IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS, VOL. SMC-5, NO. 6, NOVEMBER 1975

Learning Pattern Recognition TechniquesApplied to Stock Market Forecasting

JERRY FELSEN, MEMBER, IEEE

Abstract-Most of investment analysis involves decision making byweighing evidence. Such decision processes can be formalized with theaid of pattern recognition (PR) techniques. Specifically, we have appliedgeneralized perceptron-type PR techniques to both general marketforecasting and investment selection. And after the investment decisionsystem has been implemented and put into operation, its performanceis then gradually improved through learning from previous decisionmaking experiences. Iterative probabilistic learning algorithms (basedon stochastic approximation techniques) have been used. Decision modelsfor both investment selection and market forecasting have been realizedand tested in actual investment analysis. The experimental resultsindicate that with the aid of PR techniques we may obtain above averageinvestment performance.

I. INTRODUCTION

INVESTMENT decision making is a complex judg-mental decision process. It involves primarily decision

making by weighing evidence obtained from variousmeasurements or observations of the market and its en-vironment. For example, investment selection (securityanalysis) decisions are synthesized from observations ofearnings, dividends, earnings trends, and price earningsratios, from technical analysis, through measurements ofthe underlying psychological factors, etc. Similarly, stockmarket (SM) forecasts (investment timing decisions) aremade by weighing evidence obtained through an analysisof the market's (monetary, political, and economical)fundamentals, technical factors, psychological measure-ments, observations of the news background, and so on.We observe that if investment decisions are to be success-

ful, they must necessarily be based on a large amount ofinformation. (This follows from a basic cybernetic principlecalled the law of requisite variety [1], [2], [4].) However,when making decisions by weighing evidence and thenumber of decision parameters becomes large (e.g., exceedsfour), the quality of human made decisions rapidly deteri-orates [8]. Thus investment performance can be improvedby at least partial automation or programming of theinvestment decision process.

These decision processes can be programmed or modeledwith the aid of pattern recognition (PR) techniques: theinvestment decision situation is first numerically encodedin form of a state vector x. Through a feature space trans-formation the state vector is converted into a feature vector

Manuscript received August 20, 1974; revised April 30, 1975.This paper is based on a part of a dissertation submitted to theUniversity of Pennsylvania, Philadelphia, in partial fulfillment of therequirements for the Ph.D. degree.The author was with the Department of Computer Science, Univer-

sity of Southwestern Louisiana, Lafayette, La. 70501. He is now withthe Department of Mathematics and Computer Science, St. John'sUniversity, Jamaica, N.Y. 11439.

0(x), representing a numerical encoding of the relevanteconomic factors, the investment news background,psychological features, and various other market factors.Through generalized perceptron-type PR schemes thisinformation is then synthesized into investment decisions;and performance of the decision system is graduallyimproved through machine learning algorithms. We applycertain probabilistic iterative learning schemes that arederived from stochastic approximation methods [15].We often use concepts and tools borrowed from various

cybernetic disciplines. Therefore we sometimes use theterm cybernetic investment decision systems (CIDS) todenote fully automated or man-machine systems for in-vestment analysis that were designed with the aid of thepreceding methods, and we may refer to our generalmethodology as the cybernetic approach to investmentanalysis.The machine learning algorithms are primarily responsible

for the superior performance of the CIDS. They enable usto 1) reduce uncertainty in the investment decision process,2) gradually optimize performance of the CIDS underdirection of error-correcting feedback (derived from theanalysis of past investment decisions) after the system wasimplemented and put into operation, 3) design a "good"CIDS without a thorough initial understanding of thesituation, and 4) keep performance of the CIDS optimalat all times despite nonstationarities and changes in themarket and its environment.We have developed a learning model for both general

market forecasting as well as security analysis of individualissues. We also realized a simplified CIDS and tested it inactual investment analysis. The experimental results areencouraging. They indic.. Ie that by formalizing the essentialinvestment information processing tasks, we may be ableto derive superior investment decisions.

Before presenting the technical and mathematical details,let us briefly summarize the current state of the art ininvestment analysis and explain the difficulties faced by thehuman analyst. By doing so, we will expose the reasonswhy with the aid of PR techniques investment performancecan be improved.

II. PRESENT STATE OF THE ARTA survey of the huge volume of contemporary practical

and theoretical literature on investment analysis yields thefollowing three observations: 1) there is a great variety ofviewpoints and approaches to investment analysis, 2) thesituation is generally poorly understood, and 3) sharpdifferences of opinion exist in the financial world as to whichapproach to investment analysis is best [4].

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Before analyzing their strengths and weaknesses, let us

first briefly outline the major investment methods in the

order of frequency they are used.

A. Summary of Conventional Approaches to

Investment Analysis

The number of existing practical investment techniques

is huge, but most conventional methods and viewpoints

can be grouped into five major classes.'1) The fundamental approach is by far the most popular

investment method. It is used primarily for selection of

securities. It relies upon the evaluation of economic andfinancial statistics in an effort to determine the "intrinsicvalue" of a corporate security. (Basically, the intrinsic

value is determined by economic facts. It is usually com-

puted as a product of per share earnings of the company

and a "suitable" multiplier called price earnings ratio.)Decision rules for buying and selling individual securitiesresult from comparison of current prices with the expectedintrinsic value.

2) Technical analysis is used primarily for investmenttiming. It focuses its attention on the market itself ratherthan the companies or the economy. Its object is forecastingof market trends and security prices rather than search forintrinsic values. Investment decisions are then made throughanalysis of data created by transactions on the stock ex-

change-mainly price (and volume) measurements. Inessence, technical analysis attempts to predict future pricemovements through the study of past price (and volume)measurements.

3) Psychological techniques reflect the importance ofhuman emotions and herd instincts in the stock market.It is well known that market psychology is an important-if not the most important-cause of the dramatic rise andfall of stock prices. Thus the stock market behavior cannotbe fully understood without some psychological knowledge[7, p. 22]. The best known psychological approaches are

the principle of contrary opinion, odd-lot theory, anddivergence analysis. The principle of contrary opinion isbased on the well-known fact that at important marketturning points the majority of investors usually incorrectlyestimate the market's future direction. So the contraryinvestor attempts to ascertain the prevailing opinion aboutthe market's future, and if it is overwhelmingly polarizedin one direction, he takes the opposite viewpoint. The othertwo techniques are based on an analysis of various psycho-logical indicators including measurements of odd-lotvolume, ratio of odd-lot to round-lot volume, etc. A studyof these indicators shows that at major market turningpoints their values may sharply deviate from "normal."Corresponding investment decisions are then made when

these psychological indicators sharply diverge from their

standard ranges.

