Mean-Variance Hybrid-Entropy Model For Portfolio Selection With Fuzzy Returns

As China’s financial markets, especially the stock market booming, more and more citizens are choosing to invest in financial instruments. Investing in the financial markets, investors have to deal with trade-offs between returns and risks. In order to spread risk, the majority of institutional investors and individual investors will choose to invest in some portfolio. For China’s stock market, how to measure the return and risk when investing in the stock market are studied in this paper, and we try to establish a more suitable model to help investors make decisions. The main work is as follows:1. According to the characteristics of the fluctuation of Chinese stock market data, we choose the each ten stocks from different industries in SSE and SZSE as sample, weekly data of the samples from December 31,2010 to January 03,2014 were collected, including closing price, opening price, high price and exchange rate.2. We use the Markov method for forecasting fuzzy yields, with K-Means clustering method as auxiliary, and the yields are set as triangular fuzzy numbers. The liquidity of stock index is set as trapezoidal fuzzy numbers, calculated using the stock price and the exchange rate of the historical data.3. Give full consideration to the securities market’s random uncertainty and fuzzy uncertainty, we measure the portfolio’s future risk by both fuzzy variance and hybrid entropy, then solve the Mean-Variance Hybrid-Entropy Model using the multi-objective genetic algorithm. We exam the result by the cumulative rate of weekly return in 2014, the results show that in the premise of holding the stock for a long time, the Mean-Variance Hybrid-Entropy Model is better than the traditional Mean-Variance model and Mean-Entropy model in the stability of earnings and risks.4. According to the importance of the liquidity of the stock, and the impact of investors’subjective intention when making the investment objectives, we add the liquidity constraints to our Mean-Variance Hybrid-Entropy Model, and set all the targets as fuzzy goals, calculate and test it with the same sample data. The results implies that the effect of the model is different from the original model.This study may make contribution to the measurement of the return and risk in the stock market, the establishment and solution of portfolio, and we also want to give some practical advices to the investors in the stock with good application.