Improving Portfolio Optimization Model Based On The Notion Of Entropy

Hconomic globalization and financial integration brings unprecedented opportunities to the national investment market, but at the same time, investment risk is also growing with it. In this complex financial background, how to enhance our ability to resist market fluctuations to obtain a more stable return is determined by a reasonable pattern to capture the law of market changes, helping us to measure the accurate investment risk. In recent years, the rapid development of entropy theory makes it get more and more attention and application because of its needing no distribution assumptions and concluding high moment information of the variable among a large number of portfolio risk measurement methods.Based on Markowitz’s MV model and William Sharpe’s single-index model, we introduce the notion of entropy into the portfolio model. Using the idea of risk decomposition from single-index model and the property of entropy, we divided the entropy into two parts, mutual information and conditional information entropy respectively. The mutual information entropy of one stock represents the system risk and the conditional information entropy of one stock represents the non-systematic risk. Since Beta in single-index model measures the sensibility of the rate of returns of the asset face to the market, we use it as a weight of mutual information, so different entropy of the stocks can be added. As a result, we obtain the entropy of the portfolio as a risk measurement and establish a portfolio model based on entropy offer investors a new way of decision-making.On this basis, we select stocks as the analytical sample which performed better in Shanghai Stock Exchange of China, using the new model to establish a portfolio. Then, we compare the similarity and differences between entropy and variance in the measurement of risk. We can conclude that these two methods in measuring the risk have somehow consistency. By comparing the new model with MV model in efficient frontier and the investment weights, we verify the validity of the new model. The results show that when investors expect the same rate of return, the new model portfolio strategy is more concise contrast to the MV model. The new model can provide a less number of securities in a portfolio to achieve a similar outcome obtained by MV model. The new method not only avoids the transaction costs and management costs caused by the excessive decentralized investment, but also saves the information resources, and enhances the investors’ ability in information processing.