Alpha Trading Part 11

There are also reasons to use exit thresholds, but we have chosen not to use them. Actually, that is not a fair statement. When you exit at a value of 50, you are expecting the two legs to both come back to their relative midpoint price based on the calculation period. That is as much a positive decision as saying that we exit when the short position (entered at a stress value of 90) moves to 60 (not quite neutral) or that the short moves to 40, slightly better than neutral. Some traders would like to take as much as possible from a trade by entering a short at +90 and exiting at +10, the point where you would reverse to long. When you use a short calculation period, the indicator will swing from high to low, yet the market has no obligation to do that. If you get caught selling into a strong market, then the chances of exiting at an indicator value of +50 are far greater than exiting at +10. Risks that are very large but occur infrequently are extremely important to your final success. We can now look at some market examples.

GOLD, COPPER, AND PLATINUM.

We start by applying the stress indicator to mining stocks. With gold in the news, the higher prices and volatility are likely to cause mining stocks to move in tandem with the underlying metal. This relations.h.i.+p may be increased because some investors choose to buy a portfolio of gold mining shares rather than the metal itself.

Fundamentally, we would expect a gold mining company to show increased profits when the price of gold goes up. From one day to the next, their cost of mining and fabrication doesn't change as the price of gold changes, so better gold prices should translate into higher company profits. Along with gold, we will look at companies that mine copper and platinum. In that way, we can see if the stress indicator works across a wider range of markets and stocks, rather than just gold.

We can use the Internet to look up those companies that specialize in particular metals, but some of them produce more than one in large quant.i.ties. One web site, www.miningnerd.com, gives you a choice of both metals and companies in many countries. We could also find what we wanted on www.yahoo.com. We were able to sort by capitalization and select the largest companies to include in our test.

A well-diversified company will not perform as well as one highly focused on mining one metal. Even so, we won't try to a.n.a.lyze the fundamentals of the company but a.s.sume that successful trading means that the metal is of primary importance to the company share price. One of the uncertainties of trading stocks is that, even though a company is dependent on gold or copper, it may be that management, labor and trade contracts, or mining operations overwhelm the impact of gold prices.

Trading Rules Our test will cover both metals prices and share prices beginning in January 2000, a little over 10 years. We gave the trading rules in the previous section, but briefly: The stress indicator takes the metal price as leg 1 and the stock price as leg 2.

The stress indicator will use a 10-day calculation period.

We sell the metal and buy the company shares when the stress indicator moves over 95.

We buy the metal and sell the shares short when the stress indicator falls below 5.

We volatility adjust the position sizes of both legs in order to have the same risk.

We exit both longs and shorts when the stress indicator crosses 50.

The Dynamics of Changing Parameters The parameters used, the 10-day calculation period and the thresholds for entering and exiting, are basic values and not fitted to the best solution. Varying the short entry threshold above and below 95 should result in fewer or more trades in a predictable pattern. For example, moving the threshold from 95 to 98 might cut the number of trades by 20% but increase the unit profits (per contract and per share). Similarly, lowering the threshold would increase the number of trades but lower the unit profits; it should also increase the overall trading risk because trades would be entered earlier and held through more variation in price movement. Lowering the threshold will, at some point, cause the unit profits to fall below the transaction costs.

Changing the exit threshold has a similar dynamic. For shorts entered at 95, exiting at 50 is considered a neutral point, where both legs come back into equilibrium. If we raise the exit point to 55, we reduce the unit returns by exiting sooner, and we may increase the number of trades by a small amount. If the value of the stress indicator falls to 53, allowing an exit, then moves back up to 96, we get another trade. The chances of that happening are smaller when the calculation period is shorter because the stress indicator value will move quickly and has less definition.

The biggest changes to performance come when the calculation period is changed. By shortening the period below 10, the stress indicator will move between 100 and 0 faster, more trades will be generated, and unit returns will be smaller. Increasing the calculation period will do the opposite. But there is another dynamic affecting results-price noise.

