Fractality in market risk structure: Dow Jones Industrial components case

Abstract

We examine the Dow Jones Industrial Average index components with respect to the capital asset pricing model (CAPM), specifically its scaling properties in the sense of different investment horizons. To do so, we use the novel methods of fractal regressions based on the detrended cross-correlation analysis and the detrending moving-average cross-correlation analysis. We report three standard groups of stocks – aggressive, defensive and market-following – which are rather uniformly represented. For most of the stocks, the β parameter of the CAPM does not vary significantly across scales. There are two groups of exceptions. One of aggressive stocks which are even more aggressive for short investment horizons. These do not provide portfolio diversification benefits but allow for high profits above the market returns and even more so for the short investment horizons. And the other group of more defensive stocks which become very defensive in the long term. These stocks do not deliver short term profits but can serve as strong risk diversifiers. Apart from these direct results, our analysis opens several interesting questions and future research directions, both technical and experimental, which we discuss in more detail.