Principal Component Factor Model Of Index Tracking

As one of the popular methods of passive investment management,index tracking attracts more and more attention of investors and researchers.But due to the limit of capital,most investors prefer to reduce the number of stocks in the portfolio to track the index.Through adding a cardinality constraint to the least square model,it can be realized.However,when the sample size is small,and the market micro-structure changes radically,the precision of the model is poor.According to the factor model,we improve the precision of the model by converting Mean-Square model which tracks the rate of return directly to a new model which tracks rate of return by tracking the factor exposure coefficient indirectly.In recent years,Single-factor model,Fama-French 3-factor model,5-factor model are popular.But in reality,it is difficult to compute all factors.In order to overcome this difficulty,The main work of this paper is to extract the effective factors that impact returns of stock and index through Principal Component Analysis,and calculate risk exposure for each asset on these factor.In numerical experiment,we define tracking error and compare the stability by tracking error.First,we rewrite the factor Mean-Square model with cardinality constraint to a mixed integer programming model and solve the new model by Branch and Bound method,then verify the effectiveness of new model,but it will cost much time.So we rewrite the model into a multiple blocks target minimization problem and enhance the solving efficiency of new model by penalty Proximal Alternating Linearized Minimization method.