Question: How do you make a small fortune in the Futures Market?

Answer: Start with a large one!

This paper is a summary report based on some twelve months research during 1989/90 into the possibility of using the processes of Chaos to model short term movements in the market price of volatile financial instruments. To assist in familiarisation with some of the technicalities I will give an overview of the background to the project.

We have amused ourselves in previous Philos-o-Forum meetings with Word Association exercises. That was apposite because the name of the group itself was inspired in part by a Word Association from the venture's immediate predecessor. This trivium (singular of trivia??) might incline some of you to wonder if there exists some other project called LAPIS. There does. Its expanded acronym is Local Attractor Penetration Indicator System, and this paper sets out to explain how and why it works. 'Lapis Philosophorum' was the Philosopher's Stone of the Alchemists; it was said, among other things, to have the property of transmuting Base Metals (like lead) into Gold.

As Peter Carroll has stated "The nature of Money has changed from Land to Gold to Paper to Plastic to Pure Number". He appears to be quite correct, as I hope to illustrate. So also, it might be argued, has the nature of the Alchemist's LAPIS changed. In our own age the Philosopher's Stone may be perceived as that which transmutes Base Information into value-added Information, which, by definition, has a greater material worth.

MONEY AS PURE NUMBER AND PURE INFORMATION

The majority of people most of the time have nothing to do with what are generally termed as the "Money Markets". We transact our day to day business in barely significant amounts of a single currency - that of the country live in. There are however a few activities in which we may indulge that touch the outermost fringe of those Market Systems in a direct if barely noticeable way.

Anyone going abroad will know that exchange rates between, say, the Pound and the US Dollar can vary by a few cents over the course of a few days, or even, in exceptional cases, from one day to the next; it will also be noticed that you always lose money if you convert, say, from Pounds to Dollars and back to Pounds in near simultaneous transactions. This is because the exchange rate offered varies depending on whether you are buying or selling one currency or the other - the money-changer covers his own costs and takes his profit margin out of the difference or 'spread' in the exchange rates. When you trade with the money-changer you are exerting an effect, however infinitesimal, on the world-wide electronic Foreign Exchange market which is open and active 24 hours a day on most days of the year.

Another area of occasional contact between a relatively ordinary individual and a subset of the Money Markets occurs if you apply for shares in the 'Flotation' of a company, or of some State-owned industry, and then subsequently sell your holding or some part of it. In that instance you are exerting some infinitesimal influence on your local Stock Exchange, say, here in London, and, through the informational linkages between Stock Markets in different countries, you exert an indirect influence on Paris, Frankfurt, Wall Street, Tokyo/Osaka and the rest. If you wake up one morning and decide you want to buy or sell some shares, it will do you little good turning up at the Stock Exchange with the cash or the share certificates in your pocket. Firstly, the Trading Floor where brokers used to ply their trade in face to race transactions no longer exists, and, secondly, the major broking firms who are able to transact such business will not deal directly with you. In practice you would ask your bank to do the business on your behalf (which can take days) or open an account with one of the small number of 'Share Shops' and deal through them. If you are a very wealthy individual and/or have the right connections you may be able to open an account with a brokerage house by depositing a sum of money or some share certificates with them, and you can then trade simply by picking up a phone and giving the necessary instructions.

Another major category among the Money Markets are those which deal in Commodities. Few people will have failed to notice the recent gyrations of the Crude Oil price, or the way in which such movements are reflected in the price of petrol, albeit often in such a way that retail pump prices seem to rise very swiftly in response to rises in the Crude price, but seem to fall more slowly when the Crude price drops. This is inevitable, because just as the price 'spreads' enable the professionals to cover their trading costs in the Foreign Exchange and Stock (or Equity) Markets, so the consumer eventually picks up the tab for the market activities of the oil companies. The same principles apply for any commodity which can be bought and sold in any of the world's commodity markets - and these exist for precious and base metals, for foodstuffs like grain, sugar, soya, pork bellies, live cattle, and for raw materials like rubber.

