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It is well known that least squares estimates can be very sensitive to departures from normality. Various robust estimators such as least absolute deviations (LAD), L_p estimators provide possible alternatives to least squares when such departures occur. This paper applies a partially adaptive technique to estimate the parameters of Sharpe's market model. This methodology is based on a generalized t-distribution and includes as special cases least squares, LAD, L_p as well as some estimation procedures which have bounded and redescending influence functions.