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Market-Neutral Pairs Trading

By Erik Skyba

Senior Quantitative Analyst, TradeStation Labs

Summary

Market-neutral equity trading is a relative value investment strategy that is designed to be unaffected by the returns of the overall market (S&P 500 Index). It usually involves a long position in a security that is expected to do well and a short position in a security that is expected to do poorly, both over the same given time horizon. Ideally, at the time of the trade, the long security is undervalued and the short security is overvalued. This valuation is typically based on the type of fundamental analysis done in the hedge fund and mutual fund community. However, it’s also common to apply technical analysis to trade the market-neutral equity spread of a long/short pair.

The fascination with market-neutral equity strategies since the early 1990s largely reflects an interest in the possibility of achieving a consistent return while taking on very low levels of risk. As mentioned, traders also like these strategies because they tend to have a very low correlation to the market. By eliminating the beta component of a long/short equity pair, we are able to make it market neutral. In this paper, we focus on the beta-neutral quality of these strategies.

Introduction

In practice, most market-neutral portfolios are designed to be unaffected by overall market returns. This is typically achieved through a dollar-neutral portfolio, beta-neutral portfolio or an optimally weighted portfolio. The dollar-neutral portfolio has no dollar equity exposure because of an equal dollar amount invested in longs and shorts, e.g. $100,000 long and $100,000 short. A beta-neutral portfolio is constructed so the beta of the long positions equals the beta of the short positions. In effect, the beta of the short positions is cancelling out the beta of the long positions. In this paper, we will focus on how to make a long/short pair beta neutral, hence market neutral, by reducing the systematic risk (risk related to the market) to be close to zero.

What Is Beta Neutrality?

We can use the volatility of a security (as measured by standard deviation) to characterize its movement. For example, in Figure 1, notice that the volatilities for GS and BAC, both in the financial sector, are very different. GS has an annual standard deviation of 18.82, while BAC has a standard deviation of 20.78. Theoretically, we can say that if positive news for the financial sector hits the newswire, then BAC will have a stronger

Figure 1 Bottom Indicator Shows the Standard Deviations for GS and BAC

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percentage move than GS because it has a higher standard deviation. If the news is bearish for the financial sector, then BAC is likely to have a much larger negative move than GS. Hence volatility is a very important consideration when determining our long and short position sizes for two reasons. First, it allows us to evaluate the long and short securities on a level playing field. By cancelling out the beta risk of the pair, in effect both positions have the exact same beta risk to the market, which is close to zero. In this example, let’s say our technical trading model tells us to go long $50,000 of BAC and short $50,000 of GS, a dollar-neutral position. Now, let’s say that some negative news hits the market. BAC, the long leg, will probably go down more than the short position in GS because it has greater volatility. In effect, the pair lost money not because the valuation model was wrong but because there should have been a larger position in the short (GS) and a smaller position in the long (BAC). Instead of losing money, the pair might have made money or lost less.

This leads to the question, What is beta? Beta is similar to volatility, except that in the calculation of beta, we are incorporating the covariance and standard deviation of the market (S&P 500 Index). By reducing net beta of a position to zero, we are eliminating the influence of the overall market on the securities that we are long and short and in effect making these positions market neutral. The formula below describes beta (Ba). The numerator stands for the covariance between the security we are long (a) or short (a) and market security (p = the S&P 500 Index). The covariance is telling us how closely the returns of the security and the market security are deviating from their average returns. We are analyzing how closely the returns of both the long and short securities move together or co-vary with the market security. The denominator is the variance of the market security (p = the S&P 500 Index). We often think of beta as how sensitive a security is to market movement. A value for beta greater than 1 means that the security is more sensitive to market moves and a value less than 1 means that the security is less sensitive to market moves.

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In Figure 2 below, the column on the right shows the beta for each of the top ten components of the XLE (S&P SPDR Energy ETF) calculated and displayed in RadarScreen. The column on the right shows the beta for the XLE. In the column on the left, we can see how some stocks components have higher and lower betas than the XLE. These beta values will be factored into our beta-neutral position-size calculation for each stock.

Figure 2 Betas for the Top Ten Components of the XLE

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Creating a Market-Neutral Position

The math for creating a market-neutral position is fairly straightforward. These positions are constructed by calculating the beta of the stock component vs. the S&P 500 Index and the beta of the ETF (XLE) vs. the S&P 500 Index. As an example, in Figure 3 below, we see that APA’s beta is 1.47 and the XLE’s beta is 1.22. After adding up both of these beta values, we have 2.69, which is the Beta Total column value. We then divide the ETF’s beta by the total beta values to get the percentage position weighting for the stock component. Next, we subtract this same percentage weighting value from 100 to calculate the ETF’s position weighting. One can either go long on the stock and short the ETF or go long on the ETF and short the stock based on these weightings.

