Note on the Proportions of Financial Assets with Dependent Distributions in Optimal Portfolios

In this paper we shall study the proportions of the financial assets in optimal portfolios, where the portfolio is optimized by the maximization of its expected utility with respect to a given utility function. Our main goal is to investigate the magnitude of the proportions of the assets in optimal portfolios provided that the assets’ distributions display a certain type of stochastic dominance, which means that one asset is better in a certain sense than the other. Our main question is to understand why people buy more of an asset than of another one. For this, we introduce and study new notions of stochastic dominance which can be appropriate candidates for the study of the proportions. Based on these notions we derive new versions (and a generalization) of the results of Hadar and Seo [1], where, in case of independent asset returns, the stochastic dominance of the returns implies that the dominant asset has a larger proportion in the optimal portfolio. Our results apply to not necessarily independent returns as well. We give several realistic examples in which these new types of stochastic dominance are fulfilled.