# Value at Risk (VaR) > Value at risk estimates the loss a portfolio should not exceed with a given confidence over a set period. Learn the three methods, an example and the limits. Source: https://learn.tradelabsai.com/portfolio/value-at-risk/ Track: Portfolio and Performance · Level: Advanced · Updated: 2026-10-03 Publisher: TradeLabs AI (https://tradelabsai.com). Education, not financial advice. Cite as: TradeLabs Learn, "Value at Risk (VaR)", https://learn.tradelabsai.com/portfolio/value-at-risk/ Value at risk (VaR) is one of the most widely used risk measures in finance. It answers the question: over a given period, what is the loss we should not exceed with a certain level of confidence? A one day 99% VaR of $1 million means that on 99 days out of 100, losses should be smaller than $1 million. Banks, funds and trading desks use VaR to set limits, report risk and, for banks, historically to calculate regulatory capital. Its simplicity is its strength and its weakness: it says nothing about how bad losses can be on the remaining days. ## The three ingredients | Ingredient | Common choices | |---|---| | Time horizon | 1 day for trading desks, 10 days for some regulation, 1 month for funds | | Confidence level | 95% or 99% | | Method | Parametric, historical or Monte Carlo | ## Three calculation methods | Method | How it works | Strengths | Weaknesses | |---|---|---|---| | Parametric (variance covariance) | Assumes normal returns; VaR = z score times volatility times value | Fast, simple | Underestimates fat tails | | Historical simulation | Applies actual past daily returns to today's portfolio and takes the chosen percentile loss | No distribution assumption | Limited by the history window | | Monte Carlo simulation | Simulates many scenarios from a model | Flexible, handles options | Model dependent, computationally heavy. See [Monte Carlo Simulation](https://learn.tradelabsai.com/research/monte-carlo-simulation/) | ## A parametric example ``` VaR = z × Daily volatility × Portfolio value ``` The z score is about 1.645 for 95% and 2.326 for 99% confidence, from the normal distribution. See [Normal Distribution](https://learn.tradelabsai.com/math/normal-distribution/). **Example: One day VaR for a $1 million portfolio** A $1,000,000 portfolio has daily volatility of 1.2%. One day 95% VaR is 1.645 times 1.2% times $1,000,000, about $19,740. One day 99% VaR is 2.326 times 1.2% times $1,000,000, about $27,912. Scaling to 10 days with the square root of time rule, 95% VaR is about $19,740 times the square root of 10, roughly $62,400. The square root rule assumes independent returns and an unchanged portfolio, which may not hold. Try your own figures with the [Portfolio Volatility and VaR Calculator](https://learn.tradelabsai.com/tools/var-calculator/). ## Historical VaR in practice Take the last 500 daily returns of the current portfolio's holdings, compute what each day would mean for today's positions, sort the results and pick the 5th percentile loss for 95% VaR (the 25th worst of 500). It captures real fat tails and correlations from that window, but if the window contains no crisis, VaR will look deceptively low. ## Limitations | Limitation | Explanation | |---|---| | Says nothing beyond the threshold | A 99% VaR of $1 million is consistent with a 1% chance of losing $50 million. See [Expected Shortfall (CVaR)](https://learn.tradelabsai.com/portfolio/expected-shortfall/) | | Normal assumption | Real returns have fat tails, so parametric VaR understates extreme losses. See [Fat Tails](https://learn.tradelabsai.com/math/fat-tails/) | | Backward looking | Calm periods produce low VaR just before crises | | Not always additive | The VaR of a combined portfolio can exceed the sum of parts in some cases | | Liquidity ignored | Assumes positions can be exited at market prices. See [Liquidity Risk](https://learn.tradelabsai.com/portfolio/liquidity-risk/) | | Gaming | Positions can be structured to look safe under VaR while hiding tail risk | ## VaR in the 2008 crisis Many banks' VaR models showed moderate risk before 2008, because they relied on calm recent history and assumed liquid markets. Losses then exceeded VaR far more often than the models implied. The experience led regulators to add stressed VaR and, later, to move toward expected shortfall for bank market risk capital. See [The 2008 Financial Crisis](https://learn.tradelabsai.com/history/the-2008-financial-crisis/). ## Backtesting VaR Compare actual daily losses with VaR. At 99% confidence, losses should exceed VaR on about 1% of days, about 2 or 3 days a year. Many more exceptions mean the model underestimates risk. Banks are required to backtest their models. ## Using VaR well 1. **Use it with stress tests** and expected shortfall. See [Stress Testing and Scenario Analysis](https://learn.tradelabsai.com/portfolio/stress-testing/). 2. **Set limits** in VaR terms for desks and strategies. See [Risk, Position, Loss and Drawdown Limits](https://learn.tradelabsai.com/portfolio/risk-limits/). 3. **Decompose VaR** by position to see risk drivers. See [Risk Contribution and Risk Decomposition](https://learn.tradelabsai.com/portfolio/risk-contribution/). 4. **Never treat it as the worst case.** ## Frequently asked questions ### What is value at risk? An estimate of the loss a portfolio should not exceed over a set period with a given confidence level, such as 99% over one day. ### How is VaR calculated? With parametric formulas assuming normal returns, historical simulation using past returns, or Monte Carlo simulation from a model. ### What is the main weakness of VaR? It says nothing about the size of losses beyond the threshold, and it often underestimates risk when returns have fat tails or markets turn illiquid. Next, learn the measure that looks beyond VaR in [Expected Shortfall (CVaR)](https://learn.tradelabsai.com/portfolio/expected-shortfall/). ## Continue learning - Next lesson: [Expected Shortfall (CVaR)](https://learn.tradelabsai.com/portfolio/expected-shortfall/) - Previous lesson: [Active vs Passive Investing](https://learn.tradelabsai.com/portfolio/active-vs-passive-investing/) - Related: [Active vs Passive Investing](https://learn.tradelabsai.com/portfolio/active-vs-passive-investing/): Active investing tries to beat the market; passive investing tracks it at low cost. Learn the evidence on performance, the impact of fees and how to choose. - Related: [Expected Shortfall (CVaR)](https://learn.tradelabsai.com/portfolio/expected-shortfall/): Expected shortfall, or CVaR, is the average loss on the worst days beyond the VaR threshold. Learn the formula, a worked example and why regulators adopted it. - Related: [Portfolio Volatility and VaR Calculator](https://learn.tradelabsai.com/tools/var-calculator/): Free value at risk calculator. Enter portfolio value, daily volatility, confidence level and horizon to estimate VaR and expected shortfall in dollars. - Related: [Stress Testing and Scenario Analysis](https://learn.tradelabsai.com/portfolio/stress-testing/): Stress testing asks how a portfolio would fare in extreme but plausible events. Learn historical and hypothetical scenarios and reverse stress tests. - Related: [Fat Tails](https://learn.tradelabsai.com/math/fat-tails/): Fat tails mean extreme market moves happen far more often than the normal curve predicts. Learn the evidence, the causes, how to measure them and how to manage them. - Related: [Risk, Position, Loss and Drawdown Limits](https://learn.tradelabsai.com/portfolio/risk-limits/): Risk limits turn a risk policy into hard rules on position size, exposure, daily loss and drawdown. Learn how to set them, enforce them and avoid mistakes.