Amendment To Arbitrage Pricing Model And Empirical Test

The basic idea of arbitrage pricing theory (APT) is based on the assumptions:Firstly, any asset's prices can be expressed as some common factors' linear combination. Secondly, the distribution of asset's future return rate has been known. Thirdly, short-sale is allowed. The arbitrage pricing theory which is proposed by Ross is comparable with CAPM.Recently, both board and domestic scholars still be committed to carry on more deeply and widely applied research of the arbitrage pricing model, and have made considerable progress.The classic promotion ideas can be summarized as follows:rj-E(rj) which is the basis of security j is directly proportional to the earnings deviation I-E(I) of'common factor':Model 1:rj-E(rj)=βj(I-E(I))+εj .This promotion mode just considered simply as:The earnings deviation rj-E(rj) of the security j is a growth of earnings deviation I-E(I) of'common factors I'.In this paper, we considered the nonlinear of the basis changing.That we think that the secondary basis (I-E(I))2 (which is known as basis risk)of the'common factor I' also has influence on the earnings deviation rj-E(rj). In other words, this paper study follows model:Model2:rj= E(rj)+βj(I-E(I))+(I-E(I))2+εjThen consider the impact on the securities return caused by the skewness and kurtosis of the Stock Returns Distributions. Re-modified the arbitrage pricing model and get the following model:Model 3:rj=E(rj)+βj(I-EI)+θj (I-EI)2+λj (I-EI)3+δj (I-EI)4+εj.Based on regression analysis method, this paper gave the estimation of the model which contain the coefficient of the basis risk item(fluctuation item). According to the comparison of empirical analysis and fitting degree, we found that the model 2 joining the basis risk item and the model 3 joining the skewness and kurtosis is able to giving more reasonable explanation of return on assets. Compared with the model 1, the prices predicted by the model 2 is closer to the actual prices, and the model 2 has higher fitting degree. Compared with the model 2,the model 3 has a more reasonable explanation level for securities pricing.