ریسک هماهنگ سازی و آربیتراژ تاخیری
|کد مقاله||سال انتشار||تعداد صفحات مقاله انگلیسی||ترجمه فارسی|
|10778||2002||20 صفحه PDF||سفارش دهید|
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Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : Journal of Financial Economics, Volume 66, Issues 2–3, November–December 2002, Pages 341–360
We argue that arbitrage is limited if rational traders face uncertainty about when their peers will exploit a common arbitrage opportunity. This synchronization risk—which is distinct from noise trader risk and fundamental risk—arises in our model because arbitrageurs become sequentially aware of mispricing and they incur holding costs. We show that rational arbitrageurs “time the market” rather than correct mispricing right away. This leads to delayed arbitrage. The analysis suggests that behavioral influences on prices are resistant to arbitrage in the short and intermediate run.
It is puzzling that professional traders often mutually agree that certain assets are overvalued or undervalued and yet do not trade accordingly. An often-cited example of an overpriced stock is Priceline.com, whose market capitalization reached $30 billion in April 1999, surpassing the combined market capitalization of all major U.S. airlines.1 Stocks can also be underpriced. Brennan (1990) refers to “latent assets” and considers large takeover bid premia as evidence of underpricing. Mispricing may arise in other asset markets, too. Dammon et al. (1993) report large and persistent mispricing in the bond market based on a comparison of three high-yield bonds of RJR Nabisco that differ only in the form in which interest is paid. The cash-paying bond traded at a huge premium compared to identical pay-in-kind bonds and deferred-coupon bonds over a two-year period. Standard market imperfections cannot explain such substantial mispricing. Similarly, certain currencies in the foreign exchange market are often known to be under/overvalued over many years, but arbitrageurs are afraid to trade on this mispricing too early. The objective of this paper is to provide a rationale for why this type of mispricing can persist even when professional arbitrageurs are present in the market. One possible explanation is that not all market participants are fully rational. For example, behavioral traders can trade based on investor sentiment and ignore relevant information. Even though there is little controversy in the literature about the presence of behavioral traders, there is disagreement about whether these boundedly rational traders actually affect prices. Proponents of the efficient markets hypothesis, like Fama (1965) and Ross (2001), maintain that rational arbitrageurs will undo any mispricing caused by behavioral traders. Hence, “the price is right.” Our paper disputes this claim, offering a new reason—“synchronization risk”—for why mispricing can persist despite the presence of rational arbitrageurs. The efficient markets hypothesis is self-evident when arbitrage strategies are riskless and professional traders are willing to take unbounded positions. In reality, though, any arbitrage involves some risk since markets are not complete. Whenever a mispriced asset is not redundant, an arbitrage strategy is risky even if rational traders care only about the final payoff of the arbitrage strategy. In other words, an arbitrage trade is riskless only if a perfect substitute for the mispriced asset exists. Therefore, arbitrageurs can rarely fully hedge their arbitrage strategies. The recent literature on the limits to arbitrage has identified two broad categories of risk: fundamental risk and noise trader risk. An arbitrage strategy can be risky because the fundamental value of a partially hedged portfolio might change over time. In addition, arbitrageurs understand that their model might not coincide with the true data-generating process. Thus, arbitrageurs have to bear a fundamental risk even if they can sustain the arbitrage strategy until the final payoff is realized. While these fundamental shocks are permanent, the activity of behavioral noise traders might lead to temporary price movements. These price changes temporarily reduce the value of the arbitrage portfolio if the price moves even further away from the fundamental value. If arbitrageurs are compelled to liquidate their positions in the intermediate term, then they are forced to take losses exactly when the arbitrage opportunity is greatest. DeLong et al. (1990a) call this noise trader risk. There are many reasons why arbitrageurs have to liquidate their position before the arbitrage finally pays off. Clearly, if arbitrageurs are short-lived, as in models with overlapping generations, they only care about the price at which they will sell the asset in their final period of consumption. In practice, professional fund managers have (endogenous) short horizons because their clients evaluate them on short-term performance and relatively poor performance leads to an outflow of funds (Shleifer and Vishny, 1997). Finally, arbitrageurs might find it optimal to (partially) liquidate their position early in an incomplete market setting when the investment opportunity set changes. An important additional risk has been ignored in the literature. It derives from arbitrageur's uncertainty about when other arbitrageurs will start exploiting a common arbitrage opportunity. We term this risk synchronization risk. Note that in contrast to noise trader risk, synchronization risk does not primarily stem from the activity of other noise traders, but from uncertainty about the market timing decisions of other rational arbitrageurs. In other words, while noise trader risk reflects the risk that the price might move even further away from the fundamental value, synchronization risk pertains to uncertainty regarding the timing of the price correction. Our model builds on the framework developed in Abreu and Brunnermeier (2001). It has three key ingredients. First, we assume that a single arbitrageur alone cannot correct the mispricing. In our model, the mispricing only disappears if a critical proportion of κ<1 arbitrageurs have traded based on their information.2 Any trade imbalance of rational arbitrageurs will be absorbed by behavioral traders who interpret it as a random fluctuation in order flow. The price correction only occurs when the aggregate order imbalance of arbitrageurs exceeds the behavioral traders’ absorption capacity. The critical mass requirement introduces an element of coordination among the arbitrageurs in our model. In addition, rational arbitrageurs are also competitive since κ<1. An arbitrageur who waits too long misses the profit opportunity if the price correction occurs in interim. A second element of our model is that arbitrageurs’ opinions about the timing of the price correction are dispersed. In particular, we assume that arbitrageurs become sequentially aware of the mispricing. Some early-informed arbitrageurs immediately learn of the mispricing when the price departs from the fundamental value. Others receive this information later. After some time all arbitrageurs know that the price does not reflect the fundamental value. Note that in our setting, as is arguably the case in reality, arbitrageurs do not know how early they