Performance of Pairs Trading during a Financial Crisis

Student: Ezra van der Werff (11070633) Supervisor: Dhr. A. Lengyel University of Amsterdam

Statement of Originality This document is written by Student Ezra van der Werff who declares to take full responsibility for the contents of this document.

I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it.

The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

Abstract Pairs trading is a that takes advantage of the mispricing in markets. This paper is divided in two parts. In the first part it will compare the returns of the strategy during the last financial crisis (2007-2009) with the returns from before the crisis (2003-2005). In the second part it will examine whether the of the market is the cause of the difference in returns. A complete pairs trading strategy is developed and implemented to collect the returns using the constituents of the S&P 100. The developed strategy is based on the framework introduced by Gatev, Goetzmann and Rouwenhorst (1999). Results show average weekly returns of 0.145% and 0.512% for respectively 2003-2005 and 2007-2009. The returns of the periods did significantly differ. Regression analyses conducted show that pairs trading returns are for 15.5% explained by the volatility of the market and that pairs trading is a market- neutral strategy.

Introduction By using the trading strategy "pairs trading”, a trader tries to profit from the -term mispricing of . Pairs trading is seen as an trading strategy. This strategy aims to pair stocks whose price series highly correlate. After two stocks are paired, the trading can begin. A pairs trade is based on the historical correlation of the stocks. Traders take a short in the overperforming stock and a position in the underperforming stock when the current correlation of a pair deviates by a certain threshold from the historical correlation. A trader assumes that in the long run, the prices will converge back to their original correlation, and by unwinding the positions at that specific moment, he makes a profit. In the 1950s, Alfred Winslow Jones introduced pairs trading to the world. It was not commonly used initially, but after Nunzio Tartaglia formed a team which focused on new ways to exploit arbitrage opportunities in the mid-1890s, it became popular. From that moment on it has been a highly researched topic. Earlier papers showed that using pairs trading generates positive daily returns, but in recent years there has been a declining trend in the performance of pairs trading. Interestingly, Do and Faff (2010) found that this declining trend turned around during strong market downturns, like the 2007 global financial crisis. This paper aims to check if the performance of pairs trading is significantly higher during a period of market downturns. The 2007 subprime-mortgage financial crisis will be used to represent the period of market downturns. Especially now, a better understanding of the performance of this strategy during a crisis is relevant. As a consequence of the COVID- 19 crisis a new financial crisis is expected to occur, and pairs trading might prove to be interesting for traders. A study by Tu et al. (2016) found that during a period of high volatility, find it difficult to determine the correct value of assets. High volatility takes place during a financial crisis and if short-term misvalued assets occur more often this can be favorable for pairs trading. Given the findings of Tu et al. (2016) and Do and Faff (2010), researching the effect of volatility on the performance of pairs trading might gives new insights in the utility of the strategy. In this paper, four pairs trading periods will be constructed: two periods before the crisis (2003-2005) and two during the crisis (2007-2009). The implementation of the pairs trading strategy is constructed based on the methodology of Gatev et al. (1999). After implementing the strategy, we will compare the returns of both periods to see if there is a significant difference. Finally, we are going to regress the weekly returns against the volatility of the S&P 100 and the excess return of the S&P 100. We regress against the volatility of the S&P 100 to see if this may be the cause of potential overperformance during a crisis, and we regress the returns on the market excess return to see if pairs trading truly can be seen as a market-neutral strategy. The results of this paper are in line with the findings of Do and Faff (2010) and Tu et al. (2016). Pairs trading performs better during a financial crisis and the volatility has a significant effect on the returns of the strategy. The weekly average return before and during the crisis found in this paper were respectively 0,145% and 0,512%. The volatility of the S&P 100 explains 15.5% of the returns of pairs trading and as expected the volatility during the crisis was considerably higher. Lastly this paper found that the S&P 100 returns do not have significant effect on the returns of pairs trading. The strategy can be seen as a market-neutral strategy. Literature Review The research paper of Gatev, Goetzmann, and Rouwenhorst (1999) marks the first time the profitability of pairs trading was investigated. At the time, multiple frameworks to perform a pairs trading strategy already existed, but none of them were tested. Gatev et al. (1999) used the minimum-distance criterion to match stocks into pairs. After creating multiple portfolios existing out of a various amount of pairs they started trading according to a pre-specified rule: to open a position in a pair when prices diverge by more than two