Optimal trading strategies - a time series approach

TL;DR

This paper revisits Markowitz's mean-variance portfolio optimization using a time series approach, focusing on optimal trading strategies for a single asset that minimize market exposure given a target return.

Contribution

It introduces a time domain reformulation of portfolio optimization, incorporating spectral theory of auto-covariance matrices and addressing estimation issues from finite samples.

Findings

Optimal strategies reduce market exposure for given returns.

Auto-covariance matrix cleaning improves strategy robustness.

Framework successfully applied to real-world data.

Abstract

Motivated by recent advances in the spectral theory of auto-covariance matrices, we are led to revisit a reformulation of Markowitz' mean-variance portfolio optimization approach in the time domain. In its simplest incarnation it applies to a single traded asset and allows to find an optimal trading strategy which - for a given return - is minimally exposed to market price fluctuations. The model is initially investigated for a range of synthetic price processes, taken to be either second order stationary, or to exhibit second order stationary increments. Attention is paid to consequences of estimating auto-covariance matrices from small finite samples, and auto-covariance matrix cleaning strategies to mitigate against these are investigated. Finally we apply our framework to real world data.