Portfolio selection, has always been an
important issue for investors and financial institutions. Portfolio selection or portfolio optimization problem, which is an
important topic in finance, can be defined as selection of the optimum
portfolio by investors, under some constraint and objectives that are determined
by their strategies.
Portfolios are composed of a number of assets where their values
can be affected by different events, such as political crisis, financial turmoil
and technological improvements. Due to the uncertain nature of these events, forecasting
future prices of assets is difficult. However, with his Modern Portfolio Theory,
Markowitz introduced a new idea for portfolio optimization. According to this
approach, an investor can reduce portfolio risk simply by holding combination of
assets that are not positively correlated, and obtaining efficient portfolio
can only be achieved by focusing on portfolio return and risk simultaneously.
However, Modern Portfolio Theory is based on the assumptions that the stock return
series are normally distributed and decision makers have quadratic utility
function. Surveys conducted in markets where relevant
assumptions are not valid and where the skewness and kurtosis values of
stocks are meaningful are widely seen in the literature.
Here you can further read about portfolio selection with higher moments: A polynomial goal programming model for portfolio optimization based on entropy and higher moments
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