Research Of Stock Index Tracking Based On Lasso

Indexation investment can fully disperse non-systemic risk and get average marketreturns with low cost, so index funds, stock index futures, ETF index products has got rapiddevelopment in China. As a specific form to manage indexation investment, Index trackingcan effectively guide the stoke index arbitrage and design the products of index investment, sothis article puts forward a index tracking method based on Lasso to construct the indextracking portfolio and track the target index effectively.Lasso methods for high dimensional model have simple operation, it can be used for highdimensional stock data, and can complete the estimation problem and selection problem at thesame time, therefore this paper describes the theory of Lasso, Adaptive Lasso, Relaxed Lassomethods in detail, compares their advantages and disadvantages, then systematic describedtheir algorithm and parameter estimation. In empirical research, with the help of R languageprogramming, I use Lasso to build a tracking portfolio, chose CSI300index for trackingtarget, and use522data to build model from2012to2014, At last, the tracking performanceis evaluated in inner-sample interval and outer-sample interval two periods.The empirical results reveal that (1) From the overall perspective, using Lasso method tobuild stock portfolio can achieve good results;(2) More stocks can get better results, butconsidering the transaction cost and maintenance cost, the quantity of stocks should not be toomuch;(3) Comparing Lasso, Adaptive Lasso and Relaxed Lasso three methods, the AdaptiveLasso has obvious advantages in index tracking problem, first the weight distribution has noobvious concentration trend, secondly the Adaptive Lasso can achieved the best trackingperformance;(4) From financial perspective, build a small stock to tracking index has stronginstability, but Adaptive Lasso can make uniform weight distribution, and considering the lowtransaction cost factors, for individual investors, when market is relatively stable, it is worth atry;(5) The Adaptive Lasso can get an ideal forecasting effect in short-term and medium-term,but the long-term forecast is failure, so we suggest outer-sample interval does not exceed150 days.