The yield curve is also called the term structure of interest rates. As you move from shorter maturities to longer-for example, fed funds; 3-month T-bills or Eurodollars; 1-year bills; 2, 5, and 10-year notes; and finally, 30-year bonds-the yields form a relatively smooth curve. Based on various economic events and central bank policy, the curve can steepen (shorter-term rates move down and/or longer-term rates move up relative to the other end of the curve) or flatten (shorter-term rates move up and/or long-term rates move down). During 2009 into 2010, the economy remained depressed, and continued economic news seemed only to add to the dismal view of the future, causing the short maturities to go to near zero, while the long end held steady or began to rise in expectation of better days and future inflation due to extreme debt. When the view of the recovery dimmed, longer term rates declined, flattening the curve.

These changes in the yield curve appear to be an opportunity for a directional profit rather than a mean-reversion approach. Mean reversion is the source of large commercial profits, mainly the arbitrage of small abnormalities in the smoothness of the yield curve using various techniques, including 4-legged spreads (for example, buying the 3-month maturities, selling the 6-month, buying the 9-month, and selling the 12-month). However, the profits are very small, and costs must be near zero for this to be viable. But the risks are also very small.

Noncommercial traders can't compete with the banks using a mean reversion or stat-arb strategy, but there may be opportunities looking for shifts in the yield curve that last for a few days. We're going to use a short-term moving average applied to the differences between the U.S. 30-year bond, 10-year note, and 5-year note, three very liquid futures markets.

Trading the Short-Term Trend The first step is to create the data using continuous, back-adjusted futures. Because we will be using only a few days of data at a time, it could be done with individual contracts rather than a continuous series; however, this gives us the opportunity to conveniently backtest our method.

Being careful that the three data series, the U.S. 30-year bond (US), 10-year note (TY), and 5-year note (FV), always roll on the exact same day, we create three series, US-TY, US-FV, and TY-FV. We can't use the ratio because the back-adjusted prices can become very distorted as you go further back in their history due to compounding of the price gap on the roll dates.

Using the difference series, we apply a very short-term moving average to see what happens. No costs are applied because these may vary considerably for each trader and for spreads. We will stay aware that the profits per contract must cover costs and slippage. Results are converted to NAVs at 12% volatility, our normal benchmark, to make comparisons easier. Before starting, we test the correlations between the three series of price differences from the beginning of 2000 through May 2010 and find that they are very high, reducing our expectations of success.

Series Corr 30yr5yr 0.872 30yr10yr 0.939 10yr5yr 0.961 To make the trading system more responsive, the entry rules are: If the closing price moves above the moving average, then buy.

If the closing price moves below the moving average, then sell.

The results are shown in Table 5.4. There are a large number of trades, good returns, and good ratios, but the profits per contract are too small for our costs. An experienced a.n.a.lyst might ask if using a longer calculation period would increase the size of the profits, but as it turns out, shifts in the yield curve occur over short periods of time, and longer trends perform worse. Even in the test of 2, 3, and 4 days, the performance seems to peak at 3 days, and the profits per contract decline in the 4-day test. Results generally conform to the correlations, with the TY-FV pair showing the highest correlations and the smallest unit profits.

TABLE 5.4 Result of trading three yield-curve series using a simple moving average strategy.

Increasing Unit Profits with a Volatility Filter It should be no surprise by now that our next step is to introduce a low-volatility filter. For this application, it makes even more sense because we want to only trade when there is a significant change in the yield curve, not just the odd wiggle. There were a large number of trades, and isolating the more volatile ones might work.

The volatility filter will be a multiple of the average true range, the same method we have used before. The period of the calculation will be the same as the moving average period, also the same technique that has been used throughout the book. We define the filter, A trade is only entered if the current day volatility > average volatility factor.