 In this consideration of the Money Markets thus far there are some key points to summarise:

The Instruments considered so far are those which pertain to 'Spot Markets'. That is they represent actual currencies, stocks or quantities of a commodity being bought and sold at the time when the transaction is carried out.

Futures Markets are a little more abstract in character. They came into being originally for trading commodities, primarily to protect agricultural producers from wild price fluctuations in the Spot Markets. The idea was that a farmer could make a contract to sell his produce in 3 or 6 months time at a price fixed in advance, regardless of what the spot market was doing at the time when the produce was harvested and ready for delivery. Although the 'Future' price might not be quite as good as the Spot at any given time, at least the producer had the certainty of knowing that the price for his crop was guaranteed and could make plans accordingly. Futures Instruments can be bought and sold just like Spot Instruments, and again they can be regarded to all intents and purposes as numbers - items of information - which can go up or down in value.

Futures are not confined to commodities; such Instruments are also constructed on the future value of currencies, government bonds, and, indirectly, on shares in major companies as traded in the Stock Exchanges.

Most people are familiar with the concept of a Stock Market Index, such as the Financial Times 100 Share Index (FTSE or 'footsie'). An Index is used as an approximate means of measuring the value of the market as a whole. It is calculated as an average of the prices of the most frequently traded shares on the market in question - the 100 London 'Alpha' Stocks in the case of the FTSE. Any movement in the price of any of the shares which make up the index will be reflected in some smaller rise or fall in the value of that index. Many indices are named after the newspaper, credit agency or information service which first calculated and published it. Thus the New York Stock Exchange has the Dow Jones Industrial Index representing 30 shares in industrial companies, and the broader based Standard & Poors 500 Index (S & P).

A common strategy among major market players is to buy a portfolio of shares which includes some proportional holding in each of the companies which make up the major index for whatever market they are trading on. In that way they can keep abreast of the value of their portfolio simply by tracking the index. Moreover, Futures contracts are available against some of the indices, so that it is possible for a player effectively to insure against a sudden crash by purchasing an appropriate number of lots of the Index Future instrument, at a price which represents the best guess about where the real Index value is going to be at some fixed point in future time.

In practice Stock Index Futures can be viewed as abstract numbers which can be bought and later sold, or which can be sold and later bought back. In technical parlance buying something to sell it later (hopefully for more money) is known as taking a LONG position; selling something which you don't have in order to buy it back later (hopefully for less money) is known as taking a SHORT position. It is interesting to note that for the worlds busiest Stock Markets major movements are usually seen first in the Index Futures Instruments, with the Spot index calculated on the real share prices following some minutes behind. This is not usually due to any delay in calculating the spot index.

Brokers and major traders in the financial markets have virtual simultaneous access to the prices of all Instruments traded on the world's markets via information service screens provided by companies like Reuters, AP Dow Jones, Quotron and a host of smaller rivals. The cost of such information screens varies, but $1000 per month is not untypical. Money is Information, but the Information also costs Money.

THE LAPIS PROJECT

Since the late 1970s I have been involved professionally in the development, design, marketing and manufacture of computer equipment and communications and display systems to convey essential information from the world's money markets to the market player's desks and to their broker's dealing rooms.

In the latter phase of that activity I was involved in a long-term technical consultancy job which necessitated my having a comprehensive array of financial information terminals in my workshop here in this building. In 1989 I was made aware that my regular consultancy work was to come to an end, albeit with the prospect of some modest lump-sum payment to allow a transition to some other line of work.

Since the information terminals were in place, I was keen to investigate whether there was any process by which an individual could use the market information available, with a relatively small amount of money, to generate some sort of an income. I advertised and found someone with the necessary trading background and together we set up a feasibility-study.

