The term “portfolio” refers to any combination of financial assets such as stocks, bonds and cash. Portfolios may be held by individual investors or managed by financial professionals, hedge funds, banks and other financial institutions. It is a generally accepted principle that a portfolio is designed according to the investor's risk tolerance, time frame and investment objectives. The monetary value of each asset may influence the risk/reward ratio of the portfolio.

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When determining asset allocation, the aim is to maximize the expected return and minimize the risk. This is an example of a multi-objective optimization problem: many efficient solutions are available and the preferred solution must be selected by considering a trade off between risk and return. In particular, a portfolio A is dominated by another portfolio A' if A' has a greater expected gain and a lesser risk than A. If no portfolio dominates A, A is a Pareto-optimal portfolio. The set of Pareto-optimal returns and risks is called the Pareto efficient frontier for the Markowitz portfolio selection problem.[ Recently, an alternative approach to portfolio diversification has been suggested in the literatures that combines risk and return in the optimization problem.