Abstract
In the field of investment, how to construct a suitable portfolio based on historical data is still an important issue. The second-order stochastic dominant constraint is a branch of the stochastic dominant constraint theory. However, only considering the second-order stochastic dominant constraints does not conform to the investment environment under realistic conditions. Therefore, we added a series of constraints into basic portfolio optimization model, which reflect the realistic investment environment, such as skewness and kurtosis. In addition, we consider two kinds of risk measures: conditional value at risk and value at risk. Most important of all, in this paper, we introduce Gray Wolf Optimization (GWO) algorithm into portfolio optimization model, which simulates the gray wolf’s social hierarchy and predatory behavior. In the numerical experiments, we compare the GWO algorithm with Particle Swarm Optimization (PSO) algorithm and Genetic Algorithm (GA). The experimental results show that GWO algorithm not only shows better optimization ability and optimization efficiency, but also the portfolio optimized by GWO algorithm has a better performance than FTSE100 index, which prove that GWO algorithm has a great potential in portfolio optimization.
Highlights
Since the mean-variance (MV) model is proposed by Markowitz [1,2], the portfolio optimization problem has attracted a lot of attention
In MV model, variance is used as the risk measure, and it is assumed that returns are normally or elliptically distributed [3]
We introduce several constraints, including skewness and kurtosis, into the basic second-order stochastic dominance portfolio optimization model
Summary
Since the mean-variance (MV) model is proposed by Markowitz [1,2], the portfolio optimization problem has attracted a lot of attention. Point out that the return to the world’s fourteen major stock market is not normally distributed, which means MV model lacks effectiveness in practical applications Variance counts both upward and downward deviation, which is contrary to the definition of investment risk. Konno [6] and Speranza [7] introduce the mean absolute deviation (MAD) into portfolio optimization model as risk measure. In this paper, we take skewness, kurtosis, CVaR or VaR into SSD framework as constraints, which we called it MCVSK and MVSK model respectively. GWO algorithm is used to solve MCVSK and MVSK portfolio optimization model.
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