Statistical arbitrage

A true arbitrage is a riskless price discrepancy — the same thing trading at two prices at the same moment. Statistical arbitrage is not that, and the name is a historical accident rather than a description.

What it describes is trading a measured relationship rather than a certainty. Two assets have moved together over some past window; a position is taken on the difference between them rather than on either price. Nothing about the relationship is guaranteed to continue, and the measurement is of what already happened. It carries risk in the ordinary way, including the risk that a relationship that held for a year stops holding.

The object of interest is the spread: the difference between two assets, expressed as a ratio when the two are priced in the same currency. A position is long the spread or short it. The individual prices matter only through their effect on that difference.

This is why a ratio chart is the natural view. A chart of BTC in dollars and a chart of ETH in dollars both mostly show the same shared move; the ratio between them removes it and shows what is left.

Correlation measures whether two assets’ returns moved in the same direction over a window. It is the most common description of a pair, and on its own it is a weak one: two assets can be strongly correlated while the ratio between them drifts steadily in one direction. Moving together is not the same as staying a fixed distance apart.

The stronger property is cointegration — whether the spread itself has historically stayed within a range rather than wandering. It is a separate test, and a high correlation does not imply it. This distinction is where most introductory treatments stop, and it is the one that matters most when a relationship breaks.

Every correlation figure on this site is labelled with the window it was computed over and the time it was computed at. Both labels exist because a correlation without them is not a statement about anything in particular.

Most literature on this subject was written about equities, and three things differ on a perpetual futures venue.

Funding replaces borrow. There is no stock loan and no borrow fee. Instead each leg pays or receives funding periodically, and the position’s carrying cost is the difference between the two. That cost accrues whether or not the spread moves.

The market does not close. There is no overnight gap and no opening auction. A window of “90 days” is 90 continuous days rather than roughly 62 trading sessions, which changes what a per-day statistic is counting.

Both legs are leveraged. An equity pair trade can be held unlevered. Two perpetual legs each carry a liquidation price, so the position can be closed by either leg independently of what the spread did.

The pairs directory publishes, for each market with enough history, the correlation of daily returns over a stated window alongside the ratio and the venue figures for both legs. Those are descriptions of a past window and are presented as such.

For the mechanics of holding two legs as a single position, see what pair trading is.