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 trading strategy that takes advantage of the mispricing in stock 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 volatility 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 short-term mispricing of stocks. Pairs trading is seen as an arbitrage 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 position in the overperforming stock and a long 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, investors 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 systematic risk 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 cointegration 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 stock market. 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 dividends. Including the reinvested dividends gives a better representation of the performance of a strategy. The holding period return is calculated as follows: