## Abstract

We test a Wall Street investment strategy, “pairs trading,” with daily data over 1962–2002. Stocks are matched into pairs with minimum distance between normalized historical prices. A simple trading rule yields average annualized excess returns of up to 11% for self-financing portfolios of pairs. The profits typically exceed conservative transaction-cost estimates. Bootstrap results suggest that the “pairs” effect differs from previously documented reversal profits. Robustness of the excess returns indicates that pairs trading profits from temporary mispricing of close substitutes. We link the profitability to the presence of a common factor in the returns, different from conventional risk measures.

Wall Street has long been interested in quantitative methods of speculation. One popular short-term speculation strategy is known as “pairs trading.” The strategy has at least a 20-year history on Wall Street and is among the proprietary “statistical arbitrage” tools currently used by hedge funds as well as investment banks. The concept of pairs trading is disarmingly simple. Find two stocks whose prices have moved together historically. When the spread between them widens, short the winner and buy the loser. If history repeats itself, prices will converge and the arbitrageur will profit. It is hard to believe that such a simple strategy, based solely on past price dynamics and simple contrarian principles, could possibly make money. If the U.S. equity market were efficient at all times, risk-adjusted returns from pairs trading should not be positive.

In this article, we examine the risk and return characteristics of pairs trading with daily data over the period 1962 through December 2002. Using a simple algorithm for choosing pairs, we test the profitability of several straightforward, self-financing trading rules. We find average annualized excess returns of about 11% for top pairs portfolios. Although pairs strategies exploit temporary components of stock prices, we show that our profits are not caused by simple mean reversion as documented in the previous literature. We examine the robustness of our results to a wide variety of risk factors—including not only the widely used factors in the empirical literature but also potential low-frequency institutional factors such as bankruptcy risk. In addition, we explore the robustness of our results to microstructure factors such as the bid-ask bounce, short-selling costs, and transaction costs. Although some factors such as short-selling and transaction costs affect the magnitude of the excess returns, pairs trading remains profitable for reasonable assumptions over the sample period of study, as well as over a true out-of-sample test of four years. We interpret the results of our analysis as evidence in favor of profitable arbitrage in expectations that may accrue to market participants who possess relatively low transaction costs and the ability to short securities. We also find evidence that points to a systematic factor that influences the profitability of pairs trading over time. This unidentified latent risk factor has been relatively dormant recently. The importance of this risk factor is correlated with the returns to pairs trading, which is consistent with the view that the profits are a compensation to arbitrageurs for enforcing the “Law of One Price.”

We argue that our results reveal something about the mechanism and performance of relative-price arbitrage activities in practice. This is potentially useful to researchers because, despite considerable theory about market efficiency, economists have little empirical information about how efficiency is maintained in practice. In addition, despite the fact that hedge funds have attracted an increasing amount of investment capital over the past decade, the study of hedge fund strategies is in its infancy in the financial economics literature. This article examines the risk and return characteristics of one widely practiced active trading strategy.

One natural question to ask is whether our results imply a violation of equilibrium asset pricing. Although the documented profitability of the pairs trading rule is a robust result, it is not inconsistent with all pricing models. Indeed the reversion in relative values we find is consistent with a pricing model in prices developed and tested by Bossaerts (1988). Thus, our article at the very least suggests that this class of models merits further empirical investigation.

The remainder of the article is organized as follows. Section 1 provides some background on pairs trading strategy. The next section describes our methodology of constructing pairs and calculating returns. The empirical results are described in Section 3, and Section 4 provides conclusions and directions for future research.

### Pairs trading and contrarian investment

Because pairs trading bets on price reversals, it is an example of a contrarian investment strategy. The results of Table 4 showed that the returns to pairs are positively correlated with—but not explained by—short-term reversals documented by Lehmann (1990) and Jegadeesh (1990). In this section we further explore whether our pairs trading strategies are merely a disguised way of exploiting these previously documented negative autocorrelations. In particular, we conduct a bootstrap where we compare the performance of our pairs to random pairs. The starting point of the bootstrap is the set of historical dates on which the various pairs open. In each bootstrap we replace the actual stocks with two random securities with similar prior one-month returns as the stocks in the actual pair. Similarity is defined as coming from the same decile of previous month’s performance. The difference between the actual and the simulated pairs returns provides an indication of the portion of our pairs return that is not due to reversion. We bootstrapped the entire set of trading dates 200 times. The results are summarized in Table 6. On average we find that the returns on the bootstrapped pairs are well below the true pairs returns. In fact, the excess returns to the simulated pairs are slightly negative, and the standard deviations of the returns are large relative to the true pairs, which is a reflection of the fact that the simulated pairs are poorly matched. The conclusion from the simulations confirms the conclusion from the factor regressions that the pairs strategy does not merely reflect one-month mean reversion. In addition, in the next section, we will show that the long and short portfolios that make up a pair do not provide equal contributions to the profitability of the strategy. These three findings combined strongly suggest that our pairs trading strategy seems to capture temporal variation in returns that is different from simple mean reversion.