Pairs trading is mean reverting; therefore, markets with more noise produce better results. Entering a short on a sudden jump up in gold that has no follow-through is exactly the pattern for profitability. In Chapter 2, we discussed how to measure noise and also that viewing prices over a shorter time period magnified the noise, while longer periods emphasize the trend. Then shorter calculation periods will be better for pairs trading. If we were to use a 60-day period to generate the stress indicator, then we might see only a few buy or sell signals each year and hold that trade for weeks before exiting. We would be fighting the trend, usually unsuccessfully.

This all explains why this chapter looks at trading in a variety of commodities and stocks, all with the same parameters. If you choose to use this method, you should prove to yourself that varying the parameters has a predictable effect on results, and that most choices of parameters will be profitable. A high percentage of profitable results across markets means that you have a robust trading method.

Remember that the stress indicator has no notion of volatility. All peaks and valleys are relative to recent price swings. If prices are quiet for 10 days, the stress indicator will adjust the buy and sell zones to a narrower range. Part of this process will be to apply a volatility filter, a common solution that seems to work well.

Costs In the previous chapters, no costs have been applied to the results based on stocks, but $25 per round turn was used for futures. Per share returns in stocks were shown so that you could decide if the fees that you pay allow net profits after costs. In this chapter, we use commodities for one leg, and the cost for buying or selling a contract is larger and could change the outcome; therefore, we will charge the commodity leg $25 for each round turn. We a.s.sume stocks can be traded for less than 1 cent per share; therefore, no cost is used for the stock side of the trade.

Slippage in trading commodities can be larger than the commission costs if you throw your order into the market as a stop or a market order. Most professional traders use limit orders; that is, if they want to sell gold at $1,105.50, where the market is currently trading, they place an order to "sell 10 gold 1106," looking to do slightly better. If the order is not filled in a few minutes, they can lower that order to "sell 10 gold 1105.50 or 1105." Some amount of patience is usually rewarded with a good fill. For that reason, and because of trading experience using systematic methods, we have chosen to use $25 for each commodity trade. For some professionals, this cost can be near zero. For the novice, it might be $100.

MINING COMPANIES.

The following eight mining companies were selected, mostly by capitalization, but also for the convenience of getting the data: Symbol Company Dependency ABX Barrick Gold Gold NEM Newmont Mining Gold GG Gold Corp Gold IAG IAMGOLD Gold BVN Compania de Minas Buenaventura Gold FCX Freeport McMoRan Copper (and gold) RTP Rio Tinto Copper SWC Stillwater Mining Corp Platinum The pattern of metals prices can be seen in Figure 6.3, beginning in 1983. Older prices are not the actual cash price at the time because these are back-adjusted futures prices; however, the patterns are the same. Gold declined from its cash peak of $800 per ounce in January 1980 and kept dropping throughout the 1980s and 1990s. Anyone holding gold from the bull market of 1979 would not have recovered their investment until 2003, without including the lost interest income or adjustments due to inflation. Because of that steady decline and the a.s.sociated low volatility of prices, it would have been difficult to trade gold using any strategy and net a profit (other than holding a short position for 20 years).

FIGURE 6.3 Prices of gold, copper, and platinum from 1983, back-adjusted nearest futures.

Instead, we'll look at the more recent periods, first from the beginning of 2000 and then starting from 2007. It's important that the strategy is successful even during less volatile periods, but more interesting if we focus on the last few years, when inflation has been a concern of investors and volatility has increased. Figure 6.4 shows that although both precious metals and nonferrous metals have received a lot of press coverage during the past few years, prices for the three metals were stable from January 2006 through mid-2007. All three rallied in the first quarter of 2008, but gold was the only metal to recover; copper and platinum are now trading below their highs. The similarity in patterns, given the very different fundamentals, indicates a global market issue, in this case inflation and the change in the dollar, was driving prices. Investors, concerned about the loss of purchasing power, choose hard commodities and put their money into commodity funds containing all three metals, among others such as crude oil and wheat. By using a short calculation period, pairs trading should be able to focus on short-term market noise and distinguish between these markets, at the same time gaining valuable diversification.