One of the first areas considered was 'Arbitrage'. That is a process by which several deals are struck almost simultaneously using either real money or 'Fungible' Instruments - that is ones which can be bought in one market and sold in another. The idea would be, say, to buy Eurotunnel shares in Paris with French Francs, sell them in London for Pounds, and convert the proceeds back to Francs coming out with some profit. That is a simple example; in practice dealing chains involving five or six transactions may be more profitable because it is less easy to spot such opportunities, and therefore the transaction window is likely to exist for longer. Computers can be used to search for arbitrage opportunities, with allowances for dealing commissions and foreign exchange conversions built in, but as soon as an opportunity is spotted quick action is necessary because others will see it as well, and the subsequent trading activity will tend to reduce the profitability of the arbitrage to the point where any gains are eaten up in commission. For successful arbitrage you need accounts open with several different brokers, the best commission rates possible, large amounts of capital, excellent communications, and no mess-ups. The conclusion was that Arbitrage is best left to adventurous managers in large institutions who at least have the advantage of being able to play the game with someone else's money.

Our feasibility study next looked at 'Charting' techniques. In the simplest sense Charting involves the construction of a graph, plotting the movements in the price of an Instrument against time. Such graphs, though, are not the well behaved creatures that traditional mathematicians like to work with. They are highly discontinuous in character. The price of the instrument does not glide smoothly from one level to the next - it is quantised into price steps. Activity in the Time Domain is uneven - there may be no activity for half an hour, then a flurry of 20 price movements within a couple of minutes. There may often be significant discontinuities between one days trading and the next, caused by some activity which has taken place in other markets around the world, or some important news event overnight or during a weekend.

As a point of interest, this highlights one of the difficulties in trying to devise any coherent schema for predicting market movements by astrological means. The movements of the planets are continuous, and while there is probably a money market (apart from Foreign Exchange) open somewhere at any time on any day of the year, trading hours are limited to a small part of the day on each individual market, and the Instrument you wish to trade may well not be fungible between them. A notion that metal prices might be predicted by plotting transitory aspects to the corresponding planets (Project Agrippa) was rendered impractical by the trading patterns of the markets concerned.

The discontinuities in an Instrument's price function are incorporated by representing the function as a series of vertical price bars. Within any time period, say a day, the HIGHest and LOWest prices at which the Instrument actually trades are noted, together with, perhaps the opening and closing price for the day, and the number of transactions recorded (or the VOLUME). The graph is then plotted as a series of vertical bars, each representing a day's activity. The OPEN and CLOSE may be added as small horizontal ticks, and the VOLUME plotted separately as a bar at the bottom of the page. This style of charting predates the widespread availability of computers, and has been carried out at least -since the time of the Wall Street Crash of 1929. All that is necessary is a sharp pencil, a rule, some graph paper, and the appropriate figures extracted each day from one of the specialist newspapers - for instance the Financial Times or the Wall Street Journal. Non-specialist papers usually only give the CLOSE figure for the previous trading day.

There are two basic elements to using charts for predicting future movements in the price of an Instrument. These can be distinguished as Pattern Recognition and Cyclic Evaluation.

It is fairly easy to envisage how there might be cyclic elements in the price function of some Instruments. In the case of many commodities the price may follow an agricultural cycle, as anyone shopping in a greengrocers will have noticed. Potatoes are cheapest in the late summer at harvest time when supply is at a maximum, they then get more expensive through the winter, with the price levelling out and then dropping as the new years crop becomes available. Detailed work on long term economic cycles has been carried out, and cycles spanning 56 years (Kondratyev Cycle), 22 years (Sunspot Cycle), 8 years (Moore's Cycle) and a host of other time intervals have been identified (or at least postulated) by authors like the economist Bob Beckman and the astrologer David Williams. Although the appearance of most price functions is Chaotic in nature, it is often possible to discern what appear to be abstract lines of attraction. In a rising market the LOWs for a particular Instrument on successive days may line up, conversely, in a falling market the HIGHs for successive days may line up. These features are known as Trend Lines, and they appear to offer 'Support' in a rising trend and 'Resistance' in a falling trend. Although they are entirely abstract, Trend Lines can continue to be influential over extended time periods. If a price surges ahead taking the function away from an established line of support, it will frequently be seen, when the move runs out of steam, that the price function falls back, but only to the projected level of the old Trend Line. Plotting Trend Lines on a chart is the sort of task which comes quite naturally to anyone who has plotted Ley Lines on a map or visually searched a natal horoscope for aspects between planets.