Table 6

Returns to random pairs sorted on prior one-month return

Portfolio Top 5 Top 20 Top 100–120 All 120
A. No waiting
Fully invested
Mean excess return −0.00137 −0.00111 −0.00105 −0.00113
Standard deviation 0.05521 0.02295 0.02264 0.01200
Median −0.00192 −0.00153 −0.00156 −0.00162
Committed capital
Mean excess return −0.00083 −0.00077 −0.00089 −0.00091
Standard deviation 0.02635 0.01358 0.01443 0.00760
Median −0.00123 −0.00100 −0.00123 −0.00122
B. Wait one day
Fully invested
Mean excess return −0.00177 −0.00004 −0.00154 −0.00156
Standard deviation 0.05966 0.05310 0.02404 0.01213
Median −0.00241 −0.00172 −0.00206 −0.00201
Committed capital
Mean excess return −0.00103 −0.00094 −0.00112 −0.00112
Standard deviation 0.02811 0.01363 0.01449 0.00761
Median −0.00152 −0.00118 −0.00148 −0.00139
Portfolio Top 5 Top 20 Top 100–120 All 120
A. No waiting
Fully invested
Mean excess return −0.00137 −0.00111 −0.00105 −0.00113
Standard deviation 0.05521 0.02295 0.02264 0.01200
Median −0.00192 −0.00153 −0.00156 −0.00162
Committed capital
Mean excess return −0.00083 −0.00077 −0.00089 −0.00091
Standard deviation 0.02635 0.01358 0.01443 0.00760
Median −0.00123 −0.00100 −0.00123 −0.00122
B. Wait one day
Fully invested
Mean excess return −0.00177 −0.00004 −0.00154 −0.00156
Standard deviation 0.05966 0.05310 0.02404 0.01213
Median −0.00241 −0.00172 −0.00206 −0.00201
Committed capital
Mean excess return −0.00103 −0.00094 −0.00112 −0.00112
Standard deviation 0.02811 0.01363 0.01449 0.00761
Median −0.00152 −0.00118 −0.00148 −0.00139

Bootstrap of random pairs traded according to the rule that opens a position in a random pair when the stocks in the true pair diverge by two historical standard deviations and closes the position after the next crossing of prices. The random stocks are selected within the same last-month performance decile on the day the position is opened. The top panel gives summary statistics of the monthly excess returns on value-weighted portfolios of $$n$$ pairs of stocks where the position is opened immediately. The last column is a portfolio of all 120 top pairs. The bottom panel summarizes the performance with one day waiting before the position is opened. The statistics are computed over 200 replications of the bootstrapped sample.

### Risk and return of the long and short positions

There are at least three reasons to separately examine the returns to the long and short portfolios that make up a pairs position. First, the separate returns provide further insight into the question of mean reversion. If pairs trading simply exploits mean reversion, one would expect the abnormal returns to the long and short positions to be equal because the opening of a pair is equally likely to be triggered by either stock. Second, if the excess returns are predominantly driven by the short position, it becomes important to examine whether short-sale considerations might prevent arbitrageurs from competing away the profits. Finally, the risk exposures of the two portfolios can provide further clues to the reason for the profitability of pairs—for example, the possibility that the long and short portfolios have different exposures to common nonstationary risk factors such as bankruptcy risk.8 The returns and the risk exposures of the component portfolios are summarized in Table 7.