FIGURE 6.4 Prices of gold, copper, and platinum prices from 2006 through March 2010.

The Test The cross-market strategy was run on the eight share prices and their metal dependencies beginning in January 2000, with a 10-day calculation period, 95 short entry, 50 exit, and a $25 cost per contract for commodity trades. Results are shown in Table 6.2.

TABLE 6.2 Results of cross-market mining tests from 2000.

Overall results are remarkably good, with an average information ratio above 1.0 and an annualized return of 12.5% at an annualized volatility of 12%. The gold-copper-platinum leg averaged $114 per contract after a charge of $25, but the per share return was a marginal 5.9 cents. A few of the companies, Newmont, Barrick, and Rio Tinto, had returns that were reasonably high, but it would be much better to get the returns per share higher.

There are two ways to solve this problem: 1. Find a time period when volatility was higher.

2. Filter those trades entered when volatility was relatively low.

The more recent years, from 2007, would satisfy the first option, but if volatility were to fall, we might not have a trade for months or years at a time. By applying a volatility filter that varies with price, we gain some flexibility. Even during extended periods where volatility is low, there are bursts of activity that could produce profitable returns.

TABLE 6.3 Results of cross-market mining tests from 2007.

FIGURE 6.5 c.u.mulative profits for mining companies from 2007.

In pursuing the first option, Figure 6.4 shows that the period from 2007 had higher volatility. Table 6.3 shows the results of using our basic parameters and costs applied to that trading interval. Because the interval was slightly over 30% of the first period, we expect the number of trades to drop proportionally. Instead of 529 trades, there are now 178, 33.6% of the original, close to expectations. The higher volatility apparent from the chart translated into much better annualized returns, 23.0% compared with 12.5%. The information ratio also jumped from 1.04 to 1.92, a very large increase, indicating that this trading period yielded higher returns for the same risk. Most important, the profits per unit traded (contracts and shares) increased significantly. The metals returned $263 per contract, up more than 100%; the stocks increased to 8.7 cents per share from 5.9 cents.

One interesting result is that Rio Tinto and Stillwater show losses on the stock side of the trade but ratios near 1.0. That happens when the number of contracts times the unit metal returns is greater than the number of shares times the unit share return. The returns of the commodity metals leg overwhelms the losses of the stock. Returns per share of Barrick, Newmont, and Buenaventura exceeded 23 cents, a very safe margin of profit. Figure 6.5 shows the c.u.mulative profits for each pair from 2007. At the top are gold trading against Barrick (ABX) and Newmont, and platinum with Stillwater. Platinum shows more volatility in returns during 2008 than any of the other pairs during the entire period.

The overall impression that you get from the results in Figure 6.5 is that mining pairs work and continue to generate good returns. Copper pairs post the lowest returns but would help diversification when this is viewed as a portfolio.

Filtering Volatility Using the average true range for measuring volatility over the same period as the stress indicator, we can filter out trades entered during periods of low volatility. This may not be necessary because the results from 2007 were very good. Still, trading less often reduces your exposure to price shocks and risk in general. If you can achieve the same return by being in the market less often, you are always safer.

Higher volatility improves the performance of most arbitrage strategies. It allows the entry spreads to be larger; therefore, costs become a smaller factor. Using a momentum indicator, such as the stochastic or stress, results in self-adjusting entry thresholds because the concept of high and low is relative to recent price movement. It is not necessary to change anything in the strategy to account for increases in volatility. In addition, the number of shares traded for each commodity futures contract will vary as the two markets change in volatility relative to one another. Of course, risk increases with volatility, but the position sizes will drop to maintain a constant risk level.

Decreasing volatility is another matter. As volatility drops below some very low level, the average profit from a trade will not be enough to offset costs. Before 2006, volatility greatly reduced the rate of return. We can see this by netting the values in Tables 6.2 and 6.3. The returns from 2007 were twice the returns over the entire period from 2000, which means that the returns from 2000 through 2006 must have been very small.

