Optimal Turnover, Liquidity, and Autocorrelation

TL;DR

This paper derives an explicit formula for the steady-state turnover of trading strategies within a Gaussian process model, linking it to asset liquidity and autocorrelation of signals, providing insights for optimal trading behavior.

Contribution

It introduces a new explicit computation of steady-state turnover in a Gaussian model, relating it to liquidity and autocorrelation, which was not previously established.

Findings

Steady-state turnover is proportional to the square root of (n+1).

Turnover depends on a liquidity-adjusted risk aversion parameter.

The model links turnover to autocorrelation of alpha signals.

Abstract

The steady-state turnover of a trading strategy is of clear interest to practitioners and portfolio managers, as is the steady-state Sharpe ratio. In this article, we show that in a convenient Gaussian process model, the steady-state turnover can be computed explicitly, and obeys a clear relation to the liquidity of the asset and to the autocorrelation of the alpha forecast signals. Indeed, we find that steady-state optimal turnover is given by $\gamma \sqrt{n+1}$ where $\gamma$ is a liquidity-adjusted notion of risk-aversion, and $n$ is the ratio of mean-reversion speed to $\gamma$.