Abstract: 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.

Key words: bridge estimator, index tracking, sparse portfolios, stock selection, capital allocation