“Beta Decompositions and the Cross Section of Equity Returns: A Wavelet‐Based Approach” by Byoung KANG
The Hong Kong Polytechnic University
Tong Suk Kim
KAIST Business School
In this paper, we present a framework characterizing risk of an asset in terms of the asset's short-run, intermediate-run, and long-run exposures towards model factor. Using some fundamental results in wavelet theory, we show that standard beta can be represented as a weighted linear combination of short-run, intermediate-run, and long-run betas. The framework developed in this paper is not confined to single factor models, but can be applied to any linear factor model in general. Using the Fama-French's three factor model as an example, we demonstrate in detail how one can measure an asset's exposure towards a certain frequency movement of model factors. For the given example of Fama-French model, we find that loadings on the long-run movements of SMB and HML (i.e., long-run betas) account better for the cross section of average (monthly) returns than loadings on the short-run or intermediate-run movements of the factors (i.e., short-run or intermediate-run betas). Consistent with risk-based interpretation of SMB and HML, we find that the long-run components of SMB and HML are better proxies for the ICAPM-based risk factors than are the other frequency components of the factors.