The results are shown in Table 5.5, with the volatility factor ranging from 0.50 through 2.00. As we would like to see, there is a clear pattern from faster to slower moving averages (left to right) and from smaller to larger filters (top to bottom). The number of trades gets smaller as we go to the right and down, and the profits per contract get bigger. In the lower right box, the profits are very good, but there are only 24 trades in 10 years, less than 3 per year. Because the trades are held for only a few days, we have a very inactive trading strategy.

TABLE 5.5 Tests of three yield-curve differences using a low-pa.s.s volatility filter.

The best compromise seems to be in the middle, a 3-day moving average and a volatility factor of 1.5. That gives 118 trades for the 30-5 combination, and profits of $109 per contract. Even with less than 12 trades per year, the returns are 12.8% per annum. The 30-10 combination has smaller per contract returns but may still be acceptable; however, the 10-5 combination generates only 15 trades over 10 years and is not interesting. Although we can look at interest rates in other countries, such as the Eurobund and Eurobobl, the U.S. is the only country with a 30-year futures contract, and the Eurobund and Eurobobl are similar to the 10- and 5-year U.S. notes, which did not produce large enough profits.

If we look at the pattern of profits in the 30-5 pair, shown in Figure 5.14, we see that the interval of very low interest rate volatility, from 2005 through 2007, as the equity index markets began their rise, produced no trades. On the other hand, the subprime crisis during late 2008 was so volatile that the method was able to capture large, consistent gains. The short interval at the end again shows no trades, not because of low volatility, but because of declining volatility, which causes the filter to read positive.

FIGURE 5.14 Results of trading the 30-5 interest rate difference using a 3-day moving average and a volatility factor of 1.5.

For our purposes, the yield curve spread is another example of an event-driven market. When the volatility is high, then large profits are produced quickly. When volatility is low, there are no trades. From 2000 through most of 2004, there was a normal market generating small but steady returns. On its own, this may not seem exciting, but when combined in a portfolio with many other strategies, it could be excellent diversification.

Skewness in Volatility Filters One point needs to be discussed before moving on. In Figure 5.14, we had the case where the volatility filter worked when volatility was rising but not when it was falling. On the back side of the price rise, in mid-2009, decreasing volatility caused trades to be skipped, even though the absolute level of volatility was very high. That situation should be corrected.

One approach is to use an absolute level of volatility; that is, we trade when the dollar value of volatility, measured by the ATR, is some multiple of our costs, or above an absolute level of, say, $250.

Another approach is to calculate the volatility over a much longer time period, perhaps 1, 2, or 3 years, so that a run-up and the following decline in price lasting three months will all be recognized as high volatility. It might help to lag the volatility measure by one to three months, so that any surge in volatility is not included in the current measure. Otherwise, volatility is always chasing you.

TREND TRADING OF LONDON METAL EXCHANGE PAIRS.

As stated at the beginning of this chapter, there are markets that are correlated yet do not mean revert; that is, there may be a series of long-term shifts in the way the public values each company. The first example was Dell and Hewlett-Packard. This can also happen in commodities markets. The London Metal Exchange (LME) base metals are all tied together through the construction industry. The average correlation of all the LME pair combinations was .45 from 2000 through 2009. In Chapter 4, we used these relationships to show that the LME pairs could be traded with a short-term, mean-reversion strategy, but the results were only marginal. That is, after commissions and slippage, profits were small.

We're now going to look at relative trends in these LME metals. Consider tin and zinc, which are both noncorrosive metals used in plating steel. Stainless steel is coated with tin and galvanized steel is coated with zinc. Tin cans are actually made of a combination of aluminum and steel, bra.s.s is a product of copper and zinc, and bronze is made from copper and tin. Copper is also the choice for hot-water pipes. Uneven demand for a specific metal may drive one price more than another, or a problem with supply may cause one to become more expensive for prolonged intervals. If this turns out to be true, we can capitalize on the trends while, at the same time, hedging one against the other to take advantage of their long-term correlation. By buying one and selling the other, we still maintain a neutral position with regard to price direction. Both metals could be rising or falling, and we would be long one and short the other. This type of trade, a directional spread, offers important diversification in a broad trading portfolio.

