Multi-objective portfolio selection with skewness preference: An application to the stock and electricity markets / Karoon Suksonghong - Karoon, Suksonghong (2014)

(untitled)
The mean-variance (MV) efficient portfolios (Markowitz, 1952) are obtained by searching for portfolios that attain the global minimum variance at a given level of expected return. However, MV efficient portfolios may not yield superior result due to the fact that the distribution of returns to financial assets is not normal but skewed. Past studies proved that investors whose utility can be approximated by the third-order Taylor’s series expansion exhibit preference for positive skewness. This preference implies that portfolio selections should consider the mean-variance-skewness (MVS) model. However, studies on implications of skewness preference on portfolio selection are very limited due to computation difficulty. To overcome this difficulty, this study proposes the use of multi-objective evolutionary algorithms (MOEAs) that are applied in the field of engineering for solving the multi-objective MVS portfolio optimization problem. The superiority of this method is its ability to generate a set of MVS efficient portfolios within a single run of algorithm. The non-dominated sorting genetic algorithm II (NSGA-II), the improved strength Pareto evolutionary algorithm II (SPEA-II), and the compressed objective genetic algorithm II (COGA-II) were applied. The MVS efficient surface was graphically plotted in the three-dimension MVS space. The analysis started with an application to the stock market. Using the annualized weekly and monthly rates of return of 16 emerging market indices, expected returns of the MVS efficient portfolios are found to be smaller for those with larger skewness, at a given value iv of standard deviation. The results suggest that investors have to sacrifice expected return for skewness. At a given value of expected return, the standard deviation decreases for MVS efficient portfolios with smaller skewness. Investors have to expose themselves to a larger return dispersion in order to increase the probability of gaining extreme expected returns. This study develops a single-period model that allows for heterogeneous degree of risk aversion and skewness preference to investigate the impact of skewness preference on the efficient portfolio choice. Applying the returns of 29 component securities of Dow Jones Industrial Average index (DJIA), it was found that investors with greater skewness preference are willing to accept lower expected returns for a portfolio with higher skewness. In addition, investors with greater skewness preference are willing to accept larger return dispersion in exchange for a flatter right tail of the return distribution. The results explain why investors hold underdiversified portfolios. Investment allocations tend to concentrate on a small number of securities when the degree of skewness preference increases for a fixed level of degree of risk aversion. The MVS analysis is extended to solve the electricity allocation problem in the electricity market, where the number of trading choices is considerably small. The electricity spot prices of nine pricing zones in the Pennsylvania-New Jersey-Maryland (PJM) market were utilized. To prevent excessive under-diversification, the MVS model is modified (MVS-D) by incorporating an additional objective to increase the number of trading choices included in the portfolio solutions. COGA-II, designed for handling an optimization problem with many objectives, have good optimization performance, particularly for the MVS-D model. v While the MVS efficient portfolios are found in the efficient set of MVS-D model, the MVS strategy provides better results than the MV model to a generation company.