禁止做空机制下基于光滑桥估计的稀疏投资组合

Sparse Portfolios Based on Smooth Bridge Estimation under the No-short Sales Constraint

当目标指数包含大量成分股时,通常需要构造由少数成分股组成的稀疏组合来控制交易成本。然而,关于稀疏指数追踪的相关文献主要集中于禁止做空约束下的Lasso类估计方法。但是,Lasso类估计方法通常对大系数的惩罚过度,继而产生较大的估计偏差。桥估计是Lasso估计的推广,特别是当调节参数小于1时,其可以同时进行参数估计和变量选择。为此,引入桥估计替代Lasso估计来获取稀疏投资组合,从而实现同时进行股票选择和资本配置的指数追踪。为了更加适应股票数据的多重共线性,考虑在回归方程中引入L2罚项来增加所提方法的光滑性。模拟仿真表明所提方法相较于Lasso类估计方法在参数估计和变量选择方面表现得更好。最后,通过对上证50指数和标普500指数的追踪验证了所提方法的优越性。

When the target index contains a large number of constituents,it is usually necessary to construct a sparse portfolio consisting of a small number of constituents to control transaction costs.Nevertheless,the literature on sparse index tracking mainly focuses on Lasso-type estimation methods under the no-short sales constraint.However,the Lasso estimation method usually over-penalizes large coefficients,and then produces large estimation bias.Bridge estimation is a generalization of Lasso estimation.Especially when the tune parameter is less than 1,bridge estimation can estimate parameters and select variables at the same time.Therefore,this paper introduces bridge estimation instead of Lasso estimation to obtain sparse portfolio,so as to realize index tracking of simultaneous stock selection and capital allocation.In order to be more suitable for the multicollinearity of stock data,the L2 penalty is introduced into the regression equation to increase the smoothness of the proposed method.Simulation results show that the proposed method performs better than Lasso methods in parameter estimation and variable selection.Finally,the superiority of the proposed method is verified by the tracking of SSE 50 index and S&P 500 index.