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In this paper, we study asset selection methods to construct a sparse index tracking portfolio. For its advantage over full replication portfolio, the concept of sparse index tracking portfolio has significant attention in the field of finance and investment management. We propose useful formulations to select assets for sparse index tracking portfolio. Our formulations are described as combinatorial optimization problems, and they can yield various asset selection methods, including some existing methods, by adjusting the values of parameters. As a result, the proposed formulations can provide a well-balanced asset selection to create successful sparse index tracking portfolios. We also provide numerical examples to compare the tracking performance of resulting sparse index tracking portfolios.