Arbitrage Free Dispersion

78 Pages Posted: 14 Jan 2019 Last revised: 11 Apr 2019

See all articles by Piotr Orłowski

Piotr Orłowski

HEC Montréal; CDI

Andras Sali


Fabio Trojani

University of Geneva; University of Turin - Department of Statistics and Applied Mathematics; Swiss Finance Institute

Date Written: August 10, 2018


We develop a theory of arbitrage-free dispersion (AFD) that characterizes the testable restrictions of asset pricing models. AFD measures Jensen’s gap in the cumulant generating function of pricing kernels and returns. It implies a wide family of model-free dispersion constraints, which extend dispersion and co-dispersion bounds in the literature and are applicable with a unifying approach in multivariate and multiperiod settings. Empirically, the dispersion of stationary and martingale pricing kernel components in the benchmark long-run risk model yields a counterfactual dependence of short- vs. long-maturity bond returns and is insufficient for pricing optimal portfolios of market equity and short-term bonds.

Keywords: Arbitrage-Free Dispersion, Cumulant Generating Function, Convexity, Convex Inequalities, Jensen’s Gap, Pricing Kernel Bounds, Entropy, Long-Run Risk Models, Tests of Asset Pricing Models

JEL Classification: G12, G15, C14, C52, C58

Suggested Citation

Orłowski, Piotr and Sali, Andras and Trojani, Fabio, Arbitrage Free Dispersion (August 10, 2018). Swiss Finance Institute Research Paper No. 19-20, Available at SSRN: or

Piotr Orłowski (Contact Author)

HEC Montréal ( email )

3000 Chemin de la Cote-Sainte-Catherine
Montreal, Quebec H3T 2A7

CDI ( email )

3000, chemin de la Côte-Sainte-Catherine
Montréal, Québec H3T 2A7

Andras Sali

Alphacruncher ( email )


Fabio Trojani

University of Geneva ( email )

Geneva, Geneva

University of Turin - Department of Statistics and Applied Mathematics ( email )

Piazza Arbarello, 8
Turin, I-10122

Swiss Finance Institute ( email )

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4

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