Robust portfolio selection for sparse index tracking under no short-selling and full investment constraints

For financial index tracking, it is desirable to build a sparse portfolio of a small number of assets to save transaction costs. For all we know, a majority of the pertinent literatures on sparse index tracking are mainly concentrated on the penalized least squares estimation under the cardinality and no short-selling constraints. Nevertheless, the return series of financial index often exhibit outliers, and thus the above literatures may fail to produce a robust solution for index tracking. In this paper, we indeed to provide a general procedure to build robust portfolio that can undertake stock selection and capital allocation for financial index tracking. To be more realistic, we further take the full investment constraint (or budget constraint) into consideration. Numerical simulations indicate that the proposed method has good resistance to heavy-tailed error and outlier contamination. Finally, the out-of-sample performance of the new portfolios is compared empirically by tracking the SSE 50 index and FTSE China A50 index.