Combining backward-looking information and forward-looking information in portfolio optimization

Under the framework of mean-variance analysis, investors need to estimate the mean vector and covariance matrix of asset returns to make investment decision. The most common estimation method is called "backward-looking" method since it relies only on historical data. However, it does not use the "forward-looking" information implied by the market variables, such as asset prices, and then cannot predict the future well. In this paper, we consider the general situation that market participants are consisting of informed investors and noise traders, and extract the "forward-looking" information on asset returns implied in the equilibrium market portfolio. By combining the historical "backward-looking" information with the market implied "forward-looking" information via Bayesian analysis, we propose a "combined" method for return prediction. The theoretical analysis show that the "combined" method can adaptively select more "forward-looking" information when the informed investor has a higher market share, a lower risk-averse degree, or the noise trader has a lower noise trading intensity; otherwise, it will use more "backward-looking" information. Both the simulation experiments and the empirical tests demonstrate that the "combined" model can provide more flexible and robust prediction on asset returns in portfolio management. © 2021, Editorial Board of Journal of Systems Engineering Society of China. All right reserved.