When we looked at price noise in Chapter 2, we concluded that a long-term view of prices emphasized the trend, while a short-term view increased the effects of noise. This can be seen by first looking at a daily chart of the S&P and then converting that to weekly data. The trends will appear much clearer. Now change the daily chart to an hourly chart, and you won't be able to see any trends, only noise. In Chapter 4, we used mean reversion, holding the trade for only a few days. In this chapter, we'll take a much longer view to give the trend every opportunity to develop.

Creating the Trend Trade Trends are simple to calculate, and the most popular method is a simple moving average. We've mentioned before that a typical macrotrend system, one that attempts to profit from trends that align themselves with economic fundamentals apply calculation periods from about 40 to 80 days, sometimes longer. It isn't necessary to overcomplicate a trend strategy. Some have different risk and reward profiles, but all of them make money when markets are trending and lose when they are going sideways. For that reason we won't look any further than a moving average to identify the trend.

There are two choices in the way the data are constructed: the ratio of prices and the price difference. Because we are using back-adjusted data, we'll choose the differences. Data begins in 2000 and ends at the end of 2009.

Table 5.6 shows the information ratio from six tests where a moving average is applied to the series of price differences created from 15 LME pairs. Table 5.7 shows the corresponding profits per contract for the same combinations. Results do not reflect any commissions.

TABLE 5.6 The information ratio for six moving average calculation periods and 15 LME pairs.

TABLE 5.7 Profits per contract for the same tests shown in Table 5.6.

The first thing we notice in the tables is that nearly every test is profitable. We then believe that there are trends that can be exploited in the way the metals move in relationship to one another. The average ratios at the bottom on Table 5.6 show a slight tendency to get larger as the calculation periods get longer. The highest ratio, 0.462, occurs for calculation period 40.

Distribution of Tests Notice that the calculation periods chosen essentially doubled for each test. Doubling these values is a fast way of getting a good sample over a wide range of values without many tests. If we were to test every period from 3 days to 80 days, we would find that the greatest difference in performance came when we moved from 3 to 4 days, an increase of 1/3, while the smallest difference was from 79 to 80 days, a change of only 1.3%. If we then averaged the results of all tests, we would be heavily weighting them toward the long end. By doubling the values, all the changes are equal at 100%, and we get a much fairer sample.

Pattern of Results Table 5.7 shows the profits per contract for the same calculation periods as Table 5.6. The averages show an increase from $4 to $34 per contract. This is the right pattern when the calculation period increases, but $34 is not large enough to be comfortably above the cost of trading. If we look more closely at the results of the individual pairs, we could select five that might have per contract returns large enough to trade. But we were expecting more.

Is there anything that can be done? In the past, we have used volatility filters to select the trades that have a greater chance of larger returns. We can try to do the same thing here. But first we want to look at a sample of the NAVs. Figure 5.15 shows the results of four pairs chosen arbitrarily, lead-tin (PB-SN), aluminum-copper (AL-LP), copper-nickel (LP-NI), and nickel-lead (NI-PB). They all show that there was very little activity through 2003 followed by low volatility of returns for another two years. From 2005 on, the returns are much more active.

FIGURE 5.15 Sample NAVs for four LME pairs show little activity up to 2005.

TABLE 5.8 Return statistics for LME trend pairs from 2005 through 2009.

If we consider the data beginning in 2005 and see that the markets are currently performing at a much higher level, we can rerun the 80-day moving average test from 2005 to get the profits per contract that we can expect under current market conditions. Table 5.8 shows that the results for all pairs are far better. The number of trades was reduced by about two-thirds, but those removed were mostly losses because trends between these pairs do not appear to have been as strong. The average rate of return of 8.3% and the average ratio of 0.688 would come out much higher when these pairs are combined into a portfolio and the benefits of diversification increase leverage. It is also rea.s.suring that every pair was profitable, and the smallest ratio was for copper-nickel at 0.247. Remember that these results do not reflect costs, but an average per contract return of $129 should be enough to retain reasonable profitability.

