Costly Arbitrage : Evidence from Closed-End Funds

Textbook arbitrage in financial markets requires no capital and entails no risk. In reality, almost all arbitrage requires capital, and is typically risky. Moreover, professional arbitrage is conducted by a relatively small number of highly specialized investors using other people's capital. Such professional arbitrage has a number of interesting implications for security pricing, including the possibility that arbitrage becomes ineffective in extreme circumstances, when prices diverge far from fundamental values. The model also suggests where anomalies in financial markets are likely to appear, and why arbitrage fails to eliminate them. ONE OF THE FUNDAMENTAL concepts in finance is arbitrage, defined as "the simultaneous purchase and sale of the same, or essentially similar, security in two different markets for advantageously different prices" (Sharpe and Alexander (1990)). Theoretically speaking, such arbitrage requires no capital and entails no risk. When an arbitrageur buys a cheaper security and sells a more expensive one, his net future cash flows are zero for sure, and he gets his profits up front. Arbitrage plays a critical role in the analysis of securities markets, because its effect is to bring prices to fundamental values and to keep markets efficient. For this reason, it is extremely important to understand how well this textbook description of arbitrage approximates reality. This article argues that the textbook description does not describe realistic arbitrage trades, and, moreover, the discrepancies become particularly important when arbitrageurs manage other people's money. Even the simplest realistic arbitrages are more complex than the textbook definition suggests. Consider the simple case of two Bund futures contracts to deliver DM250,OOO in face value of German bonds at time T, one traded in London on LIFFE and the other in Frankfurt on DTB. Suppose for the moment, counter factually, that these contracts are exactly the same. Suppose finally that at some point in time t the first contract sells for DM240,OOO and the second for DM245,OOO.An arbitrageur in this situation would sell a futures contract in Frankfurt and buy one in London, recognizing that at time T he is perfectly hedged. To do so, at time t, he would have to put up some good faith money, namely DM3,000 in London and DM3,500 in Frankfurt, leading to a * Shleifer is from Harvard University and Vishny is from The University of Chicago. Nancy Zimmerman and Gabe Sunshine have helped us to understand arbitrage. We thank Yacine Ait Sahalia, Douglas Diamond, Oliver Hart, Steve Kaplan, Raghu Rajan, Jesus Saa-Requejo, Luigi Zingales, Jeff Zwiebel, and especially Matthew Ellman, Gustavo Nombela, Rene Stulz, and an anonymous referee for helpful comments. 36 The Journal of Finance net cash outflow of DM6,500. However, he does not get the DM5,000 difference in contract prices at the time he puts on the trade. Suppose that prices of the two contracts both converge to DM242,500 just after t, as the market returns to efficiency. In this case, the arbitrageur would immediately collect DM2,500 from each exchange, which would simultaneously charge the counter parties for their losses. The arbitrageur can then close out his position and get back his good faith money as well. In this near textbook case, the arbitrageur required only DM6,500 of capital and collected his profits at some point in time between t and T. Even in this simplest example, the arbitrageur need not be so lucky. Suppose that soon after t, the price of the futures contract in Frankfurt rises to DM250,000, thus moving further away from the price in London, which stays at DM240,OOO. At this point, the Frankfurt exchange must charge the arbitrageur DM5,000 to pay to his counter party. Even if eventually the prices of the two contracts converge and the arbitrageur makes money, in the short run he loses money and needs more capital. The model of capital-free arbitrage simply does not apply. If the arbitrageur has deep enough pockets to always access this capital, he still makes money with probability one. But if he does not, he may run out of money and have to liquidate his position at a loss. In reality, the situation is more complicated since the two Bund contracts have somewhat different trading hours, settlement dates, and delivery terms. It may easily happen that the arbitrageur has to find the money to buy bonds so that he can deliver them in Frankfurt at time T. Moreover, if prices are moving rapidly, the value of bonds he delivers and the value of bonds delivered to him may differ, exposing the arbitrageur to additional risks of losses. Even this simplest trade then becomes a case of what is known as risk arbitrage. In risk arbitrage, an arbitrageur does not make money with probability one, and may need substantial amounts of capital to both execute his trades and cover his losses. Most real world arbitrage trades in bond and equity markets are