What is Value at Risk,
and how do you calculate it?

What Value at Risk actually means

Value at Risk, or VaR, estimates the maximum loss a portfolio is expected to suffer over a set time horizon at a given confidence level. Every VaR number carries three pieces: an amount, a horizon, and a confidence. Say the horizon is one day and the confidence is 95%, and you get a statement like “95% 1-day VaR of $3,290.”

Read that plainly: on 95% of days, you should not lose more than $3,290. On the worst 5% of days, roughly one trading day in twenty, you could lose more. VaR draws the line at the edge of a normal day. It does not promise you will never cross it, and it does not tell you how far past it a bad day can drag you.

The three inputs

Every VaR calculation runs on the same three inputs. Get these right and the number is honest; feed it a stale volatility and the number lies to you.

First, portfolio value: how much capital is exposed. Second, volatility: the standard deviation of returns over your horizon, which is the statistical measure of how much the portfolio swings. Third, confidence level: how strict you want the estimate to be, usually 95% or 99%. A higher confidence produces a larger VaR, because you are asking about rarer, deeper losses.

The parametric formula

This is the parametric method, also called variance-covariance. It is the fastest way to a VaR number because it assumes returns follow a normal distribution and leans on the Z-score to translate your confidence level into a multiplier. The higher the confidence, the bigger the Z-score, and the bigger the loss the formula reports.

A worked example

Take a $100,000 portfolio with 2% daily volatility, and ask for 95% confidence. Plug it in: $100,000 × 0.02 × 1.645 = $3,290. That is your 1-day VaR. On a normal day you should not lose more than $3,290; on the worst 5% of days you could lose more. Push the confidence to 99% and the Z-score climbs to 2.326, so the same portfolio shows a VaR of $4,652, a stricter line for rarer, deeper days.

To stretch that one-day figure across a longer window, use the square root of time rule. A 10-day VaR is roughly the 1-day VaR times the square root of 10, so $3,290 × 3.162 = about $10,403, assuming returns are independent from day to day. Never quote a daily number as if it covered ten days; the horizon is baked into the answer.

The three ways to calculate it

The formula above is one of three standard methods, and they trade speed for realism. The parametric method is fastest but assumes a clean normal distribution, so it can miss the fat tails real markets show. The historical method uses the actual distribution of past returns, replaying what your portfolio really did, which captures the shape of real losses but is only as good as the history you feed it. The Monte Carlo method simulates thousands of possible scenarios from a model of the market, which is the most flexible for complex portfolios and the most demanding to run.

None of the three is universally correct. Parametric is a quick daily gauge, historical grounds the estimate in what actually happened, and Monte Carlo stress-tests positions a simple formula cannot describe.

What VaR does not tell you

VaR is a floor-of-normalcy gauge, not a worst-case guarantee, and treating it as the latter is how people get hurt. Three limits matter. It says nothing about how bad the loss is once you breach the threshold, so the entire tail beyond the line is invisible. Parametric VaR in particular underestimates fat tails and black-swan events, because a normal distribution does not model the rare, violent moves markets actually make. And it assumes volatility is stable, which fails exactly when markets turn, since volatility spikes in a crisis.

This is why serious risk desks pair VaR with Conditional VaR, also known as Expected Shortfall, which measures the average loss inside the tail that VaR ignores. Use VaR to size up a normal day, and remember that the days that break accounts live past the line it draws.