Generalized Stochastic Arbitrage Opportunities

45 Pages Posted: 19 Apr 2021 Last revised: 3 Apr 2023

See all articles by Stelios Arvanitis

Stelios Arvanitis

Athens University of Economics and Business

Thierry Post

Graduate School of Business of Nazarbayev University

Date Written: April 17, 2021


Concepts are introduced and applied for analyzing and selecting arbitrage portfolios in the
face of uncertainty about initial positions and risk preferences. A Stochastic Arbitrage Opportunity is defined as a zero-cost investment portfolio that enhances every feasible host 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 Appraisal Ratios, low mutual
correlation and negative exposures to the relevant host portfolios. These 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

Suggested Citation

Arvanitis, Stelios and Post, Thierry, Generalized Stochastic Arbitrage Opportunities (April 17, 2021). Available at SSRN: or

Stelios Arvanitis

Athens University of Economics and Business ( email )

76 Patission Street
Athens, 104 34

Thierry Post (Contact Author)

Graduate School of Business of Nazarbayev University ( email )

53 Kabanbay Batyra Avenue
Astana, 010000

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