Part 11 (1/2)

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, , gives you a choice of both metals and companies in many countries. We could also find what we wanted on . 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.