If you look carefully at Table 5.8, you will notice that the profits per contract seem to be inversely related to the correlation between the two legs of the pair. The largest per contract return was for the copper-tin pair, $365, which also has a correlation of 0.470 in the total range of 0.403 to 0.729 for all pairs. Figure 5.16 is a scatter diagram of correlations versus unit profits, showing that correlations over 0.60 have marginal unit returns and correlations under 0.50 have the highest values.

FIGURE 5.16 Lower correlations generate higher profits per trade for trending LME pairs after 2005.

We can conclude that the LME nonferrous metals move in a way that can be exploited using trends where the two legs are volatility adjusted to equalize risk. But in many of the other situations we've looked at, more recent price movement, which reflects higher volatility, generated much better performance. We might have been able to introduce the usual volatility filter and systematically remove the quiet period before 2005, but that did not seem necessary because these markets transitioned into a better trading period. If volatility declines, it would be necessary to stop trading when returns dropped below costs, but that is not a current problem.

SUMMARY.

Stat-arb trading, which buys and sells abnormal differences in related markets, profits from prices returning to relative normal. It is a trading approach that has withstood the test of time and evolved into one aspect of high-frequency trading. But while we can profit from these distortions in the short-term, there may be a major shift going on in the long term.

We know that noise dominates price in the very short time frames and trends surface when we look at the same prices over a long time period. Up to now we have focused on the short term, but this chapter looked at the longer term and larger moves that could occur when two fundamentally related markets diverge. Examples of this were Dell and Hewlett-Packard, gold and platinum, and the LME nonferrous metals. By going long and short according to the trend of the price ratios or price differences, and equalizing the risk of the two legs, we removed the directional risk.

Most of the opportunities in this chapter, and some in previous chapters, seem to have increased in recent years with the higher volatility a.s.sociated with economic crisis and market stress. Perhaps that's the primary consequence of more compet.i.tion. Yet, if we continue to scan these markets, there always seems to be a place that will produce profits.

To implement these strategies, you will need to put this into a spreadsheet or computer program and verify all the results. You cannot rely on anyone else's numbers when it's your money that is at risk. You will need to understand the process, do the calculations, and place the orders with precision.

We did not look at fixed-income markets in this chapter. Our experience says that they are too highly correlated. Profits would be very small, and survival would depend on extremely low transaction costs, the venue of the professional traders. However, there is a combination of interest rate markets that will work for us and is discussed in Chapter 7.

The next chapter will introduce a different relative value measurement, the stress indicator, that will correct some of the problems we faced in Chapters 3 and 4.

Chapter 6.

Cross-Market Trading and the Stress Indicator Changing times and improved technology allow more versatile trading solutions. In this chapter, we look at the stress indicator, which will allow us to identify buy and sell levels with greater flexibility than the momentum difference method used in the previous chapters, and we will apply it to some of the previous pairs. It also gives us the ability to trade across very different markets, combining physical commodities with stocks that are highly dependent upon those products.

In previous chapters, we have discussed the cla.s.sic method of statistical arbitrage (stat-arb), pairs trading. Pairs trading is based on a strong fundamental relationship between the stock prices of two companies in the same business, affected by the same events in similar ways. The correlations between their price movements may vary from as low as 0.30 to above 0.90. At the low end, there are more opportunities but at greater risk. At the high end, we need to be selective about which trades are taken because they track each other so closely that the potential profit might be too small to overcome costs.

The stat-arb represented by pairs trading has become more difficult. The method is widely known, even though there are many traders, especially novices, who do not balance the risks correctly. They can squeeze out the opportunity for others without profiting themselves.

Because of the small margin of profit in stocks, we also looked at pairs of U.S. and European index markets, pairs relating to inflation hedges, and LME metals. Some of these were quite promising; others appeared successful, but the unit returns were too small to realistically expect a profit.

