Part 10 (1/2)

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 s.h.i.+fts 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, s.h.i.+fts 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 s.h.i.+fts 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 relations.h.i.+ps 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 relations.h.i.+p 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.