historical standard deviations – as estimated during the pairs formation period – and close the position when the prices have reverted. After carrying out this complete strategy and finding positive monthly returns over periods 1962 through 1997, they regressed the monthly returns on the three- factor model of Fama-French. By executing this regression, they tried to find the exposure of the pairs trading strategy. The results showed that pairs trading returns are not significantly affected by the market return. So pairs trading can assumed to be a market- neutral strategy. Krauss (2016) published a paper about the various pairs trading frameworks. He highlighted the minimum-distance approach from Gatev et al. (1999), the approach first used by Vidyamurthy (2014), and the time-series approach introduced by Elliott et al. (2005). Each one of these methods has its pros and cons. Because of the extensive calculations none of them were suitable for this paper. Do and Faff (2010) extended the paper of Gatev et al. (1999) to a more recent time frame. They used nearly the same framework, but added one trading rule: all trades have one day delay. By adding this rule, which was initiated by Gatev et al. (1999), they tried to ease the concerns about a possible upward bias in the reported returns because of the bid-ask bounce. They implemented this framework between July 1962 and June 2009. The paper showed that pairs trading was still a profitable strategy, but that there has been a declining trend in the performance of pairs trading in recent years. Do and Faff (2010) found that the increasing competition among arbitrageurs led to smaller profits. Do and Faff (2010) also noted that the declining trend of pairs trading reversed during strong market downturns, like during the 2007 subprime-mortgage financial crisis. Jegadeesh and Titman (1995) review the contribution of stock price overreaction and delayed reaction to the profitability of contrarian strategies. A trader using a contrarian strategy purchases and sells in contrast to the sentiment of the time, because he thinks that group behavior among investors can lead to mispricing in the . In their paper, they examine the reaction of stock prices to firm-specific information and common factors. Jegadeesh and Titman (1995) found that stock prices have a delayed response to common factors, like systematic risk. This statement affects market efficiency. In other words, if the common factors are changing rapidly, for example during a financial crisis, this can create short-term mispricing. Tu et al. (2016) investigate the effect of highly expected market volatility on the willingness to engage in arbitrage. A potential decrease in the need to take advantage of arbitrage opportunities makes the market less efficient and increases the chance of misvalued stocks. The investigation found that expected volatility had a major explanatory effect on stock mispricing and that this effect emerged even more during the most recent financial crisis. During this financial crisis, current volatility overshadowed expected volatility. According to Tu et al. (2016), the current volatility had a more direct effect on the decline in arbitrage activities. Schwert (2011) used daily, monthly and intraday returns from respectively 1885-2010, 1802-2010, and 1982-2010 to show the development of stock volatility. This paper focused on financial crises. Schwert (2011) found that during the Great Depression periods of high volatility persisted for a long time, in contrast to the last financial crisis. In the previous crisis, market participants did not expect high levels of volatility to persist for long periods. Looking back, this turned out to be true, the volatility did not persist for a long period. Volatility was high in late 2008 and early 2009, but it recovered quickly. In view of pairs trading, a short period of high volatility can be a favorable circumstance: high volatility results in misaligned stocks that can recover back to their real value when volatility decreases again. This literature review gives a better insight in pairs trading. Gatev et al. (1999) were the first to research this strategy. They used the minimum-distance approach to form pairs. After trading the pairs, they found positive monthly returns which were not affected by the market. In the following years, different methods to form pairs were created: Kraus (2016) published a paper about the various approaches. Do and Faff (2010) implemented the same framework Gatev et al. (1999) used in a more recent time frame. They found a declining trend in the positive monthly returns, except for periods of significant market downturns. Pairs trading is a strategy that profits from misvalued stocks. According to Jegadeesh and Titman (1995) short-term mispricing in the stock market is partly caused by a delayed response to common factors. During a financial crisis, systematic risk is increasing, which might affect the pairs trading performance. Tu et al. (2016) found that volatility has a significant explanatory effect on stock mispricing because of a decline in arbitrage activities. Based on the previous literature study, this paper tries to explain the possible better performance of pairs trading during a financial crisis as discovered by Do and Faff (2010). According to Jegadeesh et al. (2010) and Tu et al. (2016), a potential factor that affects the mispricing of the stock market is high systematic risk, also known as high volatility. This paper combines these findings to explain more about the trading strategy pairs trading during a financial crisis.