In terms of Chaos Mathematics, chart Trend Lines can be viewed as attractors, but ones which have an elastic quality, in that the function will be drawn towards the line, and then bounce off it again. If a line is penetrated, it will continue to act as an attractor in the same way, but with the price activity on the other side of the line. Particular horizontal levels on a price chart can behave in the same way, and these attractors are often seen at 'round number' price levels. For example a market index may nudge towards a level at, say, 350 points, perhaps retreating just short of that value. That behaviour might carry on for some days or even weeks; eventually it breaks through the resistance level, but during the next few days or weeks it will fall back towards the 350 level, which now seems to act as a support.

As price functions drift in their quasi-random fashion among the lattice of Trend Lines, certain familiar patterns can be picked out, which seem to be followed by characteristic phases of activity. There are many detailed books on pattern analysis of this nature, the classic work perhaps being "Technical Analysis of Stock Trends" by Edwards & Magee originally published in 1948, though still in print in its 5th edition. Such patterns as 'Head and Shoulders' tops and bottoms, wedges, triangles, diamonds and channels are described, and carefully selected illustrations are given to show how an Instrument ought to behave after one of these patterns has occurred. Needless to say, the patterns are not infallible - the market can do the exact opposite of what it is supposed to and often does, particularly if you happen to be trading it!

A technical analysis method which incorporates both cyclic and pattern recognition elements is known as the Elliot Wave Theory. Though first postulated in the 1930s by an American accountant, Ralph Nelson Elliot, the theory has only quite recently become recognised as an important charting technique. One of the reasons may have been that Elliot embedded his Stock Market theories in much more far reaching and even cosmological treatises, which may well have led hard-nosed business people to think he was a nut-case. The definitive work on his Wave Principle, for example, appears in a book titled "Nature's Law - The Secret of the Universe" published in 1946, two years before his death.

In a nutshell Elliot's Theory says that when a market is rising it does so in a series of rising zig-zag trends, usually five in number, with each individual up and down Trend Line being termed a 'wave'. In a falling market the theory says that the dominant pattern is a three-wave zig-zag. Within these major patterns Elliot recognises features of what we might now call fractal self-replication. Each up-wave in a rising market is itself made up of five smaller (or secondary) zig-zag waves, and each of these waves is comprised of a series of tertiary waves, and so on. The theory says that to know what the market is going to do next, all you have to do is work out where in the cyclic pattern you are and sit back and wait. It is possible to subscribe to newsletters like "The Technical Trader" edited by John Piper for investment advice based on Elliot Wave interpretations across a wide spectrum of financial instruments. The importance of Elliot Wave Theory in the LAPIS project was that, by highlighting the fractal nature of price function charts, it encouraged the application of Chaos Mathematics as an analysis tool.

It was clear from the feasibility study that the secret to generating an income from a relatively small amount of capital was to concentrate on those instruments which moved relatively rapidly within the course of a trading day. Thus the same money could be put to work repeatedly without having it tied up for days or weeks at a time, as might be the case if one were taking a position in the shares of a company or in some Interest Rate related Instrument like Short Sterling. Because of this close attention was paid to the super-active Stock Index Futures such as the near term S & P 500 Future, the Japanese Nikkei and Topix Futures and the less active FTSE Future. Another feature of trading in these Instruments is that business is done "on margin".

If you buy shares in a Stock Exchange listed company you have to pay up the full amount for the shares, but if you buy a Futures Contract you are only required to stump up a small proportion of the full value of that contract; however the profit or loss when you sell the contract is calculated as if it had been made on the full value.

Considering the S & P 500 Future, an account with a broker holding approximately $8000 will allow you to trade a 'Single Lot' contract. The Instrument moves in steps of 0.05 (one twentieth) of an index point. Each time the price moves in your favour by 0.05 that Single Lot increases in value by $25 and conversely each time the price moves against you there is a decrease of $25. Movements of a full index point (i.e. 20 x 0.05) are not uncommon, even in the space of a few minutes, so clearly some technique of predicting accurately when such movements are going to occur can be potentially highly profitable. A full index point of movement correctly traded can earn a gross profit of $500 on a capital outlay of $8000 in a few minutes, with dealing costs of some $25 to $30 to be deducted. Getting it wrong however can be expensive, and if you cannot (for whatever reason) close out a position which has gone against you, then you may wind up losing more than the $8000 you had to start off with - fortunately there are trading tactics which can be employed to minimise the risk of this occurring.