1 See the 1971 Encyclopedia of Stock Market Techniques (InvestorsIntelligence, Larchmont, N.Y. 1963, 1971) for a survey of techniquesin the first five groups. For a summary of the efficient market theorysee the works of Fama [3], Jensen [9], and Vasicek and McQuown [16].

4) The creation of a great variety of specialized invest-ment techniques2 is a consequence of the extreme complexityof the stock market, the poor understanding of it, and theresulting large number of possible approaches to its analysis.Many, perhaps most of them, are of little usefulness, butsome of them can be justified by plausible arguments orvalidated experimentally. We outline only those selectthree techniques that will be mentioned later on. First, therelative strength concept in common stock selection con-tends that securities that historically have evidenced astronger price trend than the general market index willcontinue to show superior performance over some futuretime period. Secondly, the Elliott wave theory (used forgeneral market timing) draws on an analogy between thestock market and the ocean. It asserts that the generalmarket fluctuates in consistent and distinguishable wavepatterns. Finally, the general indicator approach attemptsto synthesize investment timing decisions through theanalysis ofa broad spectrum of measurements characterizingthe state of the market. They may include fundamental,technical, psychological, political, monetary, economic, andother indicators. Most of the important factors affectingthe stock market may be captured in these measures. Ifformalized and programmed, this approach may yield goodresults.

5) The efficient market theory contends that at any timeall publicly available information is already discountedinto the current market price. In other words, the currentprice always "fully reflects" the present state of knowledgein the sense that no investor can expect to obtain informationnot already discounted into the market price by actions ofother investors. The inevitable conclusion of this hypothesiswould be that neither the fundamental approach, nor

technical analysis, nor any other method that uses publicinformation can yield any consistently profitable results.In brief, according to this viewpoint, consistently out-

performing the market averages using only public informa-tion is impossible.

B. Limitations of Conventional Methods

Almost all practical investment techniques-when usedindependently of each other-suffer from several majordeficiencies that greatly limit their usefulness. For example,the fundamental approach is inaccurate, is useless for timing,and completely disregards the very important psychologicalfactors in the market. The purely technical analyst is not

aware of the "big picture" of the market: he disregardsthe important long-term relationships between the stockmarket and its economic environment. Similarly, as we willsee later, the efficient market model is an oversimplifiedand inaccurate representation of reality. However, the

2 There is some ambiguity in terminology. Usually the term "tech-nical approach" refers only to investment techniques based on an

analysis of stock price charts and possibly including also volumemeasurements. Some writers, however, use this term also for manyother stock market techniques, including those listed in this paragraph.To prevent ambiguities, we use the term "technical approach" only inthe above narrow sense and we use a different term to denote themore specialized "technical" investment techniques.

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most serious deficiency of almost all practical investmenttechniques is their low variety-they use only a very smallpart of the complex information spectrum characterizingthe state of the market. They are essentially information-destroying and variety-compressing procedures. (One ex-ception is the general indicator approach.) It can be shown[4] that decision systems with such properties are unsoundand cannot successfully cope with the complexities of thereal world.

Fortunately, fundamental, technical, and psychologicalmethods complement each other. Thus an integratedsystems approach that simultaneously includes all thesemethods would have the advantages and strong points of allmajor stock market techniques and, hopefully, wouldnot have the deficiencies and weaknesses of the individualmethods. However, then the system for investment analysisbecomes so complex that the human mind cannot copewith such complexity. Thus the various aspects of stockmarket analysis must be formalized and mechanized beforethey can be incorporated into an integrated decision system-and the design of such sophisticated investment decisionsystems can be accomplished with the aid of cyberneticconcepts and artificial intelligence techniques.

III. WHY SUPERIOR INVESTMENT PERFORMANCEIs So DIFFICULT

Studies of performance records of professional investorsindicate that most professionals are unable to outperformthe market averages. For example, the performance of mostmutual funds is not better than could be achieved by arandom selection of issues [6]. Let us now examine thereasons why consistent stock market success is so difficult.

There are at least six major reasons why it is so hard tooutperform the market. We shall group them into twoclasses: objective and subjective.

1) Objective Factors: They are "objective" in the sensethat they are beyond control of the human decision maker.There are three of them. a) Extreme competition in themarket place and its resulting high efficiency. In otherwords, since the relevant information rapidly spreadsthrough the market place, it quickly becomes publicproperty, and consequently present market prices usuallyalready reflect much of available public information.b) Inherent probabilism and uncertainty in the stock market.Stock prices are influenced by many economical, monetary,political, technical, and psychological factors. Many ofthem are unpredictable and change in a random fashion.Problems are further complicated by the fact that themarket and its environment is a nonstationary system. Inother words, some of its attributes and characteristicsunpredictably change in time. c) Psychological factors:Changes in investor sentiment are one of the chief causes

explaining the frequent lack of correlation between changesin the relevant economic factors and fluctuations in stockprices. The simple truth is that a company and its stockare not the same thing. A company has "intrinsic value."It earns profits and pays dividends; it owns plants andequipment; it has an investment in buildings, machines,

raw-materials, etc. One can form an idea about the worthof a company by evaluating these components and addingthem together. On the other hand, the correspondingcommon stock certificate is only a piece of paper: thevalue of a share is only what someone else will pay for itwhen it is offered for sale. This value depends mainly onsubjective expectations which, in turn, depend on numerouspsychological factors that change randomly over time.These psychological factors make it extremely difficult toapply the intrinsic value concept to security analysis.

