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The Math Behind Spread Arbitrage

In order to understand how a strategy can be uncorrelated to the performance of equity markets and properly assess risk in an investment, professional investors might consider the strategic drivers of each investment.

Spread arbitrage programs often determine trade execution through the use of mathematical probability tables that consider relationships between related products, time frames and pricing and may benefit when prices of related products temporarily dislocate but then revert back to the mean.1  “Spreads can trade higher or lower than a mean, but, in the normal course of events, they work back to a mean.” Schap wrote in his Spread Trading book, highlighting the core strategic driver of the strategy.

Spread Prices Can Widen and Contract In Trend Trading Behavior

Spread price variance, like outright markets, have been known to trend in price, dislocating from a price mean and potentially reverting to that mean (see related comments by Emil van Essen in this issue’s “manager profile”).  “One (contract price) can be trending in one direction, while another trends in the other direction,” noted Schap in his book.  In effect, spread trading can be subject to price momentum and persistence, just not in outright markets but rather in price relationships between contract months or related commodities. 
Spread arbitrage programs “have a basis in the economics of the markets involved,” Schap notes in his book.  For instance, if the value of the front month oil contract is below that of the back month, this might indicate markets are expecting oil prices in the future to rise in price through increased anticipated demand or reduced supply.  This “contango” occurs when a futures contract is higher in price the further it is from expiration.  It is sometimes used by economists to determine the strength of economic activity, as spread prices often exhibit movement from contango to backwardation on each leg of the trade.2  Backwardation is the opposite, when the near futures price close to expiration trades higher than the back month away from expiration.

It is important to note that the spread trade might rely on one “leg” of their trade to revert back to the mean of its normal price relationship while the other leg remains relatively consistent in price, which is sometimes utilized by program managers with the goal to provide protection against exposure to the overall market moves.  For example, the spread program outlined in this example is only a play on the relationship between oil and gasoline, not in the overall direction of the energy market either higher or lower.  Thus, if an outside market force influenced the overall price of the energy market, taking the price of both oil and gasoline dramatically higher, the spread strategy typically does not desire exposure to the overall market move, but rather only the relationship in price between related products.  This is not to say a spread strategy is less risky than an outright long or short position often taken by a trend following program, it is to say that the risks and market environments that influence performance can be different.

“What matters is that both trends responding to the same set of economic drivers,” Schap said, highlighting the importance of strategic performance drivers when evaluating strategies.  “They (spreads) exhibit a structure that responds to economic drivers.”

Strategy Risk Considerations

It is important to note in any mathematical algorithm there are points at which the strategy changes and historically consistent price relationships no longer “work.” One risk in the strategy is when prices dislocate based on historical probability tables they do not revert back to the mean.  This is where the phrase “past performance is not indicative of future results” is provided meaning.

Many economists have indicated that markets are so efficient that such opportunity for spread arbitrage may be limited, while other economic voices, such as MIT’s Andrew Lo, note that while market places may be efficient, decisions of market participants can be irrational – resulting in irrational market price movement.4  Indications are the market environments are constantly changing and risk management is tested when the formula and probability tables no longer apply to a given market environment.  When considering risk, it is also important to note that macro strategy risk is different from more complicated factors not outlined in this document involved with individual manager risk, to which investors should be aware.

Footnotes and additional reading:

1. A spread trade is commonly defined: An arbitrage technique in which a trader buys one commodity and sells another contract of the same commodity to capitalize on a discrepancy in prices.  Read more:  http://www.investopedia.com/terms/f/futuresspread.asp#ixzz1aoAwd9Lk  To understand various spread trading strategies and how mean reversion market environments impacts spread arbitrage programs: The Complete Guide to Spread Trading, Schap, Keith, McGraw-Hill, 2005; The Encyclopedia of Commodity and Financial Spreads, Jerry Toepke and Nick Colley, Wiley, Jan 3, 2006
2. Backwardation definition: As the contract approaches expiration, the near futures contract will trade at a higher price compared to the far contract from expiration. This is said to occur due to the convenience yield being higher than the prevailing risk free rate. Backwardation in futures contracts was called "normal backwardation" by economist John Maynard Keynes. This is because he believed that a price movement like the one suggested by backwardation was not random but consistent with the prevailing market conditions.  Backwardation is the opposite of contango, where the higher price away from expiration than near expiration.  Read more: http://www.investopedia.com/terms/b/backwardation.asp#ixzz1asXiI09S
3. Price Persistence definition: http://www.investopedia.com/terms/p/price-persistence.asp#ixzz1ao4Rvfen. Price persistence is also considered synonymous with price momentum.  For reading on how trend following operates, including the role price persistence and momentum plays a role:  Covel, Michael, Trend Following, Financial Times Press, 2009; Little, L.A., Trend Qualification and Trading, Wiley, 2011. 
4. For understanding of how markets can be impacted by inefficient decision making, refer to: A Non Random Walk Down Wall Street, Andrew Lo and A. Craig McKinley, Princeton Paperbacks, 1999; The Myth of the Rational Market, Justin Fox, Harper Collins; Why Markets Fail, John Cassidy, Picador, 2009.

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