In Figure 6.6, the volatility of gold and Newmont Mining are parallel at low levels from 2000 through the third quarter of 2005. Volatility is measured as the average true range of prices over the past 10 days, the same period as the stress calculation. By reading the chart, we can estimate that volatility less than $500 per day in gold and $1.50 per share in Newmont is too low to trade.

FIGURE 6.6 Comparison of gold and Newmont Mining volatility, January 2000 through February 2009.

Results Using a Volatility Filter When we apply the volatility filter, we use a multiplication factor to raise the threshold to a reasonable level. Without that, the use of 1 average true range would eliminate half the trades. To generalize the use of the volatility filter and avoid overfitting, we use the same multiplication factor for all markets, where the average true range of the price moves is converted to a percentage, ATR%, as follows: For stocks, where the ATR is calculated over 10 days, the conversion factor is 1.0 indicating 1 share minimum, and St is today's stock price. The value is multiplied by 100 to get a whole percent.

For futures, the only difference is that the conversion is the value that gives you the profit or loss based on a big point move. For example, one contract of gold is 100 troy ounces; then the conversion or big point value is 100.

By using a factor and converting the current ATR to a percentage, ATR%, we are able to use the same values for each pair. We will use only the filter factor of 3.0, which means that we will enter a trade only if the current volatility is greater than 3%, as measured previously. In our rules, both the metal prices and the share prices must have a volatility below 3% to filter the trade. In other words, if either the metal or the share price shows a volatility greater than 3%, we take the trade. If both markets have low volatility, the chance is greater that the overall market is quiet and we are not just seeing a small interval of low activity in the metal or the stock.

Filtered Results Table 6.4 shows the results of the mining pairs from 2007, applying the volatility filter with a factor of 3.0. Even though the volatility was higher during the last 3 years, we want to remove lower-volatility trades that would have generated smaller unit profits.

TABLE 6.4 Mining pairs from 2000 with volatility filter of 3.0.

Results are similar to those without the filter, but unit returns for shares increased significantly from 8.7 cents to 13.2 cents. The two pairs, copper-RTP and platinum-SWC, still show losses on the stock side, but their ratios increased slightly. Overall, the information ratio was the same, but the results are more uniform. The average returns for each metals contract remained almost the same, but those values are large enough to net a realistic profit. Figure 6.7 shows the c.u.mulative profits of the eight pairs.

FIGURE 6.7 c.u.mulative profits from mining pairs from 2007, using a volatility filter.

Alternative Rules The cross-market strategy as discussed in this section had very little testing. Only a 10-day calculation period was used, and only the 95 short entry and 5 long entry thresholds were tested. We consider the exit at 50 a nonchoice. Essentially, we used a basic set of values applied to all new markets with good success.

You can increase the size of each profit, and also the risk, by waiting until the stress indicator reaches 45 for shorts and 55 for longs, but there will be fewer trades. More trades can be generated by narrowing the entry thresholds to 90 and 10 or 85 and 15, but you reduce the potential profits. Once a trade is entered, the exit zone could be closer-for example, 55 instead of 50 for shorts-to capture more profits, but those profits will be smaller, and it will be more difficult to overcome transaction costs. You can decide to exit the trade if it's not profitable after 3 or 5 days, but that will reduce the percentage of profitable trades and turn some of the profits into losses. Using any stop or exit rule intended to cut losses also puts severe restrictions on the profits. It will require that prices move within a narrow range to satisfy the risk constraints. Markets don't like to do that and seem to know when you've placed a stop so that it can be touched before reversing back in the direction that would have posted a profit.

Mean-reverting strategies require a high percentage of profitable trades to succeed because the few losses can often be quite large. That is a natural pattern in trading. There is no free lunch. Trend-following systems have a large number of losing trades, but a few exceptional gains, called the fat tail, make up for all the losses. Mean-reverting methods are the opposite. They have a high percentage of smaller, profitable trades and a few much larger losses. There is no way to change these patterns. If you add a filter that seems to beat the odds, chances are you've overfit the data, and it won't work in real trading. You may even succeed for some time, as did Long-Term Capital, but in the end, the risk is still there.

