Mean Reversion Pays, but Costs

TL;DR

This paper derives the optimal trading strategy for mean-reverting financial instruments considering linear transaction costs, showing that the buffer width scales with the cube root of the costs, which minimizes unnecessary trading.

Contribution

It provides an explicit derivation of the optimal buffer width in mean reversion trading strategies accounting for transaction costs, with a clear mathematical relationship.

Findings

Optimal buffer width scales with the cube root of transaction costs.

Explicit formula for buffer width as a function of costs.

Minimizes trading costs while maintaining mean reversion strategy effectiveness.

Abstract

A mean-reverting financial instrument is optimally traded by buying it when it is sufficiently below the estimated `mean level' and selling it when it is above. In the presence of linear transaction costs, a large amount of value is paid away crossing bid-offers unless one devises a `buffer' through which the price must move before a trade is done. In this paper, Richard Martin and Torsten Sch\"oneborn derive the optimal strategy and conclude that for low costs the buffer width is proportional to the cube root of the transaction cost, determining the proportionality constant explicitly.