The method used to trigger signals is called relative value trading. Using a stochastic indicator, we calculated the value of each leg over the same time period and then looked to see how often the indicator values moved far enough apart to offer a profit opportunity. Overall, the results were good. In this chapter, we introduce a different way of identifying the trigger points using the stress indicator, which seems to be a more general and robust way of identifying the buy and sell points when trading pairs. With this indicator, we look at other interesting trading opportunities.

THE CROSSOVER TRADE.

The market is filled with opportunities, and it's up to us to uncover them. One of these, the most interesting one we'll discuss in this chapter, crosses over from stocks to commodities.1 There are many brokerage firms that give access to different investment vehicles, but not as many as a year ago. The consolidation of the industry in 2008 was followed by a review of both the profitability and the risk of various divisions, the result being a narrower focus for some firms, creating a less accommodative service for clients. Nevertheless, there are still firms, such as Interactive Brokers, that can facilitate trading across a wide range of markets from a single investment account.

The first step is to identify a business whose primary input is a commodity. The obvious ones are the major oil-producing companies, mining operations, and agribusiness complexes. It's important to avoid companies that are too diversified because we're looking for a dependency on the price of the underlying commodity. For example, if the gold price increases, we want that to be reflected in the share price of Barrick Gold Corp (ABX). Because we are concerned with company profits and losses, the airlines might also be candidates for this method, based on the stock price reaction to the price of crude oil (refined into jet fuel). However, this may be a temporary situation, complicated by other economic factors such as a decrease in travelers related to changes in disposable income or just an increase in fares. As the relationship between the commodity and the share price becomes less direct, the risk of the trade will increase. That's not always bad, nor is an opportunity that lasts for only six months. In Chapter 4, we saw that fear of inflation causes markets that previously had a loose relationship to move together in a way that allowed profitable pairs trading.

Trading Hours It is very important to know that futures and stock prices do not close at the same time. This was discussed in the Chapter 4, "Pairs Trading Using Futures." The main points are: There will be trading signals that are generated but not tradable when markets close at different times. If the S&P makes a move after the close of EuroStoxx, then the stochastic based on different closes will appear to be different, but the opening of the EuroStoxx will gap to correct that difference. There is no profit opportunity. It turns out that the European exchanges have all aligned their trading times with the U.S. trading hours, so this is no longer a problem.

For markets such as gold and Barrick Gold, the markets close at much different times, although the after-hours gold market continues to trade and can be captured at 4 P.M. when the stock market closes. For convenience, we will use the commodity closing price, even though it is a different time. When we studied the relationship between the U.S. and European index markets before hours were aligned, we found the results were very similar. There may be a few false trades due to the difference in closing times, but we believe the results will be representative of the performance when prices are posted at the same time.

In real trading, you must capture prices at the same time, while both markets are open, to a.s.sure a correct signal.

Capturing prices at multiple times during the day, especially following an economic report in either time zone, will increase the number of signals and the ultimate profitability. For example, capturing prices at 8:45 A.M. in New York, 15 minutes after the jobs release, should take advantage of a volatile move in the U.S. index and interest rate markets, while there is a less certain reaction in Europe.

We believe that the pair trading concept is sound and will profit as expected from real distortions in price movement that are reflected in the momentum calculations.

We will come back to this at different points during our a.n.a.lysis.

THE STRESS INDICATOR.

We can think of stress as a rubber band. As we stretch it farther and farther out of shape, it seems to pull harder to return to normal. In the previous chapters, we measured our opportunity in pairs trading by calculating two stochastic indicators, one for each leg of the pair, subtracting the indicator value for leg 2 from the corresponding value of leg 1 and then found the threshold levels based on the difference that worked for entries and exits.

The stress indicator goes one step further. When we take the difference in the stochastic values between leg 1 and leg 2, we then use that series of values as the input for another stochastic calculation. There are two advantages to this: 1. There is a single value that varies between 0 and 100.

2. This new value adjusts for volatility in the momentum difference.

By automatically adjusting the volatility, there will be more trades; however, we lose the absolute value of the volatility, so we may want to add a filter that avoids trading when the opportunity is small.

