODIFY verdicts are decision support, not investment recommendations; PreTrAIde does not place trades.