The Behavior of Beta in the 19th Century

Abstract

This paper uses completely new data to study the variations in beta when it deviates from the constancy assumption presumed by the market model. The concentration of the literature on beta is based on post 1926 data. This makes the 19 th century Brussels Stock Exchange (BSE) data a very good out-sample dataset to test beta variations. Various models proposed in the literature to capture the variations in beta were studied. Blume's correlation techniques reveal that beta is not stable at the individual stocks level and that the stability can be fairly improved by portfolio formations. Using root mean square error (RMSE) criterion, it was shown that the market model betas are weak in predicting future betas. The predictability can be improved by adjusting betas with the Blume and Vasicek mean reversion techniques. Further results from this study reveal that few stocks have lead or lag relationship with the market index. Small sized stocks were detected to be more prone to outliers. In effect betas in the 19 th century exhibits similar pattern as betas in the post 1926 era.

Market Reaction to Announcement of the Corporate Governance “Comply or Explain” Regulation and Determinants of Compliance Level

“…The beta coefficient reflects the sensitivity of a stock to market movements and is one of the parameters of time series regression. Beta is usually estimated using a standard market model, with the statistical model linking stock returns with the market index [26]. This study uses an estimation period of 210 days as the observation period for estimating beta values [27].…”

“…The regression coefficient or beta (β) can be calculated using the following regression equation: Beta estimated using the market model will be biased for an illiquid market; thus, for Indonesia, which has an illiquid market, one of the methods that can be used to correct the occurrence of bias is Dimson beta. This is calculated by summing the lead and lag coefficients in a multiple regression of market returns with the dependent variable as the time series return rate and the independent variables as the market return and the lead and lag variables on the market index [26].…”

Trading Frequency Anomalies in Infant Markets: The Test for Returns and Sensitivity of Shares and Portfolios

“…Similar finding was observed by study of Matteev (2004), and Armitage & Brzeszczynski (2011) and they stressed that beta calculated in daily and weekly returns were more stable than that of monthly returns. In recent literature, Mensah (2013) observed that beta behavior had changed, and the infrequently traded shares were more volatile than the frequently traded share. Similarly, Oprea (2015) suggested that when return interval increased, the beta of infrequently traded shares increased and that of frequency would decrease even when standard market model was applied.…”

“…The study of Mensah (2013) and Mensah (2015) both highlighted that portfolio beta decreased with the increase in portfolio size. Similarly, portfolio returns increased with the increase of portfolio size to the maximum of seven shares out of ten shares used.…”

“…Interestingly, average portfolio returns were higher in value weighted portfolio than the equal weighted portfolio, and this was due to difference of trading frequency among shares used in portfolio construction. However, both Mensah (2013) and Mensah (2015) overlooked to test differences between weighted portfolio based on increasing frequency or decreasing frequency.…”