ریسک معامله‌گران اختلال‌زا: شواهد از دوقلوهای به هم چسبیده

This paper provides new evidence regarding the magnitude and nature of noise trader risk. I examine returns for two pairs of “Siamese twin” stocks: Royal Dutch/Shell and Unilever NV/PLC. These unusual pairs of fundamentally identical stocks provide a unique opportunity to investigate two facets of noise trader risk: (1) the fraction of total return variation unrelated to fundamentals (i.e., noise), and (2) the short-run risk borne by arbitrageurs engaged in long-short pairs trading. I find that about 15% of weekly return variation is attributable to noise. Noise trader risk has both systematic and idiosyncratic components, and varies considerably over time. The conditional volatility of long-short portfolio returns ranged from 0.5% to over 2.75% per week during the 1989–2003 sample period. Noise trader risk was especially high around the failure of Long-Term Capital Management in 1998 and during the collapse of the technology bubble in 2000. I conclude that noise trader risk is a significant limit to arbitrage.

Trading that is uncorrelated with changes in fundamental or intrinsic value is known as noise trading. Noise trading may occur for exogenous reasons (e.g., portfolio rebalancing, liquidity, etc.) or it may occur when investors trade on noise (e.g., changes in sentiment) as if it were information. To the extent that noise trading moves security prices, it contributes to return volatility. Noise trading now occupies an important place in the theory of finance. It has been a cornerstone of market microstructure theory since Kyle (1985). It has been suggested as an explanation for asset pricing “anomalies” such as the “excess volatility puzzle” first documented by Shiller (1981) and LeRoy and Porter (1981). And noise trading plays a central role in the burgeoning literature on behavioral finance. For example, De Long et al. (1990) suggest that noise trader risk is a significant limit to arbitrage that may hinder informationally efficient markets. Black (1986) concludes that “Noise makes financial markets possible, but also makes them imperfect.” Despite its increasingly important role in finance, we have little empirical evidence regarding the magnitude or nature of noise trader risk. This is because it is difficult to distinguish empirically between fundamental shocks and noise shocks. In this paper, I circumvent this obstacle by exploiting a natural experiment: “Siamese twin” stocks. I examine two pairs of dual-listed securities: Royal Dutch/Shell and Unilever NV/PLC. Each of these twin stocks represents a nearly identical claim to a common cash flow stream. Thus, twin stocks have nearly identical risk exposures and should respond almost identically to news regarding fundamental value. The existence of twin stocks trading in different markets permits the investigation of two important facets of noise trader risk: (1) the fraction of total return variation unrelated to news about fundamentals (i.e., noise), and (2) the nature of the noise trader risk faced by arbitrageurs engaged in long-short pairs trading. Although twin stocks represent a very special case, the lessons learned have wider implications for asset pricing and market efficiency. Twin stocks offer a model-free approach for estimating the contribution of noise trading to stock return volatility. Previous research in this area has produced mixed results. One branch of the literature (e.g., Cutler et al., 1989; Roll, 1988; Fama, 1990) finds that news about fundamentals explains relatively little of the variation in total returns. For example, Roll (1988) reports that only 20% of the average large stock's daily return variation is attributable to fundamentals. Explained variation is less than 40% for monthly returns. Roll charges that “the paucity of explanatory power represents a significant challenge to our science.” It is unclear whether the unexplained return variation reported in these papers is due to noise trading, or whether the empirical models do not fully account for all information relevant for valuation. In simple linear regressions, I find that about 85% of weekly return variation, and up to 90% of monthly return variation, can be explained by the returns of a twin stock. This explanatory power greatly surpasses that of the ex post information models examined by Cutler et al. (1989), Roll (1988) and Fama (1990). However, a substantial fraction of return variation (about 15% for weekly returns) remains unexplained by fundamentals. I attribute this unexplained variation to noise trading. Due to their special nature, Siamese twin stocks also provide a unique opportunity to examine the role of noise trader risk as a limit of arbitrage. Because twin stocks represent nearly identical claims to a common cash flow stream, the law of one price implies that the ratio of twin stock prices should equal the theoretical parity ratio. No model of intrinsic value is required. Thus, the arbitrageur faces minimal bad-model risk and the joint-hypothesis critique (see Fama, 1970 and Fama, 1991) does not apply. The arbitrageur also faces minimal fundamental risk. An appropriately constructed long-short relative value