Statistical arbitrage consists in identifying stationary process and playing the mean reversion.

Reminder: a stationary process has the same moments (expectation, variance, etc.) in every single sample extracted from the main serie. In other words, the distribution of those samples should all be the same. See more details in the statistics notes (Time series section).

To select the group of assets to be used in a statistical arbitrage strategy, one could use the following approach approach:

1. Identify assets that have a good correlation

2. Express one asset in terms of the other through linear regression: $A_1 = \alpha A_2$. The residual is called $spread = A_1 - \alpha A_2$ and $\alpha$ the “hedge ratio”.

3. Check if the spread is stationary (e.g. using the Dickey-Fuller test)

-> If there is stationarity, the two assets can be kept for a proper backtest.

Note: the method consisting in regressing one serie on the other and applying an ADF unit-root test is called the Engle-Granger method.

Strategy

If the z-score of the spread is low (typically below 2 standard deviation of the moving average): we buy the first currency and short the second. When the spread crosses the moving average, we close the position.

If the z-score of the spread is high (typically above 2 standard deviation of the moving average): we short the first currency and buy the second. When the spread crosses the moving average, we close the position.