NELION Non-Linear Stock Prediction and Portfolio Management System

NELION: A Non-Linear Stock

Prediction and Portfolio

Management System

Am Fachbereich Mathematik und Informatik

der Freien Universität Berlin

eingereichte Dissertation

zur Erlangung des akademischen Grades

eines Doktors der Naturwissenschaften

vorgelegt von Thomas Schwerk

Berlin, 2001

Gutachter: Prof. Dr. Raul Rojas

Freie Universität Berlin

Prof. Dr. Volker Sperschneider

Universität Osnabrück

Tag der Disputation: 13. Februar 2001

This dissertation is dedicated to Victoria Malaika Bonnekamp

Preface

This thesis presents a unified Internet-based portfolio

management tool, NELION1, that combines non-linear stock

predictions and suggests the optimal portfolio for multiple

investors, based on their specific preferences.

There exist a variety of publications on different approaches to

time series analysis, especially as it pertains to financial data,

including stock prices. The bulk of the work, however,

optimized a certain technique to a specific set of data. There

also exists a wide consensus on portfolio management theory,

which describes how stocks in a portfolio should be distributed

so that it conforms to the risk and return requirements of an

investor. Until now, however, these two approaches have not

been connected to form an automated and integrated stock

prediction and portfolio management tool.

NELION connects to the Internet on a daily basis and

downloads stock prices and transaction volumes to a local

database. With this information at hand, it determines the

volatility of the stock and the correlation between any two

1 At 5188 m, Nelion is the second of the twin peaks of Mount Kenya,

the highest mountain in this East-African country. The silouette of the mountain is reminiscient of a local maximum of a stock chart.

4 Preface

stocks that are tracked on the database. The system then

calculates numerous mathematical predictor models to

forecast the stock price one day, one week and one month

into the future. These models are continually refined through

a genetic algorithm that uses the available processing power

of the computer to search the model parameter space for

improved configurations whenever no other tasks are awaiting

execution.

Investors benefit from these models through personalized

transaction suggestions, which take both their current portfolio

and their risk adversity and other preferences into account.

They can be notified by e-mail at defined intervals of the

current state of their portfolio and receive suggestions on how

to reduce its risk, while maintaining a defined return on

investment. In order to limit expensive excess trades, it takes

the minimum transaction value as defined by the investor into

account. In case NELION identifies that a particular stock has

undergone a dramatic change in stock price, the system

generates an alert for all investors who own shares in the

company by sending a short message via mobile phone.

NELION provides a Test Investor function that simulates

trades based on historic data for any number of investor

profiles. This function is designed for use with all

combinations of the adjustable parameters so that the results

of these trials can be analyzed and different categories of

investors recommended for different risk adversity levels.

Efficient Market Hypothesis 5

Additionally, the system has an Auto Investor module that acts

like an autonomous trader on real data and automatically

executes unsupervised, simulated trades at defined intervals.

These functions base all purchases and sales on the current

stock price and include transaction costs in an effort to provide

a fair measure of the success of the system.

The experiment allowed the agent to perform unlimited

transactions once every weekend with no human intervention

and ran for one year starting May 15, 1999 for a conservative

and a high-risk investor configuration. The algorithm merely

restricted negative ownership of stocks or “short” positions and

was not permitted to use more cash than the US$ 10,000

initial investment.

The results show that NELION is an effective advisor alerting

a private investor to promising opportunities and showing him

alternatives to reduce the risk of his portfolio while maintaining

a defined level of return. The portfolio management tools

provide the user with relevant information both on the portfolio

history and the recommendations for the future.

Table of Contents

Preface................................................................................. 3

1 Introduction...................................................................10

2 Predicting Stock Prices .................................................17

2.1 Efficient Market Hypothesis ....................................17

2.2 Mathematical Modeling Techniques .......................21

3 Portfolio Management ...................................................69

3.1 Return....................................................................70

3.2 Risk .......................................................................71

3.3 The Optimal Portfolio .............................................73

3.4 Applying the Theory ...............................................78

4 Methodology .................................................................82

4.1 Overview................................................................82

4.2 The HTML Interface ...............................................82

4.3 The Administration Tool .........................................83

4.4 The Database ........................................................84

4.5 The Task Agent......................................................87

5 Implementation ...........................................................105

5.1 Overview..............................................................105

5.2 The HTML Interface .............................................106


5.3 The Administration Tool .......................................110

5.4 The Database ......................................................115

5.5 The Task Agent....................................................118

6 Experimental Results ..................................................129

6.1 Test Investor Identification....................................129

6.2 Testing the Profiles ..............................................134

6.3 Model Distribution ................................................138

6.4 Daily Operation ....................................................139

7 Conclusion..................................................................140

8 Appendix A: Investor Profiles ......................................144

8.1 Conservative Investors.........................................146

8.2 High Risk Investors ..............................................152

9 Appendix B: Portfolio History.......................................158

9.1 Transactions by Conservative Investor .................158

9.2 Transactions by High Risk Investor ......................160

10 Appendix C: Screen Shots.......................................161

11 Appendix D: Conceptual Data Model .......................167

12 Appendix E: Stocks Tracked in the Simulation .........168

13 Appendix F: Bibliography.........................................173

14 Appendix G: Curriculum Vitae for Thomas Schwerk .186

Table of Figures

Figure 2.2.1: Trend Lines and Trend Channel ......................27

Figure 2.2.2: Resistance Line...............................................28

Figure 2.2.3: Momentum for n=7 ..........................................29

Figure 2.2.4: Trend Confirmation Indicator............................31

Figure 2.2.5: Comparison of the 50 and 200 Day Moving

Average ........................................................................32

Figure 2.2.6: Trend Oscillator with a 10-Day Moving Average

.....................................................................................33

Figure 2.2.7: The Over-Bought/Over-Sold Indicator with n=20

.....................................................................................34

Figure 2.2.8: Artificial Neural Network ..................................46

Figure 2.2.9: Utans, Moody Experimental Training and Test

Error .............................................................................53

Figure 2.2.10: Utans, Moody Test Error with Removed Input

Data..............................................................................54

Figure 2.2.11: Utans, Moody Experiment with Optimal Brain

Damage........................................................................55

Figure 2.2.12: Hierarchical Networks....................................57

Figure 2.2.13: Training Error for Hierarchical Networks.........59

Figure 2.2.14: Test Error for Different Prediction Horizons....60

Figure 2.2.15: The VSmart Virtual Stock Market ..................65


Figure 3.2.1: The One-in-Six Rule ........................................71

Figure 3.3.1: Risk of a Portfolio ............................................73

Figure 3.3.2: The Efficient Frontier .......................................74

Figure 3.3.3: The Utility Function..........................................75

Figure 3.3.4: The Optimal Portfolio.......................................77

Figure 4.1.1: Block Diagram NELION...................................82

Figure 4.4.1: Simplified Conceptual Data Model ...................84

Figure 4.5.1: Artificial Neural Network ..................................92

Figure 5.2.1: Porffolio Overview via the HTML Interface .....107

Figure 5.3.1: The NELION Administration Tool ...................111

Figure 5.5.1: The Task Agent Program...............................119

Figure 6.2.1: Comparison of NELION Investors with Major

Indexes.......................................................................135

1 Introduction

The rapid growth of the Internet in recent years makes

available to every investor an unprecedented wealth of

information and data used in the stock portfolio decision-

making process. However, easy access to information does

not translate into knowledge and does not automatically result

in a higher yield. In this thesis, we present NELION, a stock

prediction and portfolio management tool that takes advantage

of the Internet. NELION is designed to help small investors

improve their return on investment and achieve consistently

higher yields.

Since the introduction of the first stock market, many attempts

have been made to predict the prices of commodities. The

result of a simple calculation by Farmer and Lo impressively

underlines the motivation for these predictions: A single US

dollar invested in US Treasury bills in January 1926 and not

touched since then, would have grown to 14 dollars by

December 1996. A single US dollar invested in the S&P 500

for the same period would have grown to 1,370 dollars. In the

same period, an investor with perfect foresight and who would

have placed his cumulative fortune in the financial vehicle with

the highest yield at the beginning of every month would have

grown his one dollar investment to a staggering 2,296,183,456

dollars [Farmer, Lo 1998]. With returns like those calculated


above, it is easy to see why market prediction almost

coincides with the creation of the actual market.

As early as the late 1800’s, Charles Dow focused on simple

models to predict share prices [Bishop 1960]. One of the

components of what was later called the Dow Theory tracked

the Industrial Average and the Railroad Average. The theory

stated that when the price of both averages remains within a

band of 5% for several weeks, “a line has been drawn.” If,

thereafter, both averages break out of this band in the same

direction, the Dow Theory states that the price movement has

the momentum to continue with its trend.

Since then both the legal framework and technology

progressed. On May 1, 1975, the Security and Exchange

Commission of the U.S. ruled that security exchanges could

not fix brokerage commission rates, forcing them into a

competitive market situation. The result has been a rich

landscape of different service providers, including many

discount brokers. Unlike traditional stockbrokers, these

companies do not offer any investment advice but will manage

the stock portfolio of private investors at very competitive

prices.

The recent advances of computer technology and the

availability of diverse and comprehensive investment

information on-line have dramatically affected the domain of

the inidividual investor. For the first time, it is feasible for small

investors to manage their own investment portfolio, though not

necessarily wise. Barber and Odean show that Frank Zappa’s

12 Introduction

statement that “Information is not knowledge” applies here as

well [Barber, Odean 1999] [Zappa 1979]. They show that

access to the breadth of information that is available today

tends to give investors a false sense of confidence prompting

them to trade excessively. Additionally, the authors show that

investors tend to hold onto their losing investments

disproportionately, while selling winners.

This psychological trap seems to be the Achilles heel for most

private investors. Because most investors do not have a clear

understanding of their adversity to risk given a medium term

benefit, investors are likely to take counterproductive

decisions. Inevitably, these decisions have a negative affect

on the long-term profitability of the portfolio. Kahneman and

Tversky documented this phenomenon as early as 1979

[Kahneman, Tversky 1979]. They asked two groups of

subjects the following two questions:

1. In addition to whatever you own, you have been given US$

1,000. You are now asked to choose between A) A sure gain

of US$ 500 and B) A 50% chance to gain US$ 1,000 and a

50% chance to gain nothing.

2. In addition to whatever you own, you have been given US$

2,000. You are now asked to choose between A) A sure loss

of US$ 500 and B) A 50% chance to lose US$ 1,000 and a

50% chance to lose nothing.

Statistically, the two questions evaluate to the same result so

that neither choice affects the expected net gain. However, in


the first group 84% chose A), while 69% of the second group

chose B). The result indicates that generally, persons tend to

be risk averse when faced with a potential gain, but are willing

to take more of a risk when faced with a loss.

As Joachim Goldman, the head of the behavioral Finance

department of the Deutsche Bank explained in 1999, this

tendency leads investors to sell stocks too quickly, simply

because they have appreciated from their purchase value

[Reitz 2000]. This directly contradicts the old saying that “no

one has gotten poorer by realizing gains”, a popular saying

within the investment community. However, the development

of a portfolio depends on future movements, not on gains or

losses in the past. Unless there are clear reasons for the sale

of a commodity that has appreciated, one is better off holding

the stock than incurring transaction costs by selling it.

Similarly, investors tend to keep stocks in order to avoid

realizing a paper loss. Selling a commodity at a depreciated

level seals the loss and that seems to be a mental hurdle for

the human psychology. However, Koija Rudzio agrees with

the behavioral finance research and states that holding an

overvalued stock is liable to result in further losses [Rudzio

1999].

In this thesis, I present a system, NELION, that harnesses the

massive amounts of stock data available on the Internet and

provides an objective prediction and stock selection strategy.

The system automatically downloads select information to a

local database and uses mathematical models to predict a

14 Introduction

stock prediction using auto-regressive, Markov, k-nearest

neighbors and artificial neural network algorithms one day,

one week and one month into the future.

In order to optimize the mathematical predictors, a background

thread uses a genetic algorithm to search the input parameter

space for improved models. Since this task can be distributed

to any number of task agents running on different computers

in the network, NELION is a very powerful prediction tool that

constantly adjusts to the changing dynamics of the market.

At the same time, NELION maintains parameters set by the

investor in a profile that takes into account the desired return

in conjunction with adversity to risk. Based on these investor

profiles and the predictions for each stock, the system

suggests specific purchases or sales at defined intervals with

a selected investment horizon, that lead to an optimal portfolio.

NELION helps the investor set parameters by use of the Test

Investor function. This module simulates automatic trades

during a specified interval in the past to observe how the

investor would have fared. By choosing a profile that

corresponds to his needs, a new investor can expect relevant

suggestions in the future.

As a proof of concept, an Auto-Investor function built into the

system executed transactions for two different investor profiles

as an autonomous agent for one year in a simulation using

real data and realistic transaction costs. The results show that

without any intervention, NELION was able to out-perform the


major indexes, depending on the exact profile and the target

markets.

Though one could blindly follow the investment advice as

recommended by the system, NELION is designed as a

trading advisor that helps the investor focus on promising

opportunities and maintain a balanced portfolio. A real

investor still has to verify that these suggestions conform to his

geographical, industry and personal preferences and

estimations.

The rest of the thesis is organized as follows:

In chapter 2, I present the theory of stock price prediction and

the Efficient Market Hypothesis. Based on this, I compare

numerous examples of how different authors have

implemented stock price prediction models.

Chapter 3 addresses the theory of portfolio management

based on the Markowitz’ approach [Markowitz 1952]. After

defining the return of a portfolio and comparing it to the

inherent risk associated with investments, I introduce the

theory of optimal portfolios and how this theory can be applied.

Based on these two pillars, I describe the theoretical

foundation of NELION, in chapter 4. It describes the

mathematical models used in the system and how each

algorithm is designed.

Chapter 5 covers the implementation details of the system

from an information technical perspective, including the

interfaces to the Internet for external communication.

16 Introduction

The use of NELION is described in Chapter 6, starting with the

identification of adequate investor profiles with different risk

and return requirements. In this chapter, I also present the

promising results from a simulation using the Auto-Investor

function, working with real data, executing transactions

autonomously for one year.

Finally, in Chapter 7 I conclude on the strengths and

weaknesses of NELION and suggest further directions of

research.

2 Predicting Stock Prices

Mathematicians and economists have studied stock price

predictions for many years. In this chapter, the theory of

efficient markets presented will show that though no one can

consistently predict an exact future stock price, it is possible,

on average, to exploit inefficiencies in the commodity markets

and achieve a favorable return. With this theoretical

framework in hand, I describe various practical approaches

and conclude on what I perceive to be a promising direction.

2.1 Efficient Market Hypothesis

The ability of capital markets to reflect and react to the data

relating to a tradable security is known as the “Efficient Market

Hypothesis” (EMH). Paul Samuelson first coined this term in

seminal work [Samuelson 1965] and the fact that he was

awarded the Nobel Prize in economics shows the importance

of the EMH concept to generations of investors. Simply, the

EMH states that the price of a stock is the consensus of all

investors and other players in the market. If a disproportionate

group believes that a security is undervalued, the buyers will

outnumber the sellers, driving the price up until it has reached

equilibrium. Similarly, an overvalued commodity will attract

fewer buyers than sellers, so that its price will drop.


In a perfect market, one that is completely efficient, the price

of a commodity reflects all information that pertains to it in any

way. This includes published reports and press releases,

articles in newspapers, magazines or electronic media as well

as macro-economic trends, the political climate and strategic

as well as tactical plans of the companies. New information

and decisions would immediately lead to an adjustment of the

price of the commodity.

The efficient market hypothesis is typically formulated in a

weak, semi-strong and a strong form. The weak form of

market efficiency assumes that security prices follow patterns

with specific cycles of upward and downward trends. Analysts

subscribing to the weak form of the efficient market hypothesis

generally search for specific patterns in charts or the product

and management structure of a company to identify under- or

overvalued stocks. This includes all investment advisors who

make a living researching particular companies, markets and

industries. Prominent representatives of this guild are

Goldman Sachs, Merrill Lynch, Salomon Smith Barney and

Lehman Brothers.

Followers of the semi-strong form of the EMH assume that the

prices of all securities reflect all publicly available data. This

includes fundamental business data, press releases as well as

rumors, which possibly spread inaccurate information about

the underlying commodity. By implication, the only possible

means of consistently benefiting from the stock market would

be to act on non-public or internal information about a


company. This is usually information held by the directors of

the relevant companies and includes plans and strategies.

Much of this information can affect the stock prices if leaked to

the general investment public. However, doing business on

non-public information is called “insider trading” and is

punishable by law.

Persons subscribing to the semi-strong form of the efficient

market hypothesis build portfolios with a long-term gain in

mind, based on the assumption that the stock market has

traditionally outperformed risk-free investments over periods of

ten years or longer. The most renowned representative of this

school of thought is Warren Buffet and his Berkshire

Hathaway Mutual Fund.

In contrast, the strong form of the efficient market hypothesis

suggests that stock prices reflect all data relevant to the

security, both publicly available and non-public information.

This form is generally rejected by the investment community

and expressed eloquently by Farmer and Lo. They argue that

taken to its logical conclusion, no biotechnology company

would attempt to develop a vaccine for the AIDS virus,

because “if the market for biotechnology is efficient in the

classical EMH sense, such a vaccine can never be developed

– if it could, someone would have already done it! This is

clearly an absurd conclusion because it ignores the challenges

and gestation lags of research and development in

biotechnology” [Farmer, Lo 1998].


Much work has been done by a variety of persons on the EMH

to verify if price movements are indeed stochastic and

unpredictable.

As early as 1963, C.W.J. Granger analyzed stock behavior

based on linear models and spectral analysis and found

evidence of inefficiencies [Granger 1963]. These findings

were supported by the research from Niederhoffer and

Osborn, by showing that professional portfolio management

statistically achieved greater returns than amateur or random

selections [Niederhoffer, Osborn 1966].

As Ambachtsheer showed, only the introduction of massive

databases and complex algorithms permit reasonably

consistent investment success [Ambachtsheer 1994]. Studies

like the one by Per H. Ivarsson on inter-bank foreign exchange

trading show that there continues to be extensive interest in

the subject [Ivarsson 1997]. The conclusion of many authors

is that inefficiencies exist and can be exploited given a

coherent investment strategy.

Not surprisingly, exchanges with better infrastructure, players

that are more sophisticated and better regulatory frameworks

are more efficient than others. In general, the opportunities

are more pronounced in smaller, less developed markets like

the Bombay or Helsinki stock exchange, as opposed to the

New York Stock Exchange, as Samuelson convincingly

argued [Samuelson 1965].

Mathematical Modeling Techniques 21

Though it is unlikely that the debate regarding the efficiencies

of markets will ever have a formal conclusion, the

overwhelming evidence shows that even if stock markets are

not gold mines, they do offer opportunities, given a coherent

strategy. This view was succinctly expressed by Boldt and

Arbit: “...trading carefully and searching for opportunities

caused by a bias in conventional thinking seem to be the keys

to success for professional investors in a highly competitive,

but not strictly efficient, market” [Boldt, Arbit 1984].

