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The term “portfolio” refers to any combination of financial assets such as stocks, bonds and cash. Portfolios may be held by individual investors and/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.
When determining a proper asset allocation one aims at maximizing the expected return and minimizing 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 tradeoff 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.