LAPIS, as the acronym suggests, started off as a technique for predicting when an Instrument would experience a sudden price change -up or down - after breaking through an established Trend Line. It was discovered early on that this was most likely to happen when the frequency of price changes was particularly high. To analyse the process in more detail data was recorded on charts in 10 minute slices by manual entry of data into a standard IBM PC based charting package - MetaStock by Equis. MetaStock expects daily data slices, but it was found that it could be fooled into accepting data every 10 minutes without any major difficulty. It was possible to construct Trend Lines and to recognise patterns on 10 minute data charts in just the same way as on those constructed from hourly, daily, weekly, monthly or yearly data.

Cycles such as those described by Elliot became more difficult to discern - the very shortest defined by his theory generally last for a few days or a week. Other short term cyclic behaviour was noticeable though, albeit not so much in the performance of the Futures Instrument itself, but rather in the movement of certain ratios measuring activity on the corresponding Spot Market. This meant that while the predictive focus was on the Futures Instrument (the S & P 500 traded in Chicago), the analysis was being driven by cycle recognition applied to activity on the New York Stock Exchange.

In times of low price movement activity, say up to four moves per minute, directions of movement are reasonably predictable, but there is insufficient amplitude in the cycles to be sure of being able to take a reasonable profit after commission. Above four moves per minute the instrument becomes turbulent in its behaviour, and can swing off rapidly in either direction without prior warning; it is rarely profitable to trade during this phase. At a continuous activity rate above seven moves per minute the turbulence settles out into a cyclic pattern showing upward and downward movements (or Hemi-Cycles) which can be highly predictable both in occurrence and duration; it is during these phases of activity that LAPIS can deliver consistent repeatable results.

In mathematical terms the behaviour is analogous to that of water flowing through a pipe. This is a standard physical situation where the turbulent behaviour is modelled by Chaos Maths, as illustrated succinctly in Ian Stewart's book "Does God Play Dice". When the water pressure is low the pattern of flow through the pipe is laminar. As the pressure increases turbulent unpredictable behaviour sets in. When pressure is increased further beyond a threshold eddy patterns which behave in a predictable way start to appear. In the case of LAPIS modelling the S & P Future, the equivalent of the water pressure parameter is the number of price moves per minute.

LAPIS was operated manually from September 1989 until June 1990. During the first two months paper test results were sufficiently encouraging to lead into a preliminary phase of live trading. The brokers were intrigued by it, and not least by the numbers of BUY and SELL signals it generated. Some anomalies arose because the way in which trading is actually done in real life did not correspond exactly with the way in which the LAPIS operators had been conducting the paper tests - by this time the specialist who participated in the original feasibility study had dropped out after injury in a car wreck. The alarming discovery was also made that during periods of transition, when the current Futures Contract expires and business shifts to the next forward date in the sequence, the normal pattern breaks down. It was also discovered that trading a manual version of the LAPIS system for real is highly stressful on the operator, the experience bearing little resemblance to the relaxed ambience which obtained while it was being paper tested.

The conclusion at the end of 1989 was that the LAPIS system was viable, but that it should be automated to increase reliability and to reduce the stress levels on the operator. A specification for an Auto-LAPIS to be written in 'C' was drafted and should have been developed without further delay. The problem was (and still is) one of securing some sort of steady income during the six months or so that it would take to cut the code, particularly given the fact that it is virtually impossible to publicise a system of this type unless one is registered as a member of one of the Self-Regulatory Bodies set up under the UK Financial Services Act (FSA), and that it is difficult to get such a registration as a private individual with a relatively untried system.

