Self-Imposed Limits to Arbitrage
Phil Maymin, Assistant Professor of Finance and Risk Engineering, NYU-Poly
Columbia-JAFEE Conference on Quantitative Finance
Organized by the Mathematics of Finance program at Columbia University and the Japanese Association of Financial Engineering
I document a multi-billion dollar discrepancy that lasted from 1992 to 1999 between two otherwise identical share classes of HSBC that did not suffer from the external limits to arbitrage that traditionally explain such other mispriced pairs as 3Com/Palm or Royal Dutch-Shell. Instead, I describe how self-imposed, internal limits to arbitrage such as restrictions on position size can result in persistent mispricings.
I also show that relatively more trading volume coincides with relatively lower prices in HSBC, and the same effects holds for 3Com/Palm, Royal Dutch-Shell, and other large mispriced pairs. An increase of one standard deviation in their relative volume coincides with a decrease of about one quarter of a standard deviation in their relative price. Self-imposed limits to arbitrage explain this phenomenon as well, so long as the more expensive security also tends to have greater daily volume: a higher relative price, or a wider discrepancy, leads to more arbitrage activity, and arbitrageurs trade equal volume in both securities, bringing the relative volume down closer to one.
Finally, I distinguish self-imposed limits to arbitrage from limits imposed as a result of market transactions costs or risk measures by calculating the market implied overall maximum position size of arbitrageurs for mispriced pairs spanning different time periods and countries and having different volume characteristics. The results are roughly constant at about one hundred days of typical trading volume, consistent with self-imposed limits.
Link to paper: http://ssrn.com/abstract=1088553