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Portfolio optimisation using constrained hierarchical bayes models1

Jiangyong Yin ,

Department of Statistics, The Ohio State University, Columbus, OH, USA

Xinyi Xu

Department of Statistics, The Ohio State University, Columbus, OH, USA

Pages 112-120 | Received 20 Apr. 2017, Accepted 22 Jun. 2017, Published online: 21 Jul. 2017,
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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 Chevrier, T., & McCulloch, R. (2008). Using economic theory to build optimal portfolios (Technical report, Working paper). University of Chicago. Retrieved from http://dx.doi.org/10.2139/ssrn.1126596 [Google Scholar]) economically motivated prior (EMP) strategy. On average, our model outperforms Chevrier and McCulloch’s (2008 Chevrier, T., & McCulloch, R. (2008). Using economic theory to build optimal portfolios (Technical report, Working paper). University of Chicago. Retrieved from http://dx.doi.org/10.2139/ssrn.1126596 [Google Scholar]) EMP strategy by over 15% and outperform the ‘1/N’ strategy by over 50%.

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