Index-plus-alpha tracking under concave transaction cost

We will propose a new scheme to construct an index-plus-alpha portfolio which outperforms a given index by a small positive amount alpha. Among such methods is index tilting where the weight of an index tracking portfolio is slightly modified by taking into account the various information about individual assets. However, portfolios generated by these methods need not outperform the index, particularly when we compare the performance on the net basis, i.e., return after subtracting the transaction cost.
    The method to be proposed in this paper is to calculate a portfolio which keeps track of an index-plus-alpha portfolio with minimal transaction cost. The problem is formulated as a concave minimization under linear constraints, which can be solved in an efficient manner by a branch and bound algorithm. We will demonstrate that this method can usually outperform the given index when alpha is chosen in an appropriate manner.