Applied Research On An Improved Portfolio Method Using Principal Component Analysis

At this stage,the traditional mean-variance model proposed by Markowitz(1952)has been widely researched and promoted,but there are still many prob-lems.Part of the reason for the poor performance of market applications is due to the appearance of extreme positions.Traditional portfolio theory basically select-s portfolios from existing,correlated assets,but Partovi(2004)proposed a new method to analyze the efficient frontier portfolios under the premise that short selling is allowed.That is,the original asset set is reorganized into a set of unre-lated portfolios which is called the principal portfolios.These principal portfolios constitute a new investment environment in which assets are not correlated,and provide new research ideas for the optimization process of any portfolios.This method can increase the diversification of the portfolios.Therefore,this paper will improve the mean-variance model,risk parity model and most diversified portfolios based on the concept of principal portfolios.Traditional principal component analysis(PCA)is based on the eigenvalue de-composition of covariance matrix or correlation matrix.This paper analyzes the sensitivity and stability of the inverse matrix of the correlation matrix and finds that the inverse matrix of the correlation matrix may contain more information.Therefore,in this paper,the inverse matrix of the correlation matrix is used in the principal component analysis to establish the principal portfolios,and then we can observe the market empirical performance of the model.Firstly,the tra-ditional mean-variance model using principal component analysis is improved.In this paper,the mean-variance model using principal component analysis based on the inverse of the correlation matrix is established and recorded as I-PCMV,and compared with the traditional mean-variance model using principal component analysis(PCMV),mean-variance optimization model(MVO)and equal-weight portfolios(EM).It is concluded that the I-PCMV model performs better than the PCMV model through the analysis of the empirical results by selecting ap-propriate measurement indexes.The traditional mean-variance model only estimates the portfolio risk and does not diversify the portfolio risk.In recent years,the risk parity model,which has attracted much attention,aims at dispersing portfolio risk through equal risk contribution.Besides,the most diversified portfolio is also a strategy that can effectively diversify portfolio risk.This paper also introduces the risk parity model(RP)and most diversified portfolio(MDP)to diversify the portfolio risk.Considering that the correlation between principal portfolios is zero,this greatly facilitates the establishment of risk parity model and most diversified portfolio.In this paper,the traditional risk parity model and most diversified portfolio are improved.Based on the inverse of the correlation matrix,a improved risk parity model using principal component analysis(I-PCRP)and a improved most di-versified portfolio using principal component analysis(I-PCMD)are established.Compared with the risk parity model using principal component analysis(PCRP)and the most diversified portfolio using principal component analysis(PCMD),it concludes that the improved portfolio method using principal component anal-ysis based on the inverse matrix of correlation matrix performs better than the traditional portfolio method using principal component analysis based on the correlation matrix.The empirical part of this paper takes the constituent stocks of SSE50 Index,CSI300 Index and CSI500 Index as the research object to establish the stock pool,and uses the cumulative return,annualized return,sharpe ratio,and maximum drawdown of the strategy to measure the model's performance.The optimal in-vestment strategy of each improved portfolio method using principal component analysis is selected by retaining diferent number of principal components and changing the position adjustment cycle,the results show that the improved port-folio method using principal component analysis based on the inverse matrix of correlation matrix performs better than the traditional portfolio method using principal component analysis based on the correlation matrix.In addition,ac-cording to the investor's risk preference and the trade-offs between the transaction cost and the profit according to the adjustment of the position adjustment,the appropriate number of retained principal components and the period of position adjustment cycle can be selected.