Volume Volume can be a simple subst.i.tute for volatility or an additional measure that adds stability. When volume increases, so does the opportunity for volatility. Volume can be considered potential volatility. In Figure 6.8, the volume of gold is the total volume of all futures contracts, and the volatility is the 10-day average true range. Volume can be erratic and is normally smoothed to see if it's in an uptrend or a downtrend, but the shapes of the two curves are very similar. Volume seems to lead volatility as it moves higher in 2002, it has only a minor setback compared with volatility in 2005, and it clearly starts to decline well ahead of volatility at the end of 2008.

FIGURE 6.8 Comparison of gold volatility and volume.

For those familiar with futures, open interest is also a good measure. Open interest is the number of outstanding contracts. As public interest in a market grows, such as gold during a declining U.S. dollar period, investors enter the futures market by buying a gold contract. They are matched with someone who wants to sell a contract at the same price. If this is a new transaction, it adds one contract of open interest. If the new buyer gets the contract from a person who previously owned a contract of gold, then there is no change in open interest. During inflation periods, there are always more people wanting to buy gold. Investors currently holding gold are not interested in selling. The short-term trader, who believes that gold prices will drop slightly over the next few minutes or hours, will accommodate the new investor by selling a contract of gold, intending to get out of that trade before the end of the day by buying it back.

Open interest is said to have a pattern that confirms the trend. That is, when large numbers of investors are buying gold, then open interest rises. When gold prices suddenly turn to the downside, those investors liquidate their positions en ma.s.se, causing open interest to drop. a.n.a.lysts should consider using open interest as an alternative to volume.

AGRIBUSINESS PAIRS.

Agribusiness companies are another group of stocks that are dependent on commodities. These include Archer Daniels Midland (ADM), the biggest public company that crushes soybeans (A. E. Staley and Cargill are both privately held); Purina (part of Nestle), which uses grain for dog food; Oscar Mayer (now a division of Kraft) and Swift, which processes mainly poultry; ConAgra, which provides diversified food services; and a score of other companies. Although ADM is quite diversified, it is still highly focused on grain.

Taking soybeans as the dependent commodity, we pair it with ADM and apply the same parameters as mining, beginning in 2000 through March 2010. The first line of Table 6.5 shows the results using these same basic parameters. Results are good, but the returns per contract and per share are marginal, even after deducting $25 for each contract of soybeans traded.

TABLE 6.5 Soybean-ADM pair using the standard parameters, with and without a volatility filter.

FIGURE 6.9 The soybean-ADM pair from 2000, with and without a volatility filter.

This problem can be overcome by applying the same filter that we used for mining, a 10-day ATR with a factor of 3.0. Results then improved everywhere, while the number of trades dropped by about 40%. The ratio improved nicely, as did the annualized returns. Most important, the unit returns for soybeans rose to $122 per contact, and the ADM returns to 10 cents per share. The c.u.mulative profits for both the nonfiltered and filtered cases are shown in Figure 6.9. The two return streams are nearly parallel, but the filtered stream has intervals when it was out of the market. These can be seen as horizontal lines on the chart. The trades that were eliminated netted a total return of near zero, which can be seen in Table 6.5, because the TotPL is almost the same, even though the number of filtered trades declined substantially. Fewer trades with the same profits will result in higher unit returns, just what we were trying to achieve.

Although we tested only one stock, the result was similar to our mining results. This adds substance to the robustness of the concept.

THE MAJOR ENERGY PRODUCERS.

No cross-market trading method could be complete without looking at energy. In Chapter 3, the pairs were made up only of various major energy companies. Now we'll look at whether the price of crude oil directly affects the share prices of those companies.

