Crossover relative value trading

December 15, 2008 06:09 AM

Recent market movements should have taught us that risk has increased, and there isn’t adequate transparency to make rational decisions based on fundamentals. If you share this view, that leaves only fully systematic trading with no directional bias. By trading hedged strategies in which we are long one stock and short another, we remove most of the exposure to price shocks and economic surprises.

An ideal trade is a traditional “stat-arb,” finding distortions in two related markets, such as K.B. Homes and Pulte Homes, buying one and selling the other in anticipation of a reversion to the mean. Even though these companies target somewhat different sectors of the market, and prices may vary based on management and dividends, they are overwhelmingly moved by the same economic news.

On a larger scale, arbing all of the markets within a sector, such as home building or oil services, adds diversification and liquidity. Unfortunately, the low-hanging fruit for that method seems to have been snatched up by competition and profits are smaller and less predictable.

We can take this strategy to another level and arb the share price of companies that are highly dependent on a single commodity with the actual physical commodity. These include gold and copper mining operations, agricultural conglomerates and energy companies. The outright profitability of a firm as well as their profit margins increase as the price of the underlying commodity increases. In our example below, we will use Exxon-Mobile (XOM) and crude oil futures (CL) traded on the New York Mercantile Exchange (Nymex).

Exxon is a large, diverse company and factors other than the price of crude oil will move its share price; therefore, we shouldn’t be surprised if an arbitrage with crude is not reliable in a normal market. But this market is far from normal and it gives all the appearances that stock prices are being driven by crude prices that have reached levels that were never imagined.


Because there is no absolute price level where a stock and a commodity price are either distorted or normal, we need to create a reference point. To that end, we can formulate a stress indicator that shows when the opportunities are most ripe.

One viable tool likely is already at your fingertips. A simple stochastic indicator that measures the relative position of the current price within the recent trading range can be used for this. Stochastics is a popular overbought/oversold indicator that’s available is most charting packages. Here are the steps:

1. Find the raw stochastic of the stock price of XOM.

2. Find the raw stochastic of the crude oil price.

3. Take the difference, D, of the XOM stochastic value and the CL stochastic value

4. Find the raw stochastic of D; this is the stress indicator.

The raw stochastic over the past n days is simply:

(close_today – lowest(low,n)) / (highest(high,n) – lowest(low,n)),

where lowest(low,n) is the lowest low price of the past n days.

A plot of the stochastic of XOM, the stochastic of crude and the stress indicator can be seen in the bottom panel of “Stressed out.”

The stress indicator shows when the two markets are relatively overbought (in this case when XOM is moving up faster than crude) and oversold. By calculating the stochastic of the difference we’ve normalized the results and made it easier to assign a value to “overbought” and “oversold.” We’ll use 80 for overbought and 20 for oversold on a scale of 100 to 0.


Not so fast, however. Before we attempt to trade XOM vs. crude oil, we have to adjust for the relative sizes of the instruments. Clearly, we can’t trade one share of XOM at $55 against a contract of crude oil, which has traded as high as $147,000 and as low $55,000 in the past six months (based on the contract size of 1,000 barrels). The best chance for a profit is to make the risk the same by adjusting the position size in a way that makes the volatility equal in both markets.

Volatility = average true range over 20 days × dollar value of a one-point move

We then can divide the volatility of crude oil by the volatility of XOM to get the number of shares of XOM needed for each contract of crude. For example, if crude has a daily range of $1.10 and a contract size of 1,000 barrels, the average move is $1,100 compared to one share of XOM moving $1.50 per day. Then we need to trade 733 shares of XOM for each contract of crude. This value can change for each trade.


Logistically, it will be necessary to anticipate a buy or sell signal at the close. Arbitrage programs do not allow room for slow reactions. Many of the profits will be made in one day. While this program uses only closing prices, there are many more intraday opportunities if this method is applied to 15-minute or hourly data.

Here are the rules:

• Sell XOM and buy crude on the close when the stress indicator moves over 80.

• Buy XOM and sell crude on the close when the stress indicator falls below 20.

• Exit the trade when the stress indicator crosses 50.

• Exit the trade after three days.

While entries must be executed promptly, exits are not as critical. We enter the trade when the distortion is unusual (and therefore less frequent) but there are many more opportunities to exit when prices return to normal.

Examples of cumulative total profit curves for this method are shown in “Stress relievers.” The XOM vs. crude oil performance is shown in the top chart. There were 171 trades from March 15, 2005, through Sept. 5, 2008, of which 106 (62%) were profitable. Trades were held no longer than three days; therefore, the system is out of the market at least 50% of the time, reducing the risk of exposure to price shocks. By the end of this period, crude prices had dropped from near $150 per barrel to close to $100 per barrel, so profits were made in both directions.

The profitability of this method is not limited to major oil companies. It also extends to oil services firms. Applying the exact same rules and parameters to Schlumberger vs. crude we get the results shown in the second chart in “Stress relievers.”

Another crossover relationship using gold shows that the same concept works with other commodities as well. Again, with the exact same rules and parameters we apply the method to Barrick Gold (ABX) vs. physical gold, with the results shown in the third chart in “Stress relievers.”


You can increase the size of each profit, and also the risk, by waiting until the stress indicator reaches 40 or 30 for shorts, and 60 or 70 for longs. You can hold the trade for more than three days waiting for a profit. You can filter the trades using a minimum volatility threshold. You also could watch the correlation between these markets for better timing.

For example, in the case of XOM and crude oil, the crude market is the driving force. The impact on XOM is due to the exceptional volatility and public awareness of high crude prices. If crude fell to levels that reduced speculative interest, it is likely that XOM prices wouldn’t track as well and profits, if any, would be smaller. On the other hand, increased volatility in any commodity would add opportunity and may make traditional pairs trading (between two related stocks) profitable again.

A simple substitute for volatility would be volume. When volume increases, so does the opportunity for volatility.


All trading methods benefit from diversification and short-term trading tends to have a much lower correlation to other methods and to other markets using the same strategy. Diversification into other energy-related markets won’t do as much as introducing metals, grains or other agricultural or industrial commodities into the mix because energy trades will share the same crude oil momentum indicator. Returns also can be leveraged because futures markets require collateralized margin rather than outright payment for shares.

Keep in mind that the method shown here was not optimized. Only one calculation period was tested. There was only one volatility measurement, only one entry and exit level, only one exit based on time and only one observation period. It is possible that other choices will do much better. However, the ones chosen were based on years of experience observing markets and designing systems so it is possible that this first try will be close to optimal.

A good trader and a good technician are constantly searching for opportunities. Many of these come when prices move to extremes, attracting participation from the mainstream investors. Oil is an excellent example, but we have had similar moves in wheat, gold, non-ferrous metals and a host of other commodities. We can’t say how long these opportunities will last, but there will be others to follow. A simple relative value method can help you identify and profit when the next chance appears.

Perry Kaufman is the author of “New Trading Systems and Methods” and “A Short Course in Technical Trading.” He has traded since 1971. Read more about him at his Web site, , or e-mail him at

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