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Continuous Contracts

 

A Continuous Contract is a mathematical creation

useful for testing futures trading systems over long periods.

 

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Continuous Contracts

A way to test long-term trading systems on futures contracts

In the stock market, some stocks have history going back for half a century or more. With that much history, stock traders can test very long-term trading systems.

 

Futures contracts however, do not last very long.  The active period of a futures contract generally occurs close to expiration so the effective trading length of a futures contract may be a few months.

 

In order to test long-term trading systems for futures trading, traders use a method of stringing futures contracts together to make a continuous series. They call such a series a continuous contract. 

 

The tricky part of stringing contracts together is that they rarely trade at the same prices.  Therefore, they do not naturally splice together smoothly.  Traders have various ways to cope with the problem of making a continuous contract from individual deliveries. 

 

In a Splice Chart, when one contract ends, the next one starts, without any attempt to adjust prices to make a smooth transition. So at every join, the price jumps up or down by the price difference on the day of joining. S&P futures occur at three month intervals (Mar, Jun, Sep, Dec) so S&P splice charts typically have a price jump every three months.

In a Panama Chart: the individual deliveries float up or down so they join smoothly to their adjacent deliveries.  Panama charts provide a good proxy for actual trading since they reflect actual market changes that traders experience in actual trading. Futures contracts typically have a carry premium that shrinks as the contract nears delivery. Over time, this effect accumulates, and shows up as a downward drift in the Panama Chart, relative to the associating cash chart.

A cash chart shows the actual spot value of the underlying instrument. Traders can trade the S&P cash chart in various ways, including using the QQQQ.

Arbitrageurs sometimes trade the difference between futures and cash, say long QQQQ and short the continuous contract in order to capture the spread. The capture is about equal to the opportunity cost of carrying the positions so the trade theoretically brakes even. Arbitrageurs watch many factors such as interest rates; their bids and offers set the carry between the deliveries.

 

LME (London Metal Exchange) Charts show the price of the future at a set distance from spot.  London typically posts prices for 3-month and 6-month futures.  These charts are also seamless.  They do not, however represent trading experience.  If a trader enters a 3-month contract and keeps it on his books for a month, it becomes a 2-month contract and likely trades at a different price from the new 3-month price.

 

 

 

Simple Splicing

The simple way to join contracts is head-to-toe

The simplest way to join futures deliveries is with the splice method.  To make a splice chart, you simply wait until one contract nears expiration and then carry on with the next contract.  In this way you use, say, the March S&P delivery for a while. When March goes off the board, you continue with the June delivery.  When June goes off, you roll to September.

 

The problem with the splice method is that different futures contracts typically trade at different prices.  When the distant deliveries trade at a premium to the nearby deliveries, we say the deliveries are in contango and have a positive carrying charge.  When the nearby deliveries are at a premium to the deferred deliveries, we say the market inverts and goes to negative carry.

 

The market is almost always either in contango or inverting. Adjacent deliveries are rarely at par.  So when we try to make a continuous contract by the splice method, every time we roll out of one delivery and into the next, we get a step up or down in price equal to the difference between the prices of the adjacent deliveries on the day we switch.

 

 

 

S&P Futures - Showing Contango (Carrying Charges)

 

 2005: Sep = Black, Dec = Red

2006: Mar = Green, Jun = Blue, Sep = Violet

 

On July 29, 2005, September 2005 S&P closes at 1,236.80

with December at 1,243.40

giving Dec/Sep a contango carrying charge of 6.60,

or about 1/2% per four months.

 

A theoretically optimal system for trading a S&P splice charts buys a lot of contracts the day before the splice and then sells them the day of the splice. Traders cannot actually do this trade in the markets.

 

Another problem with back-testing with splice charts is that systems with close stops can get taken out every three months by the price steps.

 

 

 

S&P Futures: June 2000 (black) & September 2000 (red)

 

The June delivery expires on 6/15

The September delivery continues on thereafter.

 

Note: The price of the September delivery (red)

declines from 6/15 to 6/16

 

 

 

Simple Splice Chart

from S&P: June 2000 and September 2000

 

Note: The price on the splice chart

increases from 6/15 to 6/16

 

 

 

 

The Panama Method

A way to overcome the steps in the splice method.

One way to avoid the steps in the splice chart is to use a different method.  At the Panama Canal, a system of locks enables ships to float up and down so they can pass between the Pacific and Atlantic oceans, even when these two bodies of water are at different levels.

 

In like manner, a Panama Continuous contract floats deliveries up or down so that they flow into each other evenly, without a step up or down at the join point.

 

For example, say we want to create a Panama Continuous Chart for S&P Futures.  We start with the first delivery we have in our data base, in this case the June 1982 delivery.

