Mean-variance portfolio selection with tracking error penalization

TL;DR

This paper introduces a modified mean-variance portfolio optimization model that incorporates tracking error penalization, aiming to enhance robustness and benchmark tracking, with explicit solutions and empirical comparisons demonstrating improved Sharpe ratios.

Contribution

It formulates a McKean-Vlasov control problem for penalized mean-variance optimization and provides explicit solutions and asymptotic analysis for small tracking error.

Findings

Penalized portfolios often outperform standard mean-variance in Sharpe ratio.

Explicit solutions are derived for the optimal portfolio strategy.

Empirical tests show improved performance with tracking error penalization.

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.