There followed a six month phase during which I was engaged as a consultant by a firm of US based futures brokers on a commission basis to generate trading signals using the manually operated LAPIS. This was unsatisfactory partly because it paid monthly in arrears with a dollar cheque, which sometimes failed to materialise, and partly because it allowed no opportunity to concentrate on developing the automated version. The US futures brokers might have been prepared to finance such a venture, but not on terms which would have been acceptable. Some headway was made in negotiations with a Japanese financial institution whereby an Auto-LAPIS to operate on the Tokyo market would have been written for them, leaving exclusive control of a similar system to operate on the US market in the hands of the originator. These negotiations foundered when it was discovered that the Japanese regulatory authorities would not permit their market data to be fed directly into a computer; it could only be viewed on a dumb screen.

The most consistent manual trading month was May 1990 when, during a week from Thursday 10th to Wednesday 16th, the LAPIS earned $505 per lot after commissions with six positive trades, one break-even, and two going negative by a single .05 step. This was particularly encouraging because it occurred during a period when the market was generally rising, whereas experience has shown that the system usually performs better when the dominant trend is downward.

Up till now LAPIS has been shrouded in a cocoon of commercial confidentiality, partly because the reaction of brokers and market professionals who have seen it in operation has been such as to lead one to think that not only was this 'a pearl of great price' (which might be hi-jacked as so many other good ideas have been in the Financial Information sector), but also because publicising its existence might, in the very action, be considered as a breach of the Financial Services Act_s In the end my view was that the basic methodology should be protected by Copyright, which (according to legal advice) entails publishing something about the system; so what better forum to present LAPIS than Philos-o-Forum. As to the risk of a breach of the FSA, although, as an unregistered person, I am prohibited from attempting to persuade people to sink money into some investment scheme; if the attempt was being made to do that, I would have chosen any other day of the year for the publication date of this paper.

REAL MAGIC(K)

Where LAPIS is concerned the Magic is in the Maths and Information is Money is Information, but regular consumers of my lecture papers may be wondering "In all those long months didn't this sorcerous hooligan attempt even once to manipulate the Market by praeter-natural means, and then trade on any resulting movement?" The answer is "Yes", it was tried on Monday 26th March 1990 in the week before the big Poll Tax demo. The intention was to use the information screen as a conduit for a bolt of Chaos projected into the Chicago Futures Pit, and some Egyptian figurines were placed on top of the information screen and on both of the IBM PCs we were using, facing away so the effect was less likely to be the inducement of Chaos in the LAPIS operators. The Act of Will was carried out and 10 minutes later both of the phones we used for trading were dead, an hour later the information terminal crashed necessitating a service call-out, and the following morning the other phone in the house was cut off (albeit that that was not entirely unexpected). Three weeks elapsed before we were able to trade with the LAPIS again, and the exercise of real magic(k) was not repeated!

THE WAY FORWARD

So what's to become of this remarkable modern recension of the Philosopher's Stone? If Ralph Nelson Elliot's experience is anything to go by, it will sit mouldering for 30 years until, one day, someone spots it while browsing for something else in a museum library. There does tend after all to be some resistance to commercial acceptability for any idea (no matter how sensible) thrown up by an author who also freely publishes material on subjects like "The Secret of the Universe", or one who habitually heads his letters "There can be no ultimate truth" (regardless of the fact that that philosophical axiom can be derived directly from Godel's Theorem (ref 'Liber Cyber')).

Another possible outcome is that some large but irresponsible financial institution gets hold of the idea and uses it to trade huge numbers of lots being motivated by greed. They only discover when it actually happens that trading the system in that way carries the risk of runaway positive feedback, tending to drive the entire Western financial system to meltdown.

Used constructively and with restraint, an automated LAPIS could be applied to a number of instruments besides the S & P 500 Future, and could optimally generate the equivalent of a serious Pools win each week, for capital employed of no more than a few million dollars. Such an income would probably stretch beyond the needs of an individual with simple tastes, and I would venture that any surplus might usefully be applied to bankrolling an Oceanographic Institute devoted to extending the modelling potential of Chaos to the wider environment. At a pinch such a system might even be used to underwrite the budget deficit of a Chaotopian State!