Starting from the beginning, the stress indicator is calculated in the following four steps: 1. Find the raw stochastic for leg 1 over an n day period: This is effectively the position of today's closing price within the high-low range of the past n days, measured as a percentage from the bottom of the range. Note that n days is the entire n day period.

2. Find the raw stochastic for leg 2, using the same n day period: 3. Find the difference in the two stochastic values: Up to this point, we have followed the same process as in the previous chapters.

4. Find the stress indicator, the stochastic value of the differences, Diff: Even though the Diff values do not have highs and lows each day, the stress indicator can provide added value. There is also no smoothing involved in this calculation, so there is no lag, as there is in most trending indicators.

Spreadsheet Example of the Stress Indicator Calculations The stress indicator is easily calculated using a spreadsheet. In Table 6.1, there are only four steps needed once the data are loaded. In this example, we pair crude oil prices (continuous futures) with the Conoco Philips stock price. The high, low, and closing prices are loaded; the open is not used. Only 41 days will be used in this example.

TABLE 6.1 Example of stress indicator calculation.

In the two columns with the headings mom1 and mom2, we calculate the values of the raw stochastic from steps 1 and 2. For example, the 10-day stochastic, mom1, is written =(D12-min(C3:C12))/(max(B3:B12)-min(C3:C12)). The same formula is applied to the next three columns in order to get mom2. Both start in row 12 because it is the first row with 10 previous values. Column J, the mom diff, is simply H12 I12. The final column, K, the stress indicator, needs 10 values in column J, so it cannot start until row 22 on February 12, 2007. It uses column J for the high, low, and close in the momentum calculation and is written =(J22-min(J11:J22))/(max(J11:J22)-min(J11:J22)).

The momentum calculations for the first 41 days of data are shown in Figure 6.1. The first 10 days are omitted because they are needed for windup. Values of each indicator range from 0 to 100. Up until February 28, the two markets track fairly closely, but then Conoco prices decline ahead of crude (do they know something?), crude catches up, Conoco rallies to meet crude, and then crude falls ahead of Conoco. These short periods where the two markets are out of phase will create the trading opportunities.

The last step is shown in Figure 6.2, where the difference between the two momentum indicators is combined into the stress indicator. In this example, the momentum difference ranges from about 60 to +60 out of a possible 100 to +100 (100 when leg 1 is 0 and leg 2 is 100). The stress indicator has a range from 0 to 100. It reaches these extremes because a 10-day calculation is sensitive to change. That is, a 10-day high will be recorded as 100 and a 10-day low as 0. Those values occur much more often with a 10-day calculation than they would with a 30-day calculation.

FIGURE 6.1 Starting stochastic momentum calculations for crude oil and Conoco Philips.

FIGURE 6.2 Momentum difference and the stress indicator.

Rules for Trading Using the Stress Indicator The trading rules for the stress indicator are very similar to the momentum difference that we used previously. There are still two primary variables, the calculation period and the buying/selling thresholds. We always use symmetrical thresholds, even though some a.n.a.lysts argue that certain markets, such as equity indices, are biased to the upside. We want to give the longs and shorts an equal chance to profit. We could still have an exit threshold, which is nominally set at 50, but could be 55 or 60 for shorts and 45 or 40 for longs.

The main difference between the methods is that the stress indicator will find a relative peak or valley in the price movement that cannot be found using the previous method.

If the indicator is robust, then moving the threshold from 90 to 95 should reduce the number of trades and increase the size of the profits per trade, or unit profits. In the same way, holding the threshold constant at, say, 95, and increasing the calculation period from 10 to 20 should also reduce the number of trades and increase the size of the unit profits. When the threshold is very low, for example, 70, the unit profits are likely to be too small to overcome transaction costs, even though it will vary based on the volatility of the two legs. Even if there are sufficient profits, there will be many times when you enter based on a 70 threshold and prices continue in the same direction, pushing the indicator value to 90. That represents a sizable risk, even if the final accounting is a profit.