Part 10 (2/2)
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 s.h.i.+ft 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 relations.h.i.+p 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 relations.h.i.+p 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 relations.h.i.+p 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 relations.h.i.+p 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, pus.h.i.+ng the indicator value to 90. That represents a sizable risk, even if the final accounting is a profit.
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