2.2 Mathematical Modeling Techniques

Traditionally stocks were researched using fundamental

analysis, a method by which the financial health of the

company is evaluated and compared to those of competitors

in the same industry and the market as a whole.

Warren Buffet is probably the most famous investor who used

this approach successfully over decades. He has amassed a

fortune both for himself and his investors of the Berkshire

Hathaway Mutual Fund. At the annual meetings in Omaha,

Nebraska, he makes investing sound simple with statements

like his conviction to judge a company only by “its inner

values” and that they “buy if we like what we see” [Heller

2000]. However, the sheer number of potential investment

opportunities does not permit an in depth analysis of

management personalities, business models as well as

financial health. Consequently, computers were introduced


very early to analyze quantitative data from a variety of

companies to help identify potential winners.

Frequently this analysis focuses on the comparison of many

different ratios which investors weight relative to their

importance. The most common and widely quoted ratio

continues to be price-to-earnings, though all other values from

the balance sheet, profit and loss statement and cash flow can

be taken into account. Rüegg-Stürm and the training

materials from the Financial Training Company introduce all

common ratios used in the financial evaluation of companies.

Both provide an intuitive tutorial on the topic [Rüegg-Stürm

1997] [The Financial Training Company 1998]

It is worth emphasizing that the ratios do not represent

absolute quantities, but should only be used for comparison of

companies in the same industry, region or market. Also, all

ratios can only serve as one indication and should not be

viewed in isolation.

Earning

Pricemultiple P/E = Equation 2.2.1

The P/E multiple or price/earnings ratio compares the closing

price of the stock with the earnings of the last 12 months. A

high value is often a reflection of lofty expectations of stock

price and may indicate that the stock is overpriced.


Sales

Profit GrossMarginProfit Gross = Equation 2.2.2

The Gross Profit Margin determines a company’s trading

activity. It indicates a company’s profit margin by showing the

relationship between sales and direct production costs.

Sales

Profit TradingNet margin Operating = Equation 2.2.3

The Operating Margin indicates the profitability of sales, taking

into account the volume of activity. Net trading profits should

be before tax, interest paid and income from investments.

Sales

OverheadsRate Overhead = Equation 2.2.4

The Overhead Rate forms the bridge between gross profit and

trading profit to sales in the previous two ratios. If there is a

significant upward movement in this ratio, it may be a cause

for concern.

Employed Capital

ProfitNet Capitalon Return = Equation 2.2.5

This Return on Capital Employed ratio measures the overall

efficiency of the business but is only meaningful if compared

within the same industry. Manufacturing, for example, tends

to be more capital intensive than service industries and will


exhibit a lower return on capital ratio. “Capital Employed”

should include share capital, reserves and long-term loans.

sLiabilitieCurrent

AssetsCurrent RatioCurrent = Equation 2.2.6

Based on the balance sheet figures, the Current Ratio

comments on the working capital position of the company and

is generally accepted as a measure of short-term solvency.

This ratio is particularly pertinent for “dot.com” companies.

sLiabilitieCurrent

Stock less AssetsCurrent RatioQuick = Equation 2.2.7

The Quick Ratio or “Acid Test” indicates a company’s ability to

pay it debts quickly. Stock and “work-in-progress” are

generally excluded, since they are not readily convertible to

cash.

Materials ofCost

days 365Stock x TurnoverStock = Equation 2.2.8

The Stock Turnover ratio indicates the stock turnover period in

days. If this value increases, it could indicate excessive or

obsolete stock, a negative indicator, particularly for “high-tech”

companies, where the life cycle of a product is relatively short.

SalesCredit

days 365 x DebtorsTurnover Debtors = Equation 2.2.9


The Debtors Turnover indicates the average period of credit

taken by customers and is useful in determining the possible

existence of bad debts.

Fundsr Shareholde

Debt BearingInterest Gearing = Equation 2.2.10

This Gearing ratio helps measure the long-term strength of a

company. High gearing indicates a high risk and susceptibility

to economic fluctuations. It may also indicate that the

company would have difficulties borrowing additional funds.

Dividend

Profit Cover Dividend = Equation 2.2.11

The Divided Cover calculates the number of times the

company could have paid the dividend amount out of profit. A

high dividend cover may indicate that the company is

financially sound, having retained considerable amounts of

profit for investment back into the company or that the

dividend was very low. The latter may be sign of expansion.

Market Total

100 x ShareMarket ShareMarket Relative = Equation 2.2.12

The Relative Market Share measures the market share of the

company as a percentage compared to its major competitors.

Calculating ratios like these does not require significant

processing power. As computer capacity and processing


power increased, it became easier for analysts to visually

inspect graphs of individual stock prices and values derived

from them. This led to the birth of a new school of stock

analysis based on charting techniques.

2.2.1 Charting Techniques

Charting techniques work with the visual representation of the

stock price graph over a selected period. By enhancing the

diagrams with secondary time series documenting perceived

trends, the chartists identify trends or trading opportunities.

All of these charting techniques represent common analysis

tools and are frequently quoted by all major investment

magazines, including Capital, Börse and Wirtschaftswoche in

German and Forbes, Money Magazine and Barron’s in the

United States. Bookstaber describes and explains these

techniques in detail and shows which combination of triggers

he considers particularly valuable [Bookstaber 1985].

One notable proponent of these techniques is Chrystyna

Bedrij, chief investment officer at Griffin Securities in New

York. She publishes a one-page document three to four times

a week, called “The X list” and has gained notoriety for having

produced portfolio recommendations with returns in excess of

60% since 1997. Her recommendations are naturally only

available to paying customers, but frequently appear on public


web sites with a one or two week delay, including

MoneyCentral on MSN.com.

Like the many ratios discussed earlier, analysts have devised

numerous charting techniques worth consideration.

Comparable to the Price-to-Earnings ratio in importance, the

most basic enhancement used by chartists to a stock price is

the trend line. It is defined by connecting local maxima or

minima with a straight line. The area between the two lines is

called the trend channel and provides an indication of the price

tendencies.

Microsoft Stock Prices (US$)

0

40

80

120

1/1/1999 2/1/1999 3/1/1999 4/1/1999 5/1/1999 6/1/1999 7/1/1999

Trend Channel

Figure 2.2.1: Trend Lines and Trend Channel


This technique is as much an art as a science since the quality

of the implicit statement depends on the “correct” identification

of the local maxima and minima.

Another somewhat subjective indicator is the support and

resistance line. Similar to trend lines, these floors and ceilings

are usually based on psychological barriers, which are

frequently associated with round numbers.

Spiegel Corp. Stock Prices (US$)

0

2

4

6

8

10

1/1/

1999

2/1/

1999

3/1/

1999

4/1/

1999

5/1/

1999

6/1/

1999

7/1/

1999

Resistance Line at US$ 9.00

Figure 2.2.2: Resistance Line

In the example above, the Spiegel stock price has repeatedly

challenged the US$ 9.00 level, but there seems to be a barrier

preventing it from passing this value.

The momentum (Mt) of a price is defined as follows, where Pt

is the price of the stock at time t:


nt

tt P

PM

−

⋅=100 Equation 2.2.13

Using this definition, it is possible to supplement the graph of a

stock with its momentum for different values of n. The

momentum indicator can help identify trend reversals and is

designed to show the strength of the movement. A reversal in

the momentum from values smaller than 100 to bigger than

100 are interpreted as buy signals and vice versa.

Interestingly, some analysts draw trend channels into the

momentum lines to identify buy and sell signals.

Spiegel Corp. Stock Prices and Momentum

0

2

4

6

8

10

1/1/

1999

2/1/

1999

3/1/

1999

4/1/

1999

5/1/

1999

6/1/

1999

7/1/

1999

80

100

120

140

160

180

Figure 2.2.3: Momentum for n=7


Like many indicators, this technique can help identify

opportunities, though some analysts claim that it primarily

documents historic opportunities, instead of predicting the

future. On 1/12/99 and 4/30/99 the momentum value in the

diagram above climbed above 130, documenting a purchase

opportunity that would have resulted in a profitable trade. It

subsequently rose further and broke through the 140 level

confirming the momentum.

The trend confirmation indicator (TCIt) is the ratio of two

moving averages Dn and Dm, of n and m days, with n<m:

100⋅=m

nt D

DTCI Equation 2.2.14

A TCI value below 100 is usually interpreted as a signal

forecasting a change in trends. Values above 100 confirm the

current trend and provide an indication of its strength.


Spiegel Corp. Stock Prices and Trend Confirmation Indicator

0

2

4

6

8

10

1/1/

1999

2/1/

1999

3/1/

1999

4/1/

1999

5/1/

1999

6/1/

1999

7/1/

1999

80

90

100

110

120

130

Figure 2.2.4: Trend Confirmation Indicator with n=5 and m=10

We see that this indicator can, at times, provide helpful

predictions. On 4/30/99, for example, the TCI climbed to

above 110, which would have allowed for a lucrative

investment in the Spiegel stock.

Another popular indicator graphs a short and a long term

moving average on the same graph. Common values for this

moving average (MA) comparison are 50 and 200 days. A

simple trading rule states that if the short term moving average

crosses the long term moving average from below (above), the

stock price shows a trend of increasing (decreasing) strength

and promises to continue rising (falling).


0

2

4

6

8

10

1/1/

1999

2/1/

1999

3/1/

1999

4/1/

1999

5/1/

1999

6/1/

1999

7/1/

1999

0

2

4

6

8

10

Spiegel Corp.200 MA50 MA

Spiegel Corp. Stock Prices, 50 Day and 200 Day Moving Averages

Figure 2.2.5: Comparison of the 50 and 200 Day Moving Average

In this example, this MA indicator triggered a buy signal on

1/9/99 and indeed, the stock price rose from around US$ 6.00

to close to US$ 9.00. It did not, however, identify the

subsequent decrease in stock price, nor did it trigger any other

buy or sell signals in the period displayed.

Trend Oscillators (TOt) are the relationship between the

current price and a moving average.

100⋅=n

tt D

PTO Equation 2.2.15

This indicator is based on the theory that commodities

oscillate within a defined trend channel over extended periods.


Given this indicator, it is possible to fine-tune the timing of a

purchase. Values above 110 (below 90) are generally

interpreted as a “buy” (“sell”) signal.

0

2

4

6

8

10

1/1/99 2/1/99 3/1/99 4/1/99 5/1/99 6/1/99 7/1/99

80

90

100

110

120

130Spiegel Corp. Stock Prices and Trend Oscillator

Figure 2.2.6: Trend Oscillator with a 10-Day Moving Average

Again, we see that on 1/12/99 and on 4/30/99 the trend

Oscillator exceeds 110 and are followed by values up to 130.

A purchase on either of these days would have been followed

by a substantial increase in price within a few days.

The over-bought/over-sold indicator (OBOSt) is designed to

identify stocks that are currently traded at an inefficient price.

100⋅−−

=nn

tnt LH

PHOBOS Equation 2.2.16


In this equation, the values Hn and Ln are the high and low

prices in the previous n days. Generally, it is assumed that a

value over 90 forecasts a price reduction while a result below

10 indicates a price increase.

0

2

4

6

8

10

01/01/99 02/01/99 03/01/99 04/01/99 05/01/99 06/01/99 07/01/99

0

20

40

60

80

100Spiegel Corp. Stock Prices and OBOS Indicator

Figure 2.2.7: The Over-Bought/Over-Sold Indicator with n=20

The OBOSt indicator clearly reacts more sensitively than the

previous ratios, resulting in numerous buy and sell signals.

Like the previous charting techniques, it identified the 4/30/99

buying opportunity. However, there were also some “false

alarms” at the beginning of February and on March 20, 1999.

These issues showed that even the chartists are not infallible

and in 1986, Frankel and Froot suggested that it is necessary

to take the expectations from both fundamentalists and


chartists into account, if one is to understand financial markets

[Frankel, Froot, 1986]. As an example, they analyzed the

value of the US dollar and devised a meta-model, based on a

combination of models. They showed that the complex

behavior in the years before the paper was published could be

explained by the inter-play between these chartist and

fundamentalist schools of thought.

After the stock market crash on October 19, 1987, non-linear

dynamics and especially deterministic chaotic systems

became a major topic both among the financial press and

academic literature. Since the violent swings could not be

explained with the usual assumptions, this approach was seen

as an alternative model for the stock market.

Hsieh, for example, analyzed the S&P 500 Index between

1982 and 1990 and concluded that non-linear methods offer

promising new venues in the attempt to model this data [Hsieh

1990]. His extensive tests show evidence that the stock

returns tested are not independent and identically distributed.

Hutchinson also bases his work on the assumption that

financial time series are fundamentally non-linear in nature

[Hutchinson 1994]. He shows that though it is difficult to

benefit from them, models based on radial basis functions

provide better forecasts than linear predictors.

This was good news to the proponents of complex, chaotic

models and a variety have been developed and tested over

the past years. With their proliferation, a third approach to


stock evaluation evolved and Robinson and Zigomanis

propose the extension of the work of Frankel and Froot to

include the expectations of the non-linear dependence of

financial data in order to optimize these models [Robinson,

Zigomanis 1999].

The following sections address mathematical prediction

models starting with linear auto-regressive methods as a base

line. Subsequently, I focus on more advanced non-linear

approaches using k-nearest neighbors, Markov Models and

artificial neural networks.

2.2.2 Auto-Regressive Models

The literature usually distinguishes between two types of

Linear Models: AR(p) or Auto-regressive Models of degree p

have the form

∑=

−=ρ

ρϕ1

,ˆ

iitit XX Equation 2.2.17

and MA(q) or Moving Average Models of degree q are defined

as follows

∑=

−=ρ

θ1i

itit ZX Equation 2.2.18

where Zt are elements of a white noise process.


Though the two can and frequently are combined to form

ARMA (p,q) models, we concentrate on AR(p) models

because any MA(q) process can be represented as an AR(∞)

process.

The explicit representation of an AR(p) model entails the

determination of the p weights ϕip, which is frequently

accomplished with the Durbin-Levinson algorithm. Brockwell

and Davis show an elegant derivation for this method that

uses a recursive scheme to circumvent the need for a large

matrix inversion [Brockwell, Davis 1986].

The algorithm requires a stationary process with a constant

arithmetic mean and an autocovariance function such that

γ(0)>0 and γ(h)→0 as h→∞. For the algorithm, the mean

squared error of the prediction νn is defined as

( )2

11ˆ

++ −= nnn XXEv Equation 2.2.19

Using the standard definition for the estimated autocovariance

function

( ) ( )( )∑−

=+ −−

−=

hN

ihii XXXX

hNh

1

1γ Equation 2.2.20

it follows that

( )v0 0= $γ Equation 2.2.21


The coefficients of the AR models are calculated using the

following equation.

( ) ( )

1

1

1,1

−

−

=−∑ −−

=n

n

iin

nn v

inn γϕγϕ Equation 2.2.22

The AR(1) model follows immediately:

( )( )

ϕγγ1 1

1

0, = Equation 2.2.23

Given this recursive anchor and the following equations, it is

possible to compute ϕn,m for n=2, 3,… and m=1,…n as well as

νn providing the coefficients for the AR(n), n>1, models.

−

=

−

−−

−−

−

− 1,1n

1n1,n

nn,

1n1,n

1,1n

1nn,

n,1

:

:

:

:

:

:

ϕ

ϕ

ϕ

ϕ

ϕ

ϕ

ϕ Equation 2.2.24

( )2,1 1 nnnn vv ϕ−= − Equation 2.2.25

AR(n) models compute a weighted mean of past values.

Though very useful and easy to compute, the method does not

perform well when the underlying system contains non-linear

dependencies.


The results from Hsieh indicate that most financial data are

non-linear in nature resulting in a natural disadvantage for

these models [Hsieh 1990]. Additionally, due to their simple

nature they are used widely as a baseline for comparison but

consequently offer no competitive advantage.

In an effort to benefit from the extensive research done for AR

models and the numerous well-documented algorithms that

exist, it is possible to enhance the basic algorithm in various

ways. By dividing the input space into two or more regions,

defined by the Euclidean distance to their respective centers in

n-dimensional space it is possible to generate different local

linear models. Each approximates the function linearly in their

respective input spaces. The prediction is the weighted sum

of individual models, based on the distance to the input space.

This generalization requires sufficient data to generate several

local models and the quality of the results depends on the

choice of the centers used to define the separate regions, but

generally helps to reduce the model error.

Mâlâroiu, Kiviluoto and Oja proposed a different enhancement

to generic time series prediction [Mâlâroiu et al 1999]. After

preprocessing the target time series to zero mean and unit

variance, they separate it into different independent spectral

components using the FastICA package in MATLAB. Each

component is then filtered to reduce the effects from supposed

noise, by applying a high-pass and/or low-pass filter. The

individual components are then modeled using the AR method


and combined by calculating the weighted sum of each

prediction.

Hsieh developed a similar model, which decomposes

exchange rate futures contracts into a (linear) predictable and

a (non-linear) unpredictable component [Hsieh 1993]. He

focused on US dollar contracts traded on the Chicago

Mercantile Exchange for the British Pound, German Mark,

Japanese Yen and Swiss Franc. Though this approach does

not accurately calculate the expected prices, it is able to

isolate the autoregressive volatility of the data allowing him to

forecast the prediction risk.

In the Santa Fe Time Series prediction competition organized

by Weigend and Gershenfeld, Sauer concentrated on the

prediction of data set A, the intensity of a detuned NH3-FIR

Laser [Weigend, Gershenfeld 1993, Sauer 1993]. By using

delay coordinate embedding, he successfully built local-linear

models to predict the output data. In the same competition,

Lewis, Ray and Stevens modeled the time series A, B and C,

which additionally included physiological and foreign currency

exchange data. They used multivariate adaptive regression

splines in another example where a linear concept is

expanded in scope so that it can be applied to the non-linear

domain.


2.2.3 K-Nearest Neighbors Models

The k-nearest-neighbors models (KNN) search the training

data for historic points in n-dimensional space that correspond

to the current configuration. The assumption is that similar

configurations in the past are followed by values, which can be

interpreted as predictions for the future. Usually the

predictions are the weighted sum of k of these nearest

neighbors based on distance, hence the name.

In its basic form, the algorithm defines a data window ΚΚ t = (xt

... xt-n-1) where xt is the value of the time series at time t. As a

next step, it calculates the distance dt-m between ΚΚ t and ΚΚ t-m for

all m<t-n. A common metric used is the Euclidean distance,

shown in the following equation, though numerous alternatives

are possible.

( )∑−

=−−−− −=

1

0

2n

imititmt xxd Equation 2.2.26

The resulting scalars are sorted in increasing order so that the

k closest data windows ΚΚ t1 … ΚΚ tk, can be identified. Now

simply taking the value following the historic neighbors xt1+1, …

xtk+1, the system has identified k predictions for the future value

of the time series.