Table 7

Returns to long and short components of pairs

Top 5

Top 20

20 after top 100

All

Portfolio Long Short Long Short Long Short Long Short
Portfolio performance
Mean monthly return 0.01245 0.00501 0.01330 0.00435 0.01458 0.00663 0.01623 0.00908
Standard error (Newey-West) 0.00183 0.00177 0.00179 0.00174 0.00170 0.00165 0.00254 0.00231
Standard deviation 0.03875 0.03259 0.03653 0.03161 0.03437 0.03146 0.05157 0.04601
Monthly serial correlation 0.06 0.11 0.09 0.12 0.13 0.12 0.17 0.16
Regression on Market, SMB, HML, Momentum, and Reversal factors
Intercept 0.00103 −0.00442 0.00243 −0.00521 0.00287 −0.00426 −0.00101 −0.00613
$${\quad }{\quad }{\quad }{\quad }t$$-Statistic 0.47 −2.74 1.27 −3.35 2.85 −4.26 −1.32 −5.22
U.S. equity risk-premium 0.37415 0.44075 0.47617 0.50772 0.48520 0.56217 0.58571 0.73091
$${\quad }{\quad }{\quad }{\quad }t$$-Statistic 4.60 6.19 6.68 8.44 10.23 9.74 14.99 12.13
SMB −0.16764 −0.12532 −0.06506 −0.06616 0.01120 0.03453 0.22192 0.29271
$${\quad }{\quad }{\quad }{\quad }t$$-Statistic −1.74 −2.00 −0.80 −1.22 0.27 0.95 3.45 3.15
HML 0.48401 0.42661 0.52539 0.48025 0.39451 0.41175 0.25732 0.31134
$${\quad }{\quad }{\quad }{\quad }t$$-Statistic 7.12 6.92 9.36 9.47 9.76 11.54 7.49 8.11
Momentum −0.05430 −0.02625 −0.04456 0.00361 −0.10901 −0.00589 −0.08832 0.09245
$${\quad }{\quad }{\quad }{\quad }t$$-Statistic −1.48 −0.65 −1.21 0.10 −3.53 −0.21 −3.53 2.81
Reversal 0.15854 0.05662 0.09601 0.02365 0.17288 0.07830 0.39208 0.19131
$${\quad }{\quad }{\quad }{\quad }t$$-Statistic 1.83 1.13 1.26 0.55 4.33 1.90 10.44 2.98
$${\quad }{\quad }{\quad }{\quad }R^{2}$$ 0.39 0.41 0.48 0.49 0.78 0.75 0.97 0.93
Top 5

Top 20

20 after top 100

All

Portfolio Long Short Long Short Long Short Long Short
Portfolio performance
Mean monthly return 0.01245 0.00501 0.01330 0.00435 0.01458 0.00663 0.01623 0.00908
Standard error (Newey-West) 0.00183 0.00177 0.00179 0.00174 0.00170 0.00165 0.00254 0.00231
Standard deviation 0.03875 0.03259 0.03653 0.03161 0.03437 0.03146 0.05157 0.04601
Monthly serial correlation 0.06 0.11 0.09 0.12 0.13 0.12 0.17 0.16
Regression on Market, SMB, HML, Momentum, and Reversal factors
Intercept 0.00103 −0.00442 0.00243 −0.00521 0.00287 −0.00426 −0.00101 −0.00613
$${\quad }{\quad }{\quad }{\quad }t$$-Statistic 0.47 −2.74 1.27 −3.35 2.85 −4.26 −1.32 −5.22
U.S. equity risk-premium 0.37415 0.44075 0.47617 0.50772 0.48520 0.56217 0.58571 0.73091
$${\quad }{\quad }{\quad }{\quad }t$$-Statistic 4.60 6.19 6.68 8.44 10.23 9.74 14.99 12.13
SMB −0.16764 −0.12532 −0.06506 −0.06616 0.01120 0.03453 0.22192 0.29271
$${\quad }{\quad }{\quad }{\quad }t$$-Statistic −1.74 −2.00 −0.80 −1.22 0.27 0.95 3.45 3.15
HML 0.48401 0.42661 0.52539 0.48025 0.39451 0.41175 0.25732 0.31134
$${\quad }{\quad }{\quad }{\quad }t$$-Statistic 7.12 6.92 9.36 9.47 9.76 11.54 7.49 8.11
Momentum −0.05430 −0.02625 −0.04456 0.00361 −0.10901 −0.00589 −0.08832 0.09245
$${\quad }{\quad }{\quad }{\quad }t$$-Statistic −1.48 −0.65 −1.21 0.10 −3.53 −0.21 −3.53 2.81
Reversal 0.15854 0.05662 0.09601 0.02365 0.17288 0.07830 0.39208 0.19131
$${\quad }{\quad }{\quad }{\quad }t$$-Statistic 1.83 1.13 1.26 0.55 4.33 1.90 10.44 2.98
$${\quad }{\quad }{\quad }{\quad }R^{2}$$ 0.39 0.41 0.48 0.49 0.78 0.75 0.97 0.93

