Portfolio Frontier with Different Interest Rates for Borrowing and Lending

Abstract

The theory of portfolio selection of Markowitz (1952) applies mean and variance to characterize return and risk for a combination of more than two financial assets traded in a frictionless economy. Unlimited short selling is allowed and the rates of return on these assets are assumed to have finite variances. Rothschild and Stiglitz (1970, 1971) introduced the concept of second degree stochastic dominance. They showed that when there are more than two risky assets, if there exists a portfolio of assets that the second degree stochastically dominates all the portfolio with the same expected rate of return, then this dominant portfolio must have the minimum variance among all the portfolios. This observation is one of the motivations for characterizing portfolios that have the minimum variance for various levels of expected rate of return. The study of the mean-variance efficiency by Gonzalez-Gaverra (1973), Merton (1972) and Roll (1977) expanded Markowitz model to discuss various issues in portfolio management. To understand the formulation of mean-variance as return-risk, Chamberlain (1983) made an effort to characterize the complete family of probability distributions that are necessary and sufficient for the expected utility of terminal wealth to be a function only of the mean and variance of terminal wealth or for mean-variance utility functions. Epstein (1985) showed that the mean-variance utility functions were implied by a set of decreasing absolute risk aversion postulates.