How much should portfolios shrink?

Abstract

This paper develops a portfolio model that penalizes the deviation from a reference portfolio. The proposed model renders a robust portfolio that performs superior under parameter uncertainty. Penalizing the deviation also improves the performance of existing shrinkage portfolio models that are suboptimal due to model parameter uncertainty. The equal‐weight portfolio turns out to be a better reference portfolio than the currently holding portfolio even in the presence of transaction costs. A data‐driven method for determining the degree of penalization is offered. Comprehensive simulation and empirical studies suggest that the proposed model significantly outperforms various existing models.

A nonparametric approach to portfolio shrinkage

“…These models usually underperform their underlying models 0.006 0.004 0.003 0.009 0.014 0.009 0.015 0.013 0.010 0.012 0.005 0.009 TMV0+(τ * a ) 0.004 0.002 0.001 0.001 0.001 0.001 0.002 0.001 0.000 0.001 0.001 0.001 before transaction costs and perform marginally better only after transaction costs. A similar observation has been made by Han (2019), who analytically shows that the equal-weight portfolio is a more effective shrinkage target.…”

“…Branger et al (2019) develop a grouping strategy in which portfolio optimization is performed on groups of equally weighted stocks, and show that their strategy outperforms many existing strategies that aim to address estimation risks. Han (2019) develops a shrinkage model that improves upon the shrinkage models of Kan and Zhou (2007) and Tu and Zhou (2011) and finds that the proposed model outperforms the existing shrinkage models as well as the naïve strategy.…”

“…The shrinkage estimator, first proposed by Kan and Zhou (2007), optimally combines two or more portfolios so that the expected utility loss is minimized. This approach has been adopted later by Tu andZhou (2011), DeMiguel et al (2015), , and Han (2019), among others. Other approaches include imposing weight constraints (Jagannathan and Ma, 2003) or using a shrinkage method for parameter estimation (Ledoit and Wolf, 2004).…”

“…Nevertheless, shrinkage estimators suffer from shrinkage parameter uncertainty: the optimal shrinkage parameters (the coefficients on the portfolios) are functions of unknown input parameters and therefore inherit input parameter uncertainty (Han, 2019). The uncertainty of the shrinkage parameters can lead to a nontrivial utility loss.…”

“…While a closed form is always preferred,Han (2019) shows that, due to model parameter uncertainty, the closed-form solutions offered byKan and Zhou (2007) andTu and Zhou (2011) are sub-optimal even when all the assumptions are correct. He argues that the optimal shrinkage level should be higher than that suggested by these models, and cannot be determined analytically.…”