Estimates of the parameters of a linear model are usually obtained by the method of ordinary least-squares (OLS), which is sensitive to large values of the additive error term. By dividing the sample into nonoverlapping subsamples and computing the trimmed means of OLS subsample regression coefficients, we obtain a simple, consistent and asymptotically normal initial estimate of the coefficients, which protects the analyst from large values of ∈iwhich are often hard to detect using OLS on a model with many regressors. The technique is applied to the calculation of risk parameters in the capital asset pricing model for securities on the N. Y. Stock Exchange.