A compact mean–variance–skewness model for large-scale portfolio optimization and its application to the New York Stock Exchange (NYSE) market

This paper develops a portfolio optimization model that uses the first three moments of the distribution of the rate of return on investment in selecting portfolios. An alternative measure of skewness is designed for the purpose, and, in the grand scheme of compact factorization, the proposed model is transformed to an equivalent quadratic program with a quadratic constraint with 2 T nonlinear variables and terms, where usually T⩽50. Extensive computational results are obtained on a real-world dataset of the returns of about 3500 stocks that were traded in the NYSE from 3 January to 17 September 2002. In summary, the portfolios built by the proposed model gave the average return on investment of 66.85% over the course of 150 trading days, a period in time when US economy and stock markets suffered tremendously after the tragic events of September 2001.