VaR (value at risk)

What VaR (value at risk) means

Value at risk, or VaR, is a single number that estimates how much a portfolio could lose over a set time period, with a stated level of confidence. A typical statement is that a portfolio has a one-day 95% VaR of 10,000 EUR. In plain words, this means that on 95 days out of 100, the portfolio is expected to lose no more than 10,000 EUR, and on the remaining 5 days it may lose that amount or more.

The last sentence is the key point. VaR defines a threshold, not a worst case. It tells you where the bad tail of the distribution begins but nothing about how deep it goes. A 95% one-day VaR of 10,000 EUR is compatible with a bad day of 11,000 EUR and with a bad day of 200,000 EUR.

VaR is used by banks, funds and risk departments to set limits, report exposure and, in regulated institutions, to calculate capital. Retail traders meet it in portfolio-analytics tools, in some broker risk dashboards and in educational material. It condenses a large amount of information into one figure that is easy to compare across positions, which is both its appeal and its weakness.

How it works

Every VaR figure needs three inputs and a method.

• The horizon. How long the position is held, often one day or ten days.
• The confidence level. Usually 95% or 99%.
• The portfolio and its risk factors. Positions, prices, correlations and volatilities.

The three common methods are as follows.

1. Historical simulation. Take the actual daily changes in market prices over a past window, such as 500 trading days. Apply each day's changes to today's portfolio to get 500 hypothetical profit and loss figures. Sort them. For 95% VaR, read off the loss at the 5th percentile, which is the 25th worst of 500.
2. Parametric (variance-covariance). Assume returns follow a bell-shaped distribution. VaR is then roughly the portfolio value times its volatility times a multiplier for the confidence level, about 1.65 for 95% and 2.33 for 99% on one side. Longer horizons scale with the square root of time.
3. Monte Carlo simulation. Generate thousands of random scenarios from a model of how prices move, revalue the portfolio in each and read the percentile.

Each method rests on assumptions. Historical simulation assumes the past window resembles the future. Parametric methods assume a particular distribution and stable relationships between assets. Monte Carlo depends on the model chosen.

A worked example

These numbers are illustrative. A trader holds a 100,000 EUR position in a stock index ETF. Daily volatility of the index is estimated at 1.2%.

Parametric one-day 95% VaR:

1. Multiplier for 95% one-tailed = 1.65.
2. VaR = 100,000 x 1.2% x 1.65 = 1,980 EUR.

So on 95 out of 100 days, the model says the loss should not exceed about 1,980 EUR.

Scaling to ten days:

1. Square root of 10 = about 3.16.
2. Ten-day VaR = 1,980 x 3.16 = about 6,260 EUR.

Now consider the tail. If a rare market shock hits and the index falls 8% in one day, the loss is 8,000 EUR. That is about four times the one-day VaR. VaR does not say this will happen or by how much it might exceed the threshold, only that such days are expected on less than 5% of occasions under the model's assumptions. Real markets often produce larger moves than a bell curve implies.

Why it matters

VaR allows risk to be summarised in currency terms rather than percentages or Greek letters. That makes it easier to compare different positions and to see whether a portfolio's risk matches the amount you are prepared to lose. Risk managers use it to set limits, for example a maximum daily VaR for a trading desk.

For individuals, it can serve as a sanity check on position sizing. Knowing that a leveraged CFD position has a one-day VaR equal to a large share of the account balance is more informative than looking at the notional value alone. Because leverage multiplies exposure, VaR on the notional amount can rise quickly even if the margin is small.

VaR also shows how correlated holdings combine. A portfolio of ten similar stocks has a higher VaR than ten uncorrelated positions, even though the number of holdings is the same. This connects it to diversification.

How to use it in practice

• State all three parameters, confidence, horizon and method, whenever you quote a VaR number. A figure without them is not meaningful.
• Compare it with your account equity and the amount you can afford to lose, not just with the notional position size.
• Use more than one confidence level, for example 95% and 99%, to see how fast the estimate grows toward the tail.
• Pair it with stress tests that assume extreme moves, and with scenario analysis such as a repeat of a past crisis.
• Check the data window. A calm window gives low VaR, which can be misleading just before volatility rises.
• Look at expected shortfall, also called conditional VaR, which averages the losses beyond the VaR level and shows how bad the tail is on average.
• Recalculate regularly, because volatility and correlations change.

Common mistakes and misconceptions

• Reading 95% VaR as the maximum possible loss. It is the threshold exceeded on about 5% of days.
• Ignoring that a 1-in-20 event is not rare. With 250 trading days a year, a 95% daily VaR is expected to be breached around 12 times.
• Using a calm historical window and assuming it is representative.
• Applying a bell-curve assumption to assets with fat tails, such as leveraged products or crypto.
• Adding VaR figures of separate positions. Diversification effects mean the total is not a simple sum.
• Treating VaR as a forecast of what will happen rather than a model-based estimate.

Risks and limitations

VaR is only as good as its assumptions and data. It can understate risk in stressed markets when correlations jump and liquidity disappears, and it cannot capture losses from gaps, trading halts or counterparty failure. It also says nothing about the size of losses beyond the threshold, which is why many practitioners prefer expected shortfall. For leveraged retail products, losses can be large and rapid, so a VaR figure should never be read as a cap on what you might lose.

How Brokeli looks at it

VaR is a risk-measurement concept rather than a broker feature, so we mention it where broker platforms provide risk analytics or portfolio reports. In our research we focus on what a platform shows about margin, exposure and risk limits, and on how clearly those tools are explained. We treat VaR as one input for understanding risk, with all its limits, not as a reassurance.