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Opposites Attract: The Short Version on How to Pairs Trade

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April 1, 2012
Pairs trading thinkorswim
Fredrik Broden

Think Chevy vs Ford. Coke vs Pepsi. Ketchup vs mustard. You like one and don't like the other. Pairs trading is similar: you buy one stock while shorting another. On purpose. At the same time. In a pairs trade, you're long, say, 100 shares of one stock and short 100 shares of another. To get the price of a pairs trade, what we'll call the “pair difference,” take one stock price (usually the more expensive of the two), and subtract the other. If you're buying a pair, you want the pair difference to go up. If you're shorting the pair, you want the pair difference to go down. When you do a pairs trade, you want the stock you bought to outperform the one you shorted. This can happen in three ways, as we'll see using two stocks.

Stock A (long) = $50

Stock B (short) = $49

At these prices, the pair difference is $1.00 ($50 minus $49). The pair difference could move higher, from $1.00 to, say, $3.00, in a couple of ways.

First, if stock A moves to $54, and stock B moves to $51, the pair difference moves to $3.00 ($54 minus $51). Both stocks move up, and the pair difference moves up as well.

Or, stock A could drop to $48, and stock B could drop to $45. The pair difference moves up to $3.00 ($48 minus $45). Both stocks move down in this case, but the pair difference moves up. Either way, if you had bought 100 shares of stock A, and sold short 100 shares of stock B, the position would have profited $200 before commissions.

Now, if stock A rises to $55, and stock B rises to $60, the pair difference moves down to $-5.00 ($55 minus $60). If you had bought 100 shares of stock A and sold short 100 shares of stock B, the position would have lost $600 before commissions.

Calculate profit and loss by tracking the change in the price of the pair. This is straightforward if the pairs trade consists of long 100 shares and short 100 shares. In one case, the pair difference went from $1.00 to $3.00, and the trade made $200. In the other, the pair difference went from $1.00 to -$5.00, and the trade lost $600.

Now, this hypothetical example uses long and short stock positions. But, you can also pair trade using options. Instead of buying stock, you could use positive delta spreads, like short-put verticals or long-call verticals. Instead of shorting stock, you could use negative delta options spreads, like short-call verticals or long-put verticals. Even though you're using options, the underlying premise behind trading pairs is the same: you want the stock in which you have the positive delta option position to outperform the stock in which you have the negative delta option position.

Why Pairs Trading?

When trading pairs, you might have more confidence in the direction of the pair difference than you do in individual stocks or indices. Stocks can exhibit random patterns. But, certain pairs trades tend to oscillate—their price difference goes up and down around an average level or mean—though this behavior is by no means guaranteed. When it's above the level, it has a tendency to go back down to the level. When it's below the level, it has a tendency to go back up to it. Thus, pairs trades would seem attractive at one extreme or another of a trading range when they can be seen as an “overbought” or “oversold” condition.

Let's consider different time frames. For shorter-term trades, maybe intraday out to one week, pairs that exhibit wide oscillating price movement can move away, and back to an average level, quickly. If you wanted to pursue this strategy, you have to be nimble and sometimes aggressive—ready to take profits, or cut a losing position at any time. Short-term pairs trades require the greatest engagement. For short-term trades, stocks are typically the product used. The short-term pairs trades usually have smaller price targets, maybe only three or four points. When trying to capitalize on those short-term, smaller moves, stocks are typically more responsive to changes in the pair difference. The stock pairs position profit and loss changes dollar for dollar with the change in the pairs difference.

Longer-term pairs trades could be considered when there might be divergence between two stocks, or, more typically, between broad indices or industry sectors. For example, pairs trades speculating on the divergence between large-cap and small-cap stocks could be longer-term pairs trades lasting weeks or months. Rather than tracking oscillating price behavior, traders typically base longer-term pairs on fundamental or economic rationale.

For longer-term trades, you might consider options. With stocks, when a pair difference changes in price, the response is generally 1:1. With options spreads, the response is often slower. With options spreads, you could have defined risk and lower capital requirement positions for a pairs trade. But you have to understand options, and their specific risks, and how those risks are affected in a pairs-trade scenario.

How Do You Find Them?

1. Look for sector pairs. Search industry groups, like large oil stocks, or pharmaceuticals, or retail stocks. Review charts of different pairs to analyze whether the pair oscillates around a mean. If it does, do more analysis. But, start by looking at a chart to see if the oscillation is faster, i.e. more short term, or slower, covering weeks or months. You may have to go through a dozen sets of stocks before you find one you believe worth considering. Finding a good pairs trade takes time. Save them in a watch list in the thinkorswim® software. If you find a pair of stocks whose pair-difference price exhibits the behavior you like, move to more analysis.

