The Beta Heuristic from a Time/Frequency Perspective: A Wavelet Analysis of the Market Risk of the 10 S&P Sectors

Abstract

We investigate the time-scale relationships between the ten S&P sectors and the market through the use of wavelet analysis, a methodology that has widespread acceptance for investigating multi-horizon properties of time series. Our analysis of the data highlights that variation in the pattern of dependency among sector returns and market returns, even at times of market turmoil, appears differently at different time horizons and frequency intervals. The empirical evidence based on standard betas and scale betas finds that the flow of frequency changes matters for estimates of market betas at medium and higher scales for nine out of ten sectors. There are no significant differences in estimates of scale market betas at high frequency for any of the sectors, or at any scales for the energy sector. We conclude that the importance of frequency components does not remain stable over time and based on the effects of time-varying behavior at different frequencies draw implications for investors regarding the market risk of investing in specific sectors.

Keywords: Wavelet Analysis, CAPM, Equity Betas, Standard & Poor Sectors

JEL Classification: C1, G1, G10, G13, C13, C32