Estimating Beta

Abstract

We conduct a comprehensive comparison of market beta estimation techniques. We study the performance of several historical, time-series model, and option-implied estimators for estimating realized market beta. Thereby, we find the hybrid methodology of Buss and Vilkov to consistently outperform all other approaches. In addition, all other approaches, including fully implied and dynamic conditional beta, based on generalized autoregressive conditional heteroskedasticity (GARCH) models, are dominated by a simple beta estimate based on historical (co-)variances and an approach based on the Kalman filter. Our conclusions remain unchanged after performing several robustness checks.

The Choice of the Time Horizon during Estimation of the Unconditional Stock Beta

“…For the first category 14% of the stocks exhibited a beta series with structural breaks within 60 trading days. For the 2006-2007 data (columns [6][7][8][9] 117 stocks fall in the first category of Basic Materials and the average break date is now 113 with a lower standard deviation. Using first level ICB categories most of stock's beta series presented a break date once 90 trading days of information were included in the estimations.…”

“…We estimate beta by using simple returns such that, , , Returns on stocks and the market are estimated in continuous time using logarithmic differences of daily returns 6 .…”

“…5 252 daily observations were downloaded minus the 30 most recent observations allow for the estimation of 30-day betas all the way to 252 day betas. 6 The excess return specification would estimate ( ) R represents the risk free rate in period i . In the return-level specification of equation 1, alpha (α) represents the constant return earned whereas in the excessreturn specification of equation 2, the α-coefficient represents the constant return of the security in excess of the risk free rate.…”

“…While those estimates of beta reported usually originate from 7 different sources [7] they also differ substantially [5] 2 . Those 1 Numerous articles have dealt with issues of heteroscedasticity, autocorrelation and the time variation of betas through the estimation of ARCH and GARCH models, GARCH conditional betas, stochastic volatility conditional betas, Kalman Filter approaches, Flexible Least Squares, Markov switching approaches [1,2,3,4,5]; see Hollstein and Prokopczuk [6] for a recent and comprehensive comparison of market beta estimation techniques. 2 Some sites such as Bloomberg allows users to specify the period of estimation while other sites such as Compustat and Dow Jones do not.…”

Sectoral Differences in the Choice of the Time Horizon during Estimation of the Unconditional Stock Beta

“…While those estimates 1 Numerous articles have dealt with issues of heteroscedasticity, autocorrelation and the time variation of betas through the estimation of ARCH and GARCH models, GARCH conditional betas, stochastic volatility conditional betas, Kalman Filter approaches, Flexible Least Squares, Markov switching approaches [1][2][3][4][5]; see Hollstein and Prokopczuk [6] for a recent and comprehensive comparison of market beta estimation techniques. Another set of literature has concentrated on the estimation of realized betas to improve beta forecasts [7,8].…”