2) Subjective Factors: They are "subjective" in the sensethat they can be at least partially alleviated by the humananalyst. There are also three of them. a) Human information-processing limitations in decision making. Experiments haveshown that people are incapable of making effectivedecisions when they have more than a limited amount ofinformation to work with [8]. Thus a fundamental problemof the investment analyst is not getting the relevant in-formation but evaluating it and synthesizing it into a"good" investment decision. b) High complexity: The stockmarket and its environment is an extremely complexmechanism-stock prices are influenced by very manydifferent factors-and the human mind cannot cope withsuch complexity. Consequently, the process that generatesstock price changes is poorly understood. Although thereis a definite correlation between certain complex informationpatterns characterizing the present state of the stockmarket and corresponding future changes in trends of stockprices, the nature of this relationship is frequently notunderstood by most traders, at least not at the time whenthey could profit from it. c) Human psychological handicaps:Most investment practitioners agree that human nature isone of the greatest enemies to stock market success [18].Typically human traits like vanity, fear, hope, impatience,greed, etc. greatly reduce the effectiveness of investmentdecisions.

All the preceding factors contribute to impair investmentperformance, and there is nothing that can be done aboutthe objective factors since they are beyond control of theinvestor. However, investment performance can be improvedthrough reducing the difficulties caused by the subjectivefactors. Thus with the cybernetic approach we can faceproblems caused by the subjective factors on three fronts.First, through formalizing and ultimately mechanizing theinvestment decision process, human psychological handicapscan be eliminated. Secondly, by using efficient PR tech-niques to synthesize very complex information patternsinto optimal investment decisions, we can overcome humaninformation-processing limitations. Finally, by designing alearning mechanism into the cybernetic investment decisionsystem, we can at least partially alleviate problems causedby poor understanding of the decision situation and theelement of uncertainty. In this way PR techniques can beused to amplify the intellect of some human investmentanalysts to a level where they may be able to outperformthe averages.The design principles for the synthesis of such CIDS is

our next consideration.

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INVESTMENT

INVESTMENTTIMING

(A) (B)General Individualmarket securitytiming transaction

timing

ANALYSIS

INVESTMENTSELECTION

(C)Securityanalysis

(D)Efficientdiversificationof investmentportfolio

Fig. 1. Hierarchical structure of investment decision process.

IV. MATHEMATICAL APPARATUSThe investment decision problem is far too complex and

cannot be handled by any simple problem-solving procedure.Therefore we use the hierarchical approach to problemsolving. The spirit of this approach is to divide and conquer-break up a complex problem into simpler subproblemsthat are within the reach of our capabilities, developsolutions (or problem-solving systems) for these sub-problems, integrate them into a viable system, and thuscome out with a solution to the original problem.

Accordingly, our CIDS is hierarchically structured. Wefactor the global investment decision problem into two majorsubproblems-investment timing and selection. The timingproblem is further factored into two local subproblems:(A) general market timing, and (B) individual stock transac-tion timing. Similarly, the selection problem is also factoredinto two local subproblems: (C) security analysis, and (D)efficient portfolio diversification. This hierarchical structureof the investment decision process is diagrammed on Fig. 1.

Subproblems (A), (B), and (C) involve decision makingby weighing evidence. For example, general market timingdecisions (i.e., stock market forecasts) are made by weighingevidence obtained through and analysis of the market's(monetary, political, and economical) fundamentals, tech-nical factors, psychological measurements, observations ofthe news background, and so on. Similarly, investmentselection (security analysis) decisions are synthesized fromobservations of earnings, dividends, earnings trends, andprice earnings ratios, from technical analysis, throughmeasurements of the underlying psychological factors, etc.Thus subproblems (A), (B), and (C) can be programmedwith the aid of PR techniques. Subproblem (D) can behandled by mathematical (quadratic) programming methodsand therefore will not be considered any further.To each local subproblem (A), (B), or (C) corresponds a

separate decision subsystem of the CIDS. And each sub-system is again hierarchically organized. It is designed inform of a functional three-layer hierarchy so that higherlayers determine or adjust some parameters on the lowerlevels.3 That is, the system can be functionally decomposed

I For a more thorough discussion of such problems, see the book ofMesarovic, et al. [101.

Fig. 2. Functional multilayer hierarchy of investment decision system.

into three layers: 1) a layer of programmed decisionprocesses, 2) a learning layer, and 3) a layer of non-programmed decision procestes (global planning layer).This functional hierarchy erqerges naturally in referenceto three essential aspects of tl4e investment decision process:1) the search for a preferable or acceptable course of actionunder known, prespecified conditions, 2) the reduction ofuncertainties and improvement of performance, and 3) theselection of strategies to be used in investment management.The flow of information and control between these threefunctional parts of the CIDS is displayed on Fig. 2.Each level of the decision system performs a different

function. The first layer represents all those aspects of theinvestment decision process that can be automated, i.e.,it denotes formal (mechanical) "systems" for securityanalysis and market timing. The function of the secondlayer is to increase the knowledge about the system and itsstock market environment through a learning process withthe aim of improving performance of the decision systemafter it was implemented and put into operation. Thefunctions of this layer can either be automated or realizedby the human operator. The third layer represents all thoseactivities related to investment analysis that cannot bereadily formalized and mechanized on the lower layers.This includes 1) designing and subsequently modifying(if necessary) lower layers of the decision system, and 2)performing those tasks of the investment decision-makingprocess that have not been automated on the lower layers.Of course, the third layer functions are performed by man.

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Fig. 3. Anatomy of learning decision process.

A. General Approach to ProgrammingInvestment Decisions

We will develop the CIDS within the conceptual frame-work of a general model for automation of decision makingand problem solving [5]. This model factors the decisionprocess into four phases. 1) The identification activityconsists of searching the environment and numericallyencoding information for investment analysis. 2) Then inthe design phase alternative solutions to the investmentdecision problem are developed. 3) The best among thealternative solutions is then selected and implemented inthe choice phase. 4) Through a subsequent evaluation ofthe implemented solution learning feedback is generated.Hence the anatomy of this decision process can be dia-grammed by the four-stage information feedback systemon Fig. 3.

In the following subsections we now outline an applica-tion of learning PR techniques to programming the in-dividual phases of the investment decision process.

Identification Activity: The decision situation is numeric-ally encoded by the state vector x = (x1, *,x,). We definethe state of a system and its environment at any time as theinformation needed to determine the behavior of the systemfrom that time on. Hence the state variables xi, i = 1, - *,r,represent observables or measurements characterizing thevarious features (properties or attributes) of the investmentdecision situation that have some predictive significance.

