Ordering Arbitrage Portfolios and Finding Arbitrage Opportunities

Abstract

Concepts are introduced and applied for analyzing and selecting arbitrage portfolios in the face of ambiguity about risk preferences and initial positions. A Stochastic Arbitrage Opportunity is defined as a zero-cost investment portfolio that enhances every feasible benchmark portfolio for all admissible utility functions. The alternative to the existence of such investment opportunities is the existence of a solution to 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 is appealing for all risk-averse stock investors with a wide range of initial position and sufficiently low transactions costs, by mixing multiple factor portfolios with high after-cost Information Ratio, low mutual correlation and negative downside beta. The findings weaken the case for risk-based explanations for the profitability of factor investing

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

JEL Classification: C61, D81, G11