Let's begin with a futures market - Soybean Oil, or Soyoil for short - and say that there is no such thing as a continuous series of Soyoil futures prices. Futures markets are comprised of individual contracts, each with a pre-determined life-span. At any stage, the market consists of a number of contracts, or "delivery months", that have expiry dates stretching out into the future. As one contract expires, another is listed for trading, and so the cycle continues. The only way that a long-term continuous history of Soyoil prices can be examined is to access a record of cash market prices.

Of course, it's always possible to "splice" the individual Soyoil futures contracts together in some way, so as to represent their history. But it must be borne in mind that the result will merely be a representation of that history, or a computation, that is handled by a particular algorithm.

Splicing contracts together

If all delivery months in the Soyoil cycle were "equal", it would make sense to splice them together by a very simple algorithm: "when one contract expires, begin to display the next". This type of series is called a "spot-month continuous". But delivery months, particularly in commodity futures markets, are generally not equal. The delivery months that the Chicago Board of Trade offers for Soyoil trading are intended to cover the underlying agricultural cycle so as to give industry participants full scope to hedge their specific needs. They are not spread equally through the calendar year. For instance, there is a sequence of contracts expiring in July, August, September and October and then a jump to December.

A hedger may not be interested in the August, September and October contracts at all, and may prefer to trade in the December contract well before any of the intervening contracts have expired. Trading volume tends to be spread unequally between different delivery months. Sometimes an exchange introduces a new delivery month into a market cycle and the industry completely ignores it.

The same disinterest may be shown by a speculator. He may have his own reasons for trading December Soyoil "early" in the cycle. For instance, he may be discouraged by the necessity of "rolling" through all of the intervening contracts, incurring commission costs and potential "slippage" each time. If the trading volume is sufficient to allow it, why not just jump straight into December?

The "spot-month" continuous contract - how useful is it?

It is often assumed that a continuous contract has to display the "spot month" at all times in order to be "correct". This is not the case. A continuous contract is a representation and that representation is correct only in so far as it is useful. There is no single "correct" way to compute a continuous contract for any futures market. The "spot month" representation is probably the most popular, but not necessarily the most useful.

To understand why, let's consider Silver. An examination of the trading volumes in Silver futures reveals a marked decline from about a month before the expiry of each delivery month (see table below). This decline coincides with First Notice Day. If a trader remains in a contract after First Notice Day, he is at risk of having to take delivery of the underlying commodity.

A Silver contract still has a month to run after First Notice Day, but very soon only a handful of industry participants will be trading it. Is there any use in incorporating the last month of Silver prices into a continuous contract if that portion of the delivery month will never be traded? There might be, if no other prices were available, but current prices are always available from any of the subsequent delivery months.

It might be argued that the spot month prices are the most important from an "overall analysis point of view". This argument amounts to saying the following: "My next trade will be in October Cotton. But I shan't look at prices from the October contract, even though I am able to. I shall continue to study July prices, because July is the spot month, and it still has a fortnight to run." This argument becomes especially curious when it is considered that the July and October Cotton contracts virtually cover different crops!

Rolling on Volume and/or Open Interest

Another simple algorithm for constructing continuous contracts is to follow the market's lead. When volume and/or open interest become larger in a back-month, the series leaves the current contract and moves to the back-month. On the face of it, this is a clever algorithm, as it automatically circumvents liquidity problems. It may also surmount the Notice Day problem, by assuming that trading volume always leaves the current contract in time.

The trouble with the algorithm is its over-riding assumption - that liquidity is the only appropriate criterion for selecting delivery months. Let's consider the Eurodollar contract, which is one of the most heavily traded in the world. There is reasonable volume in at least the first 12 listed quarterly contracts. Furthermore, there will often be little difference between the nearby quarterly contract and the next one out in terms of volume - the volume and open interest will be huge in each.

This invites an obvious question: if the contract with the greatest volume is the "correct" one to be following, why is there so much interest in the others? The answer is that different delivery months offer different trading opportunities, both for hedgers and speculators. The Eurodollar futures market attempts to predict the level of interest rates on Eurodollar deposits at specific times into the future. The closer that the time is to "now", the more sensitive the market is to what happens to cash rates. Because of this, prices in different delivery months can move in contrasting manner. For instance, prices in the spot month may move quite sharply while back months remain relatively calm, and vice versa (see charts below). It is even possible for prices in one month to go up and in another down, although this sort of divergence is most common in commodity futures markets, where seasonal factors play a larger role.

The assumption that all delivery months are homogenous, which is implicit in the volume/open interest algorithm, is mistaken, at least for most types of futures markets. This is easily demonstrated if different roll schedules are used to construct continuous contracts for the same market. The variation in the results is often quite apparent to the naked eye.

Some system traders are happy for their continuous data to be "handed" to them by an algorithm such as rolling on volume/open interest. Others prefer to construct their own data and experiment with the results. Rolling on volume and/or open interest is a good way to construct continuous contracts, as long as the question of which delivery month appears in the series at any time is not considered an issue.

Part 2 of the article looks into a problem with simple "spliced" contracts and introduces "back-adjusted" contracts.

Click on Part 2 to continue.

Illustrations

1) The first chart below show the September 2000 Eurodollar contract trading through a 9-point range in the final 30 days of its life.

2) At the same time, the September 2001 Eurodollar contract was trading through a 39-point range.

3) The table shows volume and open interest in the September 2001 Silver contract falling away rapidly towards expiry.

Part 2 of the article looks into a problem with simple "spliced" contracts and introduces "back-adjusted" contracts.

Click on Part 2 to continue.