2. Check the correlation. Correlation measures how often stock A goes up when stock B goes up. You can measure correlation right from the Pairs Trading feature in the Trade page of thinkorswim (See Figure 1, page 38). If the two stocks always go up (or down) at the same time, the correlation between them is going to be 1.00. If stock A always drops when stock B goes up, and vice versa, the correlation is going to be -1.00. If stock A goes up or down without any measurable relation to when stock B goes up or down, the correlation is close to 0.00.

Remember that correlation results represent past performance, and as we all know, past performance does not guarantee future results. So while correlation may be valuable in evaluation of potential trades, it doesn't mean the two stocks will always cooperate. For pairs trades, you want to see correlations as close to 1.00 as possible. Now, 1.00 is pretty rare. So, look for correlations that are at least, say, .80. Why?

With a pairs trade, you're getting long one stock and short another, speculating that the stock you're long will rise faster, or fall less, than the stock you're short. So, if both stocks move up at the same time, or down at the same time, the spread difference between the stock prices tends to increase or decrease within a certain range. But if one stock heads higher and the other stock heads lower, you're hoping it's the stock you're long that's going higher and the stock you're short that's going lower.

Hope isn't a strategy. When stocks are uncorrelated, their pair difference can be much more unpredictable. In this case, you're speculating more on individual stock prices, and it isn't really a pairs trade. When stocks are correlated, and they more frequently move up together when the market's rallying, or down together when the market's falling, their spread differences tend to be more predictable, generating that oscillating price movement. If the correlation is low, it's more likely the pair difference will break down and start to move less predictably. You'll want to check the correlation frequently while you have a pairs trade on to see if it's dropping. If it is, you may want to exit the pairs trade for whatever profit or loss it has at that time.

3. Consider time frames. As previously mentioned, look at a couple different time frames for the pair. For example, look at a daily chart for a year, then look at a 20-minute chart for 20 days. The daily data will show whether the oscillation is a recent event, or has been with that pair for some time. The 20-minute data can provide a glimpse into how much that pair might swing intraday. This becomes important if you're only holding a pair for a few days.

4. Check implied volatility. Look at the implied options volatility on the stocks in the pair, particularly if you're looking at a longer-term pairs trade. If the two stocks are correlated and have betas—a measure of relative volatility comparing how much a stock moves up or down relative to a benchmark, such as an index—that are close to each other, if one stock's options have a higher implied volatility than the other stock's options, pairs trading theory would lean toward shorting a call or put vertical in the stock whose options have the higher volatility, and buying a call or put vertical in the stock whose options have the lower volatility. (Check implied volatility in thinkorswim by pulling up a stock's chart in the Charts page. In the Studies menu, select Quick Study > Volatility Studies > ImpVolatility.)

5. Pick your exits. Choose the ideal exit points for profits and losses. These mental stops can help prevent a losing pairs trade from potentially creating even larger losses when using stock positions. You may want to set a stop loss at a point just outside the recent range of the pair, to make sure the position doesn't get stopped out in a predicted oscillation. Look to take profits if the pair gets close to the average level.

Putting It All Together

Looking at a daily chart of stock A minus stock B, the pair difference between them seems to oscillate around an average of $3 for the past couple of months. The low end of the oscillation takes it down to $1 before it bounces back to around $3. The high end of the oscillation takes it up to $5 before it drops down to around $3. So, check the correlation and see that it's .85 for the past three months. Good.

Now look at the daily chart for the A/B pair, maybe the 20-minute/20-day chart. Hopefully you'll see pretty much the same oscillating behavior even in the shorter time frame. If not, reevaluate. The current pair difference is $1—the low end of the range. If you believe in the strategy, and think it will bounce back up to $3, you buy 100 shares of A and short 100 shares of B. Maybe set a stop at $-1, which would be a $200 loss for the pairs trade. If the pair difference rallies from $1 to $3, take the $200 profit by selling the long 100 shares of A, and buying back the short 100 shares of B. Now, if you see that pair difference continue to rally up to $5, and you think it will drop back down to $3, short the pair by shorting 100 shares of stock A and buying 100 shares of stock B. And place a stop to buy it back for, say, $7, for a $200 loss, or buy it back when it reaches $3, for a $200 profit. Just remember that the strategy generates multiple commissions, which you'll need to factor in when calculating overall profit or loss.

Wrapping your head around pairs trading isn't easy. But if you can't find what you like in your favorite stocks or indices, the strategy could provide new potential opportunities for those who understand it.