Methodology In order to find an answer to the question if pairs trading performs better during a financial crisis, this research is going to test the following hypothesis:

H0: The average weekly returns of pairs trading during the subprime mortgage financial crisis do not significantly differ from the average weekly returns between 2003 and 2005

H1: The average weekly returns of pairs trading during the subprime mortgage financial crisis do significantly differ from the average weekly returns between 2003 and 2005

Based on past research, it is expected the null hypothesis will not hold. Do et al. (2010) found that the declining trend of the profitability of pairs trading stopped during strong market downturns. Schwert (2011) claims in his article that one of the most visible indicators of the crisis was the extremely high level of stock volatility. Tu et al. (2016) found that high volatility causes mispricing of assets and short-term mis valued assets create more trading opportunities for pairs trading. Combining the conclusions of the above-mentioned papers the expectation is that pairs trading performs better when a financial crisis occurs. Our research starts with the implementation of pairs trading. The application is based on the same structure as Gatev et al. (1999) used. Gatev et al. (1999) examined the risk and return characteristics of pairs trading between 1962 and 1997. The implementation of pairs trading started with the selection of pairs; the so-called ‘formation period’. The formation period takes twelve months. In those twelve months stocks are matched based on the minimum sum of squared deviations between the normalized price series. After the formation period the trading period follows up. This period takes six months. The top 5 with the lowest sum of squared deviations and the top 20 pairs with the lowest sum of squared deviations are combined into portfolios. When the normalized prices of a pair diverge by more than two historical standard deviations a position is opened. Opening a position results in going short on the stock with the highest price and going long on the stock with the lowest price. The position closes when the pairs’ prices have crossed each other again. If the prices do not converge back before the end of the trading period, the profits are determined on the last trading day. This paper will deviate from the implementation of Gatev et al. (1999) at some points. There are three main differences. Firstly, a trading period will take twelve months instead of the earlier mentioned six months. By increasing the duration of the trading period, a short- term mispricing has more time to recover to his historical value. Secondly, Gatev et al. (1999) decided arbitrarily to trade a pair when the pair prices diverged by more than two historical standard deviations from the original spread, and the position would be closed again when the prices were back at the historical spread. In this paper, a trade starts when the prices diverge by more than one historical standard deviation, and the position will be closed when the pair spread is equal or smaller than one half historical standard deviation. More pairs will be traded by lowering the threshold, and positions will close earlier because the pairs’ prices do not have to converge back completely to their historical spread. More trades increase the returns, but forced closing of the positions before they are back at their original spread at the last day of the trading period can hurt the profits. Lastly, Gatev et al. (1999) used the minimum sum of squared deviations to form pairs. However, in this paper the correlation coefficient is used. Using the correlation coefficient avoids extensive calculations and still is a good measure for the co-movement of pairs. After the strategy is executed, before and during the crisis, we will compute and compare the weekly returns of pairs trading. If there is a significant difference between the returns, we will regress the weekly returns of the strategy against the volatility of the S&P 100 and the weekly excess returns of the S&P 100. By doing this, we can decide whether pairs trading is a market-neutral strategy, and we can research whether the volatility of the market can explain the possible difference in performance.

I. Formation period The first step during the formation stage is to calculate the daily holding period return for the different constituents of the S&P 100. Stocks that have gone one or more days without a trade are left out. Those stocks are left out because we are only interested in liquid stocks. The holding period return is used because when pairing the stocks based on the normalized daily price spread, the prices do include reinvested . Including the reinvested dividends gives a better representation of the performance of a strategy. The holding period return is calculated as follows:

� = (received dividends + capital gain) / closing pricet-1

The closing prices are normalized by the following formula:

Pt = (1+� ) ∙ Pt-1

Where Pt is normalized price at time t and P0 = 1

The second step is to pair the stocks. Stocks are paired based on the correlation coefficients they have. To find the correlation coefficients, Excel is used. The combinations with the highest correlation are suitable for the strategy.