We also looked at the increased correlation in certain inflation products, gold, crude oil, and the EURUSD, beginning in 2007. We would expect the relations.h.i.+p between crude oil and the oil companies to increase similarly. We make no attempt to find out how much of their profit margins are dependent on the price of crude because these companies have large downstream operations (refining and retail), as well as exploration and production, or upstream operations. We expect that a significant increase in the price of crude oil will go right to the company's bottom line because there are no costs added to their operations when prices rise.

Of these players, the first pair will be ExxonMobil (XOM) and the crude oil futures contract traded on the New York Mercantile Ex-change (NYMEX), now part of the Chicago Mercantile Exchange (CME). Because ExxonMobil is a very large, diverse company, factors other than the price of crude oil will move its share price; therefore, it shouldn't be surprising if an arbitrage with crude is not reliable in a normal market. But with the price of crude moving from $50 to $150 per barrel and back to $30, this market is far from normal. If there was ever a time that Exxon profits would track crude prices, this is it.

In Figure 6.10, we can see that crude oil and XOM prices track reasonably well until the last quarter of 2006. Crude prices take a sharp drop from about $120/bbl (these are back-adjusted futures) to near $80, while XOM continues higher. Then, when crude prices spike in mid-2008, XOM prices have already started lower. It's not clear from this chart that an arbitrage between the two will be consistent, if at all profitable, from the last quarter of 2006; however, they come back together at the end of 2008 and again seem to be tracking closely.

FIGURE 6.10 Crude oil and ExxonMobil prices, January 2000 through March 2010.

One point to keep in mind is that our trades are held for only a short time. Although we see the big trends in the chart, pairs trading holds positions only a few days, capitalizing on the noise. When using a mean-reverting system, such as pairs trading, holding a trade for a long time would be a disaster when there are sustained moves in opposite directions. Fortunately, when you view prices in the short term, there is a lot of noise.

Relative Value It would not be easy to find an absolute price level where a stock and a commodity price are both distorted or both normal. Even if there was one point where they appeared to be in equilibrium, everything would change as prices changed. An economist might be able to draw a supply-demand curve to explain the relations.h.i.+p, but econometric a.n.a.lysis has not been particularly dependable and has a time horizon that is far longer than any trader would care to think about. The empirical approach is a much more satisfying and rewarding way to solve this problem.

Stress Indicator for Crude-ExxonMobil The risk of trading crude against XOM is going to be high because both markets have been very volatile. If we were more demanding with our entry points and faster to exit, we should expect to reduce that risk, even though it would also reduce the size of our individual profits. Up to this point, we have only used a 10-day momentum and entered shorts at a 95 threshold and longs at 5. Exits are only when the stress indicator crosses 50. We will continue to use exactly those parameters and rules because success adds to the robustness of the method, and that's important for longevity.

A $25 round-turn cost per contract will be deducted from each crude trade to be more realistic about results. Although you could deduct your own costs from the unit returns, the information ratio would be highly inflated if costs were omitted. Still, with stock costs less than 1 cent per share, we have not subtracted any costs on the stock side.

Results trading the crude-XOM pair are shown in Table 6.6. Two periods are compared, 2000 through March 2010 and 2007 through March 2010. When we looked at inflation pairs, for example, gold and the EURUSD, we found that correlations increased, volatility increased, and per unit returns increased when we selected periods when there was more investor activity. The results in Table 6.6 confirm that same expectation. Over the entire 10-year period, results were good. There were a reasonable number of trades, 352, or about 35 per year, with annualized returns of 14.5% and a good information ratio of 1.21. Also important are the unit returns, which indicate the method's sensitivity to slippage and costs. Crude returned about $309 per contract net of a $25 cost, and ExxonMobil returned 31.1 cents per share (results are shown as 100 shares). Both are well within our requirements for trading. However, this pair may not be representative of other energy sector pairs, and keeping per unit returns high is an important target of system development.

TABLE 6.6 Results of trading the crude-XOM pair for two different time periods.

