# Value at risk (VaR)

Value at risk (VaR) is an estimate of the loss threshold that a position or portfolio is expected to exceed with a specified probability over a specified time horizon.

## What it means

Value at risk puts a number on a specific question: how large could a loss be over a chosen period before it enters the worst portion of a modeled range of outcomes? It is usually stated as a monetary amount alongside a time horizon and confidence level. Without both, a VaR figure is incomplete.

For example, a one-day 95% VaR of US$165 means that, under the model, the loss exceeds US$165 on about 5% of days. It does **not** mean the largest possible one-day loss is US$165. VaR describes a threshold, not the size of losses beyond it.

VaR can be calculated for one stock or an entire portfolio. Different methods—including historical simulation, parametric models and Monte Carlo simulation—can produce different estimates from the same holdings.

## How it is calculated

A simple parametric calculation assumes daily returns are normally distributed and sets expected daily return to zero:

`One-day 95% VaR (US$) = V × 1.645 × σ_daily`

- `V` is the position's current market value in US$.
- `1.645` is approximately the one-sided 95% standard-normal cutoff, with no units.
- `σ_daily` is estimated standard deviation of daily returns, expressed as a decimal per day. For example, 2% daily volatility is `0.02`.
- `VaR` is the resulting estimated loss threshold in US$ for one trading day.

The formula gives a positive loss amount, not a forecast of the next day's return. The normal-return and zero-expected-return assumptions simplify the calculation. A model with a nonzero expected return, or a different distribution, would use a different threshold. Estimating portfolio VaR also requires accounting for how holdings move together; adding individual VaR figures generally does not give portfolio VaR.

## Worked example

Assume a **hypothetical** stock position worth US$5,000 and estimated daily return volatility of 2%.

1. Convert volatility to a decimal: `2% = 0.02`.
2. Calculate one standard deviation in dollars: `US$5,000 × 0.02 = US$100`.
3. Apply the one-sided 95% cutoff: `US$100 × 1.645 = US$164.50`.

Rounded to the nearest dollar, the position's one-day 95% VaR is **US$165** under these assumptions. The modeled chance of a one-day loss larger than that threshold is about 5%. That does not say whether an actual loss beyond the threshold would be US$166, US$500 or more.

## Why it matters before you trade

A pre-trade analysis can compare a proposed position's modeled downside threshold with its size and the rest of a basket. The same percentage volatility produces a larger dollar VaR on a larger position. For a basket, correlations matter: holdings that tend to fall together can create more combined risk than their names alone suggest.

VaR is one input, not a complete description of risk. A sharp overnight gap, trading halt or unusually thin market may produce a loss unlike the returns used to estimate volatility. VaR also does not include the cost of getting an order filled or exiting a position unless the particular model explicitly incorporates those costs.

## How PreTrAIde uses it

PreTrAIde includes **one-day 95% value at risk** in its deterministic quantitative layer, alongside daily volatility, liquidity and other measures. Its pre-trade analysis assesses a user-built stock basket and each line before an order is placed, returning a GO, NO-GO or MODIFY verdict with a risk assessment and plain-language reasoning. Those verdicts are decision support, not recommendations.

PreTrAIde also offers a no-sign-up value-at-risk calculator. Its trading-cost-by-stock pages include one-day 95% VaR figures for stocks in the daily refreshed universe. The product facts do not specify the exact VaR formula used, so the simple formula above should not be read as PreTrAIde's implementation.

## Common mistakes

- **Treating 95% as a guarantee:** Losses can exceed 95% VaR; the measure does not cap them.
- **Omitting the horizon:** One-day VaR and longer-horizon VaR answer different questions.
- **Confusing VaR with expected shortfall:** VaR marks a threshold; expected shortfall estimates the average loss beyond a threshold under a specified model.
- **Ignoring assumptions:** Estimated volatility and return behavior can change, especially around events.
- **Adding stock-level figures without checking correlation:** Portfolio risk depends on how positions move together.

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Source: https://pretraide.com/glossary/value-at-risk