An application of independent component analysis in the arbitrage pricing theory

The Arbitrage Pricing Theory is a normative equilibrium theory, the theory infers that there may be a multitude of risk factors driving asset returns. Broadly speaking, three approaches can be used to identify these factors, they are fundamental model, macroeconomic model and statistical model. In the traditional approach, the statistical model applies principal components analysis (PCA) to decompose covariance matrix of asset returns. In this paper, we will (i) Discuss the relationship between macroeconomic variables and statistical factors. (ii) Apply independent component analysis (ICA) and a newly proposed ICA factor selection criterion in statistical model. Using ICA as a plug-in of statistical model, Experiments have shown that it fives a better indication of the underlying structure of stock market than PCA by using the same number of components.