A Novel Semi-Static Method for the Index Tracking Problem

With the rapid growth of index investing in wealth management, such as the exchange traded fund (ETF) market, tracking the reference index of ETF regains considerable attention because the corresponding tracking error is one of the key measurements of a fund’s performance. To improve accuracy and efficiency in minimizing tracking errors, we propose a novel approach that combines the generalized singular value decomposition (GSVD) and the constrained Kalman filter method for estimation of portfolio weights and their dynamical updates, respectively. GSVD reveals all feasible weights under a static constrained regression model for the index tracking error minimization problem. The constrained Kalman filter is applied to update the GSVD-solved weights of the optimal port-folio along with the dynamical time series of return data. This two-stage approach is semi-static. Our empirical studies demonstrate that sufficient low tracking error can be obtained under a robust top-down stratified framework that consists of 11 sector indices defined by the Global Industry Classification Standard.