Portfolio Risk Analysis From An Entropy Perspective

The securities market is an intricate dynamic system with people involved which filled with many uncertain factors, these influences the risk of investment future returns. We think the risk is the uncertainty, including random factors in market and fuzzy factors in cognition, and the geometric mean output ratio comprises random uncertainty or fuzzy uncertainty. In classical theory of portfolio model, most are only considers randomness or fuzziness, but we try developing a measure of risk based on the concept of hybrid entropy as a kind of measurement for risk.Hybrid entropy solves the limitation of the variance and VaR as the investment risk measured, a new portfolio model has been developed. The model is based on the minimum hybrid entropy and maximum valued-added entropy model by using hybrid entropy to measure risk, and making value-added entropy indicate the value-added rate of funds. Meanwhile, the model take into account the transaction costs of market friction factors, and it can be calculated by using fuzzy multi-objective decision-making theory and method. In addition, a novel portfolio model based on risk weight coefficient is proposed, by introducing risk weight parameter, the model gets more flexible and useful to individual investors have different risking preference.Finally, using 50 index stocks of Shanghai-Shenzhen 300 index, we make an authentic analysis to the decision model of combinatorial deviation based on the Matlab software and LINGO software. The result shows that the investment strategy of minimum hybrid entropy and maximum valued-added entropy model achieved a satisfactory effect on the risk aversion investors. The researches about the new model have more important theoretical value and practical significance for the portfolio. Besides, the portfolio model of introducing risk weight coefficient have positive effects on the risk seeking investors and the risk indifference investors, but it has little effect on the risk aversion investors, so the model needs further improvement.