stock, stock market trading, teaching, learning, training, financial industry, trading program, expert systems, trading strategy

Using a computer develops special skills in the same sense as driving a car or learning a new language. The process is more intimidating than it is difficult. New computer applications are much more user-friendly than they were five years ago. Most programs allow you to use a "mouse," provide pop-up help screens, and explain each option on the screen whenever you point the mouse at a special icon symbol. To our relief, it is also harder to destroy a program by hitting the wrong keys. This removes some of the concerns about learning. If you press the Enter instead of the Esc key, the computer may tell you ENTRY INVALID. TRY AGAIN, or just ignore you.

Teaching a computer the rules for a trading strategy is a learning process for both you and the computer. Unlike the human brain, the computer cannot infer a meaning, it must be told precisely. We often think that we are very clear about giving instructions, but the section on "fuzzy logic" will show how many of our expressions are vague. The following section is intended to emphasize how exact you must be in specifying rules to get the computer to give the right answer. If you have never programmed trading rules, it will be well worth your time to follow this process through the next few pages.

Because some important new technologies "teach" the computer how to solve a problem, and strategy-testing programs allow you to define spe cific rules, this chapter will show how human this process can be. An early marvel of engineering skill, the Erector Set, will be used to illus trate the steps ( Box 9-1 ).

The basic Erector Set has flat metal pieces, screws, and bolts. Our sam ple set uses only nine pieces, conveniently designed to fit together, as shown in Figure 9-1, with the pieces numbered for reference. It has 18 sets of bolts and nuts, exactly Vj the number of total corners.

Your task is to build a flat, narrow 4-inch bridge long enough to cover a 33-inch span. You must write the rules for constructing the bridge clearly enough for someone else to follow them exactly. You can start with the five rules given in the first panel of Box 9-1 .

When we apply the same process to finding a sequence of prices that results in a net move of +50 points in the DJIA, some interesting simi larities and differences appear. If we think of each "piece" as a price, we can restate some of the rules:

RULE A. Begin with a partially constructed bridge of length I (the original investment).

RULE C. You must take the prices ("pieces") in the order they come, but you may discard them if they are too small (but only if you have decided in advance, what is "too small").

Discarding a small piece is a threshold criterion that will be used later in this chapter in the section, "Neural Networks." It allows us to decide that a very small price is not relevant for determining a new trading signal.

RULE D. Prices that exceed the threshold are always attached at the same end (of the price series).

RULE F. The length cannot become less than V 2 the original size (max imum loss rule).

RULE G. The bridge must be constructed by a certain time using a fixed number of pieces (return on investment rule).

• Price changes come in more sizes. Some are exceptionally big, and
others are very small and can be ignored. When a very large positive
piece appears, the goal is successfully reached; when a very large
negative piece appears, the game is lost. The frequency of cata
strophic loss is based on the number of occurrences of large negative
pieces, or price shocks. Chapter 7 shows that there is no way to avoid
these events, but there are ways to survive them.

• If too many small pieces are used, the time spent is no longer cost-
effective.

• You cannot reach the goal in the scheduled time if too many pieces
take away from its length.

¦ There may not be a solution within the limits of the rules, time, and
objectives.

Once again: There may not be a solution. Forcing an answer from price patterns and data is not a solution. It may be necessary to look at the problem from an entirely different perspective.

Computers do not think; they simply follow your instructions. Writing the rules requires practice. When an instruction is missing, the answer is wrong, even when the results appear to be good. The only way to know that the computer has calculated everything correctly is to check the results manually for a few different cases. The more complex the trading strategy, the longer it will take to verify.

It is easy to make mistakes when specifying rules and typing formu las. It is not likely that any system has been written that did not require careful computer debugging. The following sections on new technologies will describe a number of interesting approaches to defining rules and making decisions.

The field of artificial intelligence (AI) includes many new technologies for prices forecasting, such as expert systems, neural networks, and fuzzy logic. There is still a lot to learn from the first AI methods, which centered around basic pattern recognition. Think about price changes as direction only:

What comes next? If you were taking a school test, the answer would be up. If you were investing in the market, how much would you risk on the next day being up? Nothing, because the pattern was not repeated enough times, and markets are not expected to perform with such reg ularity.

