Thin‐Trading Effects in Beta: Bias v. Estimation Error
比较了多种薄交易贝塔估计量（如Scholes-Williams和Dimson）的表现，发现减少偏差会以增大标准误差为代价，在对冲组合应用中，按规模和行业匹配比任何估计更安全。
Abstract: Two regression coefficients often used in Finance, the Scholes‐Williams (1977) quasi‐multiperiod ‘thin‐trading’ beta and the Hansen‐Hodrick (1980) overlapping‐periods regression coefficient, 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 the t ‐tests in small and medium samples, in and outside their stated assumptions, and we report their performances in a hedge‐fund style portfolio‐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.