An Emperical Study On Stochastic Portfolio Theory In Chinese Stock Market

One of the core questions in portfolio management is:how should investors invest their wealth in the financial market?Financial mathematics has tackled this problem in numerous ways,typically through the modeling of market prices and the optimization of an investment objective.In addition,Stochastic Portfolio Theory(SPT)gives a new methodology,which is descended from Markowitz's modern portfolio theory,but out of the mean-variance framework.SPT was originally proposed by E.Robert Fernholz,the main purposes of this theory is to analyze the long-term behavior of stocks and portfolios,and to explain the phenomena and internal structure of the market through some special investment portfolios.SPT has relatively general assumptions about the market,and the portfolio selection criterion is to outperform a benchmark with probability one,which will lead to arbitrage behavior in the market.The emergence of arbitrage opportunities means that SPT gives up the No-Arbitrage Hypothesis.In fact,the theory chooses Market,Diversity rather than No-Arbitrage Hypothesis.In order to construct portfolios that outperform the market portfolio with probability one,and to analyze the long-term performance of portfolios,Robert Fernholz developed Portfolio Generating Functions,which allows us to construct portfolios based on current observability.And if some conditions are imposed,which are consistent with the observable characteristics of actual portfolios and real markets,we can also use SPT to determine whether the Functionally Gen-erated Portfolios outperform the market.SPT has a complete theoretical system which has been developed for many years,and has been supported by a large number of empirical results.However,for Chinese stock market,relative researches have not been carried out yet.Based on this,this paper selects data from all constituents of SSE 50,CSI 300 and CSI 500 Index from 2004 to 2019,trying to analyze the performance of Functionally Generated Portfolios in Chinese market comprehensively,especially for several portfolios determined by measures of diversity.We discuss and study the perfor-mance of their corresponding portfolios in different asset pools in Chinese stock market,and give discussions of theoretical and empirical results.Main conclusions of this research can be made as follows:1.In the static stock pools,diversity-weighted portfolios basically outperform the market,and the performance of a portfolio is closely related to its diversity.2.When p?(log n/log(n?),0),Dp is not a measure of diversity.However,the portfolio determined by this function still outperforms the market.princi-pally because this portfolio is overweighted in the small stocks and under-weighted in the large stocks.3.In the dynamic CSI500 stock pool,the phenomenon that the diversity-weighted portfolios outperform the market is significant.4.Generally,diversity-weighted portfolios outperforms the market,after a rel-atively long time-horizon,so they are suitable for long-term holding.5.For a Functionally Generated Portfolio,the relative return is determined by its diversity and weights of small stocks.However,its absolute return depend on the overall market return.Overall,the empirical results in Chinese stock market is basically consistent with the theoretical results.Some of the conclusions are worthy of in-depth discussion,which are analyzed in detail in this thesis.