Spanning Tests for Markowitz Stochastic Dominance

TL;DR

This paper introduces a new non-parametric test for Markowitz stochastic dominance spanning, enabling better assessment of investment opportunities and challenging traditional market efficiency assumptions.

Contribution

It develops the first analytical representation of Markowitz stochastic dominance spanning and constructs a subsampling-based test with proven asymptotic properties.

Findings

Rejects market portfolio Markowitz efficiency in data

Finds equity management can outperform the market

Provides a novel test for stochastic dominance spanning

Abstract

We derive properties of the cdf of random variables defined as saddle-type points of real valued continuous stochastic processes. This facilitates the derivation of the first-order asymptotic properties of tests for stochastic spanning given some stochastic dominance relation. We define the concept of Markowitz stochastic dominance spanning, and develop an analytical representation of the spanning property. We construct a non-parametric test for spanning based on subsampling, and derive its asymptotic exactness and consistency. The spanning methodology determines whether introducing new securities or relaxing investment constraints improves the investment opportunity set of investors driven by Markowitz stochastic dominance. In an application to standard data sets of historical stock market returns, we reject market portfolio Markowitz efficiency as well as two-fund separation. Hence, we find evidence that equity management through base assets can outperform the market, for investors with Markowitz type preferences.