Thin-Trading Effects in Beta: Bias v. Estimation Error

by Sercu P; Vandebroek M; Vinaimont T.

Abstract
Two regression coeffcients often used in Finance, the Scholes-Williams (1977) quasi-multiperiod 'thin-trading' beta and the Hansen-Hodrick (1980) overlapping-periods regression coeffcient, can both be written as instrumental-variables estimators.Competitors are Dimson's beta and the Hansen-Hodrick original OLS beta.We check the performance of all these estimators and the validity of thet-tests in small and medium samples, in and outside their stated assumptions, and wereporttheir performances in a hedge-fund styleportfolio-management application .In all experiments as well as in the real-data estimates, less bias comes at the cost of a higher standard error. Our hedge-portfolio experiment shows that the safest procedure even is to simply match by size and industry;any estimation just adds noise. There is a clear relation between portfolio variance and the variance of the beta estimator used in market-neutralizing the portfolio, dwarfing the beneficial effect of bias

Keywords: Market model; Thin trading; Size; Noise; Portfolio; Variance; Estimator; Bias; Regression; Finance; Performance; Cost

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