 

 

Date           Open      High       Low    Close

19820421 116.350 117.600 116.050 117.450
19820422 117.000 118.400 117.000 117.900
19820423 118.350 119.750 118.250 119.650
19820426 119.300 120.600 118.650 120.550
19820427 120.200 120.350 118.400 118.850
19820428 118.550 119.300 117.700 118.150
19820429 117.500 118.150 117.250 117.600
19820430 117.550 118.400 117.400 117.500
19820503 117.100 117.500 116.800 117.150
19820504 117.250 118.050 117.250 117.800
19820505 117.850 118.300 117.050 117.550
19820506 118.050 119.200 118.050 119.100
19820507 119.150 120.100 119.000 119.650
19820510 119.200 119.400 118.450 118.500
19820511 118.450 119.950 118.350 119.700
19820512 119.850 120.350 119.050 119.550
19820513 119.550 119.750 118.150 118.350
19820514 118.550 118.750 118.100 118.300
19820517 118.150 118.150 116.500 116.600
19820518 116.600 116.700 115.750 116.000
19820519 115.950 116.350 114.450 114.650
19820520 114.850 115.200 114.150 114.950
19820521 115.250 115.600 114.750 114.900
19820524 114.800 115.150 114.150 115.000
19820525 115.200 115.650 113.450 113.750
19820526 114.000 114.100 112.000 112.500
19820527 112.450 112.600 111.200 111.850
19820528 111.700 112.500 110.750 111.000
19820601 110.750 111.200 109.900 110.050
19820602 110.300 111.750 109.850 111.550
19820603 111.650 112.050 109.700 110.500
19820604 110.400 110.450 108.000 108.100
19820607 108.100 109.850 107.450 109.050
19820608 108.800 109.950 107.900 108.500
19820609 108.500 109.100 107.600 108.600
19820610 108.500 109.850 108.250 109.150
19820611 110.200 111.700 110.100 111.450
19820614 110.000 110.450 108.800 108.900
19820615 109.050 110.000 108.300 109.900
19820616 109.900 110.200 108.750 108.950
19820617 108.000 108.250 107.400 107.600

 

June 1982 S&P Futures

 

Traders typically roll their contracts forward about a week before expiration.  In making the Panama Chart, we follow a similar convention.  In this case, we roll the June forward to September on 1982-06-11.  (September is the next delivery after June.) June 10 (red) is the last day we use June.  Starting with June 11, we use September.

 

Not all traders use this particular form of continuous contract.  Some like to roll earlier or later than five days before expiration.  Some like to roll when volume and/or open interest for the new contract exceeds that of the old contract.  Some like to base the adjustment factor on a combination of prices, not just on the close.  Some make a translational adjustment (plus or minus the factor) while others make a proportional adjustment (multiplication). 

 

My hunch is that the method of making a continuous contract is not very important, although I might test some different ways, as this project proceeds, to find out for sure.

 

Date           Open      High       Low    Close
19820525 115.750 116.300 113.800 114.050
19820526 114.400 114.400 112.250 112.800
19820527 112.700 112.950 111.550 112.350
19820528 112.350 113.000 111.150 111.600
19820601 111.300 111.700 109.900 110.100
19820602 110.150 111.800 109.850 111.650
19820603 111.850 112.250 109.500 110.350
19820604 110.300 110.400 107.700 107.750
19820607 107.600 109.400 106.900 108.600
19820608 108.350 109.400 107.300 107.800
19820609 107.650 108.100 106.600 108.000
19820610 107.800 109.600 107.600 109.000
19820611 111.400 112.000 110.300 111.550
19820614 110.500 110.500 108.550 108.550
19820615 108.500 110.000 107.200 109.900
19820616 109.450 110.250 107.750 108.100
19820617 105.500 106.950 105.150 105.500
19820618 105.800 106.150 104.350 104.650 
19820621 105.200 107.400 104.750 106.500
19820622 106.500 109.500 106.100 109.400
19820623 108.850 112.150 108.100 111.850 
19820624 112.100 112.600 109.750 110.200
19820625 110.000 110.800 108.800 110.350
19820628 110.050 112.350 109.650 112.200
19820629 111.850 112.450 111.100 112.250 
19820630 113.300 113.450 111.050 111.500
19820701 111.500 111.750 109.750 109.850
19820702 109.550 109.550 107.850 108.300
19820706 108.400 109.500 106.400 109.400
19820707 108.800 110.000 107.750 109.300
19820708 109.500 111.000 106.800 110.850
19820709 111.500 113.000 110.200 112.700
19820712 112.900 113.300 111.750 112.250
19820713 110.700 112.900 110.700 111.800
19820714 111.500 113.600 110.550 113.550
19820715 113.700 114.300 112.850 113.500
19820716 113.500 115.150 113.100 114.100
...

...

...

 

September 1982 S&P Futures

 

Now on June 10 (red), at the close, we compute the adjustment factor between the outgoing June and the incoming September deliveries.  In this case September closes at 109.00 while June closes at 109.15.  So September is under June by 15 points.  To make the Panama adjustment, we must adjust every September price up by 15 points.

