Portfolio Optimization Based on Funds Standardization and Genetic Algorithm

Abstract

When investing in the stock market, the first problem and one of paramount importance which investors have to face is making the proper stock selection. Selecting the stocks that simultaneously offer high return and low risk is a difficult problem that is worth investigating. However, the traditional risk calculation based on the modern portfolio theory (MPT) of portfolios has some defects. The MPT method requires the calculations of every relationship between each pair of stocks in the portfolio, entailing high computation complexity, which grows exponentially with the increased number of stocks. Besides, the traditional calculation is unable to calculate the coefficient of variation, and merely considers the relationship between each pair of stocks, so it cannot accurately assess portfolio risk. Therefore, this paper proposes a novel method, funds standardization, and utilizes it to represent the portfolio return and calculate portfolio risk. The fluctuation of portfolio funds standardization shows not only the relationships between each pair of stocks, but also the interactions among all stocks. Hence, utilizing funds standardization can accurately assess portfolio risk and completely represent the mood swings of investors. Compared with the traditional method, the proposed method significantly reduces the computation complexity because the complexity does not increase when the portfolios stock number increases. We combine the genetic algorithm, Sharpe ratio and funds standardization to find the optimal portfolio. In addition, we utilize the sliding window to avoid the over-fitting problem, which is common in this field, and test the effect of all kinds of training and testing periods. The experimental results show that the portfolio can spread the risk effectively, and that the portfolio risk can be assessed accurately by utilizing the funds standardization. Comparing with the traditional method, our method can identify the optimal portfolio efficiently and establish a portfolio that has lower risk and stable return.