The chart below shows two years of a spliced continuous contract for Lean Hogs. The most obvious thing about the chart is that it tends to consist of "clumps" of data separated by large gaps. What are these gaps and where do they come from?

The Problem with Simple "Spliced" Contracts

In Part 1 of this article, it was argued that the different contracts in a futures market are not homogenous. Each delivery month points to where cash prices might stand at a particular date in the future. Therefore each contract will tend to trade at its own level. This leads to a problem when individual contracts are spliced together. When one contract is replaced in the series by another, the difference in price between the two will manifest itself as a gap. This explains the gaps evident in the Lean Hogs chart above. For instance, the first big gap in the chart, when prices appear to "jump" from around 62.5 to 70 early in 2000, was caused by the following sequence of events:

23/3/2000 - the April 2000 contract closes at 62.525. It is now abandoned.
On the same day, the June 2000 contract closes at 69.950
24/3/2000 - the June 2000 contract, which is now the current contract in the series, closes at 70.525.

The spliced chart suggests that the Lean Hogs market jumped about 7 basis points from the 23rd to the 24th. But the June contract itself jumped only 1.25 points. It was already trading well above the level of April on the day that April was abandoned. So when did the market jump those 7 points? The answer is that it never did. The "market" is actually comprised of individual contracts that run their own course. The spliced continuous contract attempts to represent the longer-term history as best it can, but given the spurious gaps that it creates, there are obvious limitations as to what a spliced contract can achieve.

What is a spliced contract good for?

The spliced contract offers a "staccato" version of futures prices, with discontinuities evident. Nevertheless, it can be used to identify where futures prices have traded in the past. It paints the picture with a broad brush, but a spliced chart can give a good idea of whether current futures prices are high or low in an historical sense.

What is it not good for?

Any numerical price indicator run on a spliced contract will reflect the discontinuities inherent in the series. For instance, a moving average will jump along with every gap. To the extent that an indicator is used to assess market sentiment, it will provide a false reading, because the gaps in a spliced contract are not caused by market activity.

A spliced contract will distort the testing of trading systems. Unless instructed otherwise, a computerised system test based on a spliced contract will incorporate the price gaps as evidence of profit or loss.

What is the solution?

The answer is simple - take the gaps out!

The Back-Adjusted Continuous Contract

In a "gap-adjusted" continuous contract, every price gap caused by a contract "roll" is measured and removed. The procedure can work in either of two ways: it can start at the beginning of the series and work its way forwards, removing each gap in turn, or it can start at the end and work its way back. The "back-adjusting" method is preferred, because it leaves current prices intact. Only those prices prior to the last roll date are adjusted.

So how is the roll gap measured? The simplest way is to compare the closing prices on the roll day. Using the example from above, we have:

23/3/2000 - June Lean Hogs - 69.950
23/3/2000 - April Lean Hogs - 62.525
Roll gap = + 7.425

The roll gap is "up". How do we make it disappear? We can't do it by magic. What we have to do is adjust all previous prices up by 7.425 points. This effectively "closes" the gap.

Here is the back-adjustment algorithm in a nutshell: working our way backwards, we measure every roll gap and adjust all previous prices up or down according to whether the gap happens to be positive or negative. The gaps are now eliminated.

Of course, this process never ends, a point that needs to be emphasized: every time a new contract is added to the series, the back-adjusted contract is re-calculated and all previous prices are adjusted.

Now let's have a look at the result. The original spliced chart is shown on the left and the back-adjusted version appears on the right.

Misconceptions about back-adjusted contracts

Many traders are happy to see spurious price gaps removed from their continuous contracts but are unhappy with the result. They complain that the back-adjusted prices are not "real", often citing the fact that in some contracts the historical prices are actually negative.

Traders looking for real historical prices should consult their spliced charts. Prices in a back-adjusted series are adjusted deliberately, so the complaint about "unreal" prices misses the point. Gaps in a back-adjusted contract disappear because historical prices are altered. There is no other way to do it.

Trading reality versus historical price reality

If the prices in back-adjusted contracts are mostly spurious, then of what use are they? To answer this question, let's imagine that we enter a position in Lean Hogs on the first day in the series and hold it to the end, rolling the position forward from one delivery month to the next. If we ignore commission costs and execution "slippage", the back-adjusted chart can be used to calculate the exact value of the position at any time. Back-adjusted contracts represent a different type of reality - trading reality. They show exactly what would have happened to a trader who held a continuous position in any market. Therefore back-adjusted contracts constitute the perfect resource for computerised system tests.

Looking at the Lean Hogs charts above, we can say that the broad price trend in the underlying commodity has been down, but that the trend of trading activity in the futures marketplace has been up.

Spliced contracts may be differentiated from back-adjusted contracts as follows:

Spliced contracts show price levels in a futures market. As a drawback, they also display price movements that are spurious (price gaps that are unrelated to trading activity).
Back-adjusted contracts display price movements in a futures market that are due to trading activity. As a drawback, they also show price levels that are spurious.

Is there a third way?

The short answer is "no". If roll gaps are left in a continuous contract, you have a "spliced" chart. If roll gaps are removed entirely, you have a "back-adjusted" chart. The only alternative is to remove the gaps partially. The resulting series is caught between the other two methods and marred by the disadvantages of both.

Negative numbers

In futures markets that spend a large time in backwardation (e.g. Crude Oil), the back-adjustment process can cause historical prices to be pushed into negative territory. Some charting/analysis programs can display negative numbers but can't do much else with them. This is not the fault of the back-adjustment algorithm.

Part 3 of the article looks at how DataTools handles continuous contracts.
Click on Part 3 to continue.