Dynamic Sector Beta

A dynamic factor model for stock beta describes identifies that stock and sector betas are not likely to be constant through time. They vary over the long run as the composition of sectors changes and as the weight of industries in the market and economy overall changes. The pandemic shock of 2020 highlights how a significant event can significantly change market betas: discretionary sector beta increased sharply, staples sector beta decreased sharply.

The observation equation describes how a sector's returns are a linear function of the market returns include a return differential the stock risk multiple . The stock multiple is time varying, evolving as a random walk according to the observation equation. This construct is a dynamic linear regression model where the fitted regression coefficients is time varying, a Kalman Filter and Smoother is used to fit the unobserved beta, where the innovations are drawn from the covariance matrix W.

References:

• Campbell, John Y, 1996. Understanding Risk and Return, Journal of Political Economy, University of Chicago Press, vol. 104(2), pages 298-345, April.

• Adrian, Tobias & Franzoni, Francesco, 2009. Learning about beta: Time-varying factor loadings, expected returns, and the conditional CAPM, Journal of Empirical Finance, Elsevier, vol. 16(4), pages 537-556, September.