Can Turnover Go to Zero?

TL;DR

This paper investigates whether portfolio turnover can be reduced to zero as the number of alpha streams increases, revealing that the limiting turnover depends on the number of alpha clusters and the finiteness of tradable instruments.

Contribution

It introduces a factor model approach showing that the limiting turnover is determined by alpha clusters, not the total number of alphas, and discusses implications for zero turnover.

Findings

Limiting turnover is proportional to F^(-3/2) where F is the number of alpha clusters.

Turnover cannot reach zero if the number of tradable instruments is finite.

Increasing alpha clusters can reduce turnover but not necessarily to zero.

Abstract

Internal crossing of trades between multiple alpha streams results in portfolio turnover reduction. Turnover reduction can be modeled using the correlation structure of the alpha streams. As more and more alphas are added, generally turnover reduces. In this note we use a factor model approach to address the question of whether the turnover goes to zero or a finite limit as the number of alphas N goes to infinity. We argue that the limiting turnover value is determined by the number of alpha clusters F, not the number of alphas N. This limiting value behaves according to the "power law" ~ F^(-3/2). So, to achieve zero limiting turnover, the number of alpha clusters must go to infinity along with the number of alphas. We further argue on general grounds that, if the number of underlying tradable instruments is finite, then the turnover cannot go to zero, which implies that the number of alpha clusters also appears to be finite.