Commonly, these k nearest neighbors are averaged, using the

distances dt1 … dtk as a means of weighting mechanism.


∑∑=

=

+

⋅= +

k

ik

jt

ttt

j

ii

d

dxx

1

1

11 Equation 2.2.27

Frequently, the algorithm is extended by including values from

related time series yt, or zt, representing the trading volume

and general economic data like inflation, interest and

unemployment rates, as well as the price history of major

indexes or related stocks. This tends to increase the

dimensionality of the data window, but does not affect the

complexity of the remaining algorithm.

( )lttmttntt zzyyxx −−−−= ..,..,.. 1tê Equation 2.2.28

This is a general model and performs well both for linear and

non-linear time series. The results of the model can be

reconstructed because the system can list the points it used

for input, making the predictions very transparent.

The quality of the model deteriorates when the time series

enters “uncharted territory” or domain space for which no

previous examples exist. This can be avoided somewhat by

normalizing the input, though this usually increases the error

for the known input space.


2.2.4 Markov Models

Markov Models (MMs) assume that it is only possible to obtain

certain observations of the system that describe its state,

possibly incompletely. In the space-time continuum, the

system „jumps“ from one state to the next. The idea is that if

one observes the system long enough, one can note the

progression from any state σx to state σy1, σy

2... σyn. With this

information at hand, it is possible to calculate the probability

that the state following σx will be σyi for all i. If the system

should end up in state σx in the future, it is possible to

determine the likelihood for each state that it will be the next

one.

When we apply this method to time series analysis, we first

have to define our data window ω. Given a training set of N

data points we are now able to define N-ω=P training tuples.

Each of these tuples represent a move in ω-space from state

σt-1 = (st-ω, ... , st-1) to state σt = (st-ω+1, ... , st). This can also be

interpreted as the functional f(σt-1) → σt where 1 ≤ t ≤ P. In the

next step, we divide the ω-space into k ≤ P clusters. This is

done by dividing the bounded ω-dimensional hypercube into

ΚΚ=nω smaller hypercubes or by randomly selecting ΚΚ points

and attaching each tuple to its nearest representative. The

second method would necessitate the definition of a metric to

identify the “nearest” point, with all common variants possible.


Having now categorized the states, one would have to

determine the probabilities of a transition between any two

states by counting the total number of transitions from one

state to another. Once the probabilities are calculated, the

model is fully specified and can be used to predict the next

state if a new point is presented. The prediction follows from

the most probable state. Calculating the weighted mean of all

follower states can extend this model. Many schemes are

conceivable, with linear and exponential weights used most

commonly.

The state of a financial time series is frequently identified both

by the price and volume of the recent trading days. This

algorithm is also frequently enhanced by including related time

series as described in the KNN models.

Fraser and Dimitriadis used MMs in speech research and

recognized their possibilities for time series prediction when

they became aware of the Santa Fe competition [Fraser,

Dimitriadis 1993]. Their contribution focused on data set D, a

numerically generated series representing a chaotic process.

The authors describe their use of Baum’s EM algorithm, which

iteratively adjusts the model parameters to maximize the

likelihood of its observations and apply the resulting model to

forecast the data. For every point, they are able to map the

probability density making it possible to attach a confidence to

the predicted value. The latter is especially appealing for

stock trading predictions.


Poritz and Rabiner also came from the speech recognition

field and used Markov Models to forecast the likelihood of a

particular word given a certain beginning of a phrase [Poritz

1998] [Rabiner 1989]. In their work, the states described

recent words in a phrase. Given numerous historic examples,

the system is able to question every interpreted word and

replace it with one that “makes more sense”, or

mathematically expressed, where the likelihood of its

placement in a particular position is higher.

2.2.5 Artificial Neural Network Models

Artificial neural networks (ANN) are based on research of the

human brain. Here neurons receive input from n different

electrical sources, weight the inputs through an electrical

resistance and sum the results. The output of the neuron is a

transformation of this sum and is fed into the next neuron. An

ANN simulates this operation within a computer program.

The human brain consists of approximately 1010 neurons, all of

which are active simultaneously and can be interconnected.

The computer equivalent consists of only a few tens or

hundreds of the electronic "neurons" called a unit, and

normally only one is active at any one time.


Input Layer

Prediction

Hidden Layer

Figure 2.2.8: Artificial Neural Network

In the figure above, one can detect a strict hierarchy, with

clearly identifiable layers. Each layer is fully connected to the

next. Though recurrent connections are conceivable and

sometimes used, we will restrict ourselves to feed-forward

ANNs with this structure. The bottom layer in the diagram

represents the input layer. The activation of this layer is

determined by the input into the system, for example It-1, It-2,...,

It-n. The input data is then propagated to the next (hidden)

layer as represented by the connecting line in Figure 2.2.8.

Each of the four units in the middle layer sum their weighted

inputs and scale the output using the transfer function σ(h).

4,3,2,1

6

1,

=

= ∑

=

j

Iwoi

iijj σ Equation 2.2.29

The Ii in this case are the values from the input units and the

weights wj,i represent the axon or weight connection between

input i and hidden unit j. It is common to use a sigmoidal

function for σ (h), like


( ) ( )βσhe

h21

1−+

= Equation 2.2.30

or

( ) ( )σ βh h= tanh Equation 2.2.31

with the alternatives being linear or sinusoidal functions for an

input between -π and π. Similarly, the output unit or prediction

sums and transforms the activation values from the hidden

layer.

∑=

=4

1,11

jjjoWO σ Equation 2.2.32

The example in the figure contains only one hidden layer and

an output layer with one unit, though more output units and

more layers are possible.

The output unit contains the desired prediction and depends

on all the weights in the net. The ANN has to „learn“ the data

to search its configuration space for a good set of weights.

This is usually done using the back propagation algorithm. In

it, we define the error of the prediction of a particular pattern

as a function of the weight vector to the output unit as follows,

where Oi is the output of the ANN and Ti represents the target

value.


( ) ( )∑=

−=max

1

2

2

1 i

iii TOwE

v Equation 2.2.33

By now differentiating the error expression with respect to

each weight wij in Equation 2.2.33 we can determine an

expression that will reduce the error using the gradient

descent method with a step-size ç.

( ) ∑=

−=−=∆max

11'

k

kiikii

ijij OWOTO

W

EW ση

∂∂η Equation 2.2.34

The error is then propagated to the next layer of units where

the same algorithm is then used. This update routine can be

applied after the presentation of each pattern (on-line learning)

or collected for all the patterns in a training set (batch mode

learning). After running through all training patterns, the

model is verified on the test set. Training continues as long as

the test error is reduced with each iteration. This ensures that

the ANN does not start modeling stochastic noise in the

training set, a process called "overfitting." It is common for the

error to vary dramatically in the first iterations, so that many

algorithms permit the definition of a minimum number of

iterations to be tested.

From this description, it is obvious that this method is

computationally considerably more expensive than the

previous algorithms. Also, there is no easy analytical method

to determine the number of units necessary in the hidden


layers, or to make other topological decisions so that it is

necessary to find the optimal configuration using trial-and-

error. The high number of degrees of freedom poses some

difficulties as well, since it reduces the stability during the

convergence process. However, the gain, once a good

configuration is found, is a truly non-linear function predictor.

This difficulty associated with models built using artificial

neural networks is exemplified by an experiment conducted by

White [White 1989]. He attempted to predict the quarterly IBM

stock prices with a static network topology of five input and

five hidden units. The single output unit was trained with data

points from the second quarter of 1974 until the first quarter of

1978. The resulting artificial neural network was used to

predict prices from the second quarter of 1972 until the first

quarter of 1974 as well as the second quarter of 1978 until the

first quarter of 1980. Though the network was able to model

the training set well, the project had no control over the extent

of the training on the network, so that its ability to generalize

was unsatisfactory. For the two test sets, the correlation

between the predicted and the real values was 0.0751 and –

0.0699 respectively. This example shows that this powerful

tool can not be applied blindly without tailoring the network to

the specifics of the time series.

With increased complexity and consideration however, ANNs

offer good opportunities. Rehkugler and Poddig show the

potential of ANNs in an experiment, which included only three

input values and was designed to predict the movement of the


German stock index DAX [Rehkugler, Poddig 1990]. Instead

of using the prices of the index itself, the ANN was based on

the nominal interest rate, a business confidence indicator and

free liquidity, defined as follows:

GNP

M1=L Equation 2.2.35

In this equation, the money supply M1 is divided by the gross

national product, GNP. In order to eliminate seasonal swings,

the input to the ANN included only the change in value

compared to the previous year. The system was trained with

this delta data from the first quarter 1965 with 6 years worth of

information. The topology included different numbers of

hidden layers each with different number of units. The

network had five output units. One was trained to calculate a

simple rise/fall predictor with the values 1 or 0 respectively.

The remaining four output units defined index changes of

bigger than 10%, between 0% and 10%, between 0% and

–10% or smaller than –10%. During every training cycle, only

one of these four units was trained with the value 1. The

others were set to 0.

After training, the network was tested with 68 values. For the

rise/fall indicator, values of 0.5 or greater were interpreted as a

rise, while lower values were considered a falling prediction.

For the four categorization output units, the algorithm

assumed that the output with the highest value was the

“winner” and interpreted it as the prediction.


As a simple trading strategy, the program simulated a

purchase of the index as if it were a stock if the prediction was

positive and it did not already own it. Similarly, it sold the

index, if it owned it and the network predicted a decrease.

The basis for this decision was the first rise/fall indicator. The

table below summarizes the results.

Topology Rise/Fall Output Categorization Return 3-5 49 correct, 19 false 43 correct, 25 false 177.28% 3-5-5 49 correct, 19 false 47 correct, 21 false 160.23% 3-9-7-5 44 correct, 24 false 44 correct, 24 false 142.29%

Table 2.2.1: First Experiment [Rehkugler, Poddig 1990]

Interestingly, the return as well as the correct prediction

frequency responded negatively to increased complexity in the

network. Nevertheless, the average annual returns well over

100% suggest an opportunity, although transaction costs are

not considered.

Since this artificial neural network effectively produced two

different outputs, the two scientists simplified the output in a

second experiment to the simple rise/fall indicator. This

approach ensured that the secondary categorization goal did

not interfere with the desired prediction. In an effort to

improve the forecasts, the output in this second experiment

was interpreted more stringently: Only outputs over 0.9 and

under 0.1 were considered rise or fall predictors respectively.

All other values specified an undefined state and resulted in a


“hold” strategy for the hypothetical stock. The results are

shown in the table below: Topology Rise/Fall Output Return 3-1 32 correct, 13 false 225.16% 3-2-1 42 correct, 16 false 194.39% 3-3-1 43 correct, 14 false 237.65% 3-4-1 44 correct, 19 false 194.36%

Table 2.2.2: Second Experiment [Rehkugler, Poddig 1990]

The results indicate that the specialized approach increased

returns considerably, and that the number of undecided states

primarily helped reduce the number of false predictions. It is

also noteworthy that the increase in network complexity

reduced the undecided states and improved the number of

correct predictions. Though the return did not immediately

benefit from the increased quality of the predictions, one

should question whether a simple portfolio management

strategy is an adequate measure for this model.

In an attempt to improve the generalization ability of artificial

neural networks, Utans and Moody extended the methodology

in a study that was designed to predict the Standard & Poor

(S&P) rating for assorted companies [Utans, Moody 1991].

These ratings define the risk associated with an investment in

a particular company or market. S&P categorize the

companies in 18 discrete steps. Since these ratings are

updated infrequently, this ANN helped interpolate the rating

between official releases.


The ANN used ten financial ratios as input data, a hidden layer

and a single output unit, which categorized the risk rating for

the company between 2 and 19, in the order of decreasing

risk. The hidden units used sigmoidal transfer functions. In

contrast, the output unit used a piece-wise linear transfer

function in order to reduce the complexity and thereby

increasing the training speed.

=)(xf

16for 0

-1616for 2

1

32

16for 1

x

xx

x

>−

≥≥+

>

Equation 2.2.36

The authors tested this configuration with different numbers of

hidden units, in order to determine the optimal topology.

0

1

2

0 1 2 3 4 5 6 7 8 9 10

Train Error

Test Error

Experimental Training and Test Error

Figure 2.2.9: Utans, Moody Experimental Training and Test Error

The results show a pronounced change of trend in the training

error. This point coincides with the minimum test error,


indicating that the optimal configuration should include three

hidden units.

As a next step, Utans and Moody defined the importance of

the i input data by defining the sensitivity of the output to the

input.

esinput tupl ofnumber where

1

1

=

∂∂

= ∑=

N

XNS

N

p pii

µ Equation 2.2.37

By sorting the sensitivity in decreasing order, the two authors

identified the test error as more of the input data was

removed.

1.7

1.8

1.9

2

10 9 8 7 6# Input Data

Test Error with Removed Input Data

Figure 2.2.10: Utans, Moody Test Error with Removed Input Data

This approach shows that the removal of two input data

actually helped improve the test error of the resulting ANN.


In a separate effort to improve the performance of the model,

the authors applied the Optimal Brain Damage (OBD) method,

as presented by Le Cun [Le Cun et al 1990]. This approach

defined the influence of each weight in the network through

the saliency function, defined in the equation below.

( ) 2

2

2

2

1i

i

ii w

w

wEs

∂∂

= Equation 2.2.38

By resetting the weights with the lowest saliency, their effect

on the output is effectively removed. The resulting network is

retrained so that it can adjust to this “brain damage.” The

figure below shows the effect of this adjustment to the test

error.

1.7

1.8

1.9

0 3 6 9 12 15 18# Reset Weights

Err

or

Experiment with Optimal Brain Damage

Figure 2.2.11: Utans, Moody Experiment with Optimal Brain Damage


These two comparisons both showed a promising

improvement but were strangely not combined into a single

model.

The results of these two ANNs were categorized by the

deviation of the actual S&P classification. The table below

shows that percentages for each error group.

Deviation 8 Input Units, No OBD 10 Input Units, with OBD

0 31.1 % 29.1 % 1 39.3 % 39.3 % 2 15.8 % 17.9 %

>2 13.8 % 13.7 %

Table 2.2.3: Error with Reduced Input and ODB Methods

Approximately 70 % of the test set were categorized correctly

or were only off by one, resulting in reasonably accurate

predictor for the S&P risk rates.

In a different attempt to optimize the network topology and

improve the ability to generalize, Fahlman and LeBiere

introduced cascade-correlation networks [Fahlman, LeBiere

1990]. In contrast to the standard back-propagation algorithm,

in these networks the size of the hidden layer is not static.

Initially, a two-layer network is trained until the error for each

vector pair in the training set falls below a defined threshold.

When this occurs, a neuron is added to the hidden layer. The

synaptic weights between the input layer neurons and the new


neuron are adjusted to maximize the magnitude of the

correlation between its activation and the output layer error.

Deppisch, Bauer and Geisel generalize this idea in their paper

on hierarchical networks [Deppisch, et al 1991]. The concept

envisioned training an ANNs until it is no longer able to model

the complexities of input data. In a second step, a new ANN is

trained to predict the residues of the original model. Finally,

the two ANNs are used together as a predictor of the time

series.

+ =

Figure 2.2.12: Hierarchical Networks

The diagram above shows the combination of two ANNs but

this procedure could be extended indefinitely to continually

reduce the residual model. The final output is the sum of all

sub-models.

The authors tested this approach on the chaotic coupled

differential Rössler equations defined in the equation below.


( )

( )7.52.0

2.0

−+=

+=

+−=

xzdt

dz

yxdt

dy

zydt

dx

Equation 2.2.39

In order to approximate the optimal learning per network, the

first ANN had a topology using one input x value and two

hidden units to predict the next x value. Network 1 was trained

103 epochs until it produced an average test error of 10-2 and

then supplemented with a second ANN with a 1-6-1 topology

until the test error reached a minimum. In Network 2, the

original 1-2-1 ANN was trained until it produced an average

output error of 10-3 and was then supplemented with the same

1-6-1 ANN. As a comparison the following diagram include

the test error of the 1-2-1 without a secondary ANN and the

error of an ANN where all eight hidden units are trained from

the beginning.


1.E-08

1.E-06

1.E-04

1.E-02

1.E+00

1.E+02 1.E+03 1.E+04 1.E+05 1.E+06

1-2-1 Network1-8-1 Network1-2-1 + 1-6-1 Network 11-2-1 + 1-6-1 Network 2

Training Error for Hierarchical Networks

Figure 2.2.13: Training Error for Hierarchical Networks

Not surprisingly, the 1-2-1 network “learned” the data quicker

than the more complex 1-8-1 network. After several thousand

epochs it caught up and eventually produced a slightly lower

training error. The first hierarchical network initially improved

the simpler model only slightly. It only showed a significant

error reduction after 104 epochs reducing the training error by

almost two orders of magnitude. The second network

immediately caught up this level and was apparently able to

continue improving its model even in the next epochs. After

106 epochs, the training error leveled off for all models.

A possibly more significant measure of the quality of the model

was the prediction quality measured by the test error. The

diagram below shows a comparison of the most successful of

the hierarchical models in comparison to a linear predictor.


0.01

0.1

1

2 4 6 8 10 12 14 16

1-2-1 + 1-6-1 Network

Linear

Test Error for Different Prediction Horizons

Figure 2.2.14: Test Error for Different Prediction Horizons

Though significantly larger, the hierarchical predictor is an

order of magnitude better than the linear model and though

unsurprisingly both errors increase with a longer prediction

horizon, the ANN remains about ten times better throughout

the domain shown in Figure 2.2.14.

The experiment shows that hierarchical networks are able to

offer advantages in at least some cases. The difference in

training and test errors point to overfitting, an issue that would

need to be addressed, if this approach were to be used in a

system.

Artificial Neural Networks also received a big push in

popularity from two entries by Wan (data set A) and Mozer

(data set C) to the Santa Fe Time Series Prediction

Competition [Weigend, Gershenfeld 1993, Wan 1993, Mozer


1993]. The latter also showed that these models could be

applied successfully in the financial domain, an aspect of

particular relevance to this paper.

Networks based on radial basis functions have also been

applied to financial time series prediction. As early as 1986,

Hutchinson showed that these non-linear models performed

better than linear and univariate models in a simulated stock

trading comparison [Hutchinson 1986]. Building on the

theoretical foundation, he developed a system that was also

applicable to stock option pricing, showing the versatility of the

approach.

Parkinson analyzed preprocessing techniques and their

application to financial time series prediction using neural

networks [Parkinson 1999]. He proposes a method whereby it

should be possible to compare scaling, logarithmic transforms,

smoothing, differences and ratios as well as normalization.

However, the sheer number of combinations of these

preprocessing techniques makes it difficult to identify which

one of them optimally suits what kinds of data.

Nevertheless, artificial neural networks have been applied

extensively to predict financial time series. Zimmermann

enthusiastically supports their usage, because they combine

the non-linearity of multi-variate calculus with the number of

variables typically used in linear algebra [Zimmermann 1994].