Since the amount of computation needed to process aninformation pattern grows approximately exponentiallywith its size, through a mathematical feature space trans-formation (FST) the state vector x is transformed into afeature vector +(x) = ( 1(x),- ,qp,(x)). This FST greatly

reduces the size of x but without reducing too much itsinformation content. That is, the FST performs aggregation,filtering, and condensation of investment information,so as to emphasize those aspects of the situation that aredeemed important.4 In short, 0(x) is a numerical encodingof the information for investment analysis and is the inputfor the second phase of the decision process.

Design and Choice of Optimal Investment Policy: Decisionmaking is the process of converting information into action,i.e., it is a mapping from the state (or feature) space ontoa policy space. When programming decision making byweighing evidence, we can realize this mapping by per-ceptron-type PR techniques.5

Let the investment policy space be A = {aj}, where ai,i-=1s2f39- are the alternative investment policies, e.g.,buy, sell, hold, sell short, etc. Let us define linear dis-criminant functions

s

gi(X) = Wi +(X) = E Wik (Pk(X)k= 1

(1)

where Wi = (wi1, ,wjs) is the weight vector.6 Then thechoice mechanism (i.e., the mapping from investmentinformation into a course of action) can be implementedby a set of discriminant functions. Thus we associate aunique discriminant function with every investment policyai (except if the policy space has only two courses of action-then one discriminant suffices). This is expressed inmathematical terms by

a, gi(X).Then for any investment decision situation the systemselects that policy a, for which the corresponding gi(x) ishighest, i.e.,

gi(x) > max gj(x).i*j

(2)

In this way a unique investment policy is associated withevery pattern of information x.

If the policy space contains only two courses of action,we need only one discriminant g(x). Then a1 is selected ifg(x) > 0, and a2 is chosen otherwise.

Learning Mechanism: The purpose of the learning processis to gradually adjust certain system parameters so as tooptimize the decision system's performance. The learningprocess is directed by information feedback derived throughan evaluation of past investment decisions. The performancecriterion is always some measure of the expected returnand risk. It can be chosen in several ways. For our presentpurpose, we use the probability of error as the performanceindex. By "error" we mean that a wrong investment (timingor selection)- decision has been made, e.g., the expected

' See other works of this author, e.g., [5], for the technical andmathematical details of the identification phase.

I The term "perceptrons" as used here refers to both discriminanttechniques as well as to a class of probabilistic iterative learningalgorithms for performance improvement [15, ch. 4]. One such schemeis presented in the next section.

6 A good description of discriminant techniques in PR can be foundin Nilsson [12].

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Fig. 4. Structure of a perceptron-like learning PR system for two-class decision.

outcome was not attained. The decision system is thenoptimized by minimizing the probability of error, i.e., theaverage number of errors. Of course, minimizing theexpected number of wrong trading decisions is equivalent to

maximizing the expected return on investments.The performance of the decision system is measured by

a performance evaluation function V(W,x). UsuallyV(W,x) represents some measure of error. The expectedvalue of V(W,x) is the performance index I(W) of thedecision system; that is,

I(W) = E{V(W,x)}.

The objective of the learning process is to find that settingof system parameters W* for which the functional I(W)takes its extreme value, i.e., for which

grad I(W) E{grad V(W,x)} = 0

where the gradient operation is taken with respect to theweight vector W.

Learning system theory [15] provides us with the follow-

ing recursive algorithm for iteratively determining the

optimal weight vector W*:

W.+ W=W- ° grad V(W1,x") (3)n

where ao is a constant and the subscript n represents the

time when x and the corresponding V(W,x) was observed

or measured.Let us assume for simplicity that our policy space

contains only two courses of action, i.e., A = {a1,a2}.

Let us also define

V(W,x) = [y - sign g(W,x)] * g(W,x) (4)

where y = 1 if a1 was the correct decision and y = -1

otherwise, and sign z = 1 if z > 0 and sign z = -1 other-

wise. (The value of y represents the feedback informationdetermined by the performance evaluation of actually madeinvestment decisions after they were carried out. We also

observe that V(W,x) has a nonzero value only when thedecision system made an error. Thus I(W) is proportionalto the error rate and its minimization by algorithm (3) willreduce the decision system's probability of error [15].)Then substituting (4) into (3) we obtain the learningalgorithm

Wn+1= Wn + a-. [y - sign g(Wn,xn)] * (x"). (5)n

Fig. 4 shows the general structure of a two-category learningPR system. We will see later that scheme (5) provides uswith a computational procedure or program for graduallydetermining that configuration of system parameters W*for which the investment decision system's performance isbest (i.e., I(W) is minimum), that is, the probability ofmaking the wrong investment decision is smallest.

V. LEARNING INVESTMENT DECISION MODELS

We now apply the principles developed in the precedingsection to the design of investment decision systems. Thesedesign principles are applicable to both general marketforecasting as well as analysis of particular securities.

A. General Market Timing

In this article we will consider only an application toforecasting the general market, i.e., timing subproblem(A). The application to individual security transactiontiming (subproblem (B)) will be considered in subsequentpublications.With respect to general market timing, we may define the

general market state in terms of stock price trends and trendreversals. Many different states can be defined, but we findit convenient to work with four states of the market:uptrend, top, downtrend, and bottom.Now, many market practitioners are trend followers.

They prefer to buy at major market bottoms, hold duringthe uptrend, sell (or sell short) near a market top, and donothing (or hold short positions) during a downtrend.

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Thus trading in the stock market is a recurrent decisionprocess whose policy space contains four well-definedcourses of action. We can program this decision processwith the aid of PR techniques.The success of the programmed decision system depends

on its ability to predict future direction and changes oftrends in stock prices. It is apparently impossible to predictfuture price changes through an analysis of past pricechanges. However, if the information pattern for stockmarket analysis becomes very complex-and includes alsofundamental state variables, psychological measurements,news background, etc., in addition to technical factors-then prediction of future price changes appears possible.The information pattern x, which serves as a basis forinvestment decisions, must necessarily be so complex thatthe human mind is generally unable to ascertain the cor-relation between present values of x and future changes instock prices. This relationship, however, can be graduallydetermined through a machine learning algorithm.We shall discuss in detail the application of learning PR

techniques to stock market prediction (subproblem (A),cf. Fig. 1) in Section VI; but first let us consider an applica-tion to security analysis, i.e., subproblem (C).

