Research On Optimal Rebalance Strategy Based On Mutation Of Risk Characteristic Structure

Since Markowitz’s asset portfolio theory opened up modern asset allocation theory in 1952,asset allocation theory has become an important discipline,providing an important basis and method for investors to allocate assets.With the rise of computer technology,the problem of high-dimensional matrix calculation has been solved.As the characteristics of assets change over time,an important branch of the theory of asset allocation arise--the issue of rebalancing the optimal asset portfolio.Portfolio rebalancing is a powerful risk control strategy.As different investments in the portfolio produce different returns over time,the portfolio deviates from its target asset allocation and acquires risk and return characteristics that may be inconsistent with investors’ goals and preferences.Rebalancing strategies address this risk by standardizing the following criteria: determining how often the portfolio is monitored,how far asset allocations deviate from targets before rebalancing,and whether periodic rebalancing should restore the portfolio to its target or a specific value.Because each criterion affects the risk and return characteristics of a portfolio,the results of choosing a different criterion are very different.Since volatility is a well-known measure of asset risk and can be linked to the market,it is more commonly used as a basic indicator of rebalancing.For asset portfolios,according to Markowitz’s theory of optimal asset allocation,a very important input parameter is the covariance matrix.Most studies use the empirical covariance matrix as the risk index of the asset portfolio to enter the asset allocation model and obtain the optimal weight.However,Bouchaud and Potters(1997)pointed out that the empirical covariance matrix is hugely noisy,and using the empirical covariance matrix to measure the risk of asset portfolios can lead to huge deviations.The covariance matrix after noise reduction using random matrix theory(RMT)can more accurately reflect the correlation between assets.This can better measure the true risk of the asset portfolio.Therefore,using the covariance matrix after the noise reduction of RMT as the estimated covariance matrix,performing the optimal allocation and rebalancing index of the asset portfolio can achieve better results.Based on the analysis above,the research idea is determined as follows: First,use the RMT theory to remove the noise information of the variance covariance matrix,capture the real information carried by the asset covariance matrix,that is,use the RMT theory to capture the feature information of the covariance matrix,and then calculate the "clean" covariance matrix,which is used as a parameter to calculate the optimal portfolio weight.Second,the RMT theory is used to decompose the empirical covariance matrix,and the real information of the covariance matrix is abstracted as a feature factor,and the change of the feature factor is used to represent the change of the portfolio covariance matrix.Third,set the significance level,and use the Kolmogorov-Smirnov test to determine whether the characteristic factor has been mutated.Only when the characteristic factors are abruptly changed,that is,the risk structure characteristics of the asset portfolio are abruptly changed,is the asset portfolio rebalancing adjusted.In simple terms,three steps(capturing the portfolio covariance matrix information using RMT theory,constructing the eigenfactors of the covariance matrix,and rebalancing adjustments based on the mutation of the eigenfactors),jointly improve the investment strategy.The conclusions of this article are as follows: First,during the sample period,the asset portfolio after the noise reduction of RMT theory has higher returns and less fluctuations.The Sharpe ratio is higher than the benchmark portfolio based on Markowitz’s classic optimal asset allocation theory.Second,it is analyzed that the first eigenvalue of the RMT covariance matrix represents market information,and the second and third eigenvalues represent industry information.Based on this,a characteristic factor representing the real market information is well constructed,and the asset portfolio is adjusted based on real information changes in the financial market,and then the asset portfolio covariance matrix changes(through the constructed characteristic factor changes)to adjust the asset portfolio to the optimal portfolio.The rebalancing adjustment of the asset portfolio based on the mutation of the characteristic factors represents the adjustment of the asset portfolio following the changes in the financial market and macroeconomics,reducing unnecessary adjustments(the number of asset portfolio adjustments outside the sample period is reduced to 1 / 5 of the MW portfolio),reduced the handling fee(the transaction cost of about 1/4 of the MW portfolio cost),and also responded to the necessary adjustments(during the 2008-2009 global economic crisis and the 2015-2016 China stock disaster,transaction costs are rising faster).Third,it is confirmed that the covariance matrix after the noise reduction of the RMT theory is closer to the risk structure of the asset portfolio(the diversification of the RMT portfolio,Chengdu is higher),and thus the gains from diversification are improved(annualized income is5.49 times as many as MW portfolio)and risk reduction(annualized volatility is lower than MW portfolio).Therefore,it is inevitable that the Sharpe-ratio of the RMT combination is higher than that of the MW combination.Therefore,the covariance matrix after the noise reduction of RMT theory is used as the input variable of the optimal portfolio configuration,the optimal weight of the portfolio is calculated,and the asset portfolio is adjusted and rebalanced according to the change of the constructed feature factor after the covariance matrix decomposition.These facilitate to get better returns with less risk.