Timescale betas and the cross section of equity returns: Framework, application, and implications for interpreting the Fama–French factors

Abstract

We show that standard beta pricing models quantify an asset's systematic risk as a weighted combination of a number of different timescale betas. Given this, we develop a wavelet-based framework that examines the cross-sectional pricing implications of isolating these timescale betas. An empirical application to the Fama-French model reveals that the model's wellknown empirical success is largely due to the beta components associated with a timescale just short of a business cycle (i.e., wavelet scale 3). This implies that any viable explanation for the success of the Fama-French model that has been applied to the Fama-French factors should apply particularly to the scale 3 components of the factors. We find that a risk-based explanation conforms closely to this implication. This paper presents a framework that characterizes an asset's systematic risk in terms of the asset's exposures to a number of different timescale (e.g., short-, intermediate-, long-run) fluctuations in a model's factors. We call measures of such exposures timescale betas. Using two fundamental results in wavelet theory, we show that an asset's standard betas, or factor loadings, can be written as a linear combination of the asset's timescale betas. Empirically, we isolate these betas and explore their relative importance for the cross section of returns.Our exploration is motivated in spirit by the long-run consumption-risk literature, which suggests the possibility that only part of the information in the standard betas is relevant for asset pricing and the relevant part is concentrated in certain timescale betas (see, e.g.,

CO2 emissions and economic activity: A short-to-medium run perspective

“…The intuition behind using this equation is that it may help us to uncover relationships which exist between emissions and the economy at different timescales, which may not be present when analysing the relationship between the original monthly growth rate series. In the field of financial economics, several recent papers such as Ortu et al (2013), Xyngis (2017), Kang et al (2017) and Bandi et al (2019) have established that asset returns relate to macroeconomic variables and uncertainty only at lower frequencies and not at high frequencies.…”

The term structure of equity factor diversification

“…Thus, an investor who wants to diversify with the HML factor will have good diversification benefits until a three-month horizon (d6). Similarly, Kang et al (2017) found that the best estimation of the beta related to HML and SMB factors is obtained for the d3.…”

“…Our solution is to use wavelet methodology to decompose returns into a temporal series of different maturities. This filter has recently been used in portfolio management by In et al (2011), Michis (2014, Kang et al (2017) and in Jena et al (2017) and with Fama French factor as in Trimech et al (2009). Moreover, we propose to combine this approach with a parametric copula analysis.…”

Common idiosyncratic volatility and returns: From an investment horizon perspective

“…Concentrating on a timescale component of betas, rather than merely on the overall betas, can significantly improve pricing performance. Kang, In, and Kim (2017) construct a WMRA framework to interpret the returns by risk-based business cycle and document that the intermediate business cycle imposes significant effect on the price of U.S. stocks. By splitting the overall negative relationship into a positive one for long-run investors and a negative one for short-run agents, the negative relationship disappears as the wavelet scale increases.…”

“…Nikkinen, Pynnönen, Ranta, and Vähämaa (2011) indicate that the dynamic structure of exchange rate expectations may vary over different timescales by using wavelet techniques. Kang, In, and Kim (2017) construct a WMRA framework to interpret the returns by risk-based business cycle and document that the intermediate business cycle imposes significant effect on the price of U.S. stocks. Inspired by these works, we adopt WMRA analysis to examine the CIV timescales in pricing.…”