B. Investment Selection ModelThe design of every programmed investment selection

system must be tailored to requirements and conditionsexisting within individual user organizations (e.g., invest-ment research departments). Thus the first step in the designprocess is to specify the user's investment objectives inoperational terms, i.e., a selection criterion must be estab-lished. Within the decision system these investment ob-jectives are represented by a performance index.

There are many possible selection (performance) criteria.The relative strength criterion is often used. So let us use itas an example throughout this work. We define a securityto be relatively strong over a given time horizon if itappreciates more than a general market index during thattime while entailing no more than average (market) risk,and it is relatively weak otherwise. Clearly, relatively strongissues are characterized by a different information patternthan relatively weak stocks. In other words, this selectioncriterion divides the set of stocks into two classes: thosethat are in a relatively strong state and those in a relativelyweak state (during a prespecified time horizon). So a two-category pattern classifier can be used to program invest-ment selection according this criterion.7

7 We have not considered the element of risk. This was done onpurpose for several reasons. First, the commonly accepted measures ofrisk, i.e., the beta coefficient or yariance of past price changes, arenonstationary and thus are not useful measures of risk. Besides, thesequantities are not always available for many securities, such as, forexample, new issues. Secondly, and more importantly, investmentdecisions are made under conditions of uncertainty rather than risk[17], and the proper way to deal with uncertainty is to try to reduceit by increasing our knowledge and understanding of the situation.e.g., tnrougn a learning process. However, we can resolve most prob-lems of this type by limiting our selections to a prespecified range orlevel of risk as measured, for example, by the variance of past pricechanges, if it is available. Thus in our tests we assume we work with aportfolio of average (market) risk, e.g., beta = 1.

The second important design step is developing themechanism for identification of information for decisionmaking in form of the state vector x. The state variables inx represent a numerical encoding of various properties andobservables of individual securities. They include fun-damental characteristics, e.g., earnings trend, earningsstability, future earnings potential, dividend yield, dividendtrend, price earnings ratio, etc.; risk characteristics, i.e.,the variance of past price changes or the Beta coefficient;technical factors like current price trends on the charts,volume measurements, price overhang, etc.; psychologicalfactors, e.g., divergence measurements; and various otherfactors like news background, capitalization, quality ofinstitutional sponsorship of the security, company'sreputation for technical brainpower and research, qualityof management, Standard and Poor's rating of the security,and so forth.The state vector x is then mathematically transformed

into a pattern of relevant features +(x) that represent thecorresponding fundamental, technical, psychological, andother features of individual securities. This FST is designedwith the aim of greatly reducing the size of x but withoutalso reducing too much its information content.Next we will program the decision rule. Let the index n

count the number of securities considered for investment.Then the selection rule can be programmed by discriminantfunctions:

select the nth security if g(x,) > 0, and discard it otherwise.

This rule will associate a selection policy, e.g., buy (hold) orsell (discard), with any pattern of information x describingthe security. (With this scheme we can also program theindividual security's transaction timing (subproblem (B))using methods similar to those described in the next section.)

Finally, the selection rule is optimized through a learningprocess with the aim of minimizing the probability oferror. The learning process functions this way. At thebeginning we set the weights W according our best initialknowledge about what features are known to be important;or we may pick the weights arbitrarily, e.g., set them allequal to one. Afterwards the weights are changed under thedirection of error-correcting feedback derived throughperformance evaluation of actually made past stockselections. For example, suppose that the nth security hasbeen selected (bought or held), that is, g(xn) > 0. If thisstock subsequently outperforms the market during theprespecified time horizon, the system made a correctdecision. (In this case the weight vector remains unchangedbut the counter n is increased by one.) If the securityappreciates less than the market index, however, a wrongdecision was made, and the weight vector Wn is subsequentlychanged according algorithm (5). This "correction" reducesthe chance of making a similar poor selection in the future.The system is also "corrected" when a reverse error wasmade, i.e., when a relatively strong stock was not selected.The new value of the weight vector W,+1 is then used insubsequent computations until the next error is made.

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After some time, this step-by-step learning from pastexperiences may result in real performance improvement.At the start, the system's performance will most likelybe only mediocre. After about twenty learning steps(n = 20), however, the system may become close to optimaland may make better decisions than a human analystcould do intuitively. See our experimental results inSection VII.

VI. ACTUAL IMPLEMENTATION

We have implemented a cybernetic general market timingmechanism. It has been experimentally tested in actualinvestment analysis since 1970.Our scheme may be regarded as an attempt to program

the well-known general indicator approach to markettiming. This method synthesizes investment decisions byweighing evidence obtained through an analysis of a broadspectrum of indicators, i.e., measurements or observations,describing the state of the market.We observe that the CIDS is a man-machine system that

is tailored to the needs of its users. So its design willgenerally reflect the user's resources, such as the type ofinformation to which he has access, his attitudes towardrisk and expected returns on investments, available com-putational resources, etc. For these reasons there is aninfinity of possible realizations of CIDS. The choice of ourrealization has been guided primarily by the requirement ofcomputational simplicity. In fact, the present investmentdecision system is so simple that all required computationscan be efficiently performed by hand.The decision system again operates in four phases. The

first phase, the identification activity, consists of searchingthe environment and numerically encoding all informationcharacterizing the state of the general market. The relevantinformation is obtained by monitoring the various fun-damental, technical, economic, monetary, and psychologicalindicators, reading daily newspapers, watching the invest-ment news background, and so forth. All these observationsand measurements are represented by the state vectorx = (x1,5 ,x5l). So the state variables xi, i = 1,2,- ,51represent a numerical encoding of individual stock marketindicators, observations of the news background, psycho-logical measurements, etc. In short, x contains informationabout the market's past that is relevant for the predictionof its future. The encoding of state variables is doneobjectively and subjectively.8Through an FST the 51 state variables in x are transformed

into feature vectors representing the fundamental, technical,psychological, etc., features of the general market. Now,different investment policies are generally used for differenttime horizons, and different information patterns are

needed to predict the market's behavior during different

8 The inclusion of techniques for numerically encoding the statevariables xi, i = 1,-- *,51, and mathematical formulas for computingthe features pij, i = 1,2,3, andj= 1,* * *,7, would greatly increase thesize of this presentation. These schemes are described in our otherworks, e.g., [5]. A method for numerically encoding the investmentnews background can also be found in a paper by Niederhoffer [11].

