APPLICATION OF STEINE’S LEMMA IN MODERN FINANCE

Abstract. When two random variable have a bivariate normal distribution, Stein’s Lemma provides an expression for the covariance of the first variable with a function of the second. Stein’s Lemma has many application in statistics and probability and it plays an important role in modern finance. Most of these applications were initially de rived in a multivariate normal context. In finance, however, asset returns do not always display symmetry but may exhibit skewness. This paper introduced a unified multi variate skewed distribution and extend Stein’s Lemma for two version of multivariate skewed distribution. The Capital Asset Pricing Model is derived for one version of this unified form. It is shown that, under another version of the unified form, the portfolios of all investors are expected utility maximizers are located on a single mean-variance skewness surface.