II. Trading period After each formation period, we pick the fifteen pairs of stocks with the highest correlation, and add them in one portfolio. The portfolio exists out of fifteen pairs because we want to make use of diversification benefits. Trading happens as follows: a long-short position is opened in a pair when the prices diverge by more than one historical standard deviation. Based on the past relationship, a trader will expect that the prices will converge back to their original spread. When this happens, we go short on the higher-priced stock, and we go, for the equivalent cash flow, long on the undervalued stock. We unwind the positions when the spread is diverged back to less than one half historical standard deviation. If the stocks do not converge back to their historical spread before the end of the trading period, the positions close on the last day of the trading period. The portfolio's weekly return is calculated by adding up all the returns made by the pairs and dividing it by the number of pairs. The return of a pair occurs on the day the positions close. The return of the short position is subtracted from the long position's return. Depending on which stock went short and which one went long, it is multiplied by -1 or 1. In mathematical terms:

� = (� - � ) ∙ �

Where: � is the return of the pair, � is the return of stock A, � is the return of stock B and � is the short or long dummy.

0, position closed � = 1, short A: long B −1, long A: short B

III. Example of a Pairs trade Graph 1 shows the development of the normalized prices during the first month of the trading period 2008-2009. The standard deviation of the historical spread (= 0.0271) determines if an option is opened. In this month four trades are made. At trading day 2 the spread is 0.0298 so the position will be opened. You go short on the FDX share because it has the highest price and is expected to decrease relatively. This action results in a positive cash flow of $67,08. For the equivalent cash flow you go long in the UPS stock which results in a negative cash flow of $67,08. At trading day 7 the normalized price spread converged back to -0.0116 which is smaller than one half historical standard deviation so the options close. Unwinding

the options results in a positive cash flow of $66,25 as a result of selling the UPS stock and a

negative cash flow of $63,65 as a result of ending the short option. This results in a return of

5,113% on the short position and a return of -1,232% on the long position. The total return amounts to 3.88%. In table 2 the total return of the first month is calculated for this single pair.

Graph 1: Normalized price series of the FedEx-UPS pair with indication of open and close positions

Trade 1 Short or Trading Normalized Long in Cashflow Cashflow Return Return on Total Day Price Spread Price FDX Price UPS Status FDX In Out on FDX UPS Return 2 0,0298 $67,08 $55,19 OPEN SHORT $67,08 -$67,08 7 -0,0116 $63,65 $54,51 CLOSED $66,25 -$63,65 5,113% -1,232% 3,88% Trade 2 Short or Trading Normalized Long in Cashflow Cashflow Return Return on Total Day Price Spread Price FDX Price UPS Status FDX In Out on FDX UPS Return 8 -0,0448 $61,02 $54,16 OPEN LONG $54,16 -$54,16 10 -0,0001 $61,34 $52,03 CLOSED $54,44 -$52,03 3,933% 0,524% 4,46% Trade 3 Short or Trading Normalized Long in Cashflow Cashflow Return Return on Total Day Price Spread Price FDX Price UPS Status FDX In Out on FDX UPS Return 13 0,0335 $63,97 $52,46 OPEN SHORT $63,97 -$63,97 14 0,0059 $62,60 $52,78 CLOSED $64,36 -$62,60 2,142% 0,610% 2,75% Trade 4 Short or Trading Normalized Long in Cashflow Cashflow Return Return on Total Day Price Spread Price FDX Price UPS Status FDX In Out on FDX UPS Return 20 -0,0393 $60,14 $53,12 OPEN LONG $53,12 -$53,12 26 -0,0051 $62,65 $53,41 CLOSED $55,34 -$53,41 4,174% -0,546% 3,63%

Table 1: One month return calculation of the FedEx-UPS pair.

The portfolio consists of fifteen pairs like the one in table 1. To calculate the weekly portfolio return we use the committed capital return. The committed capital return equals the sum of the weekly returns of all the 15 pairs, divided by the number of pairs in the portfolio.