Monthly risk profile for the long and short positions of the pairs portfolios formed and traded according to the “wait one day” rule discussed in the text. The returns in the bottom half of the table are in excess of the 30-day Treasury bill returns. The risk adjustment includes the Fama–French factors, as well as Momentum and the Reversal factors discussed in the text. The $$t$$-statistics are computed using Newey-West standard errors with six lags. Absolute kurtosis is reported.

The table demonstrates that much of the pairs risk-adjusted excess return comes from the short portfolio, which contains the stocks that have increased in value relative to their counterparts prior to opening of the pair. By contrast, the alphas of the long portfolio containing the stocks that decreased in value relative to their counterparts are smaller, and insignificantly different from zero for the top 5 and top 20 portfolios. The asymmetry of the results provides further evidence that the returns to pairs are not due to simple one-month mean reversion. And because much of the abnormal return comes from the short position, which experienced an increase in relative value prior to opening, it is unlikely that the returns are driven by a reward for unrealized bankruptcy risk. The robustness of our results to the cost of short sales will be discussed in Section 3.9.

### Subperiod analysis and the presence of a dormant risk factor

Table 8 summarizes the profitability of pairs trading when we split the sample period at the end of 1988. A comparison between the two top halves of the two panels shows a drop in the raw excess returns to pairs trading. For example, the excess return of the top 20 strategy drops from 118 bp per month to about 38 bp per month. Has increased hedge fund activity arbitraged away the anomalous behavior of pairs since the pre-1989 period? Inspection of the risk-adjusted returns shows that this is not the case: the average risk-adjusted return of the top 20 portfolio drops by about one-third from 67 to 42 bp per month, but remains significantly positive in both subperiods $$(t = 4.41$$ and 3.77, respectively). Changes in the factor exposures and factor volatilities can explain only part of the lower returns in the early part of the sample, but not the risk-adjusted returns to pairs trading.

