آربیتراژ پر هزینه و اسطوره ریسک ویژه

Transaction and holding costs make arbitrage costly. Mispricing exists to the extent that arbitrage costs prevent rational traders from fully eliminating inefficiencies. Although the relation between mispricing and transaction costs is well-known, the relation between mispricing and holding costs is misunderstood. One holding cost, idiosyncratic risk, is particularly misunderstood. Various myths are debunked, including the common myth that idiosyncratic risk matters because arbitrageurs only have access to a small number of projects [Shleifer and Vishny, 1997. The limits of arbitrage. The Journal of Finance 52, 35–55.]. The literature demonstrates that idiosyncratic risk is the single largest cost faced by arbitrageurs.

This paper strives to debunk seven myths surrounding the impact of rational arbitrage on irrational prices. Myth 1: Arbitrage costs make arbitrage a zero-profit exercise. Myth 2: Arbitrage costs decimate all arbitrage activity. Myth 3: Arbitrageurs avoid shorting high dividend paying stocks, since the short seller must rebate all dividend payments, making a short position more expensive. Myth 4: Arbitrageurs care about idiosyncratic risk since they only have access to a small number of projects ( Shleifer and Vishny, 1997). Myth 5: Idiosyncratic risk has no impact on mispricing. Even if short-sellers are dissuaded by idiosyncratic risk, idiosyncratic risk will not affect the selling decision of sophisticated investors who already own the stock. Myth 6: Since arbitrage costs are related to mispricing, the costly arbitrage literature provides proof that markets are efficient. Myth 7: Costly arbitrage tests are subject to Fama's (1976) joint hypothesis to the same extent as classic tests of market efficiency. Arbitrage is the transaction where a rational agent tries to profit from mispricing. Mispricing continues in equilibrium since costs prevent arbitrageurs from fully offsetting the price impact of irrational investors. The relation between arbitrage costs and market inefficiencies is often misunderstood. One arbitrage cost, idiosyncratic risk is particularly misunderstood. This misunderstanding likely stems from the detailed treatment of diversification and the capital asset pricing model (CAPM) in elementary finance text books that espouse that idiosyncratic risk does not matter. This logic is often falsely extended to make erroneous claims that idiosyncratic risk should not affect arbitrage activity, since the arbitrageur can costlessly diversify away this risk. Although the text book discussion of idiosyncratic risk is correct in terms of the CAPM, this logic does not carry over to arbitrage and market inefficiencies. Regardless of an arbitrageur's access to a diversified portfolio, and regardless of the number of available arbitrage projects, the idiosyncratic risk of each project will mute the arbitrageur's position in the project. This article strives to clarify how inefficiencies may exist in equilibrium, and to illuminate the critical role played by idiosyncratic risk. This framework is useful for tests of market efficiency, since the interplay between idiosyncratic risk (as well as other arbitrage costs) and mispricing provides a testable prediction that only relies on the economic rationality of arbitrageurs, and not on the arbitrary behavior of noise traders. As will be shown in Section 5, the empirical studies that have explored such tests have affirmed the importance of idiosyncratic risk as the foremost arbitrage cost. Recent research on inefficiencies and costly arbitrage has failed to emphasize the importance of idiosyncratic risk. This lack of coverage is attributable to two factors. First, some researchers believe variants of myth 4, and thus they downplay the importance of idiosyncratic risk as only a concern for investors with limited opportunities. Second, theoretical and empirical keystone papers have focused on systematic risk to the exclusion of idiosyncratic risk. One such theoretical paper, De long et al. (1990) argues that noise trader risk creates systematic risk, and asset prices are discounted to reflect this risk. Since there is only one asset in their model and all noise-traders have the same irrational expectations, idiosyncratic risk plays no role. The literature spawned by their paper has focused on irrational comovement, but has forsaken idiosyncratic risk. Early keystone empirical work by Shiller (1989) tests whether stock index returns are too volatile relative to dividend streams. Since stock indices are not subject to idiosyncratic risk, the excess volatility calculation omits a large proportion of volatility. Pontiff (1997) estimates that 85% of closed-end fund excess volatility is idiosyncratic to a four-factor model that includes the Fama–French factors as well as the Lee et al. (1991) investor sentiment index. If this evidence is indicative of stock return excess volatility, stock return excess volatility is 6.7 times larger than implied by a Shiller-type test. 1.1. Costly arbitrage and market efficiency The term “market efficiency” describes a market where information is immediately reflected in prices. The appeal of this view of a market follows from one of two assumptions. First, as is common in economics, agents are rational. Rationality implies that no one would buy an overpriced asset and that no one would sell an under-priced asset. Thus, the equilibrium of all rational agents implies price equates to fair value, and all information is reflected in asset prices. Put another way, in this equilibrium there are no dollar bills on the floor since rational agents do not drop bills on the floor. A second assumption that is sufficient to generate an efficient market is that rational agents are able to profitably trade against mispricing until it disappears. The profit from these trades cease when price equals fair value, at which point the market is efficient (Friedman, 1953). In this equilibrium, there are no dollar bills on the floor, since all lost bills have been collected by profit-minded rational agents. For simplicity, we will call these rational agents “arbitrageurs.” Most financial economists would agree that markets are very efficient but not perfectly efficient. Thus, there may be some (but not too many) dollar bills on the floor, which begs the question, “what is wrong with our notion of a rational equilibrium?”. The answer to the question starts with the acknowledgement that not all agents are perfectly rational when it comes to financial decisions. This follows from a large body of accumulated evidence that some people make financial mistakes. For example, Barber and Odean (2000) find that individuals tend to trade positions too often. Odean (1998) shows that investors tend to realize losses later, and gains earlier than tax-optimizing would suggest. Agnew (2005) shows that employees do not fully participate in 401(k)'s, they tend to over invest in company stock, and they follow irrational allocation heuristics. Irrational decisions by some investors will not generate inefficiencies if profit-motivated investors counter their price impact. The price impact from the profit-motivated will be constrained to the extent that these traders are subject to costs, including the cost of idiosyncratic risk, that prevent them from fully taking advantage of the inefficiency. In this case, some dollar bills are left on the floor because they are too costly to pick up. This thought process leads to the notion of “costly arbitrage.” The idea of constrained rational investors goes back, at least to Shiller (1984), who models interaction between irrational and rational traders. Shiller (1984) models an effective cost by preventing rational traders from devoting more capital to their trades than they have. The costly arbitrage framework detailed here follows Pontiff (1996), which considers how various arbitrage costs affect arbitrageurs’ abilities to trade against inefficiencies. I use this framework to argue that closed-end fund anomalies (for example, Thompson, 1978, Pontiff, 1995 and Pontiff, 1997) are the manifestation of mispricing.

Holding costs force arbitrageurs to take limited positions in mispriced securities. This enables mispricing to continue. Arbitrageurs are unable to hedge idiosyncratic risk, and thus they must trade off between the expected profit from a position and the idiosyncratic risk to which the position exposes them. The fact that idiosyncratic risk is an arbitrage cost is commonly misunderstood, and because of this, very few studies of market efficiency have examined the impact of idiosyncratic risk on mispricing. The empirical studies that have pursued this course share a common thread—idiosyncratic risk appears to be the single largest impediment to market efficiency.