关键词: 贝叶斯VAR, 可预测性, 均值方差, 风险平价, Black-Litterman

Abstract: In recent years, the risk-based asset allocation models becomes so popular, especially risk parity models. One of their most common features is that they no longer use the information on returns, while the return-based asset allocation models such as mean-variance model argue that the return is important assuming the forecasts on returns is accurate. Both of these treatments on returns are doubtful. As the asset return predictability has been proved by many empirical studies, in terms of risk-based asset allocation models, a complete dropping of the returns means the useful information on returns cannot be effectively used. For the return-based models, ignoring parameter estimation errors and insensitivity to input parameter would largely offset the benefits brought up by using the returns information. Therefore whether the returns are important here or not and how to use the returns information become a key issue in asset allocation. This paper proposes the Black-Litterman model (Bayesian BL model) to answer such an important question, taking the risk parity as a benchmark for allocation and Bayesian VAR return forecasts as a subjective factor. By using the US stock and bond quarterly data from 1952 to 2016, a comparison is made between Bayesian BL model and currently available allocation models. The empirical findings show that, compared to the return-based models, the Bayesian BL model reduces the portfolio risk; while compared to the risk-based models, the Bayesian BL model enhances the portfolio returns. These features stem from that it not only makes use of the useful information brought up by the returns predictability, but also takes the advantage of risk-based models in controlling the portfolio risk. In conclusion, the Bayesian BL model featured with enhanced returns and reduced risks is a new and potential scenario for asset allocation.

Key words: Bayesian VAR, Predictability, Mean Variance, Risk Parity, Black-Litterman