Working with him, Braun developed several applications for

the prediction of the DAX, which included manual optimization


techniques like weight and input pruning as well as the

merging of hidden units and layers [Braun 1994].

2.2.6 New Approaches to Financial Market Analysis

In recent years, several new agent based approaches to the

analysis and prediction of financial data have gained

popularity. In 1997, Arthur, Holland, LeBaron and Tayler

proposed an artificial stock market (ASM) where N simulated

players, called agents, each had the option to buy, sell or keep

their current position [Arthur et al 1997]. The experiment was

permitted to run for 250,000 periods during which each agent

was permitted to execute orders once. Each agent forecast

the price of each commodity using auto-regressive models,

which it adapted using genetic algorithms. The trading rules

were based on a parameterized strategy, which was permitted

to evolve using a genetic algorithm over the course of the

experiment. This project spawned several relevant research

initiatives.

One was the experiment by Joshi and Bedau, who assume

that investors continually explore and develop expectation

models, buy and sell assets based on the predictions of the

models that perform best and confirm or discard these models

based on their performance over time [Joshi, Bedau 1998].

They used the ASM to explore the volatility of prices and

average wealth earned by the investors as a function of the

frequency of strategy adjustments.


In their experiments, they simulated a market with a fixed

number N=25 of agents. Time was discrete and in each

interval, the agents had to decide whether to invest their

portfolio in a risky stock or a risk free asset, analogous to a

Treasury Bond. There was an unlimited supply of the risk free

assets and it paid a constant interest rate of r=10%. The risky

stock, issued in S shares, paid a stochastic dividend that

varied over time governed by a process that was unknown to

the agents.

The agents applied forecasting rules to their knowledge of the

stock’s price and dividend history and performed a risk

aversion calculation and decided how to invest their money at

each time period. The price of the stock rose if the demand

exceeded the supply and fell if the supply exceeded the

demand. Each agent can submit a bid to buy or an offer to

sell fractions of shares at the previous period’s price.

Their results were classified in to four different classes of

behavior depending on the frequency of their updates using

the genetic algorithm. Genetic Interval Volatility

of Prices Average wealth

earned Complexity of

Forecasting Rules Never Low Low Low

Every Iteration Low High Very Low 102 < interval < 103 High Low Very High 103 < interval < 104 Moderate High High

Table 2.2.4: ASM Investor Types as a Function of GA Interval


Not surprisingly, the volatility of the simulated market was low,

if the investors never updated their forecasting model, since

each remained with the set of rules they were originally

endowed with. Interestingly, the volatility of the price structure

remains low when the agents update their rules at every

interval and increases dramatically as the genetic interval

increases to somewhere between 102 and 103. With this

configuration, the complexity of the forecasting rules was also

very high. At the same time, the average wealth earned by

the investors was high if they adjusted their strategy on every

iteration, then dropped to a low as soon as there are some

changes, but peaked if the investors modify their strategy

every 103 to 104 intervals.

This work was used to explain the rapid increase in volatility of

the financial markets in recent years, by implying that the

average trading strategies of the investment community has

changed. Since it is assumed that professional investors,

which represent the traditional players, do not adjust their

strategy very rapidly, the authors suggest that this increase is

due to privat investors, which tend to trade with a higher

frequency and have presumably grown their share of the

trading volume with the increasing ease of online trading via

the Internet

Also based on the ASM, Kurumatani proposes a virtual stock

market, Vsmart, where researchers worldwide can inquire

about stock prices, and can execute purchases and sales, just

like in its real world counterpart [Kurumatani et al 2000].


Unlike actual markets, no actual money will transfer ownership

and all trades, trading histories and results are open to all

participants. This results in complete transparency and

hopefully in some insights into the dynamics of stock markets,

multi-agent research and profitable trading strategies as well

as human decision-making.

To this end, the authors provide a Simple Virtual Market

Protocol, SVMP, which allows the academic community to

automate the transaction chain via the Internet. This process

allows autonomous agents to retrieve current and historic

market data, which can be processed using any kind of

algorithm. Using the resulting predictions, the agent can send

order inquiries. The central VSmart Server matches offers

and bids, thereby determining the resulting price and providing

an immediate response whether the order resulted in a

transaction.

Order Result Status

Order Inquiry

VSmart Server

V-Smart Client 1

Order Result Status

Order Inquiry V-Smart Client 2

Figure 2.2.15: The VSmart Virtual Stock Market

Since all transactions are tracked and available for all

participants, this open approach can bring together


heterogeneous agent types. A human interface via the

Internet, even allows participants, who have not fully

automated the transaction chain to interact with the server.

Due to its completely transparent design, this project promises

to provide interesting results, when it goes live.

In 1990, Granger hypothesized that trading volume and price

movements were related [Granger 1990]. Karpoff found that

stock price and trading volumes are related for bull markets,

supporting this Grangers causality [Karpoff 1987]. Taking this

work as a basis, Chen, Yeh and Liao extended the algorithms

used in the ASM to analyze the old saying on Wall Street that

“it takes volume to make price move” [Chen et al, 2000]. They

developed a similar artificial agent based stock market and

tested for Granger causality between these two components

and showed that the relationship exists in all examples tested.

This finding also emphasized the validity of the agent based

simulations and reinforced this new methodology.

Ingber and Mondescu developed an interesting alternative

based on an Adaptive Simulated Annealing (ASA) approach to

generate buy and sell signals for S&P futures contracts

[Ingber, Mondescu 2000]. The algorithm fits short-time

probability distributions to observed data using a maximum

likelihood technique on the Lagrangian. It was developed to fit

observed data to the following function.

( )tdzFdtfdF xF σ+= Equation 2.2.40


Using this equation, it defined the market momentum as

follows:

s

F

F

F

fdt

df

22σ

−=Π Equation 2.2.41

In these equations, f F represents the drift, σ the standard

deviation defining the volatility, F(t) is the S&P future price and

dz the standard Gaussian noise with zero mean and unit

standard deviation. The parameter x was used to adjust the

system to the current market conditions. The system sampled

the data with different time resolutions ∆t and averaged actual

tick data that fell into a particular sample interval.

The ASA algorithm calculated optimal parameters for the drift f

F and the parameter x in the equations above as soon as

sufficient data was available in the trading day and periodically

thereafter. By then defining the null momentum

x

FF

F

f220 σ

−=Π Equation 2.2.42

the momentum uncertainty band

dtF x

F

σ1

=∆Π Equation 2.2.43


the system was able to execute a simple trading rule for long

(“buy”) and short (“sell”) signals.

If ΠF > MΠF0 then signal = buy

If ΠF < -MΠF0 then signal = sell

The threshold parameter M was used to limit the number of

transactions by defining a momentum uncertainty band around

the null momentum value.

The system was tested with different sampling intervals ∆t,

data windows W and threshold parameters M. The σ

parameter was continually updated. The results presented in

the paper included US$ 35 transaction costs for each buy and

sell combination and show the trading profit for two specific

days, June 20 and June 22, 1999. Depending on the

parameter selection for ∆t, W and M, the system generated a

gain of up to US$ 2285 or loss of up to US$ 1125. It does not

state how much money was available for investment in total.

Nevertheless, these results show how mathematical methods

usually used in physics can be successfully applied to the

financial trading domain.

No doubt, these are not the last new prediction strategies as

scientists “keep forging ahead with always more potent

algorithms, which alone would allow them to remain ahead of

the pack” as Lequarré predicts. However, this race will

continue, as “patterns in the price tend to disappear as agents

evolve profitable strategies to exploit them” [Lequarré 1993].


3 Portfolio Management

If all stock predictions were perfect, portfolio management

would amount to the transfer of funds to the commodity that

promises the highest return in the specified investment

interval. Unfortunately, the future is not predictable to that

degree of accuracy. Consequently, portfolio management

requires a careful distribution of funds in various stocks so that

any one single incorrect prediction does not dramatically and

negatively affect the performance of the entire portfolio. On

the other hand, spreading the risk between numerous stocks

also implies that a dramatic upside gains by any one

investment only helps the portfolio proportionally.

Due to this dynamic, portfolio selection is dependent on the

risk adversity of the investor. Markowitz defined the

theoretical concept of the perfect portfolio, on which NELION

is based [Markowitz 1959]. After analyzing the concepts of

return and risk in this chapter, I present the parameterization

of the conflicting goals of high return with low risk in the

optimal portfolio theory.


3.1 Return

The return of a stock in a specified period is the percentage

increase of the value of the investment. It is defined as

follows:

1

1

−

− +−=

t

tttt P

DPPR Equation 3.1.1

In the equation above, Pt is the current price and Pt-1 is the

price at the beginning of the interval, while Dt is the dividend

within that period. The dividend can never be negative. For

periods, which do not coincide with the financial year of the

underlying stock, the dividend is calculated as a percentage of

the total accrued during the period. Following standard

investment convention, we assume that the interval is one

year. From Equation 3.1.1, it is clear that the return Rt is

positive if Pt is larger than Pt-1, or the price of the commodity

has increased.

The return of a portfolio is the weighted sum of the i individual

stock returns.

( ) ∑=i

itiPt RXXR ,, Equation 3.1.2

In this equation Xi denotes the fraction of the portfolio covered

by each investment and therefore

Risk 71

0 where11

≥=∑=

i

n

ii XX Equation 3.1.3

This requirement does not impose any restrictions on the

allocation of funds, since it allows for money kept as cash.

The return would then simply be the bank interest rate, which

may be 0%, depending on the account type.

3.2 Risk

Unlike the return of an investment, the definition of risk is more

subjective. Markowitz assumes a normal distribution of upside

and downside potential around the return of a commodity,

based on its volatility ó.

Normal Distribution

Downside Risk

Upside Potential

4/6

1/61/6

ì+ó ìì-ó

Figure 3.2.1: The One-in-Six Rule

In Figure 3.2.1, the expected return ì defines the peak of the

normal distribution with ì-σ and ì+σ defining a 2/3 margin of


return. The downside potential is 1/6, hence the name of the

rule. It is clear that a small σ reduces potential loss thereby

minimizing the associated risk of the equity. We therefore

define the risk V(X) of an investment of value X with a variance

σ as follows.

( ) 22σXXV = Equation 3.2.1

Unlike the return, the risk can not simply be calculated as the

weighted sum of the individual risks, since individual stocks

can be dependent on similar external factors. Both Daimler-

Chrysler and Ford are affected negatively by rising oil prices,

for example, so that a portfolio consisting of these two stocks

has a higher risk than one with Daimler-Chrysler and

Microsoft, for example, assuming that Microsoft and Ford have

the same volatility. Consequently, the systemic risk of a

portfolio includes the covariance ρij of the individual

investments i and j as shown in Equation 3.2.2 below.

( ) ∑ ∑∑−

= +==

+=1

1 11

22 2n

i

n

ijijji

n

iiiP XXXXV ρρ Equation 3.2.2

The first term represents the inherent risk of every individual

stock, while the second term captures the risk associated with

the correlation between stocks. Given a portfolio where the

correlation ρij between all stocks i and j is zero, the risk VP

reduces to the simple sum of individual risks for each stock.

The Optimal Portfolio 73

( )0for

1

22

=

= ∑=

ij

n

iiiP XXV

ρ

ρ Equation 3.2.3

3.3 The Optimal Portfolio

The conditions of Equation 3.2.3 are virtually impossible to

achieve for any n>1, but additionally, this approach ignored

the return of the portfolio. In order to find the optimal stock

distribution, we look at a sample portfolio with two stocks with

an equal expected return ì, where ρij = 0.2, σ1 = 0.6 and σ2 =

0.8. We can plot the risk of the portfolio as a function of the

investment in the first stock.

Risk of a Portfolio

0% 20% 40% 60% 80% 100%Stock Distribution

Ris

k

Figure 3.3.1: Risk of a Portfolio

If these two stocks were the only available choices, an

investor would ideally distribute 60% of the available capital in

stock 1 and the remaining 40% in stock 2. This example


shows that the risk of a portfolio can be minimized without

changing the expected return.

In order to calculate this optimal portfolio, we use Markowitz'

approach. He defined the objective function, which assigns a

weight between the desire for high returns and a low risk.

( )[ ] PP VREAf +−= Equation 3.3.1

In this function, A represents the risk aversion of the investor

and is dependant on his investment needs. A graph of this

function highlights a region that satisfies the investor’s

requirements for return as well as risk. The edge of this region

defines the portfolios with the highest return given a specific

risk or conversely, the lowest risk give a defined return and is

called the Efficient Frontier.

Efficient Frontier

Risk

Exp

ecte

d R

etur

n

Excessive expected risk for a given expected return

Efficient Frontier

Low expected return for a given expected risk

Figure 3.3.2: The Efficient Frontier


In the next step, Markowitz defined the Utility Function, which

is also investor dependent and describes the utility U(R) of a

specific return R. This function is used to identify the desired

return when optimizing a portfolio.

( ) 2PPP cRbRaRU −+= Equation 3.3.2

The coefficients b and c are not negative so that the resulting

graph will have a form as shown below.

The Utility Function

Return

Util

ity

Maximal Utility

Figure 3.3.3: The Utility Function

A person at the beginning of his career can generally afford to

take a larger risk since he will generally not depend on the

savings in the near future but would benefit from higher

returns later in life. Short-term downward fluctuations are

tolerable to this group of persons but not for an investor who is

close to retirement and will need his savings in the near future.

Job security, the plans for a large purchase in the near future


or personal risk aversion are other considerations, which will

affect these parameters.

Applying the expectation operator E(.) on Equation 3.3.2 we

get the following result.

( )( ) ( ) ( )2PPP RcERbERUE −+= α Equation 3.3.3

Using the definition of the variance

( ) ( ) ( )[ ]22PPP RERERV −= Equation 3.3.4

we can re-write Equation 3.3.4 as follows:

( )( ) ( ) ( )[ ] ( )PPPP RcVREcRbEaRUE −++= 2Equation 3.3.5

For a constant expected utility, C, we can solve this equation

for the expected return E(RP).

( ) ( ) 21 CCRVRE PP −+= Equation 3.3.6

where

( )2

2

12c

b

c

aCC +

−= and

c

bC

22 = Equation 3.3.7

This equation defines utility curves, which we can add to the

graph shown in Figure 3.3.2, to arrive at the optimal portfolio

as shown below.


The Optimal Portfolio

Risk

Exp

ecte

d R

etur

n

Optimal Portfolio

V(R)

Figure 3.3.4: The Optimal Portfolio

The point of tangency between the utility curve and the

efficient frontier defines the optimal portfolio for this investor.

This point can be calculated by substituting Equation 3.3.6 into

Equation 3.3.1 and solving for V(RP) or E(RP).

( )

−

−−

−

−

−

−

−= 1

2

2

11

2

2

1222

1

2

22

22 A

fC

AAA

CA

fC

A

fC

AARV P

Equation 3.3.8

( ) ( )2

24

2 22

221

ACACCCfRE P

−−

−+−+= Equation 3.3.9

This expression uniquely specifies the optimal portfolio.


The challenge of this approach is the identification of the

parameters in the utility and the objective functions since they

are highly subjective and represent relative weights and

cannot be attached to measurements in the physical world.

3.4 Applying the Theory

Most trading systems are extensions of financial prediction

experiments and have the goal of measuring the real-world

results that can be associated with the forecasts. The

simplest form was already mentioned in the experiments from

Rehkugler and Poddig: If an increase was predicted, the

system purchased one additional fictitious unit of the DAX, if a

decrease was predicted, one was sold. The system did not

permit the ownership of negative numbers of the stock, or

“short” positions.

Due to their mathematical simplicity, trading strategies based

on moving averages are probably the most widely used

technical rules. These models were prominently used by

LeBaron and became the baseline for further comparison

[LeBaron 1995].

In LeBaron’s experiment, the single moving average indicator

generated buying (selling) signals when its value was above

(below) the current stock price. The adjustment of the model

required identifying the optimal length of the data window. A

slight improvement on the basic algorithm could be achieved if

trading signals were only generated if the difference between

the moving average and the current price exceeded a

Applying the Theory 79

specified band. This reduced the number of trades and, by

implication, the transaction costs that a real world investor has

to bear.

Moving average oscillators compare a short term and a long

term moving average of the stock price against each other.

These models frequently use the commonly quoted moving

averages of five, ten, 15, 50 and 200 days for their

comparisons. Buy (sell) signals are generated only if the short

(long) term moving average rises above that of the long (short)

term. Again, frequently the difference between the two values

has to exceed a specified value in order to trigger a trading

signal, so that the number of transactions is kept at bay.

Using both of these moving average trading systems as a

foundation, Dihardjo and Tan compared artificial neural

network prediction models with an associated trading system

to predict profitability opportunities in the Australian Dollar/US

Dollar exchange rate [Dihardjo, Tan 1999]. Though they found

that both systems were profitable in the period tested, the

ANN models performed better (annualized returns between

13% and 19%) than the simple moving average approach

(returns of between 8% and 13%). The experiments showed

that both models were particularly successful in markets,

which exhibited long term trends.

Kumar, Tan and Ghosh used the same Australian Dollar/US

Dollar exchange rate data and built sophisticated financial

forecasting models. These incorporated the chaotic


components in numerous ways in an effort to optimize the

predictive powers of the models and, by implication, the

profitability of their system [Kumar et al, 1999]. The trading

system worked with two different rule patterns:

Pattern 1:

If (Current Forecast – Previous Forecast) > Delta then

Signal = “Buy”

Else If (Previous Forecast – Current Forecast) > Delta then

Signal = “Sell”

Else

Signal = “Hold”

Pattern 2:

If (Current Forecast – Current Close) > Delta then

Signal = “Buy”

Else If (Current Close – Current Forecast) > Delta then

Signal = “Sell”

Else

Signal = “Hold”

The Delta value was used to provide a threshold, which

eliminates excessive trades, since they were taken into

account with 0.1% of the transaction value in this experiment.

Interestingly, though the forecasting models were considerably

more complex than the ones used by Dihardjo and Tan, the

profitability ranged between 11% and 20% annualized return

and thus did not significantly help this goal much.

Applying the Theory 81

Notably missing from this list of trading strategies is one that

addresses the realities of an individual investor, who has to

decide not only which stocks offer good growth opportunities,

but also how to distribute his investment between the

numerous alternatives. Bookstaber describes a simple BASIC

program that combines chart analysis with a simple risk

calculation algorithm, but does not analyze the success or

failure of this approach given historic data [Bookstaber 1985].

Programs with a similar focus exist with investment institutions

or other professional investors who emphasize risk analysis,

however, this work tends to not get published since it is

considered the strategic advantage of the respective owner or

user community. Jean Y. Lequarré voiced a similar sentiment

in the conclusion of his article: “This inability to discuss their

findings in the open is often frustrating for many of those

involved in this activity and specially the ones who come from

academia” [Lequarré 1993].

