Daytrading Stock Pairs

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1 TRADING TECHNIQUES Using Volatility And Correlation Daytrading Stock Pairs Tired of trading Level II quotes and one-minute charts? Try a market-neutral strategy. by Mark Conway and Aaron Behle I t can take years of experience to discover one unique insight to exploit that can consistently pull money out of the stock market. Most traders have a bias as to market direction and position themselves accordingly; however, market-neutral strategies are becoming popular for those who are tired of trading on the gerbil wheel of Level II quotes and one-minute charts. Pairs trading is a market-neutral strategy where a long position in one stock and a short position in a correlated stock are taken simultaneously. The profit principle of the trade is based on mean reversion that is, two stocks that normally trade in the same direction become temporarily uncorrelated and eventually will revert to the mean. All of the published work on pairs trading relates to positions held over several days or as much as several months (for example, mergers and acquisitions). However, recent changes in margin requirements give the daytrader access to as much as 4:1 intraday buying power, which is perfectly suited to intraday pairs trading. This article presents a complete strategy for daytrading stock pairs. First, a definition for the spread is presented, along with a visual TradeStation indicator. Second, the volatility bands will be calculated to determine when a pairs trade is initiated. Third, the complete entry and exit rules for the intraday pair trading system are defined. Finally, examples are shown, complete with performance summaries. The allure of pairs trading is that it is a strategy with little risk; however, no stock is immune to the risk of a trading halt or an earnings warning. As with every other trading system, specific entry points, exit points, profit targets, and stop-losses need to be defined. First, I ll review the factors required for calculating the spread and the upper and lower bounds known as volatility bands. THE SPREAD The spread is a separate plot (see Figure 1) that compares the difference in price between two stocks and plots this value as a black line in real time within the volatility bands. The red line is the upper volatility band, and the green line is the lower volatility band; these bands are computed at the beginning of each trading day. When the spread line touches the upper band, the stock in the top panel (stock A) has become overvalued relative to the stock in the lower panel (stock B) a condition indicating that stock A should be shorted and stock B should be bought. When the spread touches the lower band, stock A has become undervalued relative to stock B. In this case, stock A should be bought and stock B should be shorted at the same time. The spread can be calculated according to the following formula: Spread = (Last A /Close A ) (Last B /Close B ) Divide the last price of stock A by its closing price yesterday, and do the same for stock B. Subtract the difference to obtain the current spread. VOLATILITY BANDS Let s focus on the factors needed to calculate the volatility bands. Each stock has a historical volatility (HV), which is a FIGURE 1: THE SPREAD. It s a simple calculation that compares the difference between two stocks. TRADESTATION (TRADESTATION TECHNOLOGIES)

2 percentage that measures the standard deviation of a stock s price change (the close of today compared to the close of yesterday) over a certain period of time. For example, if a stock trading at $20 has a 30-day HV of 20%, then that stock will have traded between a range of $16 and $24 over that 30-day period approximately 68% of the time based on the normal probability curve. For example, the current 30-day HV in Figure 2 is 1.13, or 113%, which is very high. The historical volatility of each stock in the pairs trade is part of the volatility band equation. The HV of all stocks can be obtained easily through websites like ivolatility.com. The site has 30-day HV readings as well as implied volatility (IV) readings. The next factor in the volatility band equation is the correlation coefficient, also known as R. This value correlates the movement of one stock price with another. A correlation of +1 means that the two stocks move in tandem, while a correlation of -1 means that the two stocks move in opposite directions. This pairs trading system is based on highly correlated stock pairs, with an R of at least 0.5. However, it is possible to reverse the signals to trade noncorrelated pairs. For further information on the correlation coefficient, go to the market-topology.com website. There, you can enter a stock symbol and the query will return a list of stocks that are most correlated. Figure 3 displays a daily chart of two highly correlated stocks with a correlation coefficient ranging between 0.75 and The next step is to calculate the volatility bands (VB) for a stock pair for one trading day. The formula is as follows (assuming 252 trading days in a year): FIGURE 2: HISTORICAL VOLATILITY. Here s a percentage that measures the standard deviation of the price change of a stock over a period of time. VB = HV 1 + HV 2 * * 1 R Let s start with an example of two highly correlated video-game software stocks, Activision (ATVI) and THQ (THQI): HV 30 of ATVI is 0.57 HV 30 of THQI is 0.70 R is 0.60 The volatility band of one standard deviation for the ATVI-THQI pair is: ( ) * * (1 0.60) = The next factor to determine is the number FIGURE 3: COEFFICIENT R. Here you see two highly correlated stocks with a correlation coefficient ranging between 0.75 and 0.95.

