Multi-Period Portfolio Optimization

62 Pages Posted: 5 May 2022

See all articles by Edmond Lezmi

Edmond Lezmi

Amundi Asset Management

Thierry Roncalli

Amundi Asset Management; University of Evry

Jiali Xu

Amundi Asset Management

Date Written: March 30, 2022

Abstract

In this article, we consider a multi-period portfolio optimization problem, which is an extension of the single-period mean-variance model. We discuss several formulations of the objective function, constraints and coupling relationships. We then derive three numerical algorithms that can be used to solve such problems: the alternating direction method of multipliers, the block coordinate descent algorithm and the augmented quadratic programming method. We illustrate the differences between single-period and multi-period solutions by considering three asset allocation problems: transition management (Rattray, 2003), total variation regularized portfolio (Corsaro et al., 2020) and trading trajectory modeling (Gârleanu and Pedersen, 2013). Finally, we solve the portfolio alignment problem of Le Guenedal and Roncalli (2022) when the fund manager has to dynamically control the carbon footprint of his investment portfolio by integrating a carbon reduction scenario. Comparing the single-period and multi-period solutions shows that the active share between the two portfolios may be greater than 25%. This figure can also reach 40% if we include carbon trends and they are increasing.

Keywords: Multi-period optimization, portfolio allocation, ADMM, block coordinate descent, quadratic programming, coupling variables, transition management, total variation regularization, optimal trading trajectory problem, portfolio decarbonization, net zero alignment

JEL Classification: C61, G11, Q54

Suggested Citation

Lezmi, Edmond and Roncalli, Thierry and Xu, Jiali, Multi-Period Portfolio Optimization (March 30, 2022). Available at SSRN: https://ssrn.com/abstract=4078043 or http://dx.doi.org/10.2139/ssrn.4078043

Edmond Lezmi

Amundi Asset Management ( email )

90 Boulevard Pasteur
Paris, 75015
France

Thierry Roncalli (Contact Author)

Amundi Asset Management ( email )

90 Boulevard Pasteur
Paris, 75015
France

University of Evry ( email )

Boulevard Francois Mitterrand
F-91025 Evry Cedex
France

Jiali Xu

Amundi Asset Management ( email )

90 Boulevard Pasteur
Paris, 75015
France

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