IV. Performance comparison The hypothesis of the comparison is as follows:

H0: � = �

H1: � ≠ �

Where � is the average weekly return during the financial crisis, and � is the weekly return before the crisis

After getting the average weekly return over the period before and the period during the subprime mortgage financial crisis, we are going to test if they significantly differ from each other. To do so, we use the T-test (mean-comparison test with unequal variances).

(� − �) � = ~�[��] � � + � �

� � + � � �� = ~�[��] � � � � + � − 1 � − 1

Where: � and � are the variances of the returns for both periods, � and � are the observations and �� are the degrees of freedom.

This T-test is conducted in Excel and a significance level of 5% is used to determine if the average returns differ.

V. Regression analysis Market volatility and high financial stress might cause the historical correlation structure to break down. More breakdowns of the historical correlation create more trading opportunities, and an increase in trades can have a significant effect on the performance of pairs trading. I will regress the weekly returns from before and during the financial crisis against the volatility of the S&P 100.

& � = �+ � � + �t

& Where: � is the weekly return of the portfolio at time t, � is the weekly volatility of the S&P 100 price index at time t, � is the constant, � is the error term of the portfolio return, �is the sensitivity of the portfolio returns to the volatility of the S&P 100 price index.

To test if pairs trading truly is a market-neutral strategy the Capital Asset Pricing Model (CAPM) is used. CAPM illustrates the relationship between systematic risk and expected return for investment objects. The � of an investment object measures how much a change in the market portfolio affects the asset returns. A � of one implies that an increase or decrease in returns from the market portfolio causes an equivalent change in the object returns. However, a � of zero indicates that a change in the market returns does not affect the returns of the asset. When the market portfolio does not affect an asset's returns, that asset is assumed to be market-neutral.

(� -� )= �+� � − � + �t

Where: � is the pairs trading excess returns sensitivity to the S&P 100 excess

return, � is the return of the S&P 100 index and � is the risk-free rate. Data description This paper consists mainly of two parts. First, we start with the implementation of the pairs trading strategy. Second, a regression is conducted based on the returns of the elaborated strategy. The following data is needed for the implementation of the strategy. We downloaded the closing stock prices and the received dividends for the companies of the S&P 100 for the periods 2002-2005 and 2006-2009. Stocks of the constituents that did not trade for at least one day are left out. By leaving out those stocks, the S&P 100 constituents only consist of liquid stocks and companies which did not go bankrupt, occurred a merger, or were taken over. This eases the process of pairing stocks. Initially, this research wanted to use the S&P 500 constituents, but the available technology was insufficient to process the data. Therefore, the S&P 100 constituents are used because it consists of the 101 largest and most established companies of the S&P 500. By reducing the data to one fifth, it could be processed. A possible consequence of the data reduction may be that the correlations of the pairs found are lower than if all the constituents of the S&P 500 were used. In practice, this does not appear to have had any major consequences on the reliability of the study. The correlations of the pairs were still sufficient enough. The closing prices and dividends received have been used to calculate the daily holding period return. Subsequently all price series of the constitutions have been normalized with the first value of the series equal to 1. Now that the price series are known, stocks can be matched, and trading starts. Period 2003 to 2005 consists of 504 trading days. The return is calculated for each trading day. A profit doesn’t occur daily. Therefore, to make the observations more organized, we use weekly returns. We collected 105 observations of weekly returns over the period 2003-2005. For the period 2007-2009, we also found 105 observations. The variables needed for regression are the weekly volatility of the S&P 100, the return of the S&P 100 and the risk-free rate. All data is collected from the database WRDS, except for the daily closing prices of the S&P 100, which were from Yahoo Finance. We used the interest paid on a three-month treasury bill as the risk-free rate.

Empirical Results I. Returns Analysis Table 2 shows the average weekly returns of the pairs trading strategy used in this study from the pre-crisis period and the crisis period. The average weekly returns after the crisis are almost four times higher than those from before the crisis. What often accompanies higher returns is a higher risk. In this case, we also see that the standard deviation from 2007-2009 is almost twice as large. Many investors are concerned with the return per unit of risk. When we compare the Sharpe ratios of the different periods, the Sharpe ratio from during the crisis is considerably higher. By performing a T-test, it can be checked whether the returns over both periods significantly differ. Those results will be discussed in the next section.

