Empirical Study On The Influence Of Marginal Distribution Setting On Copula Modeling

Asset portfolio has always been the focus of financial theory research and the core content of financial practice investment.The key point of portfolio allocation is to find the correlation between different assets,namely the joint distribution of asset returns.Copula can decompose a multi-dimensional joint distribution into multiple marginal distributions and a dependent structure to describe the correlation between marginal distributions.Meanwhile,it can also capture the non-linear,asymmetry and tail anomalies between variables,so it has a unique advantage in constructing the joint distribution structure of assets.But in fact,the properties of joint distribution come from not only the dependent structure between assets(i.e.Copula),but also the marginal distribution structure of each asset itself.However,many papers ignore the influence of marginal distribution on Copula,which may bring two problems.Firstly,some marginal distribution assumptions are not suitable for the data characteristics,so the residual sequence obtained from marginal distribution modeling may not meet the preconditions of Copula;Secondly,the final results from different marginal distribution models may be very different,so if only one marginal distribution model is used to build joint distribution,the final conclusion may not be accurate.This paper draws on Patton's empirical method of portfolio allocation using Copula,and studies the influence of different marginal distribution models on Copula modeling by selecting different marginal distribution models and comparing the differences between their final empirical results.This paper uses monthly data from January 2005 to June 2019,and considers a rational investor's asset allocation among risk-free assets,the “big cap” and the“small cap” in China stock market in order to obtain the most investment income.This process firstly uses the 12 different marginal distribution models(GARCH family and SV family)to model the “big cap” and the “small cap” in China stock market respectively.After the standardized residual of marginal distribution modeling is obtained,different joint distributions are constructed by using different Copulas.At last,the joint distribution is used to make the decision of asset allocation in each period outside the sample.The final results show that almost all the SV models perform better than the corresponding GARCH models.And in the SV and GARCH models,the best performance is the model considering the leverage effect,reflecting that the current China stock market presents the impact of the yield on the volatility asymmetry.According to the final results of all marginal distribution models,the results of different models are quite different,which also reveals that different marginal distribution settings will have a greater impact on the joint distribution constructed by Copula.In the empirical process,this paper also considers the influence of relaxing a short-sales constraint.This shows that much of the information content of these models is lost if the investor is short-sales constrained.