Strategy correlation: how to tell if two strategies are the same bet

The short answer

Take the equity curve of each strategy over the same window, same instrument, same costs, and compute the pairwise correlation between them. Anything above roughly 0.8 means the two strategies are substantially the same bet, whatever their rules look like. Above 0.95, treating them as two positions is close to a bookkeeping error.

Correlation does not tell you which is better. It tells you how many independent bets you actually hold, which is the number that determines your real risk.

What we measured on our own shelf

We keep a shelf of strategies that have passed our filters, and for the gold hourly dataset (XAUUSD H1, roughly 17,500 hourly bars, about three years) there were 55 live strategies at the time of measurement. They came from seven different discovery engines: 19 template strategies, 18 from tree-based genetic programming, 8 from linear genetic programming, and the rest from particle swarm, differential evolution and the NSGA variants. Rule sets of genuinely different families.

Across all 1,485 pairs, the correlation between equity curves ran from 0.64 to 1.00. The median was 0.91. 92% of pairs were at or above 0.8, and 55% were at or above 0.9. Not one pair was negatively correlated.

Those numbers come from different-length curves, so we re-ran the check using only curves of identical length within the same window, which removes any alignment artefact. The answer barely moved: in the 304-bar group the median was 0.97 and the minimum 0.82; in the 329-bar group the median was 0.97 and the minimum 0.89. Every pair, in every length group, was above 0.8.

Collapsing duplicates does not fix this

The obvious objection is that many of those 55 are duplicates of each other, so of course they correlate. That is true and it is worth separating, because the two effects are different problems with different fixes.

We cluster strategies whose positions overlap heavily — our disclosure threshold is a high one, and the recorded pairwise correlations inside those clusters run from 0.95 upwards. Within clusters, the median correlation is 0.98, as you would expect.

Across clusters, the median is 0.89. Take one representative from each cluster — the strongest single strategy per distinct behaviour — and the 15 pairs between those ten representatives still have a median correlation of 0.88 overall, and 0.94 among the same-length representatives.

So de-duplication solved the first problem and revealed a second one underneath it. Once you have removed strategies that are the same strategy, what is left is still, to a first approximation, the same trade. Adding them to a portfolio does not diversify the bet; it increases its size.

Why this happens, mechanically

Two strategies can hold different rules and still be exposed to the same thing. If both are long gold when gold rises and flat otherwise, their equity curves are both driven by the same price series. The rules differ in when they enter and exit; the exposure does not.

Three mechanisms push a shelf of strategies toward high correlation. They share an instrument: everything on XAUUSD H1 is a bet on gold. They share a training window: all of them were selected for working over the same years, which selects for the same opportunities. And they share a search objective: optimisers given the same fitness function converge on the same shapes, which is why seven different engines produced strategies that correlate at 0.9.

There is also an uncomfortable detail in our own numbers. Every one of the 55 had a positive total return over the window, with maximum drawdowns clustered between 7% and 15%. That uniformity is not evidence that the strategies are all excellent. Gold trended over that period, and a shelf of long-biased systems on a trending instrument looks good as a group. Correlation computed on that window partly measures the trend, not the strategies.

How to run the check on your own strategies

Get the equity curve for each strategy over an identical window, with identical costs, on the same instrument. If the windows differ, the comparison is meaningless before you start — this is the same discipline as comparing two strategies fairly.

Align them bar by bar and compute the correlation of returns rather than of equity levels. Correlating the levels of two rising curves will hand you a high number whether or not they move together; that is a well-known way to fool yourself.

Look at the whole matrix, not the average. Report the median and the minimum. The minimum is the useful one: if your worst pair is 0.9, you have one bet. If your worst pair is 0.2, you have at least two.

Then check the sign distribution. In our shelf, zero of 1,485 pairs were negative. If nothing you hold is negatively correlated with anything else, you should expect every strategy to draw down at the same time, because that is what the matrix is telling you.

Finally, re-run it on a window that is not a trend. Correlations estimated only during a directional move are structurally flattering; the same set of strategies often converges much closer together in a choppy or reversing market.

What correlation does not tell you

It is unstable. Correlation is an average over a window, and the windows when you most need diversification are exactly the ones where correlations rise toward one. A matrix of 0.3s in calm markets can become a matrix of 0.9s in a crisis.

It is not causation and it is not a ranking. Two strategies can correlate without sharing a cause, and a low correlation says nothing about whether either one is any good. Correlation constrains the portfolio, not the individual choice.

It is sensitive to the window length you choose. Short windows give noisy estimates, long windows average over regimes that no longer exist. There is no single right answer; the defensible approach is to report the window and check that the conclusion survives changing it.