time horizons. Thus, since we will work with three timehorizons-short-, intermediate-, and long-term we willneed three feature vectors 4j(x), i = 1,2,3, respectively.The elements of 4i(x) represent a numerical encoding ofthe following general market features8;

cpi1(x) aggregation of political, economical, and mon-etary fundamentals

pi2(x) technical factors, e.g., advance-decline line,volume and price trends, etc.

yP3(x) aggregation of psychological measturements as-certaining the present attitudes of the investingpublic

Pi4(x) a quantitative measure of the news backgroundunderlying stock price changes

(p,5(x) measurements derived from the Elliott wavetheory

9P6(X) market statistics like average duration and extentof stock market price trends

(pi7(X) a measure expressing the present market efficiency,i.e., this psychological measurement ascertainsthe extent to which the market's behavior isdetermined by emotional rather than fundamentalfactors.

The short-term feature vector (i = 1) contains five of theaforementioned features, the intermediate-term vector(i = 2) contains all seven features, and the long-termvector (i = 3) contains six features. All information neededfor the stock market identification activity is obtainedfrom the Wall Street Journal and Barron's.The design and choice mechanism, i.e., the mapping from

the decision situation onto the policy space, is againrealized by discriminant functions. Assume that our policyspace contains four courses of action, e.g., buy, hold, sell(sell short), and do nothing (hold short positions). Sincewe need a policy space for each time horizon, we will workwith three policy spaces: A1 = {aij}, i = 1,2,3, and j -1, ,4. For example, a12 then represents short-term hold,a31 means long-term buy, etc.We program the choice mechanism by associating a

unique discriminant with every trading policy:

aij gij(x)where

gij = Wij * Oi(X),Then for any investment decision situation the systemselects that set of trading policies aij, i = 1,2,3, for whichthe corresponding

gij(x) > maxgik(X), j,k = 1, ,4.j.k

Performance of this choice mechanism is then graduallyoptimized through a learning procedure. This learningdecision making process is summarized by the flowcharton Fig. 5. We will explain the details later.To simplify the computations, we reduce the size of our

three policy spaces to two courses of action: 1) buy (covershorts) or hold long positions if bought earlier, and 2) sell

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Initialize decision system;START set n = 1, initialize

W(1) i = 1,2,3, j = 1,..,4.

Perform SM identificationactivity; determine valueof state vector xn.

Fig. 5. Flow diagram of leamning algorithmmarket.

encoded in the state variables xi, i = 1, ,51. At regulartime intervals (e.g., every week for short-term analysis,every four weeks for intermediate-term analysis, etc.), thestate vector is transformed into feature vectors 4j(x),i = 1,2,3, and the corresponding set of trading policies iscomputed. These policies are then implemented and theresults are observed and evaluated. If the evaluation ofresults indicates that the optimal policy has been followed,no corrective actions are taken. However, if it later becomesclear that a wrong investment policy has been carried out,the decision system is corrected according algorithm (5).For instance, suppose that trading policy a21 (intermediate-term buy or hold) is carried out at time n, that is, g2(xn) > 0;but during the next several weeks the market suffers anintermediate sized decline, which results in sharp declinein value of the investment portfolio. Consequently, thevalue of W2 is "corrected" by computing

1W2(n + l ) = w2n) _ -

. 02(X )n

for trading in stock

(sell short) or do nothing (hold short positions) if soldearlier. In this case we need only three discriminant functions-one for each time horizon. Then, for example, a short-term trading strategy can be mechanized by the followingprogram:

1) buy (cover shorts) as soon as g1 (x) > 0, after a decline,then

2) hold as long as g1(x) > 0, then3) sell (sell short) as soon as g1(x) < 0, then4) do nothing (hold short positions) as long as g, (x) < 0,

and when g,(x) 0, go to 1).

Through the application of heuristic methods we can alsoprogram more complex trading strategies involving more

than one time horizon.The error-rate, i.e., the average number of wrong invest-

ment decisions, is then minimized through a learning process.

The learning mechanism is initialized as follows. The threetime counters n are set to one. (We note that for the short-term decision subsystem a unit of time is one week, for theintermediate term the unit time interval is four weeks, andfor the long term it is 16 weeks.) The weighing coefficientsao are set to one, and all weight vectors Wi, i = 1,2,3, are

initially set to one.

The learning decision process proceeds gradually in an

iterative manner. The process starts with the identificationactivity which is carried out continuously. Thus every daythe Wall Street Journal is read and other news media are

scanned for information that may be relevant to the stockmarket. Any relevant information is recorded and later

(6)

and the value of W2 is used in subsequent computations ofthe trading policy. If the market had not have declined, theweight vector would have remained unchanged (i.e.,W2("+1= W2j)), but the time counter n would be increasedby 1 four weeks later. The same correction would takeplace if the a22 policy had been in error, but the sign in (6)would be reversed. The weight vector remains unchangeduntil the next error is made. This error-correction learningprocess continues until the error rate becomes stationary.We note that the same learning algorithm is employed

for all three time horizons, but the required learning timesdiffer approximately by a factor of four between timehorizons. Thus if it takes, on the average, 20 weeks tooptimize the short-term decision system, it may take 80weeks to optimize the intermediate-term system, and itmight take approximately six years to optimize the long-term decision system. However, methods for accelerationof the learning process do exist [15, ch. 3].

VII. EXPERIMENTAL RESULTSWe have implemented a CIDS designed according the

principles outlined in this paper and tested them in actualinvestment analysis since 1970. The experimental resultsof these tests are encouraging. They seem to indicate thatwith the cybernetic approach we can 1) program someimportant judgmental aspects of investment analysis, 2)improve the quality of investment decision making, i.e.,amplify the intellect of the human analyst, and 3) attainabove average investment performance.

