Portfolio Optimization for Cointelated Pairs: SDEs vs Machine Learning

47 Pages Posted: 24 Feb 2020

See all articles by Babak Mahdavi-Damghani

Babak Mahdavi-Damghani

University of Oxford - Oxford-Man Institute of Quantitative Finance

Konul Mustafayeva

King's College London, Department of Mathematics

Cristin Buescu

King's College London, Department of Mathematics

Stephen Roberts

University of Oxford - Oxford-Man Institute of Quantitative Finance

Date Written: October 24, 2019

Abstract

With the recent rise of Machine Learning (ML) as a candidate to partially replace classic Financial Mathematics (FM) methodologies, we investigate the performances of both in solving the problem of dynamic portfolio optimization in continuous-time, finite-horizon setting for a portfolio of two assets that are intertwined.

In Financial Mathematics approach we model the asset prices not via the common approaches used in pairs trading such as a high correlation or cointegration, but with the cointelation model that aims to reconcile both short-term risk and long-term equilibrium. We maximize the overall P&L with Financial Mathematics approach that dynamically switches between a mean-variance optimal strategy and a power utility maximizing strategy. We use a stochastic control formulation of the problem of power utility maximization and solve numerically the resulting HJB equation with the Deep Galerkin method.

We turn to Machine Learning for the same P&L maximization problem and use clustering analysis to devise bands, combined with in-band optimization. Although this approach is model agnostic, results obtained with data simulated from the same cointelation model as FM give an edge to ML.

Keywords: Pairs Trading, Cointelation, Portfolio Optimization, Stochastic Control, Band-wise Gaussian Mixture, Deep Learning

Suggested Citation

Mahdavi-Damghani, Babak and Mustafayeva, Konul and Buescu, Cristin and Roberts, Stephen, Portfolio Optimization for Cointelated Pairs: SDEs vs Machine Learning (October 24, 2019). Available at SSRN: https://ssrn.com/abstract=3474742 or http://dx.doi.org/10.2139/ssrn.3474742

Babak Mahdavi-Damghani

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

United Kingdom

Konul Mustafayeva (Contact Author)

King's College London, Department of Mathematics ( email )

Strand
London, England WC2R 2LS
United Kingdom

Cristin Buescu

King's College London, Department of Mathematics ( email )

Strand
London, WC2R 2LS
United Kingdom

Stephen Roberts

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

Eagle House
Walton Well Road
Oxford, Oxfordshire OX2 6ED
United Kingdom

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