Value at Risk

What value at risk is

VaR answers one question: how much could be lost in a given time, if the next period is not one of the worst few? You pick two things. The horizon is the period, such as one day. The confidence level is how sure the statement should be, such as 95 percent. The answer is a loss amount.

Read it carefully. A one-day 95 percent VaR of $164 does not say the most you can lose is $164. It says that on a typical day the loss should not be bigger than $164, and that roughly 1 day in 20 it will be. The measure is silent on how much bigger.

Three ways to calculate it

• Parametric (variance-covariance). Assume returns follow a normal curve, estimate their standard deviation, and multiply by a fixed number for the confidence level. Quick and simple. Only as good as the normal assumption.
• Historical. Take a record of past returns, sort them from worst to best, and read off the loss at the chosen percentile. No curve is assumed. It can only see what the record contains.
• Monte Carlo. Simulate many possible paths from a model and read the percentile. It is as good as the model that generates the paths. See the Monte Carlo simulator.

For a longer horizon, the standard deviation is often scaled by the square root of the number of days. That is again an assumption: it holds only if each day is independent of the last, which is rarely true for a bot that adds to losing trades.

A worked example: $10,000 and a 1 percent daily swing

This is a made-up account of $10,000 whose daily returns have a standard deviation of 1 percent, with an average near zero. Under the normal-curve method the one-day VaR at each confidence level is the z value times 1 percent times $10,000.

Calculated by us on 29 Oct 2026, exact for these made-up inputs and the standard normal values. At 95 percent, $164.49 is 1.6449 x 1 percent x $10,000. Moving from 95 to 99 percent lifts the figure from $164.49 to $232.63, so VaR depends heavily on the confidence level chosen, and a report that does not state it is not meaningful.

A worked example: the bot that wins small and loses big

Now a made-up 100-day record for a bot of the martingale or grid kind: 96 days of +0.25 percent, 3 days of -0.5 percent, and one day of -10 percent when a ladder failed. Total over the record: +12.50 percent by simple addition. Sort the days from worst to best. The 95 percent historical VaR is the loss on the fifth worst day of the 100.

Calculated by us on 29 Oct 2026, exact arithmetic on made-up inputs. The record has a mean of 0.13 percent and a standard deviation of 1.03 percent. The tail beyond the 95 percent line holds the whole story: one day of 10.00 percent and three of 0.50 percent. The historical VaR reads off the fifth worst day, which sits right after them, so it reports nothing. Even the 99 percent normal-curve figure, 2.27 percent, is only a part of the 10.00 percent the account actually lost in a single day. On $10,000 that day cost $1,000.

How it hits bots

• Martingale and grid bots collect many small gains and rare, large losses. Their daily returns are lopsided, not bell-shaped. VaR measured over a quiet stretch will be small, and so will the confidence it inspires. See martingale and drawdown.
• Leverage. A loss bigger than the account can hold ends in a stop out or worse, which no VaR figure captures. See stop out.
• Short records. A bot with 100 days of history may not yet have met its bad day. Historical VaR can only see the days that happened.
• Gaps and thin markets. VaR assumes positions can be closed at about the quoted price. In a fast market the exit is worse. See slippage.
• Clustering. Bad days cluster. Three bad days in a row are far more likely than the independence assumption in the square-root rule says.

How to use it without being fooled

• State the horizon, the confidence level and the method every time. A VaR without those is not a number.
• Always put the tail next to it: expected shortfall, which averages the losses beyond the VaR line, and the worst day in the record.
• Check how many bad days the record contains. If it has none, the VaR is about a record, not about the strategy.
• Stress the bot with a loss it has not had: a 5 or 10 percent move against a full ladder, and see what is left. The risk of ruin calculator is one way to start.

What it does not tell you

VaR does not say what the worst case is, how long a drawdown will last, whether the strategy has an edge, or what happens when the market stops behaving like the sample. A low VaR is a statement about the common days. Bots tend to fail on the uncommon ones.