This thesis is an effort to combine the significant work on

financial time series analysis and prediction with a coherent

trading strategy that can be adjusted to the preferences and

needs of the individual investor. The resulting system is

designed to run on common PC hardware making it suitable

for personal investment advice and as a portfolio management

tool.

4 Methodology

4.1 Overview

NELION is an Internet based personal investment tool and

portfolio management software. It retrieves stock data from

the Internet, manages it and generates investment

suggestions and portfolio updates via e-Mail and alerts via

short messaging system, SMS. Additionally, an investor can

view his portfolio via a web page and can manipulate his

preferences and execute purchases or sales.

The system is separated into a task agent, an administration

tool and an HTML interface, each of which attaches to the

common NELION database.

HTML Interface

Task Agent

NELION Database

WWW

e-Mail

SMS

Internet Admin Tool

Figure 4.1.1: Block Diagram NELION

4.2 The HTML Interface

The HTML Interface provides an investor using NELION with a

means to manage his portfolio and edit his preferences. After

entering his e-mail address as a user name and the

The Administration Tool 83

associated password under www.nelion.net the investor gets

an overview of his porfolio including the current value, stocks

owned and current recommendations. A graph compares the

return on investment of his portfolio compared to the Dow

Jones Industrial Index as well as the Nasdaq.

From this main page, the investor can select hyperlinks that

allow him to maintain his investment preferences and account

parameters, buy or sell or research specific stocks.

4.3 The Administration Tool

The Administration Tool is designed for the administration of

the data, parameters and tasks on the database. As such, it is

only used by the NELION system manager and does not

require any investment experience, since it only provides a

means to maintain data but does not contain any logic for

stock prediction or portfolio distribution.

The data entry screens mirror the structure of the database

and consequently include a data entry screen for all the major

tables. For the investor data, the Administration Tool provides

one page for the data kept in the investor table. Additionally,

there are pages to view the current portfolio, its development

in a graphical format, the purchasing and sales history, as well

as the return on investment.

The stock interface includes pages with lists of the

mathematical models and current predictions with different

horizons, in addition to the standard information, such as the

company name and ticker, current price and volume. A

84 Methodology

parameter dialog allows the administrator to maintain all the

adjustable settings of the system, while the task list shows the

jobs that the task agents are currently working on, or that is

waiting for execution by one of them.

4.4 The Database

The database is the central store of information and has to

scale to several gigabytes in size in order to be able

accommodate historic data, models, recommendations and

portfolio histories for thousands of stocks and investors. The

diagram below shows a simplified conceptual data model.

The additional tables required for the model storage have not

been included for simplicity. The complete data model is

shown in Appendix D. The primary keys for each table is

included and underlined in the figure.

STOCK Stock_ID

MODEL Model_ID

CORROLATION

TODO Todo_Key Todo_Desc

PARAMETERS Parameter_ID

PREDICTION Prediction_Interval Prediction_Date

RECOMMENDATION Recommendation_Date

INVESTOR Investor_ID

PORTFOLIO

PURCHASES Purchase_ID

StockData Date

Figure 4.4.1: Simplified Conceptual Data Model

The Database 85

The historic price and volume data for each stock that is

tracked is stored in a separate table, which is created when

the stock is entered. The figure above only shows one

representative table, StockData.

The system hinges on the two main entities, stocks and

investors. For each stock, the system stores the company

name, stock exchange abbreviation called the ‘ticker” as well

as the volatility. The internal Stock_ID number is the primary

key of the table and used as a foreign key in all related tables.

The correlation between all stocks, for example, uses the two

Stock_IDs as its primary key and merely stores the correlation

as an attribute. The prediction table needs two additional

fields, the prediction interval and the prediction date, as a

primary key and stores the percentage prediction increase or

decrease as a positive or negative float as its only attribute.

The stock model component is only represented by a single

table, which defines its own internal model number Model_ID

as a primary key. The additional tables that are required to

store the assorted models are not included in the diagram.

The investor entity requires less support tables but contains

more fields within the table itself but also uses an Investor_ID

as a primary key. Besides the investor name and his e-mail

addresses for update and notification purposes as well as

SMS updates, the system stores the investment preferences

in the form of risk adversity parameters, expected minimum

annual return as well as the minimum transaction volume.

Additionally, it tracks parameters that control how frequently

the investor receives e-mails with an update of the current

86 Methodology

portfolio and purchase and sale recommendations. In order to

be able to show the change in portfolio value from one e-mail

to the next, it also stores the account value from the last

update. Furthermore, it maintains a field for the cost of each

transaction.

Lastly, each investor has an investor type, where three

different options are possible: A “Test Investor” is used to

simulate trading behavior and the resultant portfolio for

different configurations in a past period, so that a new

potential user of the system can select a configuration with the

desired characteristics. For these investors, the system

maintains a start and end date for this test. An “Auto-Trader”

is an automatic investor that autonomously acts on the

investment recommendations in a “live” simulation on current

data. This function allows the analysis of the system as a

proof of concept. Finally, there is the “Normal Investor”, who

receives regular updates, but that has to update his purchases

and sales on the system, whether they were recommended or

not.

The portfolio, purchases and recommendation tables provide

the link between investors and stocks, since each investor has

a portfolio containing zero or more stocks. Each inherits the

respective internal identifiers as foreign keys.

The purchase table shows when these stocks were purchased

and sold and at what price these transactions were executed.

The current and historic recommendations are kept in the

corresponding table along with their recommendation dates.

The Task Agent 87

The parameters are not connected to the remaining tables,

since they only store system values, which will be read by the

task agent or Administration Tool for specific functions. The

table describes the six parameters that are stored in this table. Parameter Description TimerInterval Specifies the frequency with which the Administration

Tool updates the task list on the screen BankRate Guaranteed Interest Rate from the broker or bank Diff2NY Time difference to the New York Stock Exchange.

This is used to schedule the Internet download task Mutation The likelihood of mutation in the genetic algorithm SMS Threshold If the value of a stock changes more than this

threshold, an SMS message is sent to all investors who own the stock, as well as the System Administrator

SMS for System Administrator

The SMS e-mail address of the system administrator

Table 4.4.1: System Parameters

The task table has an implicit link to the stocks and investors,

since all tasks relate to one of these two entities. Due to this

dual connection, there cannot be an explicit database

constraint and the referential integrity of the link has to be

verified by the task agent.

4.5 The Task Agent

The task agent supports the stock prediction and portfolio

management calculations, as well as the Internet interface. It

retrieves individual tasks from the task list, marks them as

“taken” until they have been executed and then deletes them

from the database.

The task agent can perform nine different tasks. The Internet

Load function to retrieve data from the World Wide Web is

88 Methodology

always the first step. Given this data, the next tasks,

calculating the volatility, mathematical models and the

correlation between stocks can be executed. These tasks can

be grouped together into a single task for a new time series.

Further tasks include sending a portfolio update, possibly

including transaction recommendations, to the investor.

Lastly, the task agent executes the test investor function and a

background thread that performs model optimization with a

genetic algorithm. All of these are explained in detail in the

following sections.

4.5.1 Internet Load

The Internet Load function connects to the Internet and

downloads historic price and volume data for each stock

tracked by NELION. If a stock has just been added to the

system so that the data table is empty, it will attempt to load

data starting from January 1, 1980. In case this function was

not invoked for several days, it retrieves missing data in one

download, bringing the stock data up-to-date.

The system stores the closing price for every day since the

stock has started trading. On weekends, public holidays and

days where the trading volume was nil, it assumes that the

price has not changed but still inserts a record into the

corresponding table. This facilitates the monthly model

calculation, which uses the last day of each month as a basis.

Additionally, it allows for consistent correlation calculations of

The Task Agent 89

stocks that are traded in different markets and with different

public holidays.

Significant changes in the stock price tend to signify dramatic

occurrences either for the stock itself or for the market as a

whole. Since this may require the attention of the investor, the

system notifies the administrator and all investors who own a

stock via a mobile phone SMS message. The sensitivity of

this threshold is controlled by the SMS threshold parameter,

which defaults to 20% so that stock price changes that exceed

that value will result in a message.

4.5.2 Calculate Volatility

The volatility of each stock is calculated using the following

equation:

( ) ∑=

−−=

n

i i

ii

x

xx

nx

1

11σ Equation 4.5.1

This value measures the mean absolute percentage change in

price over the entire interval for which the system has data.

Though it treats public holidays like regular trading days, it

ignores weekends.

90 Methodology

4.5.3 Calculate Models

For each stock, NELION calculates prediction models of four

different types: Autoregressive models of degree n (ARN),

artificial neural networks (ANN), k-nearest neighbor models

(KNN) and Markov models (MM). Since the system permits

prediction horizons of one day, seven days (one week) and 30

days (one month), it calculates models for each of these. As

input, it correspondingly uses the closing stock prices of the

last n days, weeks or months to predict the closing stock price

one prediction interval into the future.

This function serves as a bootstrap for the genetic algorithm

described below, which uses the available models to further

search the parameter space for better predictors.

The data was divided into a test and a training set but in order

to capture trends throughout the available data, each input

tuple had a 50% chance of being assigned to one of the two.

The quality of a model was measured by calculating the

normalized mean squared error (NMSE) of the predictions in

the test set.

( )

( ) ( )( )21

2

targetmintargetmax

targetprediction1

NMSEii

n

iiin

−

−⋅=

∑= Equation 4.5.2

Since each stock price time series has a different dynamic,

NELION calculates models of each type and prediction

The Task Agent 91

horizon with various parameter combinations and stores the

best two configurations of each type on the database. The

details of each model type are described in the following

paragraphs.

The autoregressive models (ARN) use the Durbin-Levinson

algorithm described in Chapter 2 to calculate a linear

prediction model. The only parameters that could be adjusted

for the model type were the number of input values, which

ranged between two and 14 values. It stored the best two

models for each prediction horizon on the database.

The artificial neural network (ANN) models in NELION use a

single hidden layer with a single output unit, which represents

the prediction of the model. The units in the input layer are

mapped to the input tuple of the network. Each unit in the

hidden and output layers is fully connected to the previous

layer and has an additional link to a threshold input, which has

a constant input of one.

Since the model is only defined for an input range of between

zero and one, all input data is normalized to a range between

zero and 0.5. This ensures that all values remain within unity,

since the stock prices in our experiments never doubled their

value within one unit of the investment horizon.

As suggested by Weigend and Nix, the hidden units have a

sigmoidal transfer function while the output unit uses a linear

transfer function [Weigend, Nix, 1994]. The artificial neural

network was trained using the back propagation network as

described in Chapter 2. The learn rate and momentum

92 Methodology

parameters were set to 0.1 for all units, but in an effort to

speed up convergence, the learn rate was left dynamic and

increased or decreased by a factor two if consecutive updates

were in the same direction.

h=2...14

2

2

i 1

1 h

o

Input Units

Linear Transfer Function

Sigmoidal Transfer Function

i=2...14

Figure 4.5.1: Artificial Neural Network

The system used batch learning so that weight updates on

each link were performed after every epoch since this proved

to be more reliable than on-line learning. Since the test error

initially tends to exhibit rather erratic behavior, NELION

imposes a minimum number of 500 epochs. Learning was

stopped after three consecutive epochs increased the test

error or until it reached a maximum number of learning

epochs. This value was set at 1000 for an investment horizon

of one day, 2000 for one week and 3000 for one month.

These values were identified through experimentation and

helped some configurations, which remained near the

minimum error but never achieved three consecutive

increases.

NELION tested all combinations of artificial neural network

models with between two and 14 input units and between two

The Task Agent 93

and 14 hidden units and stored the best two for each

prediction interval.

The k-nearest neighbors (KNN) models algorithm retrieves

each tuple in the test set and searches the training set for the

constellations, which resemble the given pattern most closely.

NELION calculates all models with between two and 14 input

values and identifies between k=2 and k=14 “nearest

neighbors.” The distance from the input tuple to the tuples in

the training set is calculated using the Euclidean metric,

though the genetic algorithms described below can select

between this and a Gaussian or constant metric.

The prediction for each tuple is the weighted average of the k

nearest neighbors, where the weight of each neighbor is

inversely proportional to the distance as shown in the equation

below.

∑=

=k

nn

ii

d

dw

1

Equation 4.5.3

The Markov models (MM) use between four and 14 input

values and select between four and 20 random states from the

training set. The system then assigns each tuple in the

training set to one of these states and then counts the number

of transitions from one state to another. Given these numbers,

it is possible to calculate the probability of each transition. The

prediction was the weighted outcome of between one and all

94 Methodology

states used in the model. The weighting algorithm is the same

as for k-nearest neighbors algorithm.

4.5.4 Calculate Correlations

The correlation between stock x and stock y measures how

closely the two time series are related and is calculated as

follows:

( )( )( )

( ) ( )∑∑

∑−−

−−=

ii

ii

iii

yyxx

yyxxyx

22,ρ Equation 4.5.4

In the formula above, xi represents the price of time series x at

a specific time i and x is the mean price for all i. The task

calculates the correlation between the given time series and

all other time series tracked in the system. If time series x

equals time series y, the correlation is unity by definition.

4.5.5 Send E-Mail Update

In order to provide the investor with an update on his portfolio,

its total value and the loss or gain for each stock currently

held, the system periodically sends an e-mail to the specified

address. The frequency of these messages is set for each

investor, though the task can be created manually at any time

for one specific or all investors.

The Task Agent 95

4.5.6 Calculate Recommendation

Given models for all stocks tracked in NELION, the system

calculates predictions for investment horizons on a daily,

weekly and monthly basis. It is assumed that the transactions

executed by the investor have a negligible influence on the

stock market as a whole. The system uses the model with the

lowest NMSE to predict the future stock price. It is worth

noting, that the MM and KNN models use the entire historic

data to predict the future stock prices and not only the test set,

as was done during the model calculation.

The predictions for each stock are stored on the database as

the percentage change from the current stock price and form

the basis of a recommendation for each investor. Additionally,

however, the recommendations take the current portfolio as

well as risk adversity parameters of the investor into account

by calculating the relative risk of all favorable future portfolios.

The parameters pertain to stock correlation, volatility, model

error and trading volume as well as a minimum transaction

amount.

The correlation between two stocks measures the likelihood of

congruent movement in response to external market forces,

like interest rate changes, new laws, political conflict or acts of

nature. The volatility measure described above measures the

variability of the stock price. Stocks with a high volatility tend

to show erratic price movements, making them a riskier

investment than those with a low volatility. NELION is able to

forecast some stocks with greater precision than others,

96 Methodology

resulting in a lower NMSE for these time series. An investor

can specify that the recommendations should favor these

stocks, since this would decrease the risk of the resulting

portfolio. A stock with a high turnover volume tends to show

greater price stability. Additionally, the transactions by the

investor affect the market price of the stock to a lesser degree

for stocks with a high volume. Consequently, this reduces the

risk associated with these kinds of stock.

In order to identify the portfolio with the lowest relative risk

given the investor parameters, NELION calculates the risk of

the current portfolio using the following equation.

∑∑= =

⋅⋅=

n

i

n

j ji

jijiji

O

ELCRisk

1 1 ,

,,, Equation 4.5.5

In this equation, the factors in the numerator (Ci,j for the

correlation, Li,j for the volatility and Ei,j for the measure of error)

increase the risk of the portfolio and the volume factor Oi,j in

the denominator decrease it.

The dependence on the correlation Ci,,j is defined as follows,

where C represents the investor specific correlation

parameter, Ii is the portfolio value currently invested in stock i

of and ρi,,j is the correlation between stock i and j.

( )( )[ ] 11,, +−= jijiji IICC ρ Equation 4.5.6

Similarly, the volatility, error and volume components are

defined as follows.

The Task Agent 97

( )[ ] 11, +−= jiji llLL Equation 4.5.7

( )[ ] 11, +−= jiji eeEE Equation 4.5.8

( )[ ] 11, +−= jiji ooOO Equation 4.5.9

In these equations, L, E and O represent the investor

parameters for volatility, model error adversity and volume

preference respectively and must be in the interval [0,1]. The

terms li, ei, and oi represent the volatility, model error and

current trading volume for the stock i.

The relative weight of each factor is determined by the

relationship between each parameter. A comparatively large

value of L, for example, increases the weight of the volatility

characteristics, which can be interpreted as a particular risk

adversity as it pertains to volatility.

Each of the individual factors is reduced to unity in case one of

the parameters C, L, E and O vanishes, making the risk

calculation independent of that component. This is equivalent

to the investor stating that the corresponding component

should not be considered in his risk calculation.

Several boundary conditions were handled as exception cases

in NELION. If the trading volume oi of a particular stock was

zero, the entire term in the double sum was disregarded. This

is equivalent to disregarding this stock completely. If all

investor parameters were set to zero, all terms in the double

98 Methodology

sum would be unity and the calculated risk would be the same

for all possible portfolios. This is equivalent to the investor not

making any statement regarding his investment preferences

and is disallowed by the system.

It is important to note that the equation above represents a

relative risk calculation and that it does not map directly to a

physical quantity. It does, however, permit NELION to

compare the relative risk associated with different portfolios by

initially calculating the relative risk value for the current

portfolio and then searching for portfolios with a lower relative

risk.

This is done using the gradient decent method over this n2-

dimensional parameter space. The standard algorithm is

restricted to prevent the recommendation of negative

ownership of specific stocks, called “short positions.” The

system starts its search with a step size of one and iteratively

calculates the resultant portfolio. In case the resultant portfolio

does not have a lower relative risk, the step size is reduced by

a factor two and the iteration is restarted. This process

repeated until the step size has diminished to 10-8.

Once the optimal portfolio is calculated, NELION filters it to

ensure that the minimum transaction limit for the investor is

not violated. This restriction prevents the system from

recommending purchases or sales, where the cost of the

transaction outweighs the benefit of it. This filter also validates

that a sale suggestion of a particular stock does not result in a

portfolio, where the sale of the remaining stocks of the same

The Task Agent 99

company would force a transaction that would fall below the

minimum transaction volume at the current price. In such a

case, the system would recommend selling all of the stocks for

this company.

For example, if NELION finds the optimum by selling 60 of the

100 stocks of company XYZ in the portfolio, and the future

sale of the remaining 40 stocks would result in a transaction of

less than the minimum transaction volume, it would

recommend selling all 100 stocks.

In order to ensure that the expected portfolio return specified

by the investor is met, the portfolio selection only includes

stocks, for which the system has predicted a price increase

greater than this threshold. This results in a customized

portfolio recommendation for each investor, which is sent to

his e-mail address for the next investment horizon. For the

auto-investors, the recommendations are “executed”

immediately, so that the purchases and the portfolio are

updated automatically.

4.5.7 New Time Series

This task combines the tasks that are necessary for each new

time series: Internet Load, Calculate Volatility, Calculate

Models and Calculate Correlations.

