Research on Mathematical Methods of Improving Fama and French Three-factor Model Based on ETF Factors

Abstract

Abstract Will ETF factors help to improve Fama and French 3 factor Model? Research has examined the Fama French model in different countries and its risk premium in different mathematical ways. This paper reconstructs the Fama-French model by replacing market capitalization size index (SMB) and book-to-market ratio index (HML) to other Exchange Traded Fund (ETF) factors to investigate whether ETF factors will improve the Fama French model. After comparing 15 ETFs, Factors EMD (GDP growth index) and SMG (factor IYC minus factor IYK) are chosen for our adapted risk model because of a relatively low rate of correlation and covariance. 20 sample stocks are selected form various industries and market capitalization size, and used to test to the performance of FFM and the new FFM. The result has been analyzed from 3 different ways: correlation and covariance, R squared, and p value. Although the new model fails to perform better than a traditional FFM, it may be improved by adding more factors or choosing factors which are more representative of the market.