# Pairs Trading Using the Hurst Exponent of Product

Pairs trading is a market-neutral trading strategy that seeks to profit from the relative movements of two correlated assets. The key to pairs trading is finding two assets that are highly correlated. This can be done by looking at historical data or using a correlation coefficient. We can also use cointegration to choose pairs that will move together in the long run. Once we have found two correlated assets, we can take a long position in the asset that is undervalued and a short position in the asset that is overvalued. We can then profit from the price differential between the two assets.

Correlation and cointegration are the most popular methods for finding pairs to trade. However, there are other methods that can be used as well. Reference [1] proposed a new approach to measure the co-movement of two price series through the Hurst exponent of the product,

… the degree of correlation of the two assets can be measured by calculating the Hurst exponent H of the product series rsn: when H is close to 0.5 the assets will have low correlation, while an H close to 1 will mean that the assets have high correlation. The Hurst exponent of the product series will be referred as HP.

Next, it will be shown that the HP of two series is able to measure the existence of a relationship between them. In particular, it will be shown that HP is significantly greater than 0.5 for correlated series, cointegrated series, as well as series with a non-linear relationship or a more complex one given by a copula, while it is close to 0.5 for uncorrelated series.

Using the new method, the authors developed pairs trading strategies that yielded better returns than the traditional approaches,

In this paper, a new method (called HP) to measure the dependence between two series was proposed. It was proven that HP is able to detect different kinds of relationships between two series: mainly correlation, but also cointegration and non-linear relationships, even when the relationship is weak or it is given by a copula. The method is especially interesting to study financial series, since it gives more weight to high increments than low increments, contrarily to other correlation measures.

To test the efficiency of this new approach, the HP method was tested through a statistical arbitrage technique for pairs selection and compared with the classical correlation method. Results show that in most cases the HP method performs better.

References

[1] José Pedro Ramos-Requena, Juan Evangelista Trinidad-Segovia, and Miguel Ángel Sánchez-Granero, An Alternative Approach to Measure Co-Movement between Two Time Series, Mathematics 2020, 8, 261; doi:10.3390/math8020261

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