Period 2003-2005 2007-2009

Observations 105 105 Average Weekly Return 0,1450% 0,5124% Standard Deviation 0,2945% 0,5740% Sharpe Ratio 0,4925 0,8927

Range 0,0249 0,0348 Minimum -0,0096 -0,0165 Maximum 0,0153 0,0182 Sum 0,1523 0,5381 Table 2: Descriptive Statistics of the weekly returns of pairs trading from before and during the financial crisis

II. Mean-comparison T-Test Table 2 shows the results of the one-sided mean-comparison test with unequal variances. This test examines whether the difference between the two means deviates significantly from 0. In this study this is the case when the p-value is less than the significance level of 0.05. The test yields a t-statistic of 5.8355, which gives a p-value of 1.5E-08. With a significance level of five percent the two means are statistically different. We can reject the null hypothesis of equal returns.

Period 2007-2009 2003-2005

Mean 0,00512 0,00145

Variance 3,3E-05 8,7E-06

Observations 105 105

Degrees of Freedom 155

T statistic 5,8355 P(T<=t) 1,5E-08

Critical T-value 1,6547 Table 3: The results of the mean-comparison T-test with unequal variances to determine the differences between the average weekly returns.

III. S&P 100 Volatility A possible cause of the better performance of pairs trading during the last crisis may be the volatility of the S&P 100. High volatility makes it difficult for arbitrageurs to estimate whether the price of a stock has the correct value. As a result, arbitrage activities decrease, which makes the market less efficient. A less efficient market offers opportunities for pairs trading because pairs trading benefits from short-term mis valued stocks. Graph 2 shows the volatility of both periods. As expected, volatility in 2007-2009 is significantly higher, especially between trading weeks 37 and 57. These weeks correspond to the dates September 2008 to approximately January 2009. A peak in volatility during this period is no surprise: autumn of 2008 was the worst period of the financial crisis. These findings are in line with the findings of Schwert (2011)

Weekly Volatility of the S&P Price index 7,0% 6,0% 5,0% 4,0% 3,0% 2,0% 1,0% 0,0% 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100 103

Volatility 2003-2005 Volatility 2007-2009

Graph 2:The weekly volatility of the S&P 100 for both periods

Table 4 shows the results of the regression of the pairs trading portfolios against the volatility of the S&P 100. A robust regression has been performed to remove positive serial correlation and to ensure that the standard errors are not biased. So, the regression accounts for heteroskedasticity of the residuals. 15.5% of the variance in pairs trading returns can be explained by the volatility of the S&P 100 index. The regression coefficient of volatility was 0.195 and is significant with a p-value < 0.01. The correlation coefficient implies that when the volatility of the S&P 100 increases by 1, the return of pairs trading increases by 19.5%. Volatility was expected to have a positive effect on returns in advance.

Pairs Trading Returns

Volatility of the S&P 100 INDEX 0.195***

(0.0425)

Constant 0.00104**

(0.000478)

Observations 210

R-squared 0.155

Robust standard errors in parentheses

*** p<0.01, ** p<0.05, * p<0.1

Table 4: The regression results of the weekly pairs returns on the weekly volatility of the S&P 100 INDEX.

IV. CAPM Table 4 shows the results of the CAPM regression. The systematic risk exposure of the pairs portfolios is similar to what Gatev et al. (1999) found. The results show that the effect of a change in the excess market return on the performance of pairs trading is small and does not differ significantly from zero. The reason for this is that the profit of pairs trading depends on the difference in the prices between two stocks. When the market in its entirety changes, this does not have to affect the relative price difference of a pair. Graph 3 clearly shows that large drops in returns from the S&P 100 do not affect excess returns from the pairs trading portfolio.

Pairs Trading Excess Returns

Excess Return of the S&P 100 INDEX -0.0178 (0.0149) Constant 0.00299*** (0.000343)

Observations 210 R-squared 0.011 Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Table 5: The regression results of the weekly excess pair returns on the CAPM factor.

