Ordering Arbitrage Portfolios and Finding Arbitrage Opportunities

Abstract

Abstract Concepts are introduced and applied for analyzing and selecting arbitrage portfolios in the face of ambiguity about risk preferences and initial portfolios. A Stochastic Arbitrage Opportunity is defined as a zero-cost overlay that enhances every feasible benchmark portfolio for all relevant risk-averse utility functions. The alternative to the existence of such opportunities is the solvability of a dual system of asset pricing restrictions based on a class of stochastic discount factors. Feasible approaches to numerical optimization and statistical inference are discussed. Empirical results suggest that equity factor investing can produce robust Stochastic Arbitrage Opportunities for all risk-averse stock investors with sufficiently low transactions costs, by mixing multiple factor portfolios with high after-cost Information Ratio, low mutual correlation and negative downside beta.

Keywords: Portfolio analysis; Arbitrage portfolios; Asset pricing; Incomplete markets; Factor Investing

JEL Classification: C61, D81, G11