Portfolio optimisation using constrained hierarchical bayes models

It iswell known that traditionalmean-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 showthat 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 na飗e 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%.