Mean-Variance Portfolio Selection with Tracking Error Penalization

29 Pages Posted: 5 Nov 2020

See all articles by William Lefebvre

William Lefebvre

Laboratoire de Probabilités, Statistique et Modélisation (LPSM); BNP Paribas

Gregoire Loeper

BNP Paribas; Monash University - School of Mathematical Sciences; Monash University - Monash Centre for Quantitative Finance and Investment Strategies; Ecole Polytechnique, Palaiseau - CMAP CNRS-UMR 7641 and Ecole Polytechnique

Huyên Pham

Sorbonne University - Laboratoire de Probabilités, Statistique et Modélisation (LPSM)

Date Written: September 16, 2020

Abstract

This paper studies a variation of the continuous-time mean-variance portfolio selection where a tracking-error penalization is added to the mean-variance criterion. The tracking error term penalizes the distance between the allocation controls and a reference portfolio with same wealth and fixed weights. Such consideration is motivated as follows: (i) On the one hand, it is a way to robustify the mean-variance allocation in case of misspecified parameters, by “fitting” it to a reference portfolio that can be agnostic to market parameters; (ii) On the other hand, it is a procedure to track a benchmark and improve the Sharpe ratio of the resulting portfolio by considering a mean-variance criterion in the objective function. This problem is formulated as a McKean-Vlasov control problem. We provide explicit solutions for the optimal portfolio strategy and asymptotic expansions of the portfolio strategy and efficient frontier for small values of the tracking error parameter. Finally, we compare the Sharpe ratios obtained by the standard mean-variance allocation and the penalized one for four different reference portfolios: equal-weights, minimum-variance, equal risk contributions and shrinking portfolio. This comparison is done on a simulated misspecified model, and on a backtest performed with historical data. Our results show that in most cases, the penalized portfolio outperforms in terms of Sharpe ratio both the standard mean-variance and the reference portfolio.

Keywords: Continuous-time mean-variance problem, tracking error, robust allocation, parameter misspecification

Suggested Citation

Lefebvre, William and Loeper, Gregoire and Pham, Huyen, Mean-Variance Portfolio Selection with Tracking Error Penalization (September 16, 2020). Available at SSRN: https://ssrn.com/abstract=3693710 or http://dx.doi.org/10.2139/ssrn.3693710

William Lefebvre

Laboratoire de Probabilités, Statistique et Modélisation (LPSM) ( email )

5 Rue Thomas Mann
Paris, Paris 75013
France

BNP Paribas ( email )

20 Boulevard des Italiens
Paris, 75009
France

Gregoire Loeper (Contact Author)

BNP Paribas ( email )

Paris
France

Monash University - School of Mathematical Sciences ( email )

Clayton Campus
Victoria, 3800
Australia

Monash University - Monash Centre for Quantitative Finance and Investment Strategies ( email )

9 Rainforest Walk
Clayton Campus
Monash University, Victoria 3800
Australia

HOME PAGE: http://https://www.monash.edu/science/quantitative-finance

Ecole Polytechnique, Palaiseau - CMAP CNRS-UMR 7641 and Ecole Polytechnique ( email )

Route de Saclay
Palaiseau, 91128
France

Huyen Pham

Sorbonne University - Laboratoire de Probabilités, Statistique et Modélisation (LPSM) ( email )

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