Mean--variance portfolio selection problem: Asset reduction via nondominated sorting

Due to recent globalization of financial markets, investors have access to large numbers of assets. It may be beneficial for them to focus on a limited number of assets filtered out by some meaningful procedure. This, however, can result in selecting portfolios which, in terms of reward and risk, are not efficient in the original set of assets. A challenge is to have ways for determining subsets of assets in which the effect of lost efficiency would be minimal. To meet this challenge, we propose a method for asset reduction, based on the notion of layers of maxima and the concept of nondominated sorting. We conduct experiments on large problems derived from the USA stock market data. Our approach resulted in a much smaller loss of efficiency compared to two representative asset reduction methods known from the literature. We test the approach viability via computational experiments on the mean–variance problem of portfolio selection, with and without the cardinality constraints, and real-life data consisting of up to 1000 assets.