Decomposing the bias in time-series estimates of CAPM betas

H. Malloch, R. Philip and S. Satchell

Applied Economics, 2016, vol. 48, issue 45, 4291-4298

Abstract: We identify two sources of bias arising from time-series regression used to compute beta. This bias arises due to the classical error in variables problem and a ‘mechanical interaction’ which exists when the index comprises the asset of interest. Assuming that the market is proxied by a fixed-weight index, we demonstrate that the relative weighting of an asset within the index, and/or the magnitude of its idiosyncratic risk, directly biases the beta estimate for the individual stock and also for all stocks within the index. Via simulations, we show that the problem is most pronounced for markets with a small number of highly concentrated assets. Finally, we propose a procedure to reduce this bias and apply the methods to equity data.

Date: 2016
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DOI: 10.1080/00036846.2016.1156233

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