Figure 3 Stock Symbol: APA (Stock Beta, ETF [XLE] Beta, Beta Total, Stock-Wght, ETF-Wght)

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RadarScreen Display

There are many factors to consider when implementing a market-neutral equity strategy. One example is the relationship between the long and short securities that make up the pair. This relationship is important because it has an effect on how co-integrated the beta-adjusted spread of the long and short security is. The concept of co-integration, however, is beyond the scope of this paper. The workspace that has been included with this paper includes a RadarScreen window that lists the top ten components of the nine-sector S&P SPDR ETFs (XLE, XLY, XLV, XLU, XLI, XLF, XLB, XLK, XLP). In a sense, the relationship between the ETF and its stock component is based on a relative value play. That is, because a percentage of the ETF is made up of the stock, if the correlation between the ETF and the stock is high, then one might want to look for periods when this relationship breaks down (where the beta-adjusted spread has widened) to consider long and short trading opportunities using some kind of valuation model.

The RadarScreen is set up so the top ten components of each ETF are listed under the ETF they represent, as shown in Figure 4. The user can compare the betas and position sizes for the stock component of the sector ETF to the ETF itself. For example, in Figure 4, we see the stock symbol COP. COP is a component of the XLE Energy sector ETF. The RadarScreen display also shows the following columns of data: Stock Beta, ETF Beta, Stock-Wght, ETF-Wght, Stk$PosSize, ETF$PosSize, Stock Shares and ETF Shares.

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Figure 5 shows the Stock Wght column, which represents the beta-neutral adjusted position weight for the stock in that row. The ETF Wght represents the beta-neutral adjusted position weight for the ETF (in this example, XLE). These values are percentages that sum to 100%. As an example, the stock component in the first row is APA. Its weighting is 45.50%, while the XLE’s weighting is 54.50%. These values sum up to 100%.

Figure 6 shows the percentage weightings converted to a dollar amount for the stock position and the ETF position. These dollar amounts are based on a total dollar amount that you wish to allocate to each individual long/short pair. In this example, we are using $100,000 as the total dollar amount that our long and short position should total. As you can see in Figure 7, this value is an input, called Total Pair Value. After you change this input, all dollar position sizes and share amounts will be updated based on the new Total Pair Value input for each stock component and its sector ETF.

Figure 6 Beta-Adjusted Position Sizes in Dollar Terms: Stock (APA) and ETF (XLE)

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Figure 7 Inputs (TotalPairValue: Allows the User to Change the Total Dollar Amount Allocated to a Long/Short pair)

Figure 8 shows the share amount that can be bought or sold short for the stock component and its designated sector ETF. By dividing the Stk$PosSize by that stock component’s last price and the ETF$PosSixe by that ETF’s last price, we are able to calculate the Stock Shares columns and ETF Shares columns.

Figure 8 Beta-Adjusted Position Sizes in Shares: Stock Components and ETF (XLE)

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Conclusion

Before risking any capital trading a market-neutral equity strategy, you must first address whether to trade the beta-neutral spread or the dollar-neutral spread. Many mutual and hedge funds that are in the market-neutral equity space are not beta neutral, but they are dollar neutral. If you want your long/short pair to be beta neutral, then you have to make sure that you use the beta-neutral spread and not the dollar-neutral spread. In this paper, we have given you the tools needed to calculate the beta-neutral position sizes for a long/short pair trade. The pair-trading relationship we have chosen to display in RadarScreen shows nine of the S&P 500 sector SPDR ETFs and their top ten components. One can go long or short either the ETF or the stock component.

If you plot the beta-neutral percentage weighting values, you will find that they are fairly stable over time. However, over a lengthy horizon of, say, one to three months, the position weightings for the long and short pair will change. So you might want to consider dynamic rebalancing on a weekly or monthly basis.

There are many other factors to consider before you start trading. For example, how does one decide on what valuation model (technical or fundamental) to use to determine which security should be held long and which should be held short? Should both the long and short legs be highly correlated or is it more important for the pair to be co-integrated? One should also consider the different risk components that might exist in a long/short pair. In reducing any of these risks, the words neutral or neutralize are often used because of the act of canceling out the risk component by shorting an opposing security with the same risk-component weighting. As discussed, beta neutral is not the only risk neutrality to consider.

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