The characteristic line of a security or portfolio relates its rate of return to that of a “market portfolio.” Several investigators have suggested the desirability of obtaining such a line by minimizing the sum of the absolute deviations rather than the sum of the squared deviations around the line. This paper presents a new algorithm for such a regression problem. The procedure has at least two virtues: it is simple, and it produces useful information as a byproduct of the solution process. Empirical evidence is also presented on the differences in the values obtained with the two regression methods (i.e., mean-absolute-deviation and least-squares). The differences appear to be relatively slight, at least for well-diversified portfolios.