The existence of a previous pattern that is identical to the current one is not enough to risk an investment. For example, you test 10 years of data and find 74 cases of identical 5-day patterns, either up, up, down, up, up or down, down, up, down, down. If the results are random, then this pattern will be followed by 37 up days and 37 down days. If there are 42 up days and 32 down days, would you consider buying each time this pattern appears? There may be an edge, but a very small one. Or there may not have been enough cases in the 10 years for the random distrib ution to have appeared.

Simple pattern recognition is a difficult tool to use in trading. Its suc cess is entirely an issue of statistics, and must be treated in that light. The following methods of artificial intelligence are much more likely to produce good results.

Applications of artificial intelligence are intended to have computers operate the way humans think. It may not be clear that the process is really desirable, but science considers the unachievable as a challenge, and sometimes pursues it without understanding why. The develop ment of the following concepts began long before everyday technology could support them.

Expert systems have the very sensible goal of duplicating expert advice and decisions. This approach has had remarkable success in medical diagnosis and could be equally applicable to financial issues.

New technology tends to create terminology to express the ideas, and expert systems are no exception. Having the proper words seems to be part of the process:

¦ Teaching the computer refers to the act of entering data and rules into the machine, such as:

¦ Inference means creating new facts from existing ones. Using facts 1
and 2, we get

• Pruning is the sorting through of all the information to find the most
relevant. Because the brain and the machine are filled with data and
rules, it is necessary to select the ones that apply to the current prob
lem. You would not want to answer the question, "Why did the stock
market drop?" with "Because of the earthquake in Armenia ." An
interesting item, but unrelated.

• An expert system is one that deals with a special area, such as medical
diagnosis, oil spills, or stock market forecasting. By listing all the
facts and rules in the specialized domain, the system is expected to
substitute for the benefits of a team of experts.

To create an expert system to make stock market decisions, first write the relationships that are facts, in any order. For example, Table 9-1 gives a set of 10 rules.

The definitions and rules in Table 9-1 combine to form a knowledge base. For convenience, the shortened names referring to data are explained in the list of variable names. Using a process called forward chaining, start with an important piece of information and follow one rule to another until you find your answer. For example, The Wall Street Journal front page reads:

and you want to know how the stock market should react. Rule 1 states that, IF interest FALLS, THEN stocks RISE. Therefore, expect the stock market to rally. If the Journal had said:

Then Rule 2 gives IF dollar FALLS, THEN interest RISE. That is chained to Rule 1, which states, IF interest RISE, THEN stocks FALL.

IF THEN	interest stocks	FALL RISE	IF THEN	interest stocks	RISE FALL
IF THEN	U.S. dollar interest	FALL RISE	IF THEN	U.S. doUar interest	RISE FALL
IF THEN	inflation interest	RISE RISE	IF THEN	inflation interest	FALL FALL
IF THEN	GNP interest	FALL FALL	IF THEN	GNP interest	RISE RISE
IF THEN	Ger Bund rate interest	FALL FALL	IF THEN	Ger Bund rate interest	RISE RISE
IF THEN	p/cap spend inventories	RISE FALL	IF THEN	p/cap spend inventories	FALL RISE
IF THEN	unemployment p/cap spend	FALL ¦ RISE	IF THEN	unemployment p/cap spend	RISE FALL
IF THEN	inventories production	FALL RISE	IF THEN	inventories production	RISE FALL
IF THEN	production GNP	RISE RISE	IF THEN	production GNP	FALL FALL

IF unemployment RISES, THEN p/cap spend FALLS, IF p/cap spend FALLS, THEN inventories RISE, IF inventories RISE, THEN production FALLS, IF production FALLS, THEN GNP FALLS, IF GNP FALLS, THEN interest FALLS, IF interest FALLS, THEN stocks RISE.

By chaining one rule to another, the computer should reach the same conclusion as an expert. The only problem is that this answer does not make sense. In this case, although all the rules are perfectly correct, the conclusion unemployment rises, therefore the stock market rises is wrong.

To be fair, it is not technically wrong. What is missing is the time delay. Unemployment will cause interest rates to be lowered, which will move the stock market higher. But not on the same day. First, the market will drop on the news. Each sequence, represented by a rule, must be assigned a reaction time or completion criterion. Rule 7b should really read:

Once the knowledge base has been established, many different ques tions can be asked: "What is the effect on the stock market when the Fed wants to increase the money supply? What is the effect of an increase in unemployment on the U.S. dollar?"

The reverse of many items in the knowledge base, but not all, may also be used: "IF interest rates DO NOT FALL and the GNP IS NOT POSITIVE, THEN the stock market WILL NOT RISE."