Table 8

Subperiod analysis

Portfolio Top 5 Top 20 20 after top 100 All Factor SD
A. Pre-1989
“Wait one day” portfolio performance
Mean excess return 0.01034 0.01181 0.01052 0.00992
Standard deviation 0.02259 0.01689 0.01527 0.01651
Regression on Fama–French factors
Intercept 0.00353 0.00670 0.00710 0.00446
$${\quad }{\quad }{\quad }{\quad }t$$-Statistic 1.72 4.41 6.54 4.19
U.S. equity risk-premium −0.43395 −0.31200 −0.28946 −0.43429 0.04580
$${\quad }{\quad }{\quad }{\quad }t$$-Statistic −4.29 −3.57 −3.80 −7.26
SMB: small minus big −0.44181 −0.33193 −0.27508 −0.40184 0.02923
$${\quad }{\quad }{\quad }{\quad }t$$-Statistic −3.75 −2.86 −2.86 −5.76
HML: high minus low book to market 0.03568 0.03162 −0.06840 −0.06983 0.02597
$${\quad }{\quad }{\quad }{\quad }t$$-Statistic 0.64 0.73 −1.84 −1.97
Momentum 0.01291 −0.01630 −0.07689 −0.15848 0.03506
$${\quad }{\quad }{\quad }{\quad }t$$-Statistic 0.29 −0.50 −2.92 −5.01
Reversal 0.43575 0.33274 0.28765 0.45222 0.07228
$${\quad }{\quad }{\quad }{\quad }t$$-Statistic 4.44 3.62 4.05 7.98
$${\quad }{\quad }{\quad }{\quad }R^{2}$$ 0.19 0.23 0.26 0.70
B. Post-1988
“Wait one day” portfolio performance
Mean excess return 0.00217 0.00375 0.00327 0.00212
Standard deviation 0.01660 0.00987 0.01121 0.01295
Regression on Fama–French factors
Intercept 0.00337 0.00417 0.00363 −0.00065
$${\quad }{\quad }{\quad }{\quad }t$$-Statistic 2.12 3.77 3.01 −0.56
U.S. equity risk-premium 0.07339 0.04804 0.00241 −0.06958 0.04390
$${\quad }{\quad }{\quad }{\quad }t$$-Statistic 1.68 1.81 0.06 −2.43
SMB: small minus big −0.00400 0.02888 0.02332 −0.06063 0.03856
$${\quad }{\quad }{\quad }{\quad }t$$-Statistic −0.10 1.32 0.69 −2.83
HML: high minus low book to market 0.03441 0.01412 0.01830 −0.08202 0.03641
$${\quad }{\quad }{\quad }{\quad }t$$-Statistic 0.61 0.45 0.50 −2.65
Momentum −0.00424 −0.02266 −0.08840 −0.12670 0.04926
$${\quad }{\quad }{\quad }{\quad }t$$-Statistic −0.13 −1.29 −4.17 −7.59
Reversal −0.06259 −0.01727 0.02404 0.18808 0.04448
$${\quad }{\quad }{\quad }{\quad }t$$-Statistic −1.76 −0.67 0.54 5.56
$${\quad }{\quad }{\quad }{\quad }R^{2}$$ 0.02 0.04 0.19 0.64
Portfolio Top 5 Top 20 20 after top 100 All Factor SD
A. Pre-1989
“Wait one day” portfolio performance
Mean excess return 0.01034 0.01181 0.01052 0.00992
Standard deviation 0.02259 0.01689 0.01527 0.01651
Regression on Fama–French factors
Intercept 0.00353 0.00670 0.00710 0.00446
$${\quad }{\quad }{\quad }{\quad }t$$-Statistic 1.72 4.41 6.54 4.19
U.S. equity risk-premium −0.43395 −0.31200 −0.28946 −0.43429 0.04580
$${\quad }{\quad }{\quad }{\quad }t$$-Statistic −4.29 −3.57 −3.80 −7.26
SMB: small minus big −0.44181 −0.33193 −0.27508 −0.40184 0.02923
$${\quad }{\quad }{\quad }{\quad }t$$-Statistic −3.75 −2.86 −2.86 −5.76
HML: high minus low book to market 0.03568 0.03162 −0.06840 −0.06983 0.02597
$${\quad }{\quad }{\quad }{\quad }t$$-Statistic 0.64 0.73 −1.84 −1.97
Momentum 0.01291 −0.01630 −0.07689 −0.15848 0.03506
$${\quad }{\quad }{\quad }{\quad }t$$-Statistic 0.29 −0.50 −2.92 −5.01
Reversal 0.43575 0.33274 0.28765 0.45222 0.07228
$${\quad }{\quad }{\quad }{\quad }t$$-Statistic 4.44 3.62 4.05 7.98
$${\quad }{\quad }{\quad }{\quad }R^{2}$$ 0.19 0.23 0.26 0.70
B. Post-1988
“Wait one day” portfolio performance
Mean excess return 0.00217 0.00375 0.00327 0.00212
Standard deviation 0.01660 0.00987 0.01121 0.01295
Regression on Fama–French factors
Intercept 0.00337 0.00417 0.00363 −0.00065
$${\quad }{\quad }{\quad }{\quad }t$$-Statistic 2.12 3.77 3.01 −0.56
U.S. equity risk-premium 0.07339 0.04804 0.00241 −0.06958 0.04390
$${\quad }{\quad }{\quad }{\quad }t$$-Statistic 1.68 1.81 0.06 −2.43
SMB: small minus big −0.00400 0.02888 0.02332 −0.06063 0.03856
$${\quad }{\quad }{\quad }{\quad }t$$-Statistic −0.10 1.32 0.69 −2.83
HML: high minus low book to market 0.03441 0.01412 0.01830 −0.08202 0.03641
$${\quad }{\quad }{\quad }{\quad }t$$-Statistic 0.61 0.45 0.50 −2.65
Momentum −0.00424 −0.02266 −0.08840 −0.12670 0.04926
$${\quad }{\quad }{\quad }{\quad }t$$-Statistic −0.13 −1.29 −4.17 −7.59
Reversal −0.06259 −0.01727 0.02404 0.18808 0.04448
$${\quad }{\quad }{\quad }{\quad }t$$-Statistic −1.76 −0.67 0.54 5.56
$${\quad }{\quad }{\quad }{\quad }R^{2}$$ 0.02 0.04 0.19 0.64

Monthly risk profile for portfolios of pairs formed and traded according to the “wait one day” rule discussed in the text, over the two subperiods between July 1963 and December 1988 (Panel A) and between January 1989 and December 2002 (Panel B). The “top $$n”$$ portfolios include the $$n$$ pairs with least distance measures, and the portfolio “20 after top 100” includes the 20 pairs after the top 100 pairs. The average number of pairs in the all-pair portfolio is 2057. The $$t$$-statistics are computed using Newey-West correction with six lags for the standard errors.

