A Multi-Period Portfolio Selection in a Large Financial Market

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This paper addresses a multi-period portfolio selection problem when the number of assets in the financial market is large. Using an exponential utility function, the optimal solution is shown to be a function of the inverse of the covariance matrix of asset returns. Nonetheless, when the number of assets grows, this inverse becomes unreliable, yielding a selected portfolio that is far from the optimal one. We propose two solutions to this problem. First, we penalize the norm of the portfolio weights in the dynamic problem and show that the selected strategy is asymptotically efficient. Second, we penalize the norm of the difference of successive portfolio weights in the dynamic problem to guarantee that the optimal portfolio composition does not fluctuate widely between periods. This second method helps investors to avoid high trading costs in the financial market by selecting stable strategies over time. Extensive simulations and empirical results confirm that our procedures considerably improve the performance of the dynamic portfolio.