Pairs Trading Returns VS S&P 100 Returns 15,0% 10,0% 5,0% 0,0% -5,0% -10,0%dec.-07 feb.-08 apr.-08 jun.-08 aug.-08 okt.-08 dec.-08 feb.-09 apr.-09 jun.-09 aug.-09 okt.-09 -15,0% -20,0% -25,0%

Returns Pairs Trading Excess Return of the S&P 100

Graph 3: The weekly excess returns of the S&P 100 and the pairs trading portfolio simultaneously.

Conclusion The main goal of this paper is to identify if pairs trading performs better during a financial crisis. To answer this question, I created a framework to execute a pairs trading strategy. This framework is based on the fundamentals which Gatev et al. (1999) introduced. The implementation of the strategy took place in two periods. Period one during 2003-2005, and period two during the subprime mortgage crisis 2007-2009. The returns of both periods were collected and compared against each other with a T-test. The result of the test did not deviate from the claims made by Do and Faff (2010). Like they stated, pairs trading performed significantly better during the last financial crisis. This was reflected in the much higher average returns and the higher Sharpe ratio during the years of the crisis. The remainder of the research focuses on finding a possible cause for the better performance of pairs trading during the subprime mortgage financial crisis. Pairs trading is a strategy that takes advantage of misvalued assets. Tu et al. (2016) found that during a period of high volatility, investors find it difficult to determine the correct value of assets. This results in fewer arbitrage activities, making the market less efficient and more mispricing of assets occur. To discover if this is the cause of the higher performance, it is examined whether the S&P 100 volatility has a significant positive effect on the pairs trading strategy's returns. Based on the regression, it appears that volatility does have a significant effect on pairs trading returns. As expected, volatility during 2007-2009 is significantly higher than during 2003-2005. In summary, based on the significant correlation of pairs trading returns with market volatility and the higher volatility during the crisis, it can be assumed that the increase in volatility partly explains the better performance of pairs trading during a financial crisis. The last part of this research is devoted to the correlation between pairs trading returns and market returns. In previous studies, the statement that pairs trading is a neutral market strategy has often been made. However, when the market underperforms during a crisis, pairs trading starts to perform better. This may be due to a negative correlation with the market. The sensitivity of a change in the market returns has been tested using CAPM. The regression shows that the � does not deviate significantly from zero, so pairs trading appears to be a market-neutral strategy. There are a few limitations to this research. At the beginning of the study, the decision was made to compare the period before the crisis with the period after the crisis. In retrospect, it would have been better to compare the period during the crisis with a more recent one. Furthermore, the study did not take transaction costs into account. Adding transaction costs will hurt the returns of the strategy. Another problem is that in some cases limitations are placed on short-sale transactions during market downturns. Not allowed to go short on a stock which is part of one of your pairs makes the pair useless. By adding transaction costs to the return calculation, implementing the strategy more recently, and by investigating the effect of the limitations on short-selling assets, a more realistic picture of the performance of pairs trading during a financial crisis would have been created.

References

Do, B., & Faff, R. (2010). Does Simple Pairs Trading Still Work? Financial Analysts Journal, 66(4), 83-95.

Elliott, R. J., *, J. V., & Malcolm, W. P. (2005). Pairs trading. Quantitative Finance, 5(3), 271-276.

Gatev, E., Goetzmann, W., & Rouwenhorst, K. G. (1999). Pairs Trading: Performance of a Relative Value

Arbitrage Rule.

Jegadeesh, N., & Titman, S. (1995). Overreaction, Delayed Reaction, and Contrarian Profits. Review of

Financial Studies, 8(4), 973-993.

Krauss, C. (2016). Pairs Trading Strategies: Review And Outlook. Journal of Economic

Surveys, 31(2), 513-545.

Schwert, G. William (2011). Stock Volatility during the Recent Financial Crisis. European Financial

Management. 17(5), 789-805.

Tu, A. H., Hsieh, W. G., & Wu, W. (2016). Market uncertainty, expected volatility and the mispricing of

S&P 500 index futures. Journal of Empirical Finance, 35, 78-98.

Vidyamurthy, G. (2004). Pairs Trading: Quantitative Methods and Analysis. Wiley Finance.

