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 the fundamental model, macroeconomic model and statistical model. In the traditional approach, the statistical model applies principal component analysis (PCA) to decompose the covariance matrix of asset returns. We discuss the relationship between macroeconomic variables and statistical factors and we apply independent component analysis (ICA) and a newly proposed ICA factor selection criterion in the statistical model, using ICA as a plug-in of the statistical model. Experiments have shown that it gives a better indication of the underlying structure of the stock market than PCA by using the same number of components.