As easy as it is to show sequences stemming from single events, it is not realistic. Two or more significant factors are usually present and often conflict with one another. Which is more important, if any? The follow ing rules can be added to help determine which government statistic is most important:

W2. IF cumulative difference of last 3 statistics minus expectations IS MOST EXTREME THEN most important.

But it is still not complete. Two or more events may be extreme in dif ferent ways. They may be cumulative or offsetting in their effect on the stock market. Rules must be written to resolve these factors. This conflict resolution can be the weak point of expert systems.

When it is all in the computer and an answer pops out, how do you know it is correct? Because the process is logical, the individual steps can be traced to prove the answer. But the example of "UNEMPLOYMENT RISES" gave the right answer but not the right time. In the end, the final decision is yours. The answer must seem right, and satisfy the test of reasonableness.

Although the idea and words for a computerized neural network come from the biological ideal of the human brain, an artificial neural network is not a model of a brain, nor does it "learn" in the human sense. It is simply very good at finding patterns. In fact, it can be so good that it "overfits" the data, finding patterns that exist only by chance. In that way, nearly all methods for finding the "best" performing systems share the same problems, whether very simple or complex techniques. A wide selection of neural network software is available for the per sonal computer. Many of these can be found through trade magazines such as Technical Analysis of Stocks & Commodities and Futures.

The brain is composed of cells called neurons, which process and store information. They are unique in the human system because they do not die, which is why we are able to remember. Neurons function in groups called networks, which have thousands of interconnected neurons, and those networks are connected to other neural networks.

Information is received through dendrites and goes directly into a neu ron. The data can be passed to other neurons through an output con nector called an axon. As the information passes from one neuron to another neuron or neural network, it may pass through a synapse, which can inhibit or enhance the importance of the data going in different directions. A synapse may also be considered a "selector." Figure 9-4 shows a biological neural network and its components.

amounts of data, store it away, and make you aware of only the most important items. This sophisticated selection process can vary for each individual and situation. For example, you may no longer hear the tick ing of a clock in your bedroom but are instantly aware of the smallest unusual sound coming from a child's room. We actually hear the clock, but the sound becomes routine and our neural networks do not alert us to action. When the clock stops, an efficient human system will notice.

Using the same structure as the biological neural network in Figure 9-4, we can show how economic and price information passes through a computerized, artificial, neural network (ANN) to produce a decision on the direction of stock prices.

The first step is shown in Figure 9-5. The system receives a wide assortment of input data, as does the human system. It must select which of these are relevant in finding the answer and assign weighting factors to represent their value. Because "Domestic Health" influences interest rates and subsequently stock prices, we select how each of the five inputs will be used. Two are discarded as irrelevant by giving a weighting factor of zero to their importance; however, all items remain stored in "neurons" for later use.

Unemployment, GDP, and inventories are all considered to con tribute to Domestic Health. The value placed on their importance will be decided by the computer neural net program. We can expect the weighting factors for GDP and inventories to be positive, because rising GDP and inventories indicate strong economic activity. Inventories are not as clear and get a smaller value. Unemployment gets a negative fac tor. When unemployment rises, domestic health declines.

Domestic health is only one element needed to forecast stock market prices. Current and anticipated interest rates may be the greatest factor. But interest rates are used to achieve an economic growth target, which may be measured by domestic health. Therefore, each feeds on the other. To make matters more complicated, world political events cause money to move to safety. If Eastern Europeans are buying the U.S. dol lar regardless of current interest rates, then rates can go lower. On the other hand, if the United States needs to attract foreign investors to sup port its debt, then U.S. interest rates must rise to attract buyers, regard less of domestic health.

Each neuron in Level 2 and 3 depends on the weighting factors of each of the neurons that feed it. Unlike the expert system, it is not told the effect

Figure 9-6. Learning by feedback. A neural network program uses the known answers as feedback to find the weighting factors that work.

of each piece of input data, but determines its use by comparing historic examples. For example, the value assigned to domestic health in Figure 9-6 is the result of many inputs, each with unique weighting factors.

The ANN arrives at an answer through a computer-intensive process of pattern recognition. The most popular method is called a genetic algorithm, because random selection in determining the importance of each input causes one solution to be better than another. This "mutation" is used in the same way that natural selection would allow a better species to survive.