It is unfortunate that this work may touch upon a con-troversy revolving around the efficient market theory [3],[9], [16]. Of course, it is not the purpose of this researchto become involved in this dichotomy. Our primary ob-jective is to demonstrate that some judgmental investmentdecision processes can be programmed and thus performedby computers highly efficiently and effectively. It is not thepurpose of this study to take sides and to refute anyparticular viewpoint. In fact, as will be seen in Section

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Probabilityof error

10 20 30 40 Time (n) in weeksFig. 6. Learning curve of short-term decision subsystem.

VII-D, our results can coexist with the efficient market modelpeacefully.

A. General Market Forecasting

We have been testing two mechanical trading strategies

designed according to principles outlined in Section VI.In the first of them (S-1), selling short is not permitted,i.e., during declining markets a "do nothing" policy isfollowed. In the second strategy (S-2), selling short ispermitted. An intermediate-term time horizon has beenused. That is, all decisions are made at intermediate marketturning points, i.e., when the sign of g2(x) changed.The two major results of our experimental testing are

summarized as follows.1) Performance of the decision system was gradually

improved by the learning algorithm. The improvement was

considerable. For instance, during a 20-week period theerror-rate of the short-term timing mechanism has droppedfrom almost 50 percent to approximately 20-30 percent.

Similar improvement of performance was observed on theintermediate- and long-term decision systems.9 The same

learning algorithm is employed for all three time horizons,but the required learning times differ approximately by a

factor of four between time horizons. The short-termlearning curve is shown on Fig. 6. During a 49-week timeperiod the short-term weight vector has changed from theinitial value WI(,- (1,1,1,1,1) to W1(49) = (1.307,1.145,1.045,0.850,0.202).

2) After some learning period, reversals of stock markettrends were usually recognized sufficiently early for profitableaction. The relationship between the values of discriminantsand the corresponding stock market trends is displayed on

Figs. 7 and 8. It is seen that near the start of an uptrend the

value of the corresponding discriminant becomes positive,it remains usually positive during the entire duration of the

uptrend, and then it becomes negative near the beginningof the next downtrend. (Of course, there are some errors

about 20-30 percent of the time.) Thus the trading policiesgenerated by the decision system appear to result in above

9 The learning procedure could also be done using past historicaldata rather than waiting for and recording current data. Historicaldata of longer duration could thus be used and the decision systemmuch improved by the longer learning time covered by past Wall

Street Journals for, say, five or ten years. One reason why we performedthe learning in "real-time" rather than using historical data is that wedid not have access to the historical data and the time to process it.

Also, results from the real-time experiment under "real-life conditions"appear to be more realistic and more credible.

Fig. 7. Sign of discriminant is usually the same as direction ofcorresponding trend. Time horizon t may be short-, intermediate-,or long-term.

66

65 NYSE Compos. Index

64

63

6Z-t / Sell Buy Sell

60Buy

58 t Sell1 g2 x)Buygl(x) Buy~ ~ ~ ~ ~~~~Bu

II I I I *II I f I II I I I EI I If

8 IS122 el 6 13 t1 Z 3 10 17 21 1 8 is 2221 5 2Z 19 26 2 9 16 UZ 2 9 16

Sept. Oct. Nov. Dec. Jan. Feb. March

1972 1973

Fig. 8. Values of short- and intermediate-term discriminants (g1(x)and g2(x), respectively) from September 1972 through March 1973with subsequent changes of stock prices.

average returns while taking no more than average risks.For example, from 1970 through 1973 strategies S-1 andS-2 were applied to the NYSE Composite Index. Thesestrategies generated net (after commissions) returns of

32.5 percent and 38 percent, respectively, while the generalmarket return during the same time period was 29 percent(dividends were discarded). A commission of 2.5 percentper round trip (in and out) trade has been assumed. The

risk of strategy S-1 is below average because approximatelyone-third of the time investible funds are held in riskless

cash, while the risk of strategy S-2 is average.

B. Automating Investment Selection

We have implemented a simple programmed scheme for

security analysis designed according the principles outlined

in Section V-B. The relative strength performance criterion

has been used.The results attainable by such programmed selection

systems appear to be indeed superior to intuitively made

.5

-4.

.3a

.2

.1

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FELSEN: PATTERN RECOGNITION

selections. For example, we have tested this scheme byparticipating in The 1972-73 Value Line Contest of StockMarket Judgment. The 25-stock portfolio selected by theCIDS has placed 342nd out of a total of 89744 entries.Within a six-month period it outperformed the averagesby almost 14 percent while taking no more than averagerisks, and it won a cash prize.

It must be pointed out, however, that these results shouldbe considered as preliminary because our experiences withthe cybernetic approach are rather limited to date. Moreresearch into this approach, and more experimental testingof our CIDS will be performed in the future.

C. Discussion of Results

One of the reasons for our successful experimental resultsis that with the aid of advanced computer-oriented tech-niques we can alleviate human information processinglimitations in decision making. For the main problem ininvestment decision making is not getting the relevantinformation but evaluating it and synthesizing it intooptimal decisions. It is well known that when makingdecisions by weighing evidence, it is difficult for the humananalyst to synthesize a multiplicity of factors into a "good"investment decision, especially if the individual decisionparameters point into opposite directions. He can easilyget lost in a maze of contradictory implications. Forexample, various experimental studies have shown thatgiving a decision maker more than four facts reduces boththe quality and speed of his decisions. In fact, as the numberof decision variables is increased, confusion increases so fastthat decision makers will perform better if some of therelevant information is omitted [8].On the other hand, a basic cybernetic principle-the law

of requisite variety-assures us that investment analysis,if it is to succeed, requires simultaneous processing of verycomplex information patterns: the investment policy mustreflect many fundamental, psychological, technical, andother factors affecting the market. In short, to succeed,investment decisions must be synthesized from scores oreven hundreds of pieces of information.

Fortunately, machines can synthesize optimal decisionsfrom any amount of information, provided that appro-priate computational resources and formal decisionalgorithms are available. Thus with artificial intelligencetechniques we can alleviate human information processinglimitations in decision making and thus amplify humanintellect. So superior processing of investment informationapparently can result in superior investment decisions.

D. Cybernetic Approach versus Efficient Market TheoriesOur experimental results indicate that with the cybernetic

approach it may be possible to consistently outperform themarket averages while taking no more than average risks-although using only public information; but this may notnecessarily conflict with the efficient market theory, providedit is properly interpreted.