Are the positive risk-adjusted returns to pairs trading a general failure of our risk model? In other words, are there reasons to believe that the risk-adjusted pairs returns are a compensation for an omitted (latent) risk factor? Inspection of the correlation between disjoint pairs portfolios provides some support for this view. Moreover, this latent risk factor seems to have been relatively dormant over the second half of our sample, which can account for the lower recent profitability of pairs trading. The full-sample correlation between the excess returns of the top 20 and the 100–120 pairs portfolios is 0.48. Because there is no overlap between the positions of these portfolios, the correlation indicates the presence of a common factor to the returns. Moreover, the correlation is 0.51 over the profitable pre-1988 period but much lower (0.18) over the lower excess return post-1988 period. These correlations are not driven by the 5 “systematic” risk factors we considered, because the correlations of the residuals from the factor regressions are very similar to the raw correlations. In particular, the correlation between the top 20 Fama–French-Momentum-Reversal (FFMR) residuals and the top 100–120 FFMR residuals is 0.41. The respective subperiod FFMR correlations are 0.42 and 0.20. This is further illustrated in Figure 4, which shows that the rolling 24-month correlation between the two portfolios was especially high during the pre-1989 period.

Figure 4

Top 20 pairs and 101–120 pairs portfolios  Rolling 24-month correlation of five-factor risk-adjusted excess returns.

Figure 4

Top 20 pairs and 101–120 pairs portfolios  Rolling 24-month correlation of five-factor risk-adjusted excess returns.

These results suggest that there is common component to the profits of pairs portfolios that is not captured by our conventional measures of systematic risk. The common component was stronger during the first half of our sample, which is consistent with higher profits (abnormal returns) than in the second half of our sample when the factor was more dormant. These results are consistent with the view that the abnormal returns documented in this article are indeed a compensation for risk, in particular the reward to arbitrageurs for enforcing the “Law of One Price.”

### Robustness to short-selling costs

Having identified and back-tested a filter rule, and subjected it to a range of controls for risk, the question of the nature of pairs profits remains. Why do prices of close economic substitutes diverge and converge? The convergence is easier to understand than the divergence, given the natural arbitrage motivation and the documented existence of relative-value arbitrageurs in the U.S. equity market. However, this does not explain why prices drift away from parity in the first place. One possible explanation is that prices diverge on random liquidity shocks that cannot be exploited by professional arbitrageurs because of short-selling costs.9

First, there are explicit short-selling costs in the form of specials. Second, D’Avolio (2002) argues that short recalls are potentially costly because they may deprive arbitrageurs of their profits. This opportunity cost is reinforced by D’Avolio’s findings that short recalls are more common as the price declines. For example, if the short stock is recalled when it starts to converge downward, then the pairs position is forced to close prematurely and the arbitrageur does not capture the profit from the pair convergence. We perform two tests for robustness of the profits that corresponds to these two types of short-selling costs.

The first test is motivated by the findings of D’Avolio (2002) and Geczy et al. (2002) that specials have minimal effect of large stocks. Correspondingly, we test for robustness of profits by trading pairs that are formed using only stocks in the top three size deciles.10 The results, given in Panel A of Table 9, can be directly compared to those in Panel B of Table 1. The comparison shows that the profits of the top 20 strategy drop by about 2 bp per month, but increase for the top five portfolios. Overall, the profits change little and remain highly significant. This shows that the pairs trading profits are not driven by illiquid stocks that are likely to be on special.

