Using properties of the cdf of a random variable defined as a saddle-type point of a real valued continuous stochastic process, we derive first-order asymptotic properties of tests for stochastic spanning w.r.t. a stochastic dominance relation. First, we define the concept of Markowitz stochastic dominance spanning, and develop an analytical representation of the spanning property. Second, we construct a non-parametric test for spanning via the use of an empirical analogy. The method determines whether introducing new securities or relaxing investment constraints improves the invest- ment opportunity set of investors driven by Markowitz stochastic dominance. In an application to standard data sets of historical stock market returns, we reject mar- ket portfolio Markowitz efficiency as well as two-fund separation. Hence there exists evidence that equity management through base assets can outperform the market, for investors with Markowitz type preferences.