Portfolio optimisation using constrained hierarchical bayes models¹

¹Present address: CapitalG, Inc.

abstract

It is well known that traditional mean-variance optimal portfolio delivers rather erratic and unsatisfactory out-of-sample performance due to the neglect of estimation errors. Constrained solutions, such as no-short-sale-constrained and norm-constrained portfolios, can usually achieve much higher ex post Sharpe ratio. Bayesian methods have also been shown to be superior to traditional plug-in estimator by incorporating parameter uncertainty through prior distributions. In this paper, we develop an innovative method that induces priors directly on optimal portfolio weights and imposing constraints a priori in our hierarchical Bayes model. We show that such constructed portfolios are well diversified with superior out-of-sample performance. Our proposed model is tested on a number of Fama–French industry portfolios against the naïve diversification strategy and Chevrier and McCulloch’s (2008) economically motivated prior (EMP) strategy. On average, our model outperforms Chevrier and McCulloch’s (2008) EMP strategy by over 15% and outperform the ‘1/N’ strategy by over 50%.

Keywords:

• Bayesian hierarchical models
• parameter constrains
• portfolio choices

Additional information

Funding

This work was supported in part by US National Science Foundation (NSF) under grant DMS-1613110.

Notes on contributors

Jiangyong Yin

Jiangyong Yin received his PhD degree in statistics from The Ohio State University, working under the supervision of Dr. Xinyi Xu and Dr. Peter Craigmile. He is currently working at CapitalG Inc.

Xinyi Xu

Xinyi Xu received his MS and PhD degrees in statistics from the University of Pennsylvania in 2003 and 2005, respectively. Currently, she is an associate professor in the Department of Statistics, The Ohio State University. Her research interests include Bayesian analysis, statistical decision theory, and high-dimensional data analysis.