It can easily be shown that the efficient market model,although a good approximation, of stock market behavior,cannot correspond to reality exactly. It probably conforms

closely with the results attained by an average professionalinvestor, but it is not compatible with a superior analyst.To capture analytically the decision behavior of a superioranalyst (whose intellect may be further amplified by acomputer) requires a more complex theory that is capableof handling judgmental decision processes. In addition itwill be necessary to study directly the dynamic informationprocesses that take place in the market. This apparentlycannot be well done with statistical tools, but we may beable to build more accurate models with the aid of cyberneticdisciplines.With the preceding background we can now interpret

our results in two ways. First, we might assume that theCIDS creates "inside information of the second kind."That is, by using advanced information processing tech-niques-that are superior to the analyses and judgments ofmost professional analysts-we can convert public in-formation into valuable private knowledge needed tooutperform the market. Secondly, there may be some im-perfections in the market. The market is apparently onlyefficient enough to prevent an average full-time professionalfrom outperforming it (using only public information),but a superior analyst may be able to do so. The stockprice setting mechanism is poorly understood, whichtogether with human information processing limitationsmake it often difficult for most investors to correctlyascertain the implications of every new piece of informationfor stock prices. Even professional analysts may not alwaysmake effective use of public information. Thus those whohave superior insight into and understanding of the situa-tion, i.e., who use superior information processing tech-niques, may be able to attain superior performance.

In either case, the results seem to support our thesis thatconsistently superior performance is possible only throughthe application of superior information processing tech-niques. In other words, if only public information is usedin investment analysis, then analysis may not succeed unlessthis information is processed by advanced methods whichare beyond the reach of most professional analysts. Ofcourse, such superior information processing may entailsubstantial costs. These costs of developing and operatingthe CIDS, i.e., the opportunity costs, must be subtractedfrom the excess returns produced by the CIDS.10We have discussed the efficient market model dichotomy

much more thoroughly in our other publications. Readerswho would like to learn more about this interesting debateare referred to the book [4].

VIII. FURTHER REMARKSAt present, there is no sound theory of stock price

formation to guide the investment analyst in building hisdecision model. That is, the scheme presented in thispaper is a model of the investment decision process carriedout by some practitioners. However the lack of underlyingtheory limits the usefulness of this approach because a

10 The actual net returns would then depend on the size of themanaged portfolio: the larger the portfolio, the less would the excessreturns be affected by costs of developing and operating the CIDS.

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IEEFE TRANSACTIONS ON SYSTEMS, MAN, ANI) CYBERNETICS, NOVEMBER 1975

sound theory of the economic processes underlying stockmarket fluctuations-including also the psychologicalfactors-might enable uls to construct better learninginvestment decision models. For example, it might guideus in the selection of the measurements in x and the FST+(x). We believe that cybernetic concepts and artificialintelligence techniques may ultimately prove to be usefulin the construction of a theory underlying stock pricechanges.We must also remember that the described model, if

used by a large number of investors, might affect themarket and result in market changes that, in turn, mightreduce the model's usefulness. This question is thoroughlydiscussed in the author's other work [4].

IX. SUMMARY AND CONCLUSIONS

In this paper we have developed a formal model of theinvestment decision process. Investment analysis as doneby practitioners-is a recurrent decision process underconditions of uncertainty, and it conforms with the generalparadigm of making decisions by weighing evidence.Using generalized learning perceptron-type PR techniques,we have outlined a conceptual framework for automatingor programming such decision processes. Within thisframework we have realized models for both securityselection and stock market forecasting. We have testedboth models in actual investment analysis, and we havefound that decisions made by the CIDS may be superior toresults obtainable by the human analyst.

TIhere are at least two reasons for the superior performanceof the CIDS. First, with the aid of forinal models we canalleviate some problems caused by human informationprocessing limitations in decision making. In other words,with the aid of efficient PR techniques we can synthesizeoptimal investment decisions from much more informationthan the human mind can handle. Thus decisions derivedfrom the formal model may be superior to the judgment ofthe human analyst.

Secondly, effectiveness of investment analysis is alsoimproved by the synergistic characteristics of the CIDS.That is, with PR techniques we can synthesize investmentdecision models involving all major existing investmenttechniques. Thus the fundamental approach, varioustechnical schemes, psychologically oriented techniques, as

well as some aspects of capital market and portfoliotheories, can be incorporated into the CIDS (as features),and thus are dynamically interacting subsystems of thecybernetic approach. Investment decisions are then basedon the entire information spectrum characterizing themarket. Hence such decision systems also derive their

strength from synergism in complex dynamic systems. Inother words, the systems are designed so that simultaneousaction of separate but interrelated parts produces a totaleffect greater than the sum of the effects taken independently.IThus decisions based only on an analysis of the fundamen-tals, or only technical analysis, or only psychologicalmeasurements, usually do not yield good results. Wheninvestment decisions are synthesized from all this informa-tion, however, and the system components are simul-taneously weighted and coordinated in an optimal fashionunder the direction of a learning process, then the decisionsystem's performance may become superior. In brief, theCIDS is more than the sum of its parts.We conclude from our results that investment analysis is a

fertile field for applications of PR techniques. These resultspresent a challenge and an opportunity for workers in bothinvestment analysis and pattern recognition. So we hopethat this research will stimulate others to further exploreapplications of PR and related disciplines to investmentselection and market forecasting. These areas clearly leavemuch room for additional research.

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1963.[2] S. Beer, Decision and Control. New York: Wiley, 1966.[3] E. F. Fama, "Efficient capital markets: A review of theory and

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[6] I. Friend, M. Blume, and J. Crocket, Mutual Funds and OtherInstitutional Investors: A New Perspective. New York: McGraw-Hill, 1970.

[7] C. W. J. Granger and 0. Morgenstern, Predictability of StockMarket Prices. Lexington, Mass.: Heath, 1970.

[8] J. R. Hayes, "Human data processing limits in decision making,"Air Force System Command, Bedford, Mass., Rep. ESD-TDR-62-48, 1962.

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[10] M. D. Mesarovic, D. Macko, and Y. Takahara, Theory ofHierarchical, Multilevel Systems. New York: Academic Press,1970.

[11] V. Niederhoffer, "The analysis of world events and stock prices,"J. Business, pp. 193-217, Apr. 1971.

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