Think of a seawall built to the 99th-percentile tide. The height of the wall is a precise, defensible number, and it says nothing about the flood on the day the water goes over the top. That is value at risk (VaR) in one picture, and we will come back to the seawall at the end.
In this guide you will learn what VaR measures, the three standard ways to calculate it, a worked example you can rebuild in a spreadsheet, the places it breaks, and why the Basel Committee moved banks toward expected shortfall. It is written for investors who already know volatility and want a working grasp of tail risk.
Basel Committee standard on minimum capital requirements for market risk, captured from bis.org on 30 September 2026.
What Is Value at Risk?
Value at risk is a single number that answers one question: how much could this portfolio lose over a set period, at a chosen confidence level, under normal market conditions. A statement such as 1-day 99% VaR of $2,326 means that on 99 days out of 100 you expect to lose less than $2,326, and on the remaining day you expect to lose at least that much.
Every VaR figure has three parts. The confidence level is usually 95% or 99%. The horizon is usually one day or ten days. The portfolio value is the amount exposed. Change any one of them and the number changes, which is why a VaR quote without all three is meaningless.
The idea went mainstream in the mid-1990s when J.P. Morgan published its RiskMetrics system, and regulators adopted it soon after. The Basel Committee on Banking Supervision has built market risk capital rules around it, and the Wikipedia entry on value at risk lists its four main uses as risk management, financial control, financial reporting and regulatory capital.
1994 is the year J.P. Morgan began distributing RiskMetrics, the framework that turned VaR from a desk tool into an industry standard.
Why Value at Risk Matters
Most investors track volatility, which treats gains and losses alike. VaR converts risk into dollars of potential loss, which is the unit you actually feel. Saying your portfolio has 14% annual volatility is abstract. Saying you should expect to lose more than $3,300 on one day in twenty is something you can plan around.
It also lets you compare unlike things. A bond ladder, an equity fund and an options overlay can each be reduced to a one-day loss threshold and summed, with correlations, into one portfolio figure. That is why banks, funds and risk desks use it as a common language.
For a self-directed investor the value is discipline. A VaR limit, such as never risking more than 2% of capital on a normal day at 99% confidence, forces you to size positions before you enter them. It pairs naturally with position sizing rules like the Kelly criterion and with the maximum drawdown view of how deep losses run.
A practical habit is to record your VaR every week alongside the number of days your actual loss exceeded it. After a few months you have your own backtest, and you learn whether your estimate is too optimistic or too cautious. That feedback loop is worth more than any single calculation, because it teaches you how your own portfolio behaves under stress rather than how a textbook portfolio behaves.
2.326 is the standard normal z-score for 99% confidence, and 1.645 is the score for 95%. Multiply daily volatility by either number and you have the parametric VaR percentage.
How to Calculate Value at Risk
There are three standard methods. They differ in how they estimate the shape of tomorrow's profit and loss, so pick one and be consistent. The steps below use a hypothetical $100,000 portfolio with a daily volatility of 1.0%, which is an assumption for illustration and not a market quote.
Step 1: Choose confidence level and horizon
Start with 99% and one day if you are sizing trades, or 95% if you want a number that gets breached often enough to learn from. At 95% over 250 trading days you expect about 12 breaches a year. At 99% you expect about 2 or 3.
Match the horizon to how fast you can act. If you can exit a liquid ETF in seconds, one day is honest. If you hold small-cap stocks or corporate bonds that take days to sell, a ten-day horizon is closer to reality, and you should widen it further for anything that trades thinly. The horizon should reflect the time you would actually need to cut the position, not the time you hope it takes.
Step 2: Pick a method
Parametric (variance-covariance) assumes returns are normally distributed and multiplies volatility by a z-score. Historical simulation replays your actual past returns and reads off the loss at the chosen percentile. Monte Carlo generates thousands of random scenarios from a model and reads the percentile from those.
Method comparison
Step 3: Run the numbers
Parametric example: daily volatility of 1.0% on $100,000 is $1,000. At 95% the VaR is 1.645 times $1,000, or $1,645. At 99% it is 2.326 times $1,000, or $2,326.
To scale to ten days, multiply by the square root of 10, about 3.162. The 10-day 99% VaR is $2,326 times 3.162, roughly $7,355. The square-root rule assumes returns are independent from day to day, which real markets violate during stress.
Historical example: take the last 500 daily returns, sort them from worst to best, and at 95% read the 25th worst day. That loss, applied to today's portfolio, is your 1-day 95% VaR. At 99% you read the 5th worst day.
Monte Carlo example: simulate 10,000 one-day outcomes using your volatility and correlation model, sort them, and at 99% read the 100th worst.
Step 4: Backtest it
A VaR model you never check is a guess. Count how often actual losses exceed the VaR over a rolling window. Under the Basel backtesting approach for a 99% model over 250 days, zero to four exceptions is the green zone, five to nine is yellow, and ten or more is red and draws a capital penalty. A model that fails that test is telling you its tails are too thin.
