Common formulations of portfolio utility functions define it as the expected portfolio return (net of transaction and financing costs) minus a cost of risk. The portfolio optimization problem is specified as a constrained utility-maximization problem. While ignoring higher moments can lead to significant over-investment in risky securities, especially when volatility is high, the optimization of portfolios when return distributions are non- Gaussian is mathematically challenging. This risk-expected return relationship of efficient portfolios is graphically represented by a curve known as the efficient frontier.Īll efficient portfolios, each represented by a point on the efficient frontier, are well-diversified. For portfolios that meet this criterion, known as efficient portfolios, achieving a higher expected return requires taking on more risk, so investors are faced with a trade-off between risk and expected return. It assumes that an investor wants to maximize a portfolio's expected return contingent on any given amount of risk. Modern portfolio theory was introduced in a 1952 doctoral thesis by Harry Markowitz see Markowitz model. 4.2 Cooperation in portfolio optimization.
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