examples of risk arbitrage in this sense. Unlike in the textbook model, such arbitrage is risky and requires capital. One way around these concerns is to imagine a market with a very large number of tiny arbitrageurs, each taking an infinitesimal position against the mispricing in a variety of markets. Because their positions are so small, capital constraints are not binding and arbitrageurs are effectively risk neutral toward each trade. Their collective actions, however, drive prices toward fundamental values. This, essentially, is the model of arbitrage implicit in Fama's (1965) classic analysis of efficient markets and in models such as CAPM (Sharpe (1964)) and APT (Ross (1976)). The trouble with this approach is that the millions of little traders are typically not the ones who have the knowledge and information to engage in arbitrage. More commonly, arbitrage is conducted by relatively few professional, highly specialized investors who combine their knowledge with resources of outside investors to take large positions. The fundamental feature of such arbitrage is that brains and resources are separated by an agency relationship. The money comes from wealthy individuals, banks, endowments, and The Limits of Arbitrage 37 other investors with only a limited knowledge of individual markets, and is invested by arbitrageurs with highly specialized knowledge of these markets. In this article, we examine such arbitrage and its effectiveness in achieving market efficiency. In particular, the implications of the fact that arbitrage-whether it is ultimately risk-free or riskygenerally requires capital become extremely important in the agency context. In models without agency problems, arbitrageurs are generally more aggressive when prices move further from fundamental values (see Grossman and Miller (1988), De Long et al. (1990), Campbell and Kyle (1993)). In our Bund example above, an arbitrageur would in general increase his positions if London and Frankfurt contract prices move further out of line, as long as he has the capital. When the arbitrageur manages other people's money, however, and these people do not know or understand exactly what he is doing, they will only observe him losing money when futures prices in London and Frankfurt diverge. They may therefore infer from this loss that the arbitrageur is not as competent as they previously thought, refuse to provide him with more capital, and even withdraw some of the capitaleven though the expected return from the trade has increased. We refer to the phenomenon of responsiveness of funds under management to past returns as performance based arbitrage. Unlike arbitrageurs using their own money, who allocate funds based on expected returns from trades, investors may rationally allocate money based on past returns of arbitrageurs. When arbitrage requires capital, arbitrageurs can become most constrained when they have the best opportunities, i.e., when the mispricing they have bet against gets even worse. Moreover, the fear of this scenario would make them more cautious when they put on their initial trades, and hence less effective in bringing about market efficiency. This article argues that this feature of arbitrage can significantly limit its effectiveness in achieving market efficiency. We show that performance-based arbitrage is particularly ineffective in extreme circumstances, where prices are significantly out of line and arbitrageurs are fully invested. In these circumstances, arbitrageurs might bail out of the market when their participation is most needed. Performance based arbitrage, then, is even more limited than arbitrage described in earlier models of inefficient markets, such as Grossman and Miller (1988), De Long et al. (1990), and Campbell and Kyle (1993). Ours is obviously not the first study of the consequences of delegated portfolio management. Early articles in this area include Allen (1990) and Bhattacharya-Pfleiderer (1985). Scharfstein and Stein (1990) model herding by money managers operating on incentive contracts. Lakonishok, Shleifer, Thaler, and Vishny (1991) and Chevalier and Ellison (1995) consider the possibility that money managers "window dress" their portfolios to impress investors. In two interesting recent articles, Allen and Gorton (1993) and Dow and Gorton (1994) show how money managers can churn assets to mislead their investors, and how such churning can sustain inefficient asset prices. Unlike this work, our article does not focus as much on the distortions in the behavior 38 The Journal of Finance of arbitrageurs, as on their limited effectiveness in bringing prices to fundamental values. The next section of the article presents a very simple model that illustrates the mechanics of arbitrage. For simplicity, our model focuses on the case where mispricing may deepen in the short run, even though there is no long run fundamental risk in the trade. We thus focus on a case that is closest to pure arbitrage, as opposed to risk arbitrage. Sect