FIGURE 6.11 c.u.mulative profits from the crude-XOM pair using a calculation period of 10 days and entry threshold (for shorts) of 95.

The second line of Table 6.6 covers only the period from January 2007 through March 2010. The number of trades drops by 66% to 118, but the unit returns for crude jump to $948, more than three times the original $309. Profits per share of XOM also increase by 71%, a healthy amount. The information ratio increases to an impressive 2.33. Keep in mind that this period from 2007 to now was selected with hindsight. Because we are in a more volatile market, this could be traded now, but it will eventually revert to the normal volatility. It simply points out that you can be more aggressive about taking positions when the market is more active. After we finish looking at the detail of the trades, we will try to simplify the selection of trades using a volatility filter. Meanwhile, Figure 6.11 shows the c.u.mulative PL for the crude-XOM pair beginning January 2000. Profits didn't begin until 2005; then they increased rapidly. From late 2008, there has been some moderation in the rate of increase, but it remains profitable.

Trade Detail Before looking at a broader selection of markets, it would be useful to review the numbers a.s.sociated with a specific trade. Table 6.7 gives a complete profile of all the calculation results needed to make a trade. Table 6.7a has the data, the stress indicator calculations used for entry and exit signals, and the volatility calculations needed to determine the position size. Table 6.7b shows all of the positions, as well as the profit and loss calculations.

TABLE 6.7 Crude-XOM pairs trades.

Table 6.7a begins with the date and then the high, low, and closing prices for crude oil (nearest futures) followed by the high, low, and close for ExxonMobil. The high and low are used for both the initial momentum calculations and the volatility, which, in turn, is used to decide the position sizes. Trades are entered on the close, so the open is not needed here. We said earlier that the markets do not close at the same time, but if you enter prices ahead of the crude close, you can trade both markets at that time. Experience shows that signals occurring anytime during the day should produce a good return.

The next two columns show the raw stochastic momentum calculations for crude and XOM. These values range from 0 to 100, as prices go from oversold to overbought. The calculation was shown earlier in this chapter, and it is the same calculation that was used in Chapter 3. All momentum values change quickly because only 10 days are used in the calculation.

Column 10, M1 M2, is the momentum difference, which becomes the input to the stress indicator, given in the next column. Although the momentum difference can range from 100 to +100, the stress indicator resets those values to the range 0 to +100. This is the column used to determine a short entry (greater than 95), a long entry (less than 5), and an exit (crossing over 50).

The last two columns are the volatility calculated using the average true range and expressed in dollars. You'll notice that the stocks are based on trades of 100 shares, so when we see the results, it will show unit profits in whole cents rather than in dollars (i.e., a 12 cent unit profit will be shown as 12.00 rather than 0.12).

The first trade shown is a long (long crude, short XOM) taken on the close of December 3, 2008, when the stress indicator drops from 15.14 to 0. That happens when today's low is the lowest of the past 10 days. The entry prices are the close of trading in each market. The position size is always 10 contracts for crude and the number of shares in XOM needed to make the ATR equal for both legs. Remember that we are using stock units of 100, so a position size of 93 is actually short 9,300 shares. We get those shares by dividing the volatility of crude, $4,243, by the volatility of 100 shares of XOM, $458.30, for a position size of 9.258 for each contract of crude. We trade 10 contracts; therefore, the XOM position is 93 (100 share units) or 9,300 shares.

Following the profits and losses for the trade is straightforward. Crude was entered at 75.51 per barrel and XOM at 76.85 per share. The stress indicator rises steadily until on December 9, 2008, it reaches the value 55.24, above the exit threshold of 50, triggering an exit on the close. The exit price for crude is 70.79 for a net loss of 10 contracts (70.79 75.51) 1,000 per big point for a loss of $47,200 less $25 per contract for a net loss of $47,450. XOM was sold short at 76.85 and bought back at 76.12 giving a profit of 9,300 (76.85 76.12), or $6,789. That nets to a loss on the pairs trade of $40,661. Well, not every trade can be a profit.