Arbitrage and Beliefs∗ Paymon Khorramiy Alexander K. Zentefisz May 4, 2021 Abstract We study a segmented-markets setting in which self-fulfilling volatility can arise. The only requirements for this volatility to come about are (i) asset price movements re- distribute wealth across markets (e.g., equities rise as bonds fall) and (ii) a stabilizing force keeps valuation ratios stationary (e.g., cash flow growth rises when valuations rise). We prove that when self-fulfilling volatility exists, arbitrage opportunities must also exist, and vice versa. The tight theoretical connection between price volatility and arbitrage is detectable in currency markets by studying deviations from covered interest parity. JEL Codes: D84, G11, G12 Keywords: limits to arbitrage, segmented markets, volatility, self-fulfilling prices, multiple equilibria, covered interest parity ∗We are very grateful to Nick Barberis, Jess Benhabib, Harjoat Bhamra, Wenxin Du, Stefano Giglio, Daniel Grosshans, Stefan Nagel, Jung Sakong, Andre Veiga, Pietro Veronesi, Raman Uppal, and especially Stavros Panageas and Dimitri Vayanos for extremely helpful comments. We would also like to thank conference participants at CESifo’s Macro/Money/International conference and seminar participants at Imperial College and INSEAD for valuable feedback. yImperial College London,
[email protected] zYale School of Management,
[email protected] Arbitrages exist. Empirical research has documented several examples of trades fea- turing positive profits with zero hold-to-maturity risk. Moving beyond the neoclassical frictionless model of financial markets, a theoretical literature emphasizing limits to ar- bitrage aims to rationalize such trades.1 More broadly, limits to arbitrage help reconcile high asset returns and extreme price volatility under tame levels of fundamental risk, helping bridge an important gap in financial economics.