A Bayesian information criterion for portfolio selection

The mean–variance theory of Markowitz (1952) indicates that large investment portfolios naturally provide better risk diversification than small ones. However, due to parameter estimation errors, one may find ambiguous results in practice. Hence, it is essential to identify relevant stocks to alleviate the impact of estimation error in portfolio selection. To this end, we propose a linkage condition to link the relevant and irrelevant stock returns via their conditional regression relationship. Subsequently, we obtain a BIC selection criterion that enables us to identify relevant stocks consistently. Numerical studies indicate that BIC outperforms commonly used portfolio strategies in the literature.

► We investigate the problem of portfolio selection for risk minimization.
► We obtain the necessary and sufficient condition for the theoretically optimal portfolio.
► A BIC-type criterion is proposed to identify the optimal portfolio.
► We prove theoretically that the proposed BIC criterion is selection consistent.