Analysis Of Portfolio Based On Advanced Tsallis Generalized Entropy Principle

In today’s society,"investment" is no longer a word seems as mysterious as before, especially with the coming of Internet Finance in recent several years. the concept about investment has been blowed to a lot of common people. There are quite a few people want to realize investment hedge through reasonable investment by using their income and assets. As a core theory of modern financial theory, portfolio management is dedicated to solving the problem that how to choose assets to conduct portfolio and how to allocate weights of different assets so that investors can gain the most or suffer the least. According to the modern portfolio theory, diversified portfolio provides convenience to eliminate the non-systemic risk. Thus portfolio management is the focus content of investment decisions.At the same time, the choice of indicators to measure risks is also an important research. In1952, Markowitz, the pioneer of portfolio theory, proposed using variance to measure risk. In the1990s, JP Morgan putted forward VaR with favorable statistical properties. There are some shortcomings, such as VaR indicators itself does not reflect the tail of the information, so that risk with small probability that will make a loss cannot be predicted. Therefore Rockafellar and Uryasev (1999) proposed a new indicator based on VaR which is named CVaR risk measure.With the development of cross-disciplinary in the theoretical study, foreign scholars applied entropy and generalized entropy to measure risks in investment securities. Entropy is a measure of uncertainty, larger entropy value indicates less information about the target and more uncertainty. Thus this paper pulls Minimum-Torsion Bets which can reduce correlation of assets while remaining the maximization of market information, into Tsallis generalized entropy, then proposes this advanced Tsallis generalized entropy to measuring portfolio risk. This method allows short selling so that it can apply to margin trading in the near future. The advanced model not only Improves the practicability of Tsallis generalized entropy, but also reduce portfolio risk.An empirical example with eight stocks at shanghai securities exchange is offered, which from January5,2009to October8,2013. Firstly, comparing the element correlation matrix with sample correlation matrix, which shows that correlations of elements tend to be zero. Then after calculating portfolio weights and variance of MV model and advanced Tsallis generalized entropy separately, we get a conclusion that advanced Tsallis generalized entropy truly achieves short celling and reduces portfolio risk at the same time.