What Is Value at Risk? VaR in Plain Language, and the Tail It Hides

Value at Risk, usually shortened to VaR, is an estimate of how much a portfolio could lose over a given period, at a given level of confidence. A one day 95 percent VaR of ten lakh rupees means the model expects losses to stay below ten lakh rupees on about 95 out of every 100 days.

It is the most institutionally embedded risk number in finance, used in bank capital rules, risk committee packs and trading limits. It is also the number with the most famous blind spot, because it draws a line and then declines to describe anything on the far side of it.

What it measures

Every VaR figure carries three parts, and quoting it without all three is meaningless:

• A horizon. One day, ten days, one month. VaR is always over a period.
• A confidence level. Commonly 95 percent or 99 percent. This is the fraction of periods in which losses are expected to stay within the threshold.
• An amount. Expressed either in currency or as a percentage of portfolio value.

Put together: “the one day 99 percent VaR is 2 percent of portfolio value” means that on roughly 99 out of 100 days, the model expects the portfolio to lose less than 2 percent. Equivalently, on about one day in a hundred, it expects the loss to exceed that.

VaR is therefore a percentile of the loss distribution. Nothing more exotic than that.

The three ways it is computed

Historical simulation. Take the portfolio’s actual returns over some past window, sort them from worst to best, and read off the value at the relevant percentile. For a 95 percent VaR over 500 days, that is roughly the 25th worst day. This method makes no assumption about the shape of the distribution, which is its main appeal. Its limitation is that it can only produce losses that resemble ones that already occurred in the window chosen.

The parametric or variance-covariance method. Assume returns follow a known distribution, usually a bell curve, estimate the volatility, and calculate the threshold that corresponds to the chosen confidence level. This is fast and convenient. It is also only as good as the assumption, and market returns are known to have fatter tails than a bell curve, which makes this version prone to understating extreme losses.

Monte Carlo simulation. Specify a model for how the portfolio’s drivers behave, then generate a large number of simulated future paths and read the percentile from the simulated outcomes. This handles complex, non-linear portfolios that the other two struggle with, and it is more flexible about distributional shape. It is also the most dependent on the modeller’s assumptions, a point taken up in Monte Carlo simulation in investing.

The three methods can produce noticeably different answers for the same portfolio on the same day. That divergence is information, not a defect.

How to read it

Never quote it without horizon and confidence. A number alone is uninterpretable. Scaling also matters: a one day figure is often stretched to ten days using the square root of time convention, which assumes independence between days and therefore tends to understate risk in trending or crisis conditions.

Read 95 percent and 99 percent together. The gap between them describes how quickly the loss distribution deepens as you move into the tail. A portfolio where the 99 percent figure is only slightly worse than the 95 percent figure has a different shape from one where it is several times worse.

Backtest the number. The honest test of a VaR model is counting breaches. If a 95 percent daily VaR is well calibrated, losses should exceed it roughly 5 percent of the time, spread out rather than bunched. Far fewer breaches means the model is too conservative and the risk budget is being wasted. Far more, or breaches that arrive in clusters, means the model is missing something.

Pair it with expected shortfall. Expected shortfall, also called conditional VaR, answers the question VaR refuses to: given that the threshold has been breached, how large is the loss on average. It is now preferred in several regulatory frameworks precisely because it looks inside the tail.

Put it next to a realised measure. VaR is a model output. Maximum drawdown is a recorded fact. Reading a modelled tail threshold beside the deepest fall the portfolio actually suffered keeps the model honest.

Understand aggregation. Portfolio VaR is not the sum of position VaRs, because positions do not all lose money at the same time. The diversification benefit that reduces the total depends entirely on the correlation assumptions used, which is why a correlation matrix sits underneath most VaR systems.

What it does not tell you

It is silent about the size of the tail. This is the central criticism. A 99 percent VaR tells you where the worst 1 percent of days begin and nothing about how bad they get. Two portfolios can share an identical VaR while one’s worst outcomes cluster just past the line and the other’s run far beyond it. The losses that destroy portfolios live in exactly the region VaR does not describe.

It is not a maximum loss. It is routinely, and dangerously, spoken of as if it were. A one day 99 percent VaR will be exceeded, by design, on roughly one day in a hundred. Being exceeded is not a model failure. It is the model working as specified.

It assumes tomorrow resembles the estimation window. Historical simulation cannot produce a shock that never occurred in its window. Parametric VaR inherits whatever volatility regime it was estimated in. Both compress during calm periods, so risk appears to fall just as the conditions for a large move are building. That procyclicality is a well documented behaviour of the measure.

It assumes stable correlations. Diversification benefits in a VaR model come from assets not falling together. In severe market stress, correlations across risky assets have historically tended to rise, so the diversification the model was counting on can thin out at the moment it is needed most.

It ignores liquidity. VaR is computed from marked prices and assumes positions can be valued and, implicitly, exited at those prices. In a stressed market, exiting a large or illiquid position moves the price against you. That cost is real and does not appear anywhere in the calculation, which is why slippage and impact cost is a separate discipline.

It does not add up neatly. VaR is not what mathematicians call subadditive, meaning the VaR of a combined portfolio can in some constructed cases exceed the sum of the parts. This makes it awkward to use for allocating risk limits across desks, and it is one of the technical reasons expected shortfall gained ground.

It cannot see the risks that are not in the return series. Governance failure, fraud, regulatory change, a counterparty default: none of these appear in a price history until after they happen. VaR describes the statistical behaviour of past prices, not the set of things that could go wrong.

It invites false precision. A VaR figure printed to the rupee gives an impression of accuracy that the underlying assumptions cannot support. It is an estimate with wide uncertainty around it, and dressing it up as a measurement is how risk numbers get trusted more than they deserve.

The productive way to hold VaR is as one lens among several. It is genuinely useful for comparing risk across time, across desks and across portfolios on a consistent basis. It is not a promise, not a worst case, and not a substitute for asking what happens when the assumptions fail. That last question belongs to stress testing, which exists precisely because VaR stops where the trouble starts.

Related reading

• Portfolio metrics explained: the hub connecting every risk and return measure.
• What is maximum drawdown: the realised loss measure to read alongside a modelled one.
• Stress testing a portfolio: deliberately examining the scenarios VaR does not describe.
• Volatility and standard deviation explained: the input most parametric VaR models rest on.
• Monte Carlo simulation in investing: what simulation adds and the assumptions that make it fragile.

This article is educational. Altys Labs is not a registered research analyst or investment adviser, and nothing here is investment advice or a recommendation to buy, sell, or hold any security.