What it means
The method works by taking a window of past market data, often one to four years of daily moves, and applying each day's percentage changes to the portfolio you hold right now. That produces one hypothetical profit or loss figure per historical day, and sorting those figures from worst to best gives you a distribution of outcomes.
The loss at your chosen confidence level is simply read off that sorted list. Its main attraction is that it makes no assumption about the shape of returns.
Real markets produce more extreme days than a normal distribution predicts, and historical simulation captures those days automatically because they are in the data. It also handles the way different assets moved together in past stress episodes without anyone having to estimate correlations.
The weaknesses follow from the same design. The method can only produce a loss it has already seen, so a portfolio can look calm simply because the chosen window happened to be quiet, and results change abruptly when a large past shock rolls out of the window.
Many risk teams respond by weighting recent days more heavily or by running a second window that deliberately includes a known crisis period. In practice, the output is used for far more than a regulatory number.
Trading desks use it to size positions, treasurers use it to judge how much liquidity to hold, and boards use it as one input into risk appetite. The number is best treated as a rough ordering of how risky different portfolios are, not as a precise forecast of a loss.
In practice
Real-world examples.
Example
A commodities trading firm runs historical simulation over four years of data and finds its value at risk doubles when a period of extreme energy price moves enters the window. Rather than dismissing the jump, the risk committee uses it to cut position sizes ahead of a volatile contract expiry.
Example
A corporate treasurer applies the method to a portfolio of currency hedges and discovers that the worst simulated days all involve the same two currency pairs moving together. The finding leads the team to diversify its hedging counterparties and instruments rather than to change the overall hedge ratio.
Example
A wealth manager compares two client portfolios with the same expected return and finds one shows a 99% daily value at risk of $18,000 and the other $41,000. The comparison gives the adviser a concrete way to discuss risk tolerance without resorting to abstract language about volatility.
Think of it
“Historical simulation uses real past data to estimate risk-what actually happened before.
Formula
Calculation
Value at risk by historical simulation: apply each of the past N daily percentage moves to the current portfolio, sort the resulting profit and loss figures from worst to best, and take the loss at the position N x (1 - confidence level).
A fund holds a $10,000,000 portfolio and uses 500 trading days of history at a 99% confidence level. The cut-off position is 500 x (1 - 0.99) = 5, so the answer is the fifth-worst day in the sample.
Suppose the five worst simulated daily returns for today's portfolio are -4.2%, -3.8%, -3.5%, -3.1% and -2.9%. The fifth-worst is -2.9%, so the one-day 99% value at risk is $10,000,000 x 2.9% = $290,000. The interpretation is that on roughly one trading day in a hundred, based on the past two years of market behaviour, the fund would expect to lose more than $290,000.Case study
Seen in the real world.
This example is illustrative and fictional. Pemberton Ridge Asset Management, an invented mid-sized fund manager, reported a steadily falling value at risk across 2019 and treated it as evidence that its portfolio had become safer.
In fact, the two-year window it used had rolled past an earlier period of market stress, so the calmest possible history was doing the work. When markets moved sharply the following year, the fund's actual losses breached the modelled figure on eleven days in a single quarter, against an expectation of roughly one breach in a hundred days.
In this fictional account, the firm kept historical simulation as its main method but added two changes: a second calculation using a fixed stressed window that always includes a severe past episode, and a rule that any material fall in the risk number must be explained by a change in positions, not merely reported.
Watch out
Common mistakes.
- Treating the result as the worst possible loss. A 99% value at risk says nothing about how bad the remaining 1% of days can be, and those days are exactly the ones that hurt.
- Choosing the data window for convenience. A short, calm window flatters the portfolio, and quietly using it because the number looks better is one of the most common failures in risk reporting.
- Forgetting that the portfolio, not the past, is the variable. The simulation applies old market moves to today's positions, so the number changes the moment holdings change, even if no market data has been updated.
Questions
People also ask.
How much history should the window contain?
One to four years of daily data is typical, with shorter windows reacting faster to current conditions and longer ones giving a steadier but slower-moving figure.
How does it differ from Monte Carlo simulation?
Historical simulation replays real past moves, while Monte Carlo generates artificial scenarios from an assumed statistical model, which allows more scenarios but adds model assumptions.
Does the method work for options and other non-linear positions?
It can, provided each position is fully revalued under each historical scenario rather than approximated, which is slower to compute but far more accurate.
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