Research On Kelly Policy Optimization Based On Shrinkage Estimation Method

Although Kelly’s portfolio theoretically maximizes the logarithmic growth rate of wealth and has the highest growth rate of return compared to any other portfolio.However,in practice,it is not the case,especially with greater risk and instability in short term,and short-term investors in the stock market are the majority.Therefore,in this case,it is necessary to reduce the short-term volatility and risk of Kelly ’s portfolio.The traditional Kelly model is risky.One of the main reasons is that most of its model parameters are estimated through sample data,but the sample parameters themselves have large estimation errors.Therefore,to some extent,it increases the risk of the model.Since most of the input parameters of the traditional investment model are estimated from the sample parameters,which has a large risk,many researchers have proposed corresponding correction methods.At present,the most popular method on the market is the shrinkage estimation method.The common shrinkage estimation form is to introduce another element estimator to revise the sample parameters.De Miguel & Utrera(2013)proposed to rewrite the target mean estimator as the weighted average of the original sample mean estimator and the constant vector,and proposed that the shrinkage estimation method may have a large performance improvement to aggressive portfolios;Ledoit & Wolf(2000)proposed a method for market matrix shrinkage estimation,and the introduction of market matrix is also conducive to reducing the error of traditional portfolio covariance matrix estimates,and also play a large role for aggressive portfolios.Then,Ledoit& Wolf(2003)introduced a shrinkage estimation method of constant coefficient correlation matrix on this basis.In terms of weight shrinkage,most literatures still use traditional investment portfolios models combined in pairs.Therefore,considering the aggressive characteristics of Kelly’s portfolio,on the basis of previous scholars’ research,this paper studies the impact of different shrinkage estimation methods on the traditional Kelly model and the differences between different shrinkage methods.estimation error of sample parameters,this paper adopts different shrinkage estimation methods according to the basic characteristics of Kelly model.The estimation of different parameters adopts a unified shrinking method,that is,the parameter form after shrinking estimation is expressed as the weighted average of the original sample moment and another shrinking moment,so as to realize the optimization of the traditional Kelly model.In the selection of shrinkage estimation method,the constant vector proposed by De Miguel & Utrera(2013)is used for the mean shrinkage estimation.In the covariance matrix shrinkage estimation method,combined with the characteristics of the Kelly model,the method proposed by Ledoit & Wolf(2003)is used.Market matrix and constant coefficient correlation matrix shrinkage methods and the most common shrinkage estimation method of identity matrix,among the sample weight shrinkage estimation methods,the minimum variance portfolio and equal weight portfolio shrinkage estimation methods are used.In order to better understand the impact of the shrinkage estimation method on the model,this paper firstly conducts a simulation,using the fama-french threefactor model to simulate different asset return data,in order to initially understand these different shrinkage estimates.The characteristics of the model.The market studied in the empirical analysis is the Chinese stock market,and the daily data of20 industry indices in China from January 1,2006 to December 31,2021 are selected,and the corresponding Kelly investment portfolio is constructed on this basis.,and use the control variable method to explore the impact of different shrinkage estimation methods on the traditional Kelly model,and further compare different shrinkage models,so as to provide investors with certain suggestions.The main conclusions of this paper are as follows:(1)In the simulation study,all Kelly models using the shrinkage estimation method have better performance than the traditional models,whether in terms of return,volatility,Sharpe ratio,maximum return withdraw.(2)In the empirical study of a single shrinkage estimation method,the shrinkage estimation method that introduces a constant vector is better than other shrinkage methods.(3)In the pairwise mixed shrinkage estimation model,when the mean constant vector shrinkage and the constant coefficient correlation matrix shrinkage are performed on the traditional Kelly model,the shrinkage estimation method at this time is the best.(4)In the three shrinkage estimation models,when the traditional Kelly model is subjected to mean constant vector shrinkage,market matrix shrinkage and equal weight combination shrinkage,the performance of the model is compared to the other three shrinkage estimation models.The effect is the best,but considering that there are three shrinking directions at this time,the performance of the model is actually lower than the traditional Kelly model,which is caused by excessive shrinkage to a certain extent.(5)In China’s stock market,the method of shrinking the mean and covariance matrix of the traditional Kelly model is better than the weight shrinking estimation method to a certain extent.The main innovations of this paper include:(1)This paper verifies and illustrates the possible shrinkage estimation methods for aggressive portfolios proposed by existing scholars De Miguel & Utrera(2013)and Ledoit & Wolf(2003).By solving nonlinear Planning problems to carry out asset allocation,which to a certain extent enriches the framework theory of traditional Kelly model performance improvement.(2)From the perspective of the direction of shrinkage estimation,most of the literature currently chooses to optimize the traditional model for single shrinkage estimation,but this paper is based on constant vector mean shrinkage,market matrix,constant coefficient correlation matrix,unit matrix,etc.The traditional model adopts the research on the shrinkage estimation of all three,which is innovative to a certain extent,which further enriches the theoretical system of the shrinkage estimation method.(3)This paper comprehensively analyzes and studies the impact of each shrinkage estimation direction on the traditional Kelly model,and uses the control variable method to analyze the performance of different shrinkage estimation models.It provides certain investment advice for Chinese and even global investors to apply aggressive investment portfolios in the Chinese market.There are still some deficiencies in this paper:(1)Although this paper applies the corresponding shrinkage estimation method for Kelly’s portfolio,there are many other shrinkage estimation methods for the portfolio that have not been applied.(2)Although the research object of this paper is the Chinese stock market,because the selected asset allocation is an industry index,for the analysis of individual stocks,whether the Kelly strategy using the shrinkage estimation method is still applicable to individual stocks with more missing data,Further research is needed.(3)The different shrinkage estimation methods used by the traditional Kelly model in this paper are all existing methods.In the follow-up research,innovative shrinkage estimation methods can be further proposed for the Kelly model,so as to further improve the Kelly model optimization theory system.