The neural network uses the genetic algorithm to "learn" how to arrive at the best answer in a feedback process called training. This method compares the random use of input data and indicators with a known answer until it finds the combination that comes closest to being correct. Figure 9-6 shows the "feedback loop" that mutates weighting factors, using random numbers, until the answers match a large sample of historic situations.

Because this is a trial-and-error process, rather than an analytic approach, the best results could be caused by a coincidental occurrence of data, rather than cause and effect. Keep in mind the famous warning, Post hoc ergo prompter hoc (literally, "After this, therefore because of this"), which refers to the error in thinking which assumes that because one event followed another, the second event was caused by the first.

• Each input is given an adjusted value, from +100 to —100, indicating
whether the current state is strong or weak, high or low, or neutral.

• Buy signals are given when the total value is above 120; sell signals
occur when the value is below —120.

The initial test has only two training cases, that is, the computer is given two sets of input data and the correct answers. History tells us that, when evaluated correctly, Case 1 will give a strong signal and Case 2 a weak signal. To begin, the weighting factors are all set to 1.0. As seen in Table 9-2(a), both Case 1 and Case 2 produce neutral results, which are wrong.

Through the process of random assignment of weighting factors (which was chosen as the "genetic algorithm"), the network "mutates" the pat tern. When the ANN arrives at a wrong answer, by comparing it against the historic facts, an error signal is produced and the neural net is told to try again. This is the feedback process. The system then changes the weighting factors until it stumbles on the reverse sign for interest rate and unemployment values (minus instead of plus). The neural net had started by assuming that "low" meant negative and "high" meant posi tive. But the effect of low or high interest rates is the reverse in the stock market. By changing the weighting factor to —1.0, a correct answer is generated in Table 9-2(b).

Because there were only two cases, many combinations of weighting factors would have given the correct answers. For example, interest rates could have been assigned a factor of -5.0 while all other inputs were given a value of zero. These ambiguities are quickly removed when the number of training cases increases.

(a) First Test with Unit Weights
		Casel				Case 2
Input	Relative	Value	Wgt	Net	Relative	Value	Wgt	Net
GNP	Strong	50	1.0	50	Weak	-60	1.0	-60
Unemployment	Low	-25	1.0	-25	High	40	1.0	40
Inventories	Low	-50	1.0	-50	Neutral	15	1.0	15
U.S. dollar	VryStrg	75	1.0	75	Neutral	0	1.0	0
Interest rates	Falling	-25	1.0	-25	Rising	45	1.0	45
Total of all test values				75				40
Buy/sell threshold levels				±125				±125
Computer training answer			Neutral				Neutral
Actual answer should be				Strong				Weak
(b) Training Cases with Mutated Weighting Factors
		Casel				Case 2
Input	Relative	Value	Wgt	Net	Relative	Value	Wgt	Net
GNP	Strong	50	1.0	50	Weak	-60	1.0	-60
Unemployment	Low	-25	-1.0	25	High	40	-1.0	-40
Inventories	Low	-50	1.0	-50	Neutral	15	1.0	15
U.S. dollar	VryStrg	75	1.0	75	Neutral	0	1.0	0
Interest rates	Falling	-25	-1.0	25	Rising	45	-1.0	-45
Total of all values				125				-130
Buy/sell threshold levels				±125				±125
Computer training answer			Up signal			Down signal
Actual answer should be				Strong				Weak

Relative values assigned in a range from -100 to 100. WGT is the weighting factor, set to 1.0 to start. Actual is the response you want to get, or the actual price change over the next 10 days.

Training the neural network can be a very long process. Allowing the computer to assign weighting factors to countless data items, and con tinually comparing the answers with the correct one, can take longer than we are prepared to wait. To control the process, it is necessary to put limits on the training and help it along.

Preprocessing. Rather than giving the system all the data possible, select the most significant information. Rather than using automobile and department store sales separately, use a single retail sales figure. Eliminate similar items; each piece of information will continue to be analyzed by the computer over and over again without distinguishing whether two items are the same. Combine some items into indicators and eliminate the less important elements as redundant. If an index is more complicated than a simple weighting of its elements, then the neural network will not include it properly. Include a trend of prices; the ANN cannot create one itself.

Break the Problem into Clear Steps. Solving the problem in a single step may be overly complicated. More important, it becomes very difficult to validate the results. For example, separate forecasts into components. Before looking at the expected move in the stock market, forecast interest rates one week out, or forecast a cut or rise in the prime rate. If the stock market direction is dependent on interest rates, verifying the decision process for rate changes should be a necessary step.

