基于随机因子模型的增强型指数基金

创新性的假设传统的Fama-French三因素模型中的三因素为服从正态分布的随机变量,进而获得了股票收益随机变量的分布信息.采取部分复制的原则建立增强型指数基金随机投资组合优化模型,通过引入投资组合风险概率约束给出增强型指数基金的绝对风险上限,针对增强型指数基金建立基于VaR的超额收益概率约束.引入最买入门槛限制降低增强型指数基金的管理费用,增强其流动性.最后,根据股票收益的概率分布特征,获得基于上述约束的指数基金和增强型指数基金的确定性优化模型,并同时基于上证A股进行了实证分析.

Enhanced Index Fund Based on Stochastic Factor Model

This paper treats securities return as a random variable,which follows a stochastic Fama-French three factor model.By assuming these three factors to follow a normal distribution,we could acquire the distribution knowledge of securities' return.Then,a stochastic investment portfolio optimization model based on partial replication strategies is constructed.The absolute risk upper limit of the investment portfolio is controlled by probabilistic constraint in the model.In terms of EIF,a lower bound on the excess return is given by imposing a VaR stochastic constraint.A buy-in threshold constraint is also taken into consideration in the purpose of reducing the management fees and increasing the liquidity. Finally,the stochastic optimization model is transformed into a deterministic model according to the distribution information of the securities' return and the empirical research based on the China stock market is conducted.