A condition for asset redundancy in the mean-variance model of portfolio investment

The mean-variance approach to portfolio investment exploits the fact that the diversification of investments by combination of different assets in one portfolio allows for reducing the financial risks significantly. The mean-variance model is formulated as a bi-objective optimization problem with linear (expected return) and quadratic (variance) objective functions. Given a set of available assets, the investor searches for a portfolio yielding the most preferred combination of these objectives. Naturally, the search is limited to the set of non-dominated combinations, referred to as the Pareto front. Due to the globalization of financial markets, investors nowadays have access to large numbers of assets. We examine the possibility of reducing the problem size by identifying those assets, whose removal does not affect the resulting Pareto front, thereby not deteriorating the quality of the solution from the investor’s perspective. We found a sufficient condition for asset redundancy, which can be verified before solving the problem. This condition is based on the possibility of reallocating the share of one asset in a portfolio to another asset without deteriorating the objective function values. We also proposed a parametric relaxation of this condition, making it possible to removemore assets for a price of a negligible deterioration of the Pareto front. Computational experiments conducted on five real-world problems have demonstrated that the problem size can be reduced significantly using the proposed approach.