Appendix

Rank Pairs 2003-2004 Correlation Rank Pairs 2004-2005 Correlation 1 AXP C 0,97884945 1 HPQ TXN 0,94697035 2 CVX MCD 0,972961 2 BDK NSC 0,94488904 3 INTC RTX 0,96721472 3 GD RTN 0,94488904 4 GS MCD 0,96677978 4 ETR SO 0,94412024 5 INTC NSM.2 0,96513958 5 NSC ROK 0,937599 6 AVP RSHCQ 0,96328335 6 INTC UIS 0,9304898 7 AA.3 UIS 0,96248088 7 GD JNJ 0,92834267 8 ATI HIG 0,96189663 8 FDX ROK 0,92560889 9 JPM TGT 0,96138383 9 GD XOM 0,92151727 10 DELL.1 HD 0,9597416 10 EMC ORCL 0,91740761 11 AES WMB 0,95961094 11 ATI BA 0,91493393 12 DD FDX 0,95903914 12 ALL S.3 0,91185232 13 INTC ROK 0,95799807 13 CSCO INTC 0,91181865 14 AXP JPM 0,9562349 14 FDX XOM 0,91124697 15 C JPM 0,9556724 15 AES DXC 0,91090832

Rank Pairs 2007-2008 Correlation Rank Pairs 2008-2009 Correlation 1 MET MEU 0,99391327 1 FCX WMB 0,98011555 2 CVX XOM 0,98554087 2 COP NOV 0,97294962 3 HGM XGM 0,98541771 3 HIG XRX 0,97221562 4 BEM OXY 0,97883589 4 BA RTX 0,97177702 5 COP CVX 0,96731335 5 AXP VIAC 0,96943038 6 FCX WMB 0,96641214 6 FDX UPS 0,96808481 7 CVX SLB 0,96499303 7 CAT FCX 0,96634073 8 BEM WMB 0,964927 8 DD MET 0,96181781 9 FCX SLB 0,96339657 9 BA TXN 0,9607584 10 OXY WMB 0,96099063 10 BEM HAL 0,9594566 11 AAPL OXY 0,96083984 11 MRK UNH 0,9590578 12 COP XOM 0,9596807 12 AEP ROK 0,95670201 13 SLB XOM 0,95927299 13 GE MS 0,95535278 14 DVN OXY 0,95704756 14 HON HIG 0,95498769 15 MO NKE 0,956413 15 ATI MMM 0,95388457

Pairs trading Portfolios including correlation coefficient

Durbin-Watson test for first order serial correlation Durbin-Watson d-statistic( 2, 210) = 1.621774 Ciritcal region (1.653-1.693)

Conslusion: No autocorrelation Durbin-Wartson test for first order serial correlation For the volatility regression on pairs trading returns

Breusch-Pagan / Cook-Weisberg test for heteroskedasticity Ho: Constant variance

chi2(1) = 23.85 Prob > chi2 = 0.0000

Conslusion: Reject null hypothesis Breusch-Pagan / Cook-Weisberg test for heteroskedasticity For the volatility regression on pairs trading returns

Returns 2003-2005 2,0%

1,5%

1,0%

0,5%

0,0%

-0,5% 05-dec.-0305-feb.-0405-apr.-0405-jun.-0405-aug.-0405-okt.-0405-dec.-0405-feb.-0505-apr.-0505-jun.-0505-aug.-0505-okt.-05 -1,0%

-1,5%

Pairs trading returns before the crisis Returns 2007-2009 2,0%

1,5%

1,0%

0,5%

0,0%

-0,5% dec.-07 feb.-08 apr.-08 jun.-08 aug.-08 okt.-08 dec.-08 feb.-09 apr.-09 jun.-09 aug.-09 okt.-09 -1,0%

-1,5%

-2,0%

Pairs trading returns during the crisis

Weekly Pairs Trading Returns Volatility Market Return σ 0,00294491 0,002291523 0,013520423 Mean 0,15% 0,63% 0,05% SUM 15,23% 66,54% 5,30% Descriptive Statistics 2003-2005

Weekly Pairs Trading Returns Volatility Market Return σ 0,00573998 0,011729117 0,040237958 Mean 0,51% 1,67% -0,28% SUM 53,81% 175,17% -28,99% Descriptive Statistics 2007-2009