 

 

Date           Open      High       Low    Close

19820520 114.850 115.200 114.150 114.950
19820521 115.250 115.600 114.750 114.900
19820524 114.800 115.150 114.150 115.000
19820525 115.200 115.650 113.450 113.750
19820526 114.000 114.100 112.000 112.500
19820527 112.450 112.600 111.200 111.850
19820528 111.700 112.500 110.750 111.000
19820601 110.750 111.200 109.900 110.050
19820602 110.300 111.750 109.850 111.550
19820603 111.650 112.050 109.700 110.500
19820604 110.400 110.450 108.000 108.100
19820607 108.100 109.850 107.450 109.050
19820608 108.800 109.950 107.900 108.500
19820609 108.500 109.100 107.600 108.600
19820610 108.500 109.850 108.250 109.150
19820611 111.550 112.150 110.450 111.700
19820614 110.650 110.650 108.700 108.700
19820615 108.650 110.150 107.350 110.050
19820616 109.600 110.400 107.900 108.250
19820617 105.650 107.100 105.300 105.650
19820618 105.950 106.300 104.500 104.800
19820621 105.350 107.550 104.900 106.650
19820622 106.650 109.650 106.250 109.550
19820623 109.000 112.300 108.250 112.000
19820624 112.250 112.750 109.900 110.350
19820625 110.150 110.950 108.950 110.500
19820628 110.200 112.500 109.800 112.350
19820629 112.000 112.600 111.250 112.400
19820630 113.450 113.600 111.200 111.650
19820701 111.650 111.900 109.900 110.000
19820702 109.700 109.700 108.000 108.450
19820706 108.550 109.650 106.550 109.550
19820707 108.950 110.150 107.900 109.450
19820708 109.650 111.150 106.950 111.000
19820709 111.650 113.150 110.350 112.850
19820712 113.050 113.450 111.900 112.400
19820713 110.850 113.050 110.850 111.950
19820714 111.650 113.750 110.700 113.700
19820715 113.850 114.450 113.000 113.650

...

...

...

 

Continuous Contract by Panama Method

 

Note that June 10 (red) contains the last of the June prices.  Thereafter (blue) the prices are September prices plus the adjustment factor of 15 points.

 

Readers who would like to follow along with this exercise and the tutorials can download the S&P Panama data here:  SP----C.CSV

 

 

The Drift Effect

Panama charts accumulate the adjustment factors.

S&P futures typically trade in contango with the distant deliveries trading at a premium to the nearby deliveries. The example above is an exception.

 

The example above shows only two deliveries. We start with June 1982 and roll forward to September 1982.  When September 1982 expires, we must roll again, this time to December 1982. Then we have to roll to March 1983. Since S&P futures has a contract every 3 months, we have to roll four times per year.

 

On July 29, 2005 September 2005 S&P closes at 1,236.80 with December at 1,243.40 giving Dec/Sep a contango carrying charge of 6.60, or about 1/2% per four months.  To roll from September to December on this date we have to reduce the December prices by 6.60.

 

These Panama price adjustments accumulate and the Continuous Contract chart develops an overall downward bias or Drift Effect. 

 

In about 20 years of applying the Panama method to create a Panama S&P chart, we have about 80 rolls. Overall we accumulate about 400 handles (40,000 points) of downward drift. This comes to about 500 points per roll, a little less than the Dec/Sep carry on July 29, 2005.

 

In the example below, the simple splice chart and the continuous chart both cross 200 at the end of 1985.

 

By late 2005, the splice chart is at about 1200 while the continuous chart is at about 800.

 

 

 

S&P Cash Chart

This is the actual value - not futures.

 

 

 

S&P Splice Chart

Different deliveries appear in different colors.

 

 

 

S&P Continuous Contract Chart

Compare with the Cash and Splice Charts to see the Drift Effect

 

See a comparison chart: Cash, Splice, Panama by David Meyer.

Note: The Magenta Splice line is mostly behind the Green Cash line

and only shows through where it differs from Cash.

 

 

 

First True and Last True

Traders find ways to cope with the drift effect.

Some traders do not like the fact that the current prices of the Panama Chart are down to about 2/3 of the prices of the associating futures contracts.

 

To remedy this, they compute the Panama chart from the other end.  That is, instead of starting with the first delivery and working forward, they start with the last delivery and work backward.  Starting with the first delivery is the First True Method and starting with the last delivery is the Last True Method.

 

The main purpose of the continuous contract is to provide a way to measure long-term trends in a way that reflects trading experience.  As long as the trading algorithm does not depend on the actual price of the deliveries, both forms of the continuous contract provide a pretty good synthetic instrument for back-testing.

 

In cases where the trading algorithm does depend on the actual price of the instrument, the continuous contract can still provide useful trend information. The testing software must, however, also refer to the original contract data for accurate price level information.