  This article proposes a new method for the estimation of the parameters of a
simple linear regression model which accounts for the role of co-moments in
non-Gaussian distributions being based on the minimization of a quartic loss
function. Although the proposed method is very general, we examine its
application to finance. In fact, in this field the contribution of the
co-moments in explaining the return-generating process is of paramount
importance when evaluating the systematic risk of an asset within the framework
of the Capital Asset Pricing Model (CAPM). The suggested new method contributes
to this literature by showing that, in the presence of non-normality, the
regression slope can be expressed as a function of the co-kurtosis between the
returns of a risky asset and the market proxy. The paper provides an
illustration of the method based on some empirical financial data referring to
40 industrial sector assets rates of the Italian stock market.