Table 9

Robustness to short-selling costs

Portfolio Top 5 Top 20 20 after top 100 All
A. Top three deciles
Mean monthly return (fully invested) 0.00835 0.00914 0.00728 0.00690
Standard error (Newey-West) 0.00112 0.00096 0.00075 0.00064
$$t$$-Statistic 7.47 9.48 9.66 10.85
Excess return distribution
Median 0.00800 0.00793 0.00614 0.00508
Standard deviation 0.01904 0.01464 0.01579 0.01294
Kurtosis 0.02 0.98 0.80 1.77
Skewness 7.01 8.20 6.46 11.67
Minimum −0.10894 −0.05646 −0.03803 −0.02680
Maximum 0.10144 0.10003 0.10642 0.10478
Observations with excess return < 0 32% 26% 33% 27%
Mean excess return on committed capital 0.00493 0.00514 0.00462 0.00401
B. Short recalls on high volume
Mean monthly return (fully invested) 0.00619 0.00854 0.00665 0.00585
Standard error (Newey-West) 0.00115 0.00094 0.00085 0.00098
$$t$$-Statistic 5.39 9.07 7.81 5.95
Excess return distribution
Median 0.00592 0.00703 0.00531 0.00312
Standard deviation 0.02210 0.01488 0.01505 0.01555
Skewness 0.15 0.48 1.03 2.82
Kurtosis 5.39 6.00 7.39 18.98
Minimum −0.09611 −0.06594 −0.04408 −0.03465
Maximum 0.10504 0.07255 0.10084 0.14173
Observations with excess return < 0 39% 26% 34% 37%
Mean excess return on committed capital 0.00304 0.00347 0.00296 0.00202
Portfolio Top 5 Top 20 20 after top 100 All
A. Top three deciles
Mean monthly return (fully invested) 0.00835 0.00914 0.00728 0.00690
Standard error (Newey-West) 0.00112 0.00096 0.00075 0.00064
$$t$$-Statistic 7.47 9.48 9.66 10.85
Excess return distribution
Median 0.00800 0.00793 0.00614 0.00508
Standard deviation 0.01904 0.01464 0.01579 0.01294
Kurtosis 0.02 0.98 0.80 1.77
Skewness 7.01 8.20 6.46 11.67
Minimum −0.10894 −0.05646 −0.03803 −0.02680
Maximum 0.10144 0.10003 0.10642 0.10478
Observations with excess return < 0 32% 26% 33% 27%
Mean excess return on committed capital 0.00493 0.00514 0.00462 0.00401
B. Short recalls on high volume
Mean monthly return (fully invested) 0.00619 0.00854 0.00665 0.00585
Standard error (Newey-West) 0.00115 0.00094 0.00085 0.00098
$$t$$-Statistic 5.39 9.07 7.81 5.95
Excess return distribution
Median 0.00592 0.00703 0.00531 0.00312
Standard deviation 0.02210 0.01488 0.01505 0.01555
Skewness 0.15 0.48 1.03 2.82
Kurtosis 5.39 6.00 7.39 18.98
Minimum −0.09611 −0.06594 −0.04408 −0.03465
Maximum 0.10504 0.07255 0.10084 0.14173
Observations with excess return < 0 39% 26% 34% 37%
Mean excess return on committed capital 0.00304 0.00347 0.00296 0.00202

Summary statistics of the monthly excess returns on portfolios of pairs. We trade according to the rule that opens a position in a pair when the prices of the stocks in the pair diverge by two historical standard deviations. Panel B reports the summary statistics for the rule that waits one day before opening and closing the position. The “top $$n”$$ portfolios include the $$n$$ pairs with least distance measures, and the portfolio “20 after top 100” includes the 20 pairs after the top 100 pairs. The average number of pairs in the all-pair portfolio is 2057. There are 474 monthly observations, from July 1963 through December 2002. The $$t$$-statistics are computed using the Newey-West standard errors with six-lag correction. Absolute kurtosis is reported.

The second test is motivated by the evidence in Chen et al. (2002) and D’Avolio (2002) that short recalls are driven by dispersion of opinion. We use high volume as proxy for divergence of opinion and perform pairs trading under recalls, where we simulate recalls on the short positions, and subsequent closing of the pairs position, on days with high volume. High-volume days are defined as days on which daily volume exceeds average daily volume over the 18 months (both split-adjusted) by more than one standard deviation. Panel B of Table 9 summarizes the profits of pairs trading with the high-volume recalls. The profits decline slightly by 4–13 bp per month, yet they remain large and positive. For example, the top 20 pairs portfolio earns an average of 85 bp per month with short recalls, with a Newey-West $$t$$-statistic of 9.07. The results in Panel B can be interpreted as an estimate of the opportunity cost of short recalls.