position should hedge out nearly all fundamental shocks. Yet, we have observed large relative mispricings between twin stocks. These mispricings are often cited as puzzling violations of the law of one price (e.g., Shleifer, 2000). Rosenthal and Young (1990) document “significant and persistent” deviations from theoretical parity for Royal Dutch/Shell and Unilever NV/PLC for the period from September 1979 to December 1986. Froot and Dabora (1999) document mispricing through 1995 and find that “the relative price of twin stocks is highly correlated with the relative stock-market indexes of the countries where the twins’ stocks are traded most actively”.1Froot and Dabora (1999) examine a number of potential fundamental (i.e., rational) explanations for the observed deviations from parity. These fundamental explanations include discretion in the use of dividend income, differences between parent company expenditures, voting rights, foreign exchange risk exposure between dividend announcement and ex-dividend dates, differences in ex-dividend dates, and cross-border tax-induced investor heterogeneity. They conclude that none of these fundamental explanations is sufficient to explain the magnitude of the observed deviations from parity. Violations of the law of one price are fascinating because they pose a fundamental empirical challenge to the efficient market hypothesis (EMH). The EMH implies that security prices should, on average, reflect fundamental value. In a frictionless and informationally efficient market, two essentially identical assets should trade for the same price. In theory, the law of one price is enforced by arbitrageurs. Arbitrageurs are rational traders who profit from simultaneously buying and selling essentially identical assets at different prices. The existence of such traders is perhaps the strongest theoretical foundation for the EMH. Shleifer (2000) neatly summarizes three theoretical arguments, each with progressively weaker assumptions, that justify the EMH. The first, and least plausible, argument assumes that all investors are rational. The second argument admits the existence of irrational traders, but assumes that their trades are random (i.e., uncorrelated) and, thus, do not affect equilibrium prices. The third argument admits the existence of irrational investors whose noise trading may be correlated. In such a market, prices could temporarily deviate from fundamental value. However, the third argument also assumes the existence of rational, well-capitalized arbitrageurs whose trades restore an equilibrium in which prices reflect intrinsic value. If arbitrage is limited, then correlated noise trading can move stock prices for reasons unrelated to news about fundamentals. Shleifer (2000) argues that violations of the law of one price suggest: (1) the presence of irrational investors (i.e., noise traders), and (2) limits to arbitrage. Potential limits to arbitrage include risks and trading costs. The risks, as described by Lamont and Thaler (2003), include bad-model risk, fundamental risk, and noise trader risk.2 The trading costs include transaction costs, information costs, and financing costs. The role of noise trader risk as an important limit to arbitrage is developed by De Long et al. (1990), Shleifer and Vishny (1997), and Liu and Longstaff (2004). Liu and Longstaff (2004) consider the optimal investment decision of a risk-averse arbitrageur facing realistic collateral requirements. They show that the variance of long-short portfolio returns is an important determinant of the optimal arbitrage position. They conclude that it is often optimal to underinvest in arbitrage (i.e., take a smaller position than collateral requirements allow). I employ a simple limited arbitrage-noise trader model to motivate my empirical framework. In this model, stock returns can be decomposed into four unobservable and orthogonal components: systematic fundamental shocks, firm-specific fundamental shocks, systematic noise shocks, and firm-specific (i.e., idiosyncratic) noise shocks. Barberis et al. (2005) suggest that noise traders invest in only a subset of available securities (i.e., their habitat). If arbitrage is limited, then noise trading induces systematic, sentiment-based comovement in the stock returns of a given habitat. These noise shocks are systematic in the sense that they are not diversifiable. However, systematic noise shocks for twin stocks trading in different habitats need not be correlated. Motivated by Rosenthal and Young (1990) and Froot and Dabora (1999), I assume that twin stocks are fundamentally identical (i.e., they respond identically to news about fundamental value). The most appealing aspect of this assumption is that no asset pricing model is required. A long-short portfolio of twin stocks should hedge the fundamental shocks (both systematic and firm-specific) and isolate the noise shocks. When twin stocks trade in distinct noise trader habitats, long-short portfolio returns will, in part, reflect the relative change in noise-trader sentiment (both systematic and firm-specific) across habitats. At short horizons, long-short portfolio returns will also include microstructure-induced noise.

