A new optimal portfolio selection strategy based on a quadratic form mean–variance model with transaction costs

A new optimal portfolio selection method within the Markowitz mean–variance framework is presented in this paper. The model proposed in the paper includes expected return, trading risk, and in particular, a quadratic form in the transaction costs of the portfolio. Using this model yields an optimal portfolio solution that maximizes return and minimizes risk as well as the transaction costs by moderating the transaction volume and smoothing the volume of traded securities in the trading process. A set of first-order autoregressive (AR) models is utilized to estimate the future returns of the securities in the portfolio, and the AR parameters are estimated by the least-squares method with a moving window. The optimization problem that results from this approach is convex and can thus be solved by quadratic programming (QP). A case study demonstrates the effectiveness and the significant performance improvements of the proposed optimal portfolio selection strategy.