Overall, the small effects confirm that the profits persist when trading pairs of large stocks as well as when shorts are recalled. These results show that pairs trading profits are robust to short-selling costs. For better-positioned investors, for example, large institutions and hedge funds, the pairs trading profits are likely to remain essentially unaffected by potential shorting costs. Getczy et al. (2002) argue that for large traders, who have better access to most stocks at “wholesale prices,” direct shorting costs of the rebate rate on short sales are low (4–15 bp/year). The main implicit shorting cost stems from limited availability and is relevant mostly for general retail investors. The impact of such potential short sales constraints on the profitability of pairs trading by large investors is mitigated by our use of liquid stocks that trade every day over a period of one year.

## Conclusion

We examine a hedge fund equity trading strategy based on the notion of co-integrated prices in a reasonably efficient market, known on Wall Street as pairs trading. Pairs are stocks that are close substitutes according to a minimum-distance criterion using a metric in price space. We find that trading suitably formed pairs of stocks exhibits profits, which are robust to conservative estimates of transaction costs. These profits are uncorrelated to the S&P 500; however, they do exhibit low sensitivity to the spreads between small and large stocks and between value and growth stocks in addition to the spread between high- and intermediate-grade corporate bonds and shifts in the yield curve. In addition to risk and transaction cost, we rule out several explanations for the pairs trading profits, including mean reversion as previously documented in the literature, unrealized bankruptcy risk, and the inability of arbitrageurs to take advantage of the profits because of short-sale constraints.

One view of the lower profitability of pairs trading in recent year is that returns are competed away by increased hedge fund activity. The alternative view, taken in this article, is that abnormal returns to pairs strategies are a compensation to arbitrageurs for enforcing the “Law of One Price.” We present two pieces of empirical evidence that supports this view. First, although raw returns have fallen, the risk-adjusted returns have continued to persist despite increased hedge fund activity. Second, our results suggest that the change in risk-adjusted returns of pairs trading is accompanied by the diminished importance of a common factor that drives the returns to pairs strategies. A further examination of the nature of this common factor and its link to the profitability of pairs trading is an important question for future research.

1

Froot and Dabora (1999) consider “twin” stocks that trade in different international markets to examine the issues of market integration.

2

Note that the case $$n {\gg } k$$ corresponds to the standard finance paradigm where in the large universe of $$n$$ stocks, expected returns are driven by a few, namely $$k,$$ common factors. This paradigm is supported by existing empirical work, for example, see Connor and Korajczyk (1993) for references, which generally finds less than 10 common nonstationary components.

3

We thank an anonymous referee for this example.

4

The profits are robust with respect to this delisting assumption. A potential problem arises if inaccurate and stale prices exaggerate the excess returns and bias the estimated return of a long position in a plummeting stock. To address this potential concern, we have reestimated our results under the extreme assumption that only a long stock experiences a –100% return when it is delisted. This zero-price extreme includes, among other things, the possibility of nontrading due to the lack of liquidity. Because selective loss on the long position always harms the pair profit, this extreme assumption biases the results against profitability. However, pairs trading remains profitable under this alternative: for example, the average monthly return on the top 20 pairs portfolio is 1.32% with a standard deviation of 1.9%.

5

This is a conservative approach to computing the excess return, because it implicitly assumes that all cash earns zero interest rate when not invested in an open pair. Because any cash flow during the trading interval is positive by construction, it ignores the fact that these cash flows are received early and understates the computed excess returns.

6

The optimal trigger point in terms of profitability may actually be much higher than two standard deviations, although we have not experimented to find out.

7

The construction is similar to Carhart’s (1997) momentum factor, but the performance-sorting horizon here is one month.

8

We thank a referee for suggesting this explanation.

9

We are grateful to the editor Maureen O’Hara for pointing out this plausible explanation and for suggesting the way to test it.

10

Using large liquid stocks also mitigates the problem of stocks that are hard to short and can be overvalued, see, for example, Jones and Lamont (2002).

We are grateful to Peter Bossaerts, Michael Cooper, Jon Ingersoll, Ravi Jagannathan, Maureen O’Hara, Carl Schecter, and two anonymous referees for many helpful discussions and suggestions on this topic. We thank the International Center for Finance at the Yale School of Management for research support, and the participants in the EFA’99 Meetings, the AFA’2000 Meetings, the Berkeley Program in Finance, and the Finance and Economics workshops at Vanderbilt and Wesleyan for their comments.

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