The Impact Of Parameter Uncertainty On The Mean-variance Forefront Combination And Solution Studies

With the increasing development of the domestic capital market, more and more financial investment products are on the market and the growing institutional investors, managing the increasing scale of products at the same time and holding s a large number of securities positions, are considering how these positions are distributed? In theory, Markowitz’s (1952) mean-variance model theory is a "perfect" Asset Allocation theory, which is seeking to maximize expected yield with a combination of certain risk control or minimize risk under certain expected yield. However, this theory is a "post-optimal", that is, seeking ex post optimal allocation when the yield of risk asset has been achieved. Therefore, it is difficult to avoid estimated error from parameters of risk assets when applying the mean-variance model. Unfortunately, the mean-variance model is extremely sensitive to estimated error and a slight change of the parameters will cause an intense changes on the weight of portfolio. At the same time, there are existing other defects, such as non-intuitive and error amplification. Therefore, in the actual investment applications, few investors use mean-variance model. This article is basing on such a specific problem, trying to give a quantitative asset allocation method.This article firstly proves the existing of parameters time-varying problem by empirical method. The parameters estimated from historical data cannot be directly applied to traditional mean-variance model and we found that the higher the degree of uncertainty of the expected yield, the greater the efficiency loss of the portfolio, but this is not in the case about covariance matrix. From the perspective of the loss of Sharpe ratio, the impact from the uncertainty of the covariance matrix is low. So, the use of historical data to estimate volatility in practical applications is relatively reliable.Secondly, on the basis of the above discussion, this article summarizes the Bayesian algorithm as the core portfolio model system under the framework of the mean-CVaR. Then, through the use of Monte Carlo simulations and stress test, it discussed parameter estimation accuracy from loss, bias and effectiveness three aspects, finding that the models which base on Bayesian algorithm can improve expected yield estimation accuracy, but fail to improve volatility estimation accuracy. Later, it discussed the models’ efficiency from the loss of Sharpe rate, resulting in that in the case of the same views and the same confidence, robust method and full perspective method are quite excellent and very suitable for the actual investment demand.Finally, this article focused on back-test of the full perspective model, using the investment logic "invest in high-β stock when market rise, and low-β stock when market fall" and estimating the β value from historical data, observing that excess revenue can be obtained by full perspective method under different confidence and different CVaR.Therefore, the portfolio model under Bayesian algorithm can avoid the efficiency loss of portfolio created by parameters estimated error and can become a powerful tool for asset allocation.