Identifying Factors within the APT: A New Approach

Abstract

In the framework of the Arbitrage Pricing Theory (APT), this paper estimates a new set of factors from stock return data by adopting an estimation procedure advocated in the chaos literature. Specifically, I view the principal components analysis as feature extraction step, and then estimate the factors as the driving forces of the principal components. This estimation procedure identifies two sources of underlying risk which can be captured by five empirical factors. This new set of factors outperforms the existing benchmarks in explaining cross-sectional returns, and it can be well explained by the commonly used macroeconomic variables. In particular, the Fama-French three factors leave out a significant part of the risk information that this new set of factors proxy for, indicating an omitted variable problem when use Fama-French factors as a benchmark. The additional risk information captured by the new set of factors is not the momentum factor, suggesting at the bottom line that it is not equivalent to the currently adopted Fama-French and momentum four factors. As an alternative risk benchmark, this new set of factors suggests that the seasoned equity offering firms do not underperform in the long run, providing support for the bad-model argument of Fama (1998).