Gradual Arbitrage¤ Martin Oehmkey Columbia University This version: February 1, 2009 Abstract Capital often flows slowly from one market to another in response to buying oppor- tunities. I provide an explanation for this phenomenon by considering arbitrage across two segmented markets when arbitrageurs face illiquidity frictions in the form of price impact costs. I show that illiquidity results in gradual arbitrage: mispricings are generally corrected slowly over time rather than instantaneously. The speed of arbitrage is decreas- ing in price impact costs and increasing in the level of competition among arbitrageurs. This means arbitrage is slower in more illiquid markets for two reasons: First, there is a direct e®ect, as illiquidity a®ects the equilibrium trading strategies for a given level of competition among arbitrageurs (strategic e®ect). Second, in equilibrium fewer arbi- trageurs stand ready to trade between illiquid markets, further slowing down the speed of arbitrage (competition e®ect). Jointly, these two e®ects may help explain the observed cross-sectional variation of arbitrage speeds across di®erent asset classes. Keywords: Illiquidity, Limits to Arbitrage, Strategic Trading, Strategic Arbitrage, Im- perfect Competition ¤I thank Markus Brunnermeier, Jos¶eScheinkman and Hyun Shin for helpful conversations. I also thank Zhiguo He, Konstantin Milbradt and seminar participants at the Princeton Finance Lunch Workshop for comments. yColumbia Business School, 3022 Broadway, 420 Uris Hall, New York, NY 10027, e-mail:
[email protected], http://www0.gsb.columbia.edu/faculty/moehmke There is now a large body of empirical evidence showing that capital flows only slowly between markets to exploit buying opportunities.