Value at Risk (VaR)

What is value at risk (VaR)?

Value at risk (VaR) is a statistical estimate of the most money a portfolio could lose over a set period, at a given confidence level, under normal market conditions. VaR stands for value at risk. A one-day 95 percent VaR of 50,000 means there is a 95 percent chance the portfolio loses no more than 50,000 tomorrow, and a 5 percent chance it loses more.

It compresses three things into one number: a time horizon (one day, ten days, one year), a confidence level (usually 95 or 99 percent), and a currency loss amount. That is why risk managers, treasurers and bank regulators lean on it. It puts a single, comparable figure on exposures that would otherwise be hard to weigh against each other.

How value at risk works: a worked example

VaR answers a plain question: how bad could a normal bad day be? Read a 99 percent one-day VaR as the loss you would exceed on only about one trading day in a hundred. The example below shows the same portfolio at two confidence levels.

The maths behind the figures is the variance-covariance shortcut: multiply the portfolio value by its daily volatility, then by the z-score for the confidence level (1.65 for 95 percent, 2.33 for 99 percent). So 1,000,000 times 2 percent times 1.65 gives roughly 32,900, and the same figures with 2.33 give roughly 46,500. Raising the confidence level always raises the number, because you are reaching further into the tail of bad outcomes.

How to read a VaR figure correctly

Three details decide what a VaR number actually means, and getting any of them wrong makes the figure useless. Quote a VaR without all three and you have a number that cannot be compared to anything.

To stretch a one-day figure to a longer horizon, analysts scale it by the square root of time: a ten-day VaR is roughly the one-day VaR multiplied by the square root of ten, about 3.16. So the 46,500 one-day 99 percent figure above becomes roughly 147,000 over ten days. The third detail is the most often forgotten, because a calm-looking VaR says nothing about a disorderly market, which is precisely when the assumption behind it breaks down.

How is value at risk calculated? The three methods

There are three standard ways to calculate VaR: historical simulation, the variance-covariance (parametric) method, and Monte Carlo simulation. They answer the same question but make different assumptions, and the right one depends on the data you have and how unusual your risks are.

Historical simulation is the most intuitive and makes no claim about the shape of returns, but it assumes the future resembles the past. The variance-covariance method is fast and clean, yet its normal-distribution assumption understates the odds of extreme moves. Monte Carlo is the most flexible and handles complex instruments well, at the cost of heavy computation and a reliance on the distributions you feed it. Many risk teams run more than one and compare.

Value at risk in accounts receivable

The same logic applies to a receivables book, where it is usually called credit VaR. Credit value at risk estimates the largest loss a company could face from customers failing to pay, over a set period and confidence level. Instead of market volatility, it leans on a different set of inputs.

Concentration is the part finance teams underrate. A book where one customer owes 40 percent of the total carries far more tail risk than the headline balance suggests, because a single default would be severe. This is exactly what good receivables risk management and credit risk management are built to control: setting limits, spreading exposure, and watching the accounts most likely to slip. Strong accounts receivable reporting gives you the exposure and aging data those estimates depend on.

Most small and mid-sized businesses will never compute a formal credit VaR, and they do not need to. The instinct behind it is what matters: ask not just what you are owed, but how much you could lose if your largest or weakest customers stopped paying at once. That single question, asked regularly, catches the concentration risk a healthy-looking total can hide.

Why banks and regulators rely on VaR

VaR became a standard because regulators needed a common yardstick for risk. Under the Basel framework, banks calculate VaR on their trading books and hold capital against it, so the figure directly shapes how much reserve a bank must set aside. A higher VaR means more capital tied up, which gives institutions a real incentive to measure and manage their exposures rather than just report them. The same number lets a board, a regulator and a risk desk talk about risk in one currency, which is much of why it spread from trading floors into treasury and credit functions across finance.

The limits of value at risk

VaR's biggest weakness is the question it does not answer: how bad is bad when the threshold is breached. A 99 percent VaR tells you the loss you should beat 99 days in 100, but says nothing about the size of the loss on the hundredth. That blind spot is why many institutions now pair VaR with expected shortfall, also called conditional VaR, which averages the losses in the tail beyond the VaR point.

It trusts the recent past

VaR also leans on the recent past and on its modelling assumptions, so it can lull teams into false comfort just before a shock, when correlations jump and history stops being a guide. The honest way to use it is as one input among several, backed by stress testing and scenario analysis rather than treated as a hard limit on what can go wrong.