100 Methodology

4.5.8 Test Investor

In order to identify parameters that correspond to the risk and

return expectations of an investor, NELION provides the Test

Investor function. This task simulates the behavior of an

investor for a specified period in the past so that the outcome

of the resulting portfolio can be analyzed.

This function is designed with the assumption that test

investors with all different parameter combinations are created

on a specific database. The investors are then tested in a

defined interval of sufficient length to be able to analyze their

behavior.

Assuming that the dynamics of the past hold in the future, one

can then aggregate the results from many different parameter

combinations. It is then possible to make statistical

statements about investors with certain parameter

combinations so that a potential user of NELION can select

the risk and return structure suitable for his needs.

4.5.9 Parameter Selection with the Genetic Algorithm

Since the computer running the task agent only responds to

requests entered into the task list on the database, it spends

the majority of its time waiting for new jobs. This processing

time is nevertheless available for productive tasks at no

incremental costs. In order to take advantage of this power,

NELION starts a background thread to search the parameter

The Task Agent 101

space of the prediction models using a genetic algorithm if no

other tasks need to be addressed immediately.

Genetic algorithms imitate the gene selection process from

nature to mix different traits from two parents, in the hope of

generating a child that can outperform either parent, as

defined by some fitness function. Much like in its biological

equivalent, where an animal, the genotype, is defined by its

genetic makeup, its phenotype, a mathematical model can be

specified by a series of parameters. These parameters are

encoded in a string of bytes of a finite length.

Biological reproduction entails the selection of specific genes

from the two parental phenotypes. Similarly, a mathematical

genetic algorithm maps this crossover function to the random

selection of bytes from the phenotypes of the two parents

resulting in a child phenotype, which has inherited some

features from either of its parents.

Biological mutation is a process by which a specific gene was

not inherited from either parent but is randomly generated,

frequently through some sort of defect or external influence.

In the overwhelming majority of cases, this leads to children

with undesirable characteristics. However, occasionally, this

leads to a new trait that increases the likelihood of survival and

begins to dominate the population thereafter. This dynamic

can be imitated in genetic algorithms by selecting random

bytes instead of inheriting them from one of the parents on

occasion.

102 Methodology

The child phenotype can be used to generate a new

mathematical model, which can be trained and tested. If the

model error is lower than either of its parents, it is apparently

superior and can replace one of the two parents.

For each stock and model type (ANN, ARN, MM and KNN) the

system stores two models with the lowest test error as

parents. Using these two models, the algorithm uses

crossover and mutation to generate new models, calculate the

predictive quality of them and to replace the worse of the

existing parent models if the child test error is lower than either

of them. The likelihood of mutation is controlled through a

system parameter, which can be anywhere between 0% (no

mutation) and 50%, meaning that on average every second

byte is randomly selected with no heritage from either parent

phenotype.

The resulting phenotype is converted back to a genotype by

interpreting the string and populating the parameters of a new

model. These parameters are validated to ensure a valid and

sensible configuration. The specific parameters and validation

depends on the model type and are shown in the table below.

The Task Agent 103

Model Parameter Validation

ARN # input values

• Can not be more than twice the # of input values of either of the parent models

• Can not be more than 32 • Must be at least 1

# input values (units)



# hidden units



ANN

Transfer Function • Must be 1 or 2 representing the constant a in the transfer function

# input values



# of nearest neighbors (“k”)

• Can not be more than twice the # of nearest neighbors of either of the parent models


Metric • Must be 1, 2 or 3 representing Euclidean, Gaussian or Constant functions

KNN

Weighting • Must be 1, 2 or 3 representing Euclidean, Gaussian or Constant functions

# input values



# states

• Can not be more than twice the # of states of either of the parent models


# states used to calculate prediction

• Can not be more than # states • Must be at least 1

MM

Weighting • Must be 1, 2 or 3 representing Euclidean, Gaussian or Constant functions

Table 4.5.1: Genetic Algorithm Parameter Validation

104 Methodology

Given the verified parameters, the system calculates the

model and if its test error is lower than that of either of the

other two models, the system replaces it on the database.

5 Implementation

5.1 Overview

While many mathematical models concentrate on the

prediction of stock prices, few use these predictions to

manage a portfolio given the theoretical basis described in

Chapter III. I have developed a system, NELION, based on

non-linear stock prediction models and this investment theory.

It uses the many different possibilities that the Internet offers

both for data retrieval as well as user interaction.

NELION is designed to manage the portfolios for numerous

investors and to suggest customized purchases and sales for

each, in an effort to achieve an optimal portfolio. Investors

can request to receive portfolio recommendations on a daily,

weekly or monthly basis, depending on their preference.

Correspondingly, these recommendations are based on

mathematical models, which take into account daily, weekly or

monthly stock data.

As described in Chapter 4, NELION is divided into four

components that are shown in Figure 4.1.1. The database is a

Microsoft SQL Server 7 running on MS Windows 2000 and the

Task Agent and Administration Tool are two applications

written in Microsoft Visual C++ 6.0. The User Interface runs

106 Implementation

on MS Internet Information Server and uses Active Server

Pages. All components connect to the database via an ODBC

interface, which is used to manage the entire data pool. Both

Visual C++ programs require the ODBC Data Source Name

(DSN) of the NELION database as an input parameter and

use MS Windows authentification to ensure access rights.

5.2 The HTML Interface

The HTML Interface runs on MS Internet Information Server

5.0 and provides the investor with a means to manage his

portfolio. Since this web server is not connected to the

Internet continuously, the domain www.nelion.net is hosted on

an Internet service provider and when the web server logs

onto the Internet it updates a link on the welcome page to it.

After a successful log in using the e-mail address as a user

name and a password, the investor is shown an overview his

current portfolio.

The HTML Interface 107

Figure 5.2.1: Porffolio Overview via the HTML Interface

The upper half of the page is devided into two columns: The

left side contains basic portfolio information including the e-

mail address, the sum of all stocks currently owned, the cash

reserves in the portfolio and the sum of these two figures,

which represents the total value of the portfolio. It also shows

the gain or loss in portfolio value both in US dollar and in

percentage terms. The right side contains a graph comparing

the return of the portfolio with the developments of the Dow

Jones Industrial Index and the Nasdaq.

Below these two components, the web page shows a list of all

stocks in the current portfolio, including the ticker symbol, the

full stock name, the current price and quantity as well as the

product of these two values, which represents the total

108 Implementation

investment in this stock. Lastly, the table shows the total gain

or loss that the investor has incurred with this stock.

Finally, the web page contains a further table with the current

recommendation for the investor. This component contains

the same column as the portfolio table, with the exception of

the gain. A positive quantity represents a buy, a negative

quantity a sell recommendation.

From this page, the investor can select numerous links that

permit him to manage and adjust his portfolio.

5.2.1 Stock Search

The stock search link opens a new window that permits the

entry of a stock ticker symbol, a company name or a part of a

company name. After completing this information and

pressing the “Search” Button, NELION will attempt to locate a

stock with the specified stock symbol.

If it can not find the corresponding company, it will list all

companies that contain the word specified in the search field.

The ticker symbol for each company in the list also serves as

a link to the relevant stock, so that the investor can view all

relevant company details.

The HTML Interface 109

5.2.2 Buy/Sell Stock

This link is used to update the portfolio after a transaction.

NELION will open a dialog in the menu window when the link

is pressed and will request the investor to specify whether a

stock was bought or sold. Additionally, it needs the

transaction date, the ticker symbol, the amount, purchase or

sales price as well as the transaction costs. The latter will be

defaulted with the value specified in the investor parameters.

5.2.3 Deposit/Withdraw Cash

If the investor changes the cash reserves by depositing or

withdrawing cash from the account, he will need to update the

portfolio accordingly with this link. The system will respond

with a dialog in the menu window requesting information on

whether cash was deposited or withdrawn from the account,

the transaction date and the cash amount.

5.2.4 Password

In order to change the NELION password, an investor has to

enter the current password and type the new password in

twice. The double entry is necessary since none of the

passwords are shown in clear text but only with a star (“*”) for

every character entered.

110 Implementation

5.2.5 Parameters

This page is used to specify all investor preferences and

parameters. For each parameter, the system offers an

explaination on the usage of this parameter. Besides the

investor name, e-mail and SMS e-mail address, the system

requires information on the investment horizon and the e-mail

frequency. The transaction cost field is used to populate the

“Buy/Sell Stock” dialog with a correct default value. The

remaining parameters focus on the risk adversity of the

investor and include the minimum transaction amount, as well

as the volatility, error, volume and correlation risk adversity.

This same page is used for the online application of new

investors. It allows a new applicant to specify all relevant

parameters when he opens an account without intervention by

the NELION administrator.

5.2.6 Log Out

The log out link removes a session token from the web server

so that no additional transactions are possible and returns the

investor to the NELION welcome page.

5.3 The Administration Tool

The NELION Administration Tool is the primary tool for the

administrator of the system. It contains all common features


of an MS Windows application including a menu, icon bar for

short cuts and a status bar at the bottom of the screen.

Figure 5.3.1: The NELION Administration Tool

The program is written using a multi document interface (MDI)

so that the administrator can open multiple windows, each

displaying information for a specific investor or stock.

Additionally, it is possible to open a window for the system

parameters. The task list is also implemented as a MDI

window but, unlike the others, it remains open on the left side

of the screen as long as the application is running.

Following the MS Windows standard, the Administration Tool

uses multiple tabs in documents in order to make optimal use

112 Implementation

of the available screen real estate. Some of these allow the

user to enter or update data pertaining to the corresponding

entity, while others show historical, calculated data or

parameters. They are described in detail in the following

sections. Full screen prints are included in Appendix C.

5.3.1 Investors

The “General” tab for the investors contain the basic investor

information like the name, e-mail address, investment horizon,

e-mail notification interval, transaction costs and minimum

transaction amount, as well as all investor risk adversity

parameters. The investor type is maintained here as well and

for test investors the data entry fields for the beginning and

end of the test have to be entered. The investor number

cannot be modified and represents the internal system

number. Similarly, the portfolio value is calculated from the

current stock prices held by the investor.

The “Portfolio History” tab displays a graph of all the stocks

that the investor owned since he started tracking his account

on NELION. The proportional value of each stock as well as

the overall value of the portfolio is visible at a glance for the

entire portfolio history.

On the “Purchases” tab, the Administration Tool provides a list

of a purchases and sales undertaken within the portfolio.

Each transaction is one record and includes the ticker and


company name, date, stock price, amount, and the product of

these two, representing the total transaction value.

The “Portfolio” tab displays a list where every record

represents one stock that is currently held. Each line contains

the ticker and stock name, the current stock price, the amount

held and again the product of these two, representing the total

value of the stock. The sum of these values is shown on the

header of this column representing the total portfolio value.

Finally, the list contains a column for the value gained or lost

with this stock.

The “Return” tab shows the actual return on the investment for

three different periods: Since the portfolio was included in

NELION, since the beginning of the calendar year and in the

last 12 months.

5.3.2 Stocks

The “General” tab for a stock includes the ticker and stock

name and the web site for data download. At present, the

latter only offers one option, which is “Quote Central.” If more

sites provide historic stock data, especially for European and

Asian stocks, this list and the additional required functionality

would be expanded. The ticker name is used to create a table

on the database to store the daily price and volume

information for the stock.

114 Implementation

The two additional pieces of information on the tab, current

price and volatility are read-only fields since the former is

downloaded from the Internet and the latter is calculated.

For a new stock in NELION, this is the only tab available.

When editing an existing stock, three further tabs with

information are available. The “Models” tab shows a list with

the header information of the mathematical models stored for

this stock. Each model has a name, the number of data input

values used, the prediction interval as well as the NMSE.

The “Graph” tab displays the price movement over time of the

stock. The graph auto scales the y-axis to ensure that the

entire data is visible on the screen.

Finally, the “Correlation” tab shows a list for the correlations of

the chosen stock with all other stocks in the system. The list is

sorted in decreasing order, so that the selected stock will

always be at the top with a correlation of “1”.

5.3.3 Parameters

The “Parameters” data entry screen permits the maintenance

of the system parameters. The “Refresh Interval” parameter

controls how often the Administration Tool will update the task

list. The entry is interpreted in seconds, so that a value of 60

will result in a refresh rate of once a minute.

The “Bank Interest Rate” represents the return on cash kept

with the broker or with another bank. Since this can be viewed

The Database 115

as a risk-free investment, any stock purchase, which is by

definition risky to a greater or lesser degree, is only

recommended by the system if the prediction for it exceeds

the bank interest rate.

The “Time Difference to New York” parameter records the time

difference from the current location to the home of the New

York Stock Exchange. Since “Quote Central”, the Internet

source of our data, does not update the historic stock price

and volume list until approximately 4:00 a.m. local time in New

York, we use this value to calculate the time for the Internet

data download.

The “SMS Threshold” defines a band of uncritical price

swings. If the price of a stock changes by an amount, which

exceeds the SMS threshold, all investors who own the stock

as well as the NELION system administrator are notified

through an e-mail. The e-mail address is different from the

one used for regular updates and should be tied to a

messaging provider that forwards the e-mail to a specified

mobile phone via short messaging system, SMS. The system

administrator’s SMS e-mail address is defined in the

corresponding system parameter.

5.4 The Database

The NELION database server runs on MS Windows 2000 and

employs MS SQL Server 7.0. This software infrastructure

ensures scalability to a multi-gigabyte installation, while

permitting an individual investor to work with standard PC

116 Implementation

hardware on a single, modern workstation. The database

platform includes functionality to ensure referential integrity, by

including counters, stored procedures, triggers, primary and

foreign keys and other constraints.

In order to harness the power of these tools effectively, I used

S-Designor DataArchitect 5.1 to design and document the

database, which only required a few manual adjustments for

installation. The graphical tool permits relating tables

graphically and generates an SQL script for different database

types. The database creation is then limited to the execution

of this script and assigning user access rights.

DataArchitect also allows the definition of data types, which

map to types supported by the underlying database. In a first

design, I defined a type “Geld”2, which mapped to the data

type “money”. At a later stage, I reduced the number of

different data types and mapped “Geld” to “float”, in an effort to

reduce complexity. This merely required creating a new

database and transferring the data to it, with an appropriate

mapping from “money” to “float”.

MS SQL Server offers scheduled tasks, which I used to

automatically generate tasks in the task list for e-mail updates

of the portfolio value and recommendations for the investors.

Similarly, the system inserted an “Internet Download” task into

the task list once a weekday. In order to adjust the

2 "Geld“ is the German word for „money.“

The Database 117

mathematical models to the changing dynamics of the market,

NELION autonomously increased the error of all models by

5% every Sunday. This gave new models calculated by the

genetic algorithm a better chance of undercutting the existing

models, with no loss of generality. In a worst-case scenario, it

identified a model with the same parameters as optimal again,

so that it merely overwrote itself.

A trigger on the “Purchases” table secured referential integrity

between transactions, investor portfolio and the investor

header tables. When a purchase or sale was entered, either

through the Administration Tool or directly on the database,

the trigger updated the “Portfolio” table and reduced the

portfolio value on the investor table to reflect the associated

transaction cost.

Since the data tables for each stock were created dynamically

and represented the bulk of the tables in the database, I did

not include the same trigger on each of these to keep the

current value of the header table updated. Instead, I wrote a

stored procedure that was called from the Administration Tool

and updated both the data table and the stock header table

when data was downloaded from the Internet.

A number of tables used to store the mathematical models

contained a database-internal counter as the primary key,

since this key was a foreign key in subsequent tables. This

design reduced the data requirements in the database and

normalized the tables effectively. When storing a model on

the database, it was necessary to save the model header

118 Implementation

information and then to retrieve the counter because it was a

required piece of information on the detailed tables. Here, I

also used stored procedures to save the record and

immediately deliver the ID as the return value, because it

reduced the database accesses from two to one, thereby

optimizing the system.

Though the insert function automatically increments the

counter for a table, I manually added a stock with the counter

“0”, which is defined as “Cash”. It is used to maintain the cash

held by the individual investors in their respective portfolios

and is automatically adjusted to account for purchases and

sales. Similarly, on the Purchase table, each transaction

results in an entry for this “stock” to account for the transaction

costs, as they are defined for each investor.

5.5 The Task Agent

The Task Agent is a separate program with a simple interface

that consists of an “Exit” button as well as nine check boxes,

which allow the user to define which actions this instance of

the program should perform. When the program exits, the

current configuration is stored in the MS Windows registry and

is restored the next time the program is started to ensure that

the same configuration is retained.

The Task Agent 119

Figure 5.5.1: The Task Agent Program

Two text boxes provide the user with a description of the

current object and the actions on that object that are currently

executed. The objects are either the stock or an investor from

the corresponding table.

The server process typically “sleeps” until either the

Administration Tool or a scheduled task enters a record in the

task list. In this state, it could start a second thread that

benefited from the idle processing time to search for improved

prediction models using a genetic algorithm. While performing

this optimization, a progress bar is updated every second to

show that the system is still running and checking for new

tasks every six seconds.

If it found an “Open” task in the task list, it marked the task as

“Working” so that no other Task Agent on the network begins

executing them. After performing the relevant task, it deleted

the task from the task list and the cycle starts afresh.

120 Implementation

The Task Agent can perform nine different functions, which

are described in detail in the following section.

5.5.1 Internet Load

The Internet Load function assumes that a permanent

connection to the Internet exists and downloads data from a

site called “Quote Central”, which has its Internet homepage at

www.wallstreetcity.com. Navigating to the “Stocks” tab on this

site allows the user to enter a stock ticker name to retrieve

stock data and charts with a 20-minute delay. On the left-

hand side of the screen, it also provides the option to view

historical quotes. Choosing this function, the site provides

options to enter the stock, the start and end dates of the

historic data requested, the data interval as well as eight

different formats for the historical stock data. After selecting

the appropriate parameters, pressing the “Get Quotes” button

performs the request.

By analyzing the URL that results from this request, one can

automate the retrieval by generating it within NELION and

executing it directly. The Internet Load function builds the

correct URL, using a daily interval and requests historic stock

data in the “HEADER 5 – Super Charts” format. In order to

limit the data download, it sets the start date to the day of the

last date available in the system and overwrites it in case it

has been updated. All new data is appended to the stock data

The Task Agent 121

table. For newly created stocks, NELION attempts to

download all data since January 1, 1980.

After sending the request to the Internet site,

wallstreetcity.com responds with a new page, which contains a

temporary link to a page with the “Historical Quote Header 5

Export File”. NELION extracts this link and executes it. The

result is a comma deliminated ASCII file, which contains the

date, open, high, low and close prices as well as the daily

volume. From this page, it extracts the close price and volume

for each day and stores them on the database. For days,

which do not have an entry on the web site, like public

holidays and weekends, NELION generates a fictitious record

using the previous stock price and volume figures. In case the

price changes more than a specified percentage from one day

to the next, the system automatically sends an alert to all

investors, who own the stock as well as the system

administrator. The e-mail address of this alert can be different

from the address used for regular updates, so that the investor

receives it as an SMS notification on his mobile phone. The

technical details of this function are described in section 5.5.5

below.