This paper provides new evidence regarding the magnitude and nature of noise trader risk. I study the returns for two pairs of “Siamese twin” stocks: Royal Dutch/Shell and Unilever NV/PLC. These twin stocks are exposed to the same fundamental risk factors and should respond identically to news about intrinsic value. Thus, they present a unique opportunity to learn about noise trader risk. I examine two facets of noise trader risk: (1) the fraction of total return variation unexplained by fundamentals (i.e., noise), and (2) the short-run risk borne by arbitrageurs engaged in long-short pairs trading. In simple regressions of stock returns on the returns of a twin stock, I find that about 85% of weekly return variation is explained by fundamentals. I attribute the remaining 15% to noise. The explained variation climbs to about 90% for monthly returns. The explained variation from this model-free approach greatly surpasses that reported by Cutler et al. (1989), Roll (1988) and Fama (1990). However, I conclude that noise trading contributes substantially to stock return volatility. The relative mispricings between “Siamese twin” stocks are often cited as a puzzling violation of the law of one price and a challenge to the efficient markets hypothesis. I find that the significant and persistent deviations from theoretical parity previously documented by Rosenthal and Young (1990) and Froot and Dabora (1999) persisted and even increased in the 1990s despite the trading activity of well-capitalized hedge funds such as LTCM. Long-short arbitrage positions in these “Siamese twin” stocks are free of bad-model risk and fundamental risk. However, they are exposed to noise trader risk, and analysis of hypothetical long-short portfolio returns yields valuable insights into the nature of noise trader risk. Using a limited arbitrage-noise trader model of stock returns, I show that long-short portfolio returns reflect relative changes in noise trader sentiment across habitats. I find evidence that noise trader risk faced by arbitrageurs is substantial, that it has both systematic and firm-specific components, and that it varies considerably over time. As in Froot and Dabora (1999), I find that long-short portfolio returns covary excessively with the stock market indices and currencies of the markets where the twin stocks are traded most actively. The limited arbitrage-noise trader model attributes these correlations to comovements in noise shocks, not comovements in fundamental shocks. I find that the volatility of noise shocks is substantial and highly persistent. The level of noise trader risk varied from 0.5% to 2.75% per week over the sample period. Noise trader risk was especially high during the failure of LTCM in 1998 and peaked at the height of the internet/technology bubble in 2000. Since transaction and financing costs are relatively low for large, liquid stocks like the twins, it is likely that noise trader risk is a significant limit to arbitrage. This view is consistent with Pontiff (2006), who suggests that idiosyncratic risk is the single largest cost faced by arbitrageurs. These results raise important questions about the broader issue of market efficiency. If noise trader risk can prevent arbitrageurs from eliminating relative mispricing between pairs of nearly identical assets, then what effect does noise trader risk have on absolute mispricings? The EMH relies on arbitrageurs to enforce an equilibrium in which prices, on average, reflect fundamental value. How efficient can financial markets be if, as Shleifer and Vishny (1990) predict, arbitrageurs are unwilling to commit capital to long-term assets?