Choose the Number of Decision Levels. Two or more inputs are given weights and may be combined into a single item in a new decision level. If all the inputs can be taken two at a time, combined, and then used with the combination of two other inputs, the computer creates an exces sive number of "hidden layers." More hidden layers allow more combi nations and increase processing time. They allow the solution to be more specific and require much more data to offset possible overfitting. A four- layer system will also take much longer to process than a three-layer one, therefore the three-layer is highly recommended.

Choosing the Smallest Number of Neurons. Although limiting the number of "hidden" layers will make the solution faster and more gener al, the number of neurons that hold intermediate results also can be spec ified. Just as fewer layers create a more general and faster solution, a small number of neurons in each layer has the same effect. Fewer neurons mean a more general solution.

Trade-Offs. As with conventional optimization, neural networks can produce a result that is overfit. Too much data, much of it irrelevant, and too many hidden layers and neurons allow the computer to find spurious patterns. Too few data items, levels, and neurons may make the result so general that it is useless. The analyst must find the proper compromise.

The neural network responds to combinations of events in the manner in which it was "taught." A drop in interest rates without the associated poor economic news (e.g., a flight to the safety of the U.S. dollar) results in a signal to buy equities. The neural network learns that this situation is still good for stocks. But one day, interest rates drop sharply when investors move their money fearing a plunge in stock prices. You are a buyer of stocks because the move to lower interest rates satisfies the rules. The trade is a large loss as more stock is liquidated. The neur al network adds a rule to bypass trades that begin under high volatility conditions.

The system continues to learn. There is no way to know how many dif ferent situations will be added to the list of conditions that build a complete network. A synthetic neural network is a technical achievement of large proportions. It can find patterns that cannot be identified by conventional methods (such as multiple regression used in econometrics). It can train itself to determine the importance of each input. But there are many problems it cannot resolve. It will recognize only those inputs that it expects and may not respond properly to combinations of inputs that it has not "seen" before. If there are too many inputs, the network may respond correctly, but to the wrong events. It is the best so far, but it does not guarantee the results within the limits of your investment.

Fuzzy logic is not a brand name, or a description of scatterbrain thinking; it is a formal area of mathematics. Along with neural nets, fuzzy logic pushes the bounds of science. The idea of "fuzziness" describes the lack of precision in normal human conversation and thought. The concept will allow human uncertainty to be introduced to artificial intelligence methods. Think about most casual conversations:

Although these conversations do not include specific numbers, we accept and understand what the other person is saying. In fuzzy logic, all is not true or false, 0 or 1, there or not there. It will answer questions such as "If a half-eaten apple is still an apple, how much do you have to eat before it stops being an apple?"

The fuzziness concept includes fuzzy numbers, such as "small," "about 8," "close to 5," and "much larger than 10," as well as fuzzy quantifiers, such as "almost," "several," and "most." The phrase "Surprise government reports cause big moves" is a common fuzzy expression.

"Fuzzy events" and "fuzzy statistics" are combined into fuzzy reasoning. Surprisingly, answers to the following examples are remarkably clear to a brain, but not to a machine:

Example 3: It is not quite true that the quarterly earnings were very bad. It is not true that quarterly earnings were good. How bad were the quarterly earnings?*

Fuzziness is not intended to describe the same concepts that can be explained precisely by probability (referred to a crisp logic.) Because fuzzy logic and possibility theory are new, mathematicians believe that practical applications will use both (fuzzy) possibilities and (crisp) probabilities. Up to now, the fuzzy part has been assigned ranges to represent commonly used values. For example, in expressing the S&P price change, we might have the following:

Fuzzy logic may bring a better solution than other methods that are now being used to develop trading models. By its very nature, a fuzzy solution must be general. Writing fuzzy rules for a trading program will not have to be as precise as traditional specifications. That also means there should be fewer rules and a more robust solution. No matter how hard we try, it may be impossible to overfit the solution using fuzzy data.

Fuzzy systems have been combined with neural networks and expert systems, which provide a framework for "learning." Neural nets pro vide the behavioral structure so that correct answers are reinforced and incorrect ones are rejected. Expert systems give the program a knowl edge base.

Japanese firms have led the financial industry in the application of fuzzy expert systems. It is said that programs already exist for financial dealing, especially stock market trading. These models have been based entirely on price information, but may soon include expectations, or "feelings," about political outcome. It seems that, once the idea is plant ed, the technology moves forward at a furious pace.