Reference · method

Monte Carlo simulations

What Monte Carlo simulations bring — and their blind spot on trend strategies.

The principle

A backtest tells ONE story: the one that happened. A Monte Carlo simulation manufactures thousands of others, drawing returns at random under a chosen rule, to observe not one trajectory but a DISTRIBUTION of trajectories — median, worst cases, probability of ruin. The idea is honest in intent: the realised path is only one draw among the possible paths, and judging a strategy on a single draw is to confuse the outcome with the process.

Three families

Everything depends on the drawing rule. The PARAMETRIC method assumes a law (often normal) and draws returns from it: simple, but it underestimates the tails — real crashes are more frequent and more violent than the bell allows. The HISTORICAL BOOTSTRAP resamples the returns actually observed, one by one, independently: the tails are real, but the ORDER is destroyed. The BLOCK BOOTSTRAP resamples whole slices of history to preserve short-term sequences — the best compromise, and the least used.

What it is really for

Monte Carlo's natural ground is DECUMULATION: for someone living off withdrawals, two trajectories with the same average return are not equivalent — a crash in the first decade ruins, the same crash in the last decade merely disappoints. This is the sequence-of-returns risk, and it appears only in a distribution of paths, never in an annualised return. Testing a withdrawal rate against thousands of sequences is the method's most defensible use.

The limits — including one that goes unsaid

First the general limit: a Monte Carlo cannot invent regimes absent from its raw material — it remixes the past it is given, it does not create new futures. Its "probabilities" are those of a model, not of the world. Then the specific limit, rarely written: INDEPENDENT drawing destroys the autocorrelation of returns — the trends that chain together, the declines that persist. Yet that is precisely what a momentum strategy exploits and sidesteps. Applying a naive bootstrap to a momentum strategy is to measure the risk of a strategy stripped of its reason for being: the filter has nothing left to filter, and the result describes neither the strategy nor the market. Only long blocks — which preserve the trends — produce a meaningful test, at the cost of far less diversity in the draws.

Monte Carlo and this site

This site chose another route to validation: not to remix one window, but to LENGTHEN the history — real instruments over ten then twenty-five years, Fama-French series over a century. A century of genuinely chained regimes (deflation, wars, stagflation, bubbles) contains the time dependence that resampling destroys, and that is what the strategy exploits. The two approaches answer different questions: Monte Carlo asks "what if the same process had drawn other cards?", long history asks "did the process survive the cards actually dealt, in the order they were dealt?". For a trend strategy, the second question is the right one.