Value at risk defined as an estimate of how much a set of investments might lose, captured from Wikipedia on 30 September 2026.
Real Examples
The clearest real test of a normal-distribution VaR is Black Monday, 19 October 1987, when the S&P 500 fell about 20.5% in one session. If daily volatility were 1%, that move sits roughly 20 standard deviations from the mean, an event a normal model says should essentially never occur in the life of the universe. It happened. Fat tails are a feature of markets, not an error in the data.
20.5% was the one-day S&P 500 drop on Black Monday, 1987, a move no parametric VaR with normal tails would have allowed for.
The 2008 crisis repeated the lesson. After Lehman Brothers filed for bankruptcy on 15 September 2008, correlations between assets jumped toward one, so diversification benefits that VaR models had counted on disappeared at the moment they were needed. Banks reported more backtesting exceptions in a few weeks than their models implied for decades.
Here is what the gap looks like in numbers. For the $100,000 portfolio with 1% daily volatility, a normal model puts 99% VaR at $2,326 and 99% expected shortfall at about $2,665, only 15% higher. Real portfolios with fat tails often show a much wider gap, which is exactly the information VaR alone hides. When the two numbers diverge, your tail is heavier than your model believes.
That experience drove the regulatory rethink. The Basel Committee's Fundamental Review of the Trading Book, finalised in January 2016, replaced the 10-day 99% VaR with expected shortfall at 97.5% confidence, and added a stressed calibration period. The Basel market risk standard sets the framework banks now work toward.
VaR versus expected shortfall
Common Mistakes
Mistake 1: Treating VaR as a maximum loss
VaR is a threshold, not a ceiling. A 99% VaR of $2,326 says nothing about whether the bad day costs $2,400 or $40,000. This is the seawall problem. Always pair VaR with a stress test that asks what happens in the tail.
Mistake 2: Trusting normal returns
The parametric method is tidy because it assumes bell-curve returns. Real returns have fatter tails and volatility that clusters, so parametric VaR understates the 99% loss in most real portfolios. If you must use it, cross-check with historical simulation.
Mistake 3: Using a calm sample
Historical VaR built on two quiet years will report a low number right before a volatile regime. Extend the window to include at least one stress period, or weight recent observations more heavily, as the RiskMetrics approach does.
Mistake 4: Scaling to ten days blindly
The square-root-of-time rule assumes independent daily returns. In a crash, losses compound and liquidity dries up, so the true 10-day loss is usually larger. Illiquid positions make the gap wider because you cannot exit at the modelled price.
Mistake 5: Ignoring that VaR is not additive
Adding the VaR of two positions overstates risk if they diversify and understates it if they crowd into the same trade. Compute VaR on the combined portfolio using a covariance matrix, and revisit it whenever correlations shift. Related measures like the Sortino ratio and the Sharpe ratio help you judge whether the risk is being paid for.
Frequently Asked Questions
What is a good value at risk number?
There is no universal good number. It depends on your risk tolerance and time horizon. A common personal rule is to keep 1-day 99% VaR below 2% of portfolio value, then tighten it if losses of that size would change your behaviour.
How do you calculate value at risk for a portfolio?
Estimate portfolio volatility from asset weights and the covariance matrix, multiply by the z-score for your confidence level, then multiply by portfolio value. For a non-normal portfolio, use historical simulation or Monte Carlo on the combined return series instead.
What is the difference between VaR and expected shortfall?
VaR gives the loss threshold at a confidence level. Expected shortfall, also called conditional VaR, gives the average loss on the days beyond that threshold. Expected shortfall is more sensitive to the shape of the tail, which is why regulators prefer it.
Is value at risk still used after the Basel changes?
Yes. VaR remains common for daily risk reporting, limit setting and backtesting because it is simple to communicate. Regulatory capital for trading books has moved to expected shortfall, but many desks still run both side by side.
Expected shortfall, the tail-sensitive alternative to VaR, captured from Wikipedia on 30 September 2026.
Key Takeaways
- VaR is a threshold, not a worst case. It names the loss you should exceed only on the 1-in-20 or 1-in-100 day.
- State all three parts every time: confidence level, horizon and portfolio value.
- Parametric VaR is fast but assumes normal tails. Historical VaR is honest about the past but blind beyond it. Monte Carlo is flexible but model dependent.
- Backtest against actual losses. Five or more exceptions in 250 days at 99% is a warning sign.
- Pair VaR with expected shortfall and stress tests so you see the flood, not just the wall.
- Basel moved trading book capital from 99% VaR to 97.5% expected shortfall because VaR ignores what happens past the line.
- Like the seawall, VaR is useful precisely because you know its height, and dangerous if you forget what lies beyond it.
This article is educational and is not personalised investment advice.