Stochastic Dominance With a Riskless Asset: An Imperfect Market

Abstract

The assumption that investors can borrow and lend at a riskless interest rate reduces the Mean-Variance (M-V) efficient set to only one optimal unlevered portfolio. However, once we realize that the market is generally imperfect and that the borrowing rate is higher than the lending rate, we can no longer use the mean-variance Separation Theorem. Instead, a number of unlevered portfolios must be included in the efficient set, while the optimal unlevered portfolio is selected on the basis of the investor's preference. The size of the efficient set of unlevered portfolios is a function of the type of empirical data used and of the disparity between the borrowing and lending interest rates.