3 of standard deviations required to take a pairs trading system signal. We have selected 1.5 standard deviations as the default value, because prices have at least an 80% chance of reverting to the mean. We then multiply the volatility band value by the number of standard deviations to obtain the volatility band values. In the example in Figure 4, 1.5 * = Pairs trading system calculations Set the volatility factor (VF); default value is 1.5 Obtain the 30-day volatility of stock A (HV A ) Obtain the 30-day volatility of stock B (HV B ) Calculate the 30-day correlation of stock A and stock B (R AB ) Calculate the volatility band (VB) Calculate the spread (S). Entry rules 1 Long A Short B Entry S crosses above -VB Buy stock A the next bar one tick above the high Sell short stock B when stock A triggers. FIGURE 4: VOLATILITY BAND EXAMPLE. Volatility bands are important indicators when applying the pairs strategy. 2 Short A Long B Entry S crosses below VB Sell short stock A the next bar one tick below the low Buy stock B when stock A triggers. Exit rules 1 Long A Short B Exit Profit target: S crosses above zero Sell stock A Cover stock B Stop loss: S < (VF * -VB) Sell stock A Cover stock B 2 Short A Long B Exit Profit target: S crosses below zero Cover stock A Sell stock B Stop loss: S > (VF * VB) Cover stock A Sell stock B FIGURE 5: LONG ABGX/SHORT MEDX. When the spread crosses back above the lower VB, buy ABGX and sell short MEDX. EXAMPLES The following examples will clarify the pairs trading system. Some tips and techniques for pairs trading will be presented afterward. An example of a long A short B entry is displayed in Figure 5. Stock A (ABGX) has become undervalued relative to stock B (MEDX) because the spread has fallen below the lower volatility band (in green). As soon

4 as the spread crosses back above the lower VB, we would buy 1,000 shares of ABGX at a price of and sell short 1,000 shares of MEDX at (TradeStation does not allow simultaneous signals in two different plots, so the symbols have to be reversed to show the short signal in MEDX see the next example). The spread crosses above zero at 4 pm, at which point the ABGX long trade is exited at for a profit of 93 cents. Simultaneously, cover MEDX at 31 for a profit of 2.24 on the short leg of the trade. Together, the pairs trade nets = 3.17 points on 1,000 shares for a total profit of $3,170, not including slippage and commissions. The example in Figure 6 shows the reverse leg of the ABGX-MEDX pairs trade shown in Figure 5 and is a short A long B entry. Note the symmetry of the volatility bands in the Acme spread indicator. Essentially, this spread is a mirror image of the spread shown in the previous example, but the VB value is the same (0.065). The TradeStation performance reports after trading both legs of the ABGX-MEDX pairs from November 6, 2000, to August 31, 2001, are displayed in Figure 7. The New York Stock Exchange is an excellent vehicle for trading highly correlated pairs, especially among the oil service companies. The APA-APC pair displayed in Figure 8 has a correlation usually above 0.9, and exhibits smooth multiday swings between the volatility bands. In this example, there are two pairs trades. In the first trade (long APA/short APC), APA stays relatively flat while APC goes down sharply the ideal scenario. In the second trade, both stocks trade higher (they are correlated), but APC moves sharply higher and the spread plummets. This is the typical scenario for a pairs trade one profitable leg and one unprofitable leg but the objective is to capitalize on the price difference with proper position sizing. An excellent pairs trading strategy consists of selecting a correlated pair where one stock is a leader and the other is a laggard. Typically, the leader is a growth stock, and the laggard is either a value stock or a blue-chip stock with little volatility. In Figure 9, two insurance companies, Allstate and Progressive, have been selected to compose the ALL-PGR pair. The second pairs trade on April 6 gets stopped out when the spread goes half a band below the lower VB (-1.5 * 0.03 = ). The spread actually hit before reversing. The final pairs trade is taken on the cross above the lower VB. FIGURE 6: SHORT ABGX/LONG MEDX. Although the spread is a mirror image of that in the previous figure, the volatility bands remain the same. FIGURE 7: PERFORMANCE REPORTS. Here are the results of trading both legs of the ABGX/MEDX pairs trade from 11/6/00 to 8/31/01.

5 TRADING TIPS Here are a few more tips to keep in mind: 1 There is an almost infinite number of possible pairs in the stock market, but trading this strategy requires both liquidity and volatility. Filter out those stocks with little volume and low ADX readings. The key is to find two stocks in the same industry with high volatility. This list shows some of the more popular pairs: ABGX-MEDX ALL-PGR APA-APC ATVI-THQI BLDP-FCEL COF-PVN CPN-DYN GS-MWD HGSI-MLNM MERQ-MUSE UNH-WLP 2 When legging into a pairs trade, initiate the short trade first to make sure you can get an uptick, unless you have a forward conversion or bullet that allows you to short without an uptick. FIGURE 8: ONE PROFITABLE LEG AND ANOTHER UNPROFITABLE LEG. Both these stocks are highly correlated. When APC moves sharply higher, the spread drastically declines. 3 There are several alternatives for closing out a pairs trade. Some traders prefer to close out all trades at the end of the trading day, while others prefer to let the spread go to the opposite volatility band to a period of a few days. 4 If one of the stocks in the pairs trade has significant news, then the pairs trade may not be feasible because the spread may widen dramatically; however, the system rules preclude entering a trade until the spread starts reverting to the mean. 5 Find stock pairs that fit the leader/laggard criterion within a specific industry niche. Mark Conway and Aaron Behle are general partners of Groundswell Capital LP, a hedge fund based in Waltham, MA. For further information on pairs trading and other advanced trading systems, refer to the Acme Trader website ( RELATED READING Conway, Mark [1998]. Daytrading Stocks, Technical Analysis of STOCKS & COMMODITIES, Volume 16: August. See Traders Glossary for definition S&C FIGURE 9: A LEADER AND A LAGGARD. You can select a highly correlated pair of stocks where one is a leader and the other is a laggard. Find stock pairs that fit the leader/ laggard criterion within a specific industry niche.