Since the system does not download any images, the data

volume of the download is kept at a minimum so that the daily

update per page can be accomplished within one second,

given the necessary bandwidth to and within the Internet.

Since the system is tailored to this specific site map, it is clear

122 Implementation

that a change in the structure at wallstreetcity.com will require

an adjustment of the NELION Internet Load function

Though other sites also offer historic stock quotes, many are

fee-based and require a log in process, which complicates the

retrieval. Of those that were free of charge none that I found

offer the simple ASCII format and several tests showed that

parsing an HTML page is considerably more complex and

error prone.

It is worth noting that the system does not retrieve dividend

and stock split notices, so that these would have to be entered

manually. The former would merely be an adjustment to the

available cash. For the latter, stocks are normally split in a

ratio of 2:1 or 3:1, so that one can expect a drop in the stock

price by approximately 50% or 66% respectively. The investor

database administrator will be alerted to drastic changes in

price through the SMS notification so that he can take

appropriate action.

5.5.2 Calculate Volatility

Calculating the volatility of a stock is a straightforward

implementation of the equation described in 4.5.2. To this

end, NELION retrieves all of the data of a particular stock and

executes the loop described in the section. This task is

performed when a new stock is created and can be repeated

periodically thereafter.

The Task Agent 123

A single task in the task list, for stock ID “0” performs this for

all stocks. Since this stock counter refers to “Cash” and no

data table exists for this dummy stock, the instruction is well

defined.

5.5.3 Calculate Models

Before a forecast for a stock can be calculated, it is necessary

to calculate predictors. The Calculate Models task performs

this task for a specific stock for all investment horizons (one

day, one week and one month) and all model types (ARN,

ANN, KNN and MM), keeping only the two models for each

combination that have the lowest NMSE. The algorithm for

the model calculation follows from section 4.5.3.

It is worth noting that though the database only stored all

model and financial parameters as floats, all models employed

the data type double in RAM, in order to ensure greater

precision for internal calculations, potentially increasing the

quality of the results.

Given the models as a basis, the system was able to make

predictions for each horizon. In an effort to continually improve

the quality of the models, however, the fine-tuning of these

predictors took place in the genetic algorithm implemented in

the background thread described in section 5.5.9.

124 Implementation

5.5.4 Calculate Correlations

To calculate the correlations for a stock, the system loaded the

historic data into memory, excluding weekends. It then

iteratively loaded the data for the remaining time series into

memory and started calculating the correlation as specified in

section 4.5.4 starting with the later of the two beginning dates.

The function did not disregard public holidays, because this

does not significantly affect the calculation and helps reduce

the complexity of the application.

5.5.5 Send E-Mail Update

The Send E-Mail Update function is designed to keep the

investor informed on the status of his portfolio. The subject of

the message contains the current total account value and in

parentheses the change from the last e-mail.

The body of the e-mail contains a table with all the stocks that

the investor currently holds in his portfolio. For each stock, the

message shows the number of shares, the current price and

the product of these two, representing the value held in this

stock. The last column shows the total gain or loss that the

investor has incurred to date with this investment. The last

row is always the current cash holdings of the portfolio. At the

bottom of the table, the message shows the sum of all

investments representing the total portfolio value.

The Task Agent 125

All dollar amounts are displayed with three significant digits, to

ensure that eights of dollars (US$ 0.125) can be represented

accurately.

NELION generates a plain-text e-mail and needs a MAPI

compliant e-mail client to send it. The application uses the

default profile to access the e-mail services. The MAPI client

does not have to be running, but its behavior and settings

determines how the message is treated thereafter. I tested

the task agent with Outlook Express 5 running under Windows

2000 as well as Outlook 2000 running under Windows 2000

and Windows 95. The OS did not affect the operation, but

although both e-mail clients were set to send e-mails

immediately, only Outlook Express 5.0 performed this action,

even if it was not started. Outlook 2000 needed to be started,

but only sent the message because it was configured to send

and receive new messages every ten minutes.

In order to provide a consistent appearance, I registered the

domain name NELION.NET. All e-mail was sent using the e-

mail address [email protected].

5.5.6 Calculate Recommendation

In the recommendation calculation for a specific investor,

NELION attempted to load the prediction with the specified

investment horizon for each stock into memory. If the

prediction did not exist on the database, it proceeded to load

all historic stock data and the model with the lowest NMSE

126 Implementation

into memory and calculated the prediction. To make this

prediction available for subsequent recommendations, it was

stored on the database.

With the predictions in memory, NELION identifies the stocks,

which promise to achieve an annual return bigger than the

bank interest rate and uses the algorithm described in section

4.5.5 to identify the optimum portfolio.

The investor subsequently receives an e-mail similar to the e-

mail update described in the previous section. In addition,

however, the system adds a line for each purchase or sale

recommendation, specifying the stock and the recommended

number of shares. For Auto-Investors, the transactions were

simulated, using the most recent stock price and included

transaction costs in order to provide a realistic scenario for

comparison. In this case, the e-mail indicated exactly which

transactions were performed.

5.5.7 New Time Series

This task combines the tasks that are necessary for each new

time series: Internet Load, Calculate Volatility, Calculate

Models and Calculate Correlations. This was necessary in

case more than one Task Agent accessed the database,

because combining these tasks into a single function ensured

that they were executed sequentially. If they were executed in

parallel, one Task Agent might be downloading the historic

data from the Internet, while a second might start calculating

The Task Agent 127

its volatility, models or correlations with incomplete data, which

would have falsified the results.

5.5.8 Test Investor

The Test Investor function is necessary to identify parameter

combinations, which result in investment recommendations

that suit the preferences of each investor. The implementation

follows from the theoretical discussion in section 4.5.8.

In order to provide a realistic test environment, I created a

separate database, deleted all stock data after the beginning

of the test interval, and recreated all prediction models.

Thereafter, task agents on two computers spent two weeks

optimizing the models using the genetic algorithms of the

background thread.

The test investor results are discussed in detail in chapter 6,

where the experimental results show the quality of our Internet

trading system.

5.5.9 Parameter Selection with the Genetic Algorithm

If the Background Thread check box was set on the interface

and the task list of the database only contained functions that

the instance of the Task Agent was not requested to perform,

it started a program thread to calculate new predictors for a

randomly selected stock.

128 Implementation

In the foreground, the application continued updating the

progress bar every second and checked the task list every six

seconds. In case a new task was entered while the

background thread was active or the Exit button was pressed,

the program completed the calculation of the current model in

the background before ending the thread.

The symmetric multi-processor (SMP) architecture of Windows

2000 ensured that the two threads were executed on different

processors in multi-processor machines so that no

degradation in execution speed was noticeable. On a single

processor computer, the two threads had to share the

resources, so that two computing intensive tasks increased

the execution time.

The additional models calculated by the background task used

the genetic algorithm described in section 4.5.9, using

inheritance and cross-over to generate new model parameters

and then checking whether this model was able to achieve a

lower NMSE than either of its parents. If this was the case, it

replaced the worse of the two existing models and became a

parent for future calculations. This regenerative process was

facilitated by increasing the NMSE value of all models by 5%

every Sunday, because this permitted new models, which

capture new market dynamics, to replace outdated predictors.

6 Experimental Results

In order to test the trading system we described in the

previous two chapters experimentally, I first executed the Test

Investor function with different parameter configurations in

order to identify promising candidates for high risk and

conservative investment profiles. Once these investment

profiles were identified, I used them in a “live” simulation to

test their performance under realistic circumstances with the

“Auto Investor” function in NELION. In this chapter, I present

the results of these two steps. Additionally, I show the

distribution of the four different model types that were used in

the simulation.

6.1 Test Investor Identification

The “Test Investor” function in NELION is designed to identify

the optimal investor configuration for a high risk and

conservative investor. This option allowed the user to specify a

test interval to simulate the actions of investors with specific

parameters. I limited the parameter space to [0,1] for the

volatility, correlation, volume and error parameters and tested

weekly investors for the period from January 1, 1998 to

December 31, 1998. A second test included the period of

January 1, 1999 to December 31, 1999 with an initial capital of

US$ 10,000 and a minimum transaction volume of US$


250.00. The cost of each transaction was set at US$ 9.99,

which corresponds to the charges at the online broker

Datek.com and exceeds the cost at AmeriTrade.com. The

minimum expected return was 6%. The trials included all

combinations of parameters with values with an increment of

0.125.

As a measure of the risk profile, I examined the final portfolio

of each test investor and discarded parameter combinations,

which had more than 75% of the portfolio value invested in

one stock. Investors with between 50% and 75% invested in a

single stock at the end of the investment period were

considered “High Risk” combinations, while those with less

than 50% invested in one stock were considered

“Conservative” Investors.

This separation resulted in two sets of parameter

configurations, which I analyzed to identify a promising

combination by creating a cross tab query on every

combination with two of the four parameters. The resulting six

tables for each set and both test intervals for the subsequent

calculations are shown in Appendix A.

From the tables, I identified the parameter combination that

occurred the most frequent in each set and used this to define

two of the four parameters. This value is highlighted on the

tables in Appendix A a dark grey background. The table

below summarizes these results.

Test Investor Identification 131

Investor Parameter 1 Parameter 2 Conservative 1998 Volume=0.875 Error=0.75 Conservative 1999 Volume=0 Volatility=1 High Risk 1998 Volume=0 Volatility=0.875 High Risk 1999 Volume=0 Correlation=0.25

Table 6.1.1: Sample Investor with two Parameters identified

In a second iteration, I used these two values to identify the

parameter combination in the remaining four tables that

occurred the most frequently to define the third parameter. To

simplify the search, I highlighted all relevant columns and rows

in the tables of Appendix A with a light grey background and

identified the largest values with dark grey characters. This

specifies a third parameter as shown in the following table. Investor Parameter 1 Parameter 2 Parameter 3

Conservative 1998 Volume=0.875 Error=0.75 Volatility=0.875 Conservative 1999 Volume=0 Volatility=1 Error=0.625 High Risk 1998 Volume=0 Volatility=0.875 Correlation=0.875 High Risk 1999 Volume=0 Correlation=0.25 Volatility=0

Table 6.1.2: Sample Investor with three Parameters identified

Finally, using the three defined parameters, I identified the

combination from the last three tables that occurred the most

frequently to set the last parameter. The relevant columns

and rows are displayed with a medium grey background in the

tables in Appendix A, which had not been used and included a

medium grey line at the bottom or the left hand side of the two

columns or rows that had already been identified in the second

iteration.

For the conservative investor 1998, this did not uniquely define

the correlation parameter, because a volatility of 0.875 and a


volume 0.875 both had 14 occurrences in the correlation

parameter at 0.5 and 0.375 respectively. This seemed to

indicate that the maximum is somewhere between these two

values. Comparing the number of occurrences at 0.375 and

0.5 for each of these two parameters respectively indicated a

score of eleven versus ten occurrences, so that I opted for the

0.375 value. This is supported by the tests for the

conservative investor in 1999.

The results from this third and final iteration are summarized in

the table below. Investor Correlation Error Volatility Volume

Conservative 1998 0.375 0.750 0.875 0.875 Conservative 1999 0.375 0.625 1 0 High Risk 1998 0.875 0 0.875 0 High Risk 1999 0.250 0.500 0 0

Table 6.1.3: Sample Investor Parameters

The results show considerably more consistency for the

conservative than for the high-risk investors. The correlation,

error and volatility parameters changed only slightly between

the tests for 1998 and 1999, while the volume parameter

dropped from 0.875 to 0. For the high-risk investors, only the

volume parameter remained the same at 0, while the

remaining parameters underwent significant adjustments.

This is caused by two factors. Firstly, in 1998 the high-risk

investor selection only contained 150 investors, compared to

3774 in 1999. For comparison, the conservative investors in

1998 and 1999 had 1218 and 1360 profiles respectively in

their analysis. Consequently, the analysis in 1999 allows for a

Test Investor Identification 133

significantly higher degree of confidence, since it is based on

25 times more investor.

Secondly, the volatility in the markets rose in this period, most

notably for the Nasdaq, which had an increase of 17%

between 1998 and 1999. As a result, a number of profiles,

which had a volatility parameter of 0 in 1998, were spread

evenly between all investor profiles, so that the profiles with a

volatility value of 0.875 were able to dominate. In 1999, the

profiles with a volatility parameter of 0 were concentrated in

the high-risk selection and defined this set.

The conservative investor profile shows a consistently strong

adversity toward high volatility and stocks where the system

cannot effectively predict future movements. At the same

time, it does not disregard the need for a well balance

portfolio, as exemplified by the correlation parameter. This is

to be expected, since the portfolios in that conservative set

were chosen so that no more than 50% of the invested value

remained in a single stock at the end of the interval.

The high-risk investors disregarded the transaction volume

and, in 1999, volatility of the stocks completely. This is

consistent with the approach of relying on the raw predictions

since that parameter had the biggest weight in the 1999 test.

The result was a portfolio, which fluctuated, at times widely, as

one might expect.


6.2 Testing the Profiles

Using the results from the previous section, I tested the quality

of the system for one year starting May 15, 1999 with the

NELION test investor function. I configured a high-risk and a

conservative investor with the parameters calculated from the

1998 investor profiles. Each had a starting capital of US$

10,000, expected a return of at least 6% annually and required

a minimum transaction volume of US$ 250. The transaction

costs were calculated at US$ 9.99 per trade. On the January

15, 2000, I updated the profiles, which resulted from 1999 test.

Every weekend, the system had the opportunity to

automatically perform fictitious but unverified purchases and

sales. A detailed list of purchases and sales is included in

Appendix B. The portfolio development is shown in the

diagram below. The Nasdaq, Dow Jones Composites as well

as the S&P 500 indexes are included for comparison.

Testing the Profiles 135

80%

100%

120%

140%

160%

180%

200%

5/15

/199

9

6/15

/199

9

7/15

/199

9

8/15

/199

9

9/15

/199

9

10/1

5/19

99

11/1

5/19

99

12/1

5/19

99

1/15

/200

0

2/15

/200

0

3/15

/200

0

4/15

/200

0

5/15

/200

0

NELION High Risk

NELION Conservative

Nasdaq Composite

Dow Jones Composite

SP 500

Figure 6.2.1: Comparison of NELION Investors with Major Indexes


This diagram is not adjusted for inflation, which amounts to

approximately 1.6% in the test interval. For easy comparison,

the return on investment calculation for the interval is

summarized in the table below. NELION

High Risk

NELION Conser- vative

NELION Average

Nasdaq Composite

Dow Jones Composite

S&P 500

5/15/1999 $10,000 $10,000 $10,000 $2,528 $3,306 $1,338

5/15/2000 $15,323 $9,736 $12,530 $3,607 $3,143 $1,452 Return 53.2% -2.6% 25.3% 42.7% -4.9% 8.6%

Table 6.2.1: NELION Test Investor Comparison

The results exhibit a pronounced difference between the high-

risk and the conservative investor, the former achieving a

53.2% return, while the latter lost 2.6% of the portfolio value.

This follows from the portfolio held. The high-risk investor

disregarded the model error in the first half of the trial and

volatility in the second so that his investment choices

gravitated toward stocks traded on the Nasdaq because they

tended to exhibit comparatively erratic behavior. This

correlation is apparent from Figure 6.2.1, where the portfolio

value of the high-risk investor and the Nasdaq remained close

during the entire year. NELION beat the index the first six

months, trailed it slightly at the beginning of 2000 and

regained the edge shortly before the correction in March 2000.

Though this adjustment did not pass by the NELION portfolio,

the drop was not as pronounced as for the Nasdaq.

The conservative portfolio consistently emphasized good

predictability of the stock, as one might expect. Consequently,

Testing the Profiles 137

it chose fewer volatile stocks resulting in a mix between Dow

Jones and Nasdaq stocks. The fact that the “old economy”

stocks did not perform well is documented by the 4.9% decline

of the Dow Jones Composite during our simulation interval.

Two changes in the portfolio value are worth noting here: On

November 21, 1999, the conservative portfolio held 1072

stocks of Angeion Corporation at US$ 0.88 a stock. Within

two days, the price had jumped to US$ 2.25 and continued

climbing up to a peak of US$ 3.94 on February 18, 2000. This

increase pushed the value of portfolio up 16% within two days

and is clearly visible in on the graph above. On the other

hand, the conservative investor purchased 80 shares from

Fruit of the Loom on May 15, 1999 for US$ 11.88 each, for a

total investment of US$ 950.40. Unfortunately, the company

sought protection under Chapter 11 of the bankruptcy law on

December 28, 1999 so that this investment was lost

completely.

The average of the two NELION portfolios achieved a healthy

25.3% return on investment, well above the S&P 500.

Compared to a risk-free investment in government bonds,

which returned about 6%-8% annually, these portfolios

represent a very attractive alternative. Bearing in mind that

the returns already account for transaction costs, they

compare favorably to many mutual funds, which state the

return on investment without mentioning their charge of

between 3% and 5% of the invested value.


6.3 Model Distribution

In the test above NELION selected the weekly trial portfolios

from the total list of stocks tracked, which is included in

Appendix E. However, since the system is designed for

investment horizons of one day, one week and one month, it

calculated models for all of these intervals. For the

overwhelming majority of the stocks, NELION was best able to

predict future values using the k-nearest-neighbor models.

For a detailed list, please see the table below. Model Type Daily Weekly Monthly

ANN 0 1 7 ARN 11 2 1 MM 0 3 5 KNN 96 101 94

Table 6.3.1: Model Type Usage

The low success rate of auto-regressive models is not

surprising, given the complexity of stock price movements.

The dominance of k-nearest-neighbor models over the Markov

and Artificial Neural Network models seems to indicate that

the stocks used in this experiment exhibit low–dimensional

chaotic behavior, since the complexity that KNN models are

generally able to model is lower than the other two non-linear

predictors. Hsieh supports this by showing that stock market

data is a low-dimensional deterministic system [Hsieh 1990].

The ANN models require considerably more processing time

than any of the other models. This poses a challenge, since

the algorithm tends to spend as much time calculating these

Daily Operation 139

models, as it requires for all the others together.

Consequently, the initial model calculation does not search the

parameter space of these models as extensively as it does for

the remaining model types, which may have further helped the

dominance of the KNN models.

6.4 Daily Operation

The application evolved over the months and years in

response to the specific requirements of private investors and

addresses their immediate needs in its current form. Several

distinguishing features were emphasized repeatedly, beside

the obvious guidance with specific suggestions.

Overall, the investment recommendations were considered

valuable because they helped direct attention to opportunities

that are beyond the scope of an individual investor.

The customization of the suggestions instilled a significant

amount of trust, because each investor felt that he was getting

individual attention. It was clear that the recommendations

were not of one mold and independent of the personal goals of

the investor, so that there was no cause for suspicion that the

recommendations were motivated by NELION’s personal gain.

The recommendation and update intervals differ widely

between persons who actively participate on a daily basis and

investors with a long-term horizon and each appreciate the e-

mail frequency.

