application of steine’s lemma in modern finance

Abstract. when two random variable have a bivariate normal distribution, stein’slemma provides an expression for the covariance of the first variable with a functionof the second. stein’s lemma has many application in statistics and probability and itplays an important role in modern finance. most of these applications were initially derived in a multivariate normal context. in finance, however, asset returns do not alwaysdisplay symmetry but may exhibit skewness. this paper introduced a unified multivariate skewed distribution and extend stein’s lemma for two version of multivariateskewed distribution. the capital asset pricing model is derived for one version of thisunified form. it is shown that, under another version of the unified form, the portfoliosof all investors are expected utility maximizers are located on a single mean-varianceskewness surface.