receive this information relative to other traders. This sequential awareness element, together with the critical mass requirement, introduces a temporal dimension to the coordination problem. A synchronization problem arises because no individual arbitrageur knows when other traders will trade based on their information and hence they do not know when the price correction will occur. Finally, we argue that arbitrageurs incur explicit and implicit holding costs in order to exploit an arbitrage opportunity. For example, several explicit costs arise when an overpriced asset is sold short. Short-sellers must hold the short-sale proceeds in a margin account that pays minimal or no interest. Moreover, if the stock is “on special,” that is, if it is difficult to locate shareholders who are willing to lend the share, short-sellers will receive a negative interest rate on their short-sale proceeds. In other words, the short-seller is indirectly paying a lending fee. Furthermore, margin requirements force short-sellers to put additional money into low interest bearing margin accounts. This can bind a large amount of an arbitrageur's capital, which could be used for alternative investment opportunities. Note that short-sale costs also arise if an asset is undervalued. In this case, the arbitrageur goes long on the underpriced asset, but shorts assets with correlated payoffs in order to hedge the position. In addition, arbitrageurs also face implicit holding costs. For example, they cannot fully hedge their arbitrage strategy in a world where a perfect substitute for the mispriced asset does not exist. Other examples include the relative performance evaluation of fund managers and the risk that the lender of a security might recall the asset.3 The fundamental result of our analysis is that the combination of synchronization risk with holding costs typically causes arbitrageurs to delay acting on their information. However, they eventually do trade and while arbitrage does occur, it can be significantly delayed. This result holds despite our assumption that the price correction occurs with certainty within a finite horizon. Thus, the classical backward induction argument does not apply. The reason is that at no point in time is the mispricing common knowledge among the arbitrageurs. It might be the case that all arbitrageurs know of the mispricing, and all arbitrageurs know that all know that the price is too high or too low, but it is never the case that all arbitrageurs know that everybody knows that everybody knows and so on ad infinitum. We also obtain a variety of comparative statics results. As one would expect, we find that the duration of the mispricing increases with the size of the holding costs, the dispersion of opinion among arbitrageurs, and the absorption capacity of the behavioral traders. The larger the mispricing, the larger is the incentive of each individual arbitrageur to trade based on that information, and the sooner the price will revert towards the fundamental value. When the mispricing exceeds bounds, determined by dispersion of opinion among arbitrageurs and other model parameters, arbitrageurs will act on their information without delay. The fundamentals serve as an anchor around which the price can fluctuate. Thus, Black's (1986) (half-serious) suggestion that the fundamental value is between half and twice the current value is a description that is consistent with our model. The model can be extended to allow for asymmetric holding costs which, as has been widely noted, are higher for a short position than for a long position. Since arbitrageurs who receive bad news have to sell an asset short in order to exploit its overpricing and conversely for good news, our model provides a simple explanation of why “bad news travels slowly.” Our model also explains why fads and fashions in the acquisition and use of information are compatible with rational optimizing behavior. The coordination aspect of our model creates a strong incentive for individual arbitrageurs to act only on information that other arbitrageurs are acting upon, and to ignore information that is being generally ignored, even when such information is more important in terms of fundamentals. It does not pay to research or use “sleepy news” even when such news is known to be important. Our results are also robust in a generalized model in which partial price adjustments occur whenever the trading pressure exceeds a smaller threshold. Arbitrageurs update their information based on price movements. However, this inference is imperfect since no arbitrageur knows whether the price movement was due to trading pressure from rational arbitrageurs or a shift in investor sentiment. Therefore, opinions remain dispersed. Note that trading immediately after a partial price adjustment can be costly since the price might reverse if it was only due to a temporary shift in investor sentiment. In this setting, arbitrageurs might trade against each other. Some arbitrageurs bet on a price reversal and buy (sell) the asset even though they know that the asset is overpriced (undervalued). Other arbitrageurs, who became aware of the mispricing earlier, think that it is more likely that the price move will trigger a full price correction, and trade in the direction of the fundamentals. In summary, our analysis shows that arbitrage ultimately works, but that it occurs with a delay. While markets are not fully informationally efficient, the departure from the fundamental value is constrained. Prices are governed by the fundamental value in the long term, but behavioral biases might affect prices in the intermediate and short term.
نتیجه گیری انگلیسی
This paper presents a new explanation—synchronization risk—for why arbitrage might be limited and behavioral biases in prices persist. The distinctive feature of synchronization risk compared to noise trader risk is that it is not directly caused by behavioral traders. It is each arbitrageur's uncertainty about the timing of other arbitrageurs’ actions, combined with the desire to minimize holding costs, that causes each trader to delay an arbitrage trade. As a consequence, and contrary to the prediction of the efficient markets hypothesis, there can be significant and long-lasting departures from efficient prices. Nevertheless, our analysis suggests that the price of an asset is (loosely) anchored to its fundamental value since in our model mispricing is corrected more quickly the larger it is. Apart from the basic result of delayed arbitrage, the model also provides an explanation for fads and fashion in the acquisition and use of information and for why “bad news travels slowly.” Many extensions of the basic model could be usefully pursued. Perhaps the most challenging is to model the price process more explicitly than we have done. Another task that merits future research is to model the behavioral traders’ decision-making based explicitly on well-documented psychological biases. In that setting, arbitrageurs who want to “read the mind of the market” would not only have to predict the behavior of other rational arbitrageurs, but would also have to take account of the evolving behavior of irrational traders. Such models would combine synchronization risk with endogenous noise trader risk.