7 Conclusion

There exist numerous articles and papers on various

approaches to the prediction of financial time series. Each of

these focuses on the specific qualities of the data at hand and

attempts to optimize the predictions for it based on historic

values. On the other hand, the theory of portfolio

management is documented and widely agreed, in its basic

form. Though these two components must be combined to

form a coherent portfolio management system, academic

papers have largely ignored this comprehensive approach.

The goal of this thesis was to build a fully integrated Internet-

based system that helps a private investor focus on promising

opportunities from the vast amount of financial data that is

available. NELION retrieves historic stock data from the World

Wide Web, stores it on a local database and uses four

mathematical model types to predict stock prices at different

intervals in the future.

At the same time, it allows an investor to choose from four risk

adversity parameters to establish a risk profile that matches

his needs. Given the investor preferences and stock

predictions, the system calculates the optimal portfolio for the

investor and sends him an e-mail with these

recommendations. The investor can then evaluate these

Daily Operation 141

suggestions based on qualitative indicators, which cannot be

captured in the mathematical models. NELION tracks his

portfolio, provides regular transaction recommendations, and

updates via e-mail and alerts via SMS to his mobile phone in

case any one of the stocks in his portfolio undergoes dramatic

swings.

The Auto-Investor function in NELION autonomously

simulates the trading behavior without intervention, providing

an objective means to evaluate the success of the system as a

real world application. Our comparisons of the U.S. markets

show that on average our fully automated investment agents

performed better than the major indexes in our test period of

one year.

As an initial experiment, these are promising results.

However, the system has also shown that a number of further

features could increase the flexibility and profitability of the

system.

Increased Diversity in the Input Data Set

The models are currently only based on historic data of the

time series itself. It is reasonable to assume that adding other

information to the input vector of the model will improve the

quality of the predictions by reducing the model error. This

information can include stock prices and trading volumes of

other stocks or indexes as well as price/earnings or other

ratios. A genetic algorithm can then search for effective input

combinations for each stock.

142 Conclusion

Generalized Data Pre-processing

Parkinson proposed an idea of pre-processing the input data

of time series analysis in order to improve the model quality

[Parkinson 1999]. By generalizing this approach and allowing

any number of combinations of both pre- and post-processing,

one can assume that the quality of the models can be

enhanced. Again, a genetic algorithm could be used to search

the parameter space for the best combinations.

Identifying Appropriate Age of Historic Input Data

Presently, NELION uses all available historic data to generate

models. This is likely to include periods where the dynamic of

the stock has undergone changes, leading to reduced overall

performance. It is possible to shorten the input data to an

appropriate length by identifying specific, current

characteristics of it. This measure would improve the model

quality and will reduce computation time, offsetting the

increase in parameter space proposed by the previous

suggestions.

Additional Attributes for each Stock

Each stock can be associated with a region and industry. By

allowing each investor to assign a subjective risk factor for

these categories and factoring this value into the risk equation,

the investor can focus on opportunities that conform to his

preference or that, in his estimation, promise above-average

returns.

Daily Operation 143

Including a Prediction Error for each Forecast

The current approach defines the reliability of the model by

using the out-of-sample error. By enhancing all models to

associate an error with each specific prediction, it should be

possible to identify stocks, which have entered a phase of

unpredictability.

Include Qualitative Explanation Module

With its current functionality, NELION offers valuable

assistance to the informed investor, by directing his attention

to promising opportunities. In order to appeal to novices as

well, the system would need to include a qualitative

explanation module. This function would support the

recommendations with copies or links to articles on the

Internet that shed more light on the suggestion. Additionally,

the module could automate the explanation of financial ratios

and charting techniques, helping less experienced investors

judge the validity of the forecasts by the system.

NELION represents a first attempt to automate a stock

prediction and portfolio management system. In its present

form, it shows promise and can be used effectively as a tool.

Based on the experiences gained from the extensive tests, it is

possible to refine the first version and take this integrated

approach to the next level of sophistication.

8 Appendix A: Investor Profiles

In order to specify his risk adversity, an investor has to define

numeric values for four parameters. The Correlation

parameter specified the emphasis NELION should place on

the correlation between the stocks when identifying the

optimal portfolio. The Error and Volatility parameters

determined if stocks where the model error or the volatility was

low were favored. Lastly, the Volume parameter performed

the same function based on the trading volume of the previous

trading day.

Chapter 6 explains the details of how the experiments were

conducted. The results were a collection of conservative and

high-risk investor profiles for 1998 and 1999. For each of

these four categories, I created cross tab queries, which

compare two of the four parameters, resulting in the six tables

shown in this appendix.

By selecting the combination that occurred the most frequently

in the six tables, it was possible to identify the first two

parameters for each category. It is highlighted with a dark

grey background.

Given these two parameters, I highlighted the four columns

and/or rows of the remaining five tables that contained either

of the two parameters with a light grey background. From

these, I chose the combination with the highest occurrence,

thereby defining the third parameter.

Daily Operation 145

Lastly, the fourth parameter was selected in the same manner

from remaining three tables. The rows and columns were

defined by the first three parameters and highlighted with a

medium grey background, or a medium grey strip on the left

side of the column or bottom of the row, if it had been

identified with a light grey background already.


8.1 Conservative Investors

8.1.1 January 1, 1998 – December 31, 1998

Error

0.000 0.125 0.250 0.375 0.500 0.625 0.750 0.875 1.000

0.000

0.125 4 3 4 8 1

0.250 4 4 2 1 10 2

0.375 4 7 1 3 10 5 4 1

0.500 3 9 3 4 2 3 4 1

0.625 1 6 5 4 4 1 1

0.750 2 2 3 2 7 1

0.875 6 2 9 2 1 3

Cor

rela

tion

1.000 4 3 2 5 2 5 10

Volume

0.000 0.125 0.250 0.375 0.500 0.625 0.750 0.875 1.000

0.000

0.125 4 3 3 10

0.250 2 2 2 13 4

0.375 2 1 4 11 2 14 1

0.500 1 5 1 1 6 5 10

0.625 1 1 4 4 4 4 4

0.750 2 2 5 7 1

0.875 3 6 2 4 5 3

Cor

rela

tion

1.000 1 2 2 1 9 8 2 6

Conservative Investors 147

Volume

0.000 0.125 0.250 0.375 0.500 0.625 0.750 0.875 1.000

0.000 2 4 2 8 4

0.125 1 1 3 5 12 4 8

0.250 4 2 2 4

0.375 7 2 4 3 3 4

0.500 18 6 7

0.625 2 6 1

0.750 37 5

0.875 2 16 4 3

Err

or

1.000 2 2

Correlation

0.000 0.125 0.250 0.375 0.500 0.625 0.750 0.875 1.000

0.000 1 1 1 2 2

0.125 2 3 2 2 2 1 6

0.250 1 1 3 4 1 2 3 5

0.375 3 3 2 1 2 4

0.500 2 5 3 1 2 2

0.625 3 3 1 1 1 1 3

0.750 11 8 10 1 11 5 4 4 0.875 2 5 11 14 2 6 9 5

Vol

atili

ty

1.000 4


Error

0.000 0.125 0.250 0.375 0.500 0.625 0.750 0.875 1.000

0.000 1 1 4 1

0.125 4 1 3 3 1 3 3

0.250 4 4 1 1 6 3 1

0.375 2 1 1 3 3 1 2 2

0.500 5 5 2 1 2

0.625 2 3 1 2 1 4

0.750 6 6 2 9 11 3 17

0.875 6 12 2 2 11 10 11

Vol

atili

ty

1.000 4

Volume

0.000 0.125 0.250 0.375 0.500 0.625 0.750 0.875 1.000

0.000 1 2 4

0.125 1 2 2 1 2 4 4 2

0.250 1 1 2 5 2 8 1

0.375 2 1 2 3 4 2 1

0.500 2 1 4 3 2 3

0.625 3 1 3 1 4 1

0.750 2 8 3 7 10 4 18 2

0.875 4 2 4 12 9 21 2

Vol

atili

ty

1.000 4



Error

0.000 0.125 0.250 0.375 0.500 0.625 0.750 0.875 1.000

0.000

0.125 3 4 4 2 4 4 2 2 2

0.250 1 1 3 8 4 3 1 2 3

0.375 2 5 3 5 4 2 1 2

0.500 2 7 3 4 6 4 3 1 2

0.625 2 4 4 3 5 4 1 2 1

0.750 1 2 3 3 6 2 3 3 3

0.875 2 5 3 2 4 5 3 3 1

Cor

rela

tion

1.000 1 3 4 6 4 6 3 5 2

Volume

0.000 0.125 0.250 0.375 0.500 0.625 0.750 0.875 1.000

0.000

0.125 13 1 1 1 2 2 2 5

0.250 10 1 1 3 6 5

0.375 14 1 1 5 3 4

0.500 8 1 6 5 6 6

0.625 11 1 4 3 2 5

0.750 13 2 1 1 4 5

0.875 12 3 1 5 3 4

Cor

rela

tion

1.000 12 2 5 4 5 6


Volume

0.000 0.125 0.250 0.375 0.500 0.625 0.750 0.875 1.000

0.000 10 1 2 1

0.125 9 2 5 2 2 6

0.250 8 3 5 6 7

0.375 5 2 2 9 7 6

0.500 6 4 1 5 5 9 8

0.625 17 2 2 4 7

0.750 9 1 2 3 3

0.875 13 1 1 2 2

Err

or

1.000 12 1 1 1 1

Correlation

0.000 0.125 0.250 0.375 0.500 0.625 0.750 0.875 1.000

0.000 2 2 1 3 2

0.125 2 3 4 1 1 4 4 5

0.250 2 6 4 6 7 2 4

0.375 4 3 4 4 2 2 3 8

0.500 2 4 2 8 2 4 1 3

0.625 4 4 6 2 3 1 4 1

0.750 3 2 1 4 7 2 4 6

0.875 4 2 1 3 1 3 3 3 4 2 4 5 4 3 4 2

Vol

atili

ty

1.000


Error

0.000 0.125 0.250 0.375 0.500 0.625 0.750 0.875 1.000

0.000 1 2 1 1 1 3 1

0.125 1 7 5 4 1 3 1 2

0.250 3 6 6 8 2 1 4 1

0.375 1 4 5 5 7 4 2 1 1

0.500 1 2 3 5 5 5 1 2 2

0.625 3 1 6 6 2 4 1 2

0.750 1 4 5 2 4 9 3 1

0.875 1 3 2 2 1 2 6 3

Vol

atili

ty

1.000 10 5 1 7 1 1 3

Volume

0.000 0.125 0.250 0.375 0.500 0.625 0.750 0.875 1.000

0.000 1 1 3 1 4

0.125 7 2 4 3 2 6

0.250 8 2 4 1 7 9

0.375 11 1 3 5 3 7

0.500 12 1 1 2 7 3

0.625 11 1 1 6 2 4

0.750 10 1 2 2 5 5 4

0.875 10 1 3 1 2 3

Vol

atili

ty

1.000 19 2 1 2 2 2


8.2 High Risk Investors


Error

0.000 0.125 0.250 0.375 0.500 0.625 0.750 0.875 1.000

0.000

0.125 1 2 1

0.250 1

0.375 1 1

0.500 2 1 1

0.625

0.750 1 1

0.875 6 1

Cor

rela

tion

1.000 1 1

Volume

0.000 0.125 0.250 0.375 0.500 0.625 0.750 0.875 1.000

0.000

0.125 2

0.250 3

0.375 2

0.500 3 1

0.625

0.750 2

0.875 7

Cor

rela

tion

1.000 2

High Risk Investors 153

Volume

0.000 0.125 0.250 0.375 0.500 0.625 0.750 0.875 1.000

0.000 6

0.125

0.250 4

0.375 2

0.500 2

0.625

0.750 2 1

0.875 4

Err

or

1.000 1

Correlation

0.000 0.125 0.250 0.375 0.500 0.625 0.750 0.875 1.000

0.000 1 2 1 1 1 1

0.125

0.250 1 1

0.375

0.500 1 1

0.625

0.750 1

0.875 1 6 1

Vol

atili

ty

1.000 2


Error

0.000 0.125 0.250 0.375 0.500 0.625 0.750 0.875 1.000

0.000 2 1 3 1

0.125

0.250 2

0.375

0.500 2

0.625

0.750 1 6 2

0.875

Vol

atili

ty

1.000 1 1

Volume

0.000 0.125 0.250 0.375 0.500 0.625 0.750 0.875 1.000

0.000 6 1

0.125

0.250 2

0.375

0.500 2

0.625

0.750 1

0.875 8

Vol

atili

ty

1.000 2


January 1, 1999 – December 31, 1999

Error

0.000 0.125 0.250 0.375 0.500 0.625 0.750 0.875 1.000

0.000

0.125 9 8 10 11 10 10 10 6 8 10 10 9 9 13 8 9 6 10

0.250

0.375 9 9 10 9 12 9 8 8 8

0.500 9 6 8 8 10 8 8 8 11

0.625 7 7 9 9 8 8 8 8 8

0.750 8 8 9 9 9 10 8 8 7

0.875 7 9 9 7 12 7 10 7 10

Cor

rela

tion

1.000 9 6 8 10 11 7 8 8 9

Volume

0.000 0.125 0.250 0.375 0.500 0.625 0.750 0.875 1.000

0.000

0.125 65 2 3 3 6 3

0.250 69 1 3 3 2 3 3

0.375 67 2 2 1 4 6

0.500 67 1 1 3 4

0.625 67 2 3

0.750 64 1 1 1 2 4 3

0.875 65 1 3 9

Cor

rela

tion

1.000 65 1 2 2 1 5


Volume

0.000 0.125 0.250 0.375 0.500 0.625 0.750 0.875 1.000

0.000 62 3 2 1

0.125 57 1 1 4

0.250 59 1 2 5 5

0.375 60 1 2 1 1 3 4

0.500 65 2 2 2 2 1 4 7

0.625 55 2 4 6

0.750 61 1 2 3 2

0.875 50 2 2 5

Err

or

1.000 60 4 4 3

Correlation

0.000 0.125 0.250 0.375 0.500 0.625 0.750 0.875 1.000

0.000 10 11 11 9 8 8 9 7

0.125 7 9 7 9 7 6 7 7

0.250 8 6 9 10 8 7 9 8

0.375 8 10 5 7 10 8 9 8

0.500 11 8 7 7 7 8 9 9

0.625 7 6 9 6 8 10 10 9

0.750 9 10 10 10 7 10 8 8

0.875 11 12 13 8 9 8 9 9

Vol

atili

ty

1.000 11 12 11 10 8 11 8 11


Error

0.000 0.125 0.250 0.375 0.500 0.625 0.750 0.875 1.000

0.000 9 8 8 6 11 8 6 8 9

0.125 10 4 5 8 6 7 7 6 6

0.250 8 8 8 7 9 7 7 3 8

0.375 7 7 6 10 7 6 9 6 7

0.500 7 7 9 8 9 6 7 7 6

0.625 8 7 8 7 8 8 4 8 7

0.750 8 8 6 7 10 6 7 11 9

0.875 9 8 11 8 12 11 11 1 8

Vol

atili

ty

1.000 2 6 11 11 13 8 11 9 11

Volume

0.000 0.125 0.250 0.375 0.500 0.625 0.750 0.875 1.000

0.000 67 1 1 2 2

0.125 56 1 1 1

0.250 63 1 1

0.375 59 2 1 1 2

0.500 59 1 1 1 2 2

0.625 59 1 5

0.750 57 2 1 1 6 5

0.875 57 2 1 6 4 9

Vol

atili

ty

1.000 52 1 3 3 4 8 11

9 Appendix B: Portfolio History

This appendix shows all transactions for the two test investors.

The first column contains the ticker abbreviation of the stock

as defined in Appendix E. The second column shows the

transaction date. The amount in the third column is positive

for purchases and negative for sales. Finally the stock price at

the time the transaction took place is shown in the last column.

Please note that these prices are adjusted for stock splits as of

May 15, 2000.

9.1 Transactions by Conservative Investor Ticker Date Amount Price

MADGF 5/15/1999 208 $ 3.50 GAP 5/15/1999 23 $ 31.56 IBM 5/15/1999 2 $239.25 SPGLA 5/15/1999 70 $ 8.50 DOW 5/15/1999 7 $135.31 FTLAF 5/15/1999 80 $ 11.88 AAPL 5/15/1999 28 $ 44.38 AOL 5/15/1999 10 $125.25 BI 5/15/1999 13 $ 11.00 COMS 5/15/1999 4 $ 28.56 AXP 5/15/1999 6 $120.75 BS 5/15/1999 118 $ 9.13 CSCO 5/15/1999 2 $115.44 CRUS 5/15/1999 32 $ 7.56 EK 5/15/1999 3 $ 77.63 IT 5/15/1999 5 $ 24.06 IBM 5/23/1999 1 $230.38 BA 5/23/1999 3 $ 44.94 DOW 5/23/1999 -2 $126.19 AOL 5/23/1999 -4 $126.44 AXP 5/23/1999 1 $120.25 CSCO 5/23/1999 1 $113.25

Transactions by Conservative Investor 159

DOW 9/11/1999 5 $113.13 AAPL 9/11/1999 -5 $ 77.44 AOL 9/11/1999 -5 $ 96.31 AXP 9/11/1999 -2 $140.00 CHV 9/11/1999 4 $ 95.88 DOW 9/19/1999 -6 $115.63 AAPL 9/19/1999 -17 $ 76.94 AXP 9/19/1999 -4 $139.88 CVD 9/19/1999 48 $ 8.75 EBF 9/19/1999 46 $ 8.56 DZB 9/19/1999 17 $ 24.00 HSIC 9/19/1999 18 $ 15.81 MADGF 11/14/1999 -208 $ 2.44 GAP 11/14/1999 -23 $ 27.25 IBM 11/14/1999 -3 $ 95.88 SPGLA 11/14/1999 -70 $ 12.44 DOW 11/14/1999 -4 $118.56 AAPL 11/14/1999 -6 $ 90.63 BI 11/14/1999 72 $ 4.75 COMS 11/14/1999 28 $ 33.38 BS 11/14/1999 -67 $ 6.06 CHV 11/14/1999 -4 $ 91.38 CSCO 11/14/1999 -3 $ 83.44 IT 11/14/1999 32 $ 11.44 ANGN 11/14/1999 536 $ 1.56 CVD 11/14/1999 -48 $ 11.25 EBF 11/14/1999 46 $ 9.00 DZB 11/14/1999 -17 $ 22.38 SHN 11/14/1999 846 $ 1.50 UMGI 11/14/1999 28 $ 70.19 DAB 11/14/1999 48 $ 10.31 HBNK 11/14/1999 60 $ 18.56 BS 1/23/2000 -101 $ 7.50 DAB 1/23/2000 -95 $ 6.88 BI 2/12/2000 -85 $ 3.56 BