3 – M2L6 04 Pairs Trading V3

Let’s take a closer look at pairs trade. When two companies have economic links, this implies that their stock prices may also move in a similar manner. For example, company A sells frozen green peas, and company B cells frozen carrots. Since frozen peas and carrots are often combined and sold together, we can see how an increase in sales of peas and carrots would affect both companies. Most of the time we see the two stocks moving similarly. However, we may see the two start to diverge. When this happens, we use our assumption about their economic ties, and also our assumption about mean-reversion. We assume that the divergence is temporary and that the two stock values will revert back to their original long-term relationship. The pairs trade involves going long the asset that is priced relatively low. At the same time, the strategy involves going short the asset that is priced relatively high. If and when the prices start to converge we can close our positions. When I say we close our positions, I mean that we sell the asset that we originally buy and we buy the asset that we initially shorted. Also, if we see the stocks do not converge but continue to diverge over a period of time, we may also decide to close our positions to cut our losses. You may be wondering how long we should wait before expecting to see the pairs converge. It helps to look at historical trends. Sometimes pairs of socks diverge and then converge in cycles that may last weeks or months. Some traders may decide to trade in shorter time horizons such as in days or even hours. For these shorter time periods traders may look for smaller movements to determine what they consider diverging, or converging trends. There are benefits to trading a pair rather than a single stock. Trading a pair reduces our exposure to the overall market. For example, with a single stock, we may expect a stock’s recent price decline to be temporary. However, if a negative jobs report causes most stocks to decline then this overall market movement would carry this single stock downward with it. With partnering, we reduce some of the impact of large market movements. So, even if both stocks in the pair are pulled down by a general market downturn, what matters to us is the relative difference between the pair of stocks. To describe this relative difference between a pair of stocks we will look into the spread and the hedge ratio. While the pair of stocks are still converged or linked, we can imagine holding a long position in stock A and a short position in stock B. Our positions are in a certain proportion so that our combined position has a constant value over time. In other words, movements in our long position and short position cancel each other out. The proportion that lets us create this neutral position is called the hedge ratio. There are two ways to calculate the hedge ratio and they tend to have similar results. One way is to take the price of stock B divided by the price of stock A, or the price ratio. A second way is to run a linear regression in which stock A is the independent variable and stock B is the dependent variable. The coefficient of this regression is our hedge ratio and is similar to the price ratio. The difference is that the regression accounts for a series of previous prices while the price ratio uses just the most recent price of each stock. Once we have a hedge ratio we can calculate the spread. The spread is the price of B minus the product of the hedge ratio and price of A. This may look familiar from our studies of regression. When we used a regression model to estimate the dependent variable we compared the prediction with the actual value and called it a residual or error term. Here, we can think of using the hedge ratio to estimate the price of B using the price of A. We still expect a difference between the estimation and the actual price of B. This difference between the estimation and actual value is called the spread.