Efficient Portfolios Computed via Moment-Based Bounding-approximations: Part II - DBFS

We develop and analyze a new second-order upper bound on the expectation of convex function of random variable with finite support. If the finite support is extended to infinite interval then we prove that the new upper bound tends to an upper bound already available in the scientific literature. We apply the upper bound as a second-order lower bounding approximation on the expected value of a concave utility function. We prove that the optimal solution of the approximate optimization problem yields mean-variance efficient portfolio. We illustrate how to use the resulting portfolios in practice by designing a daily trading strategy with stocks traded on the New York Stock Exchange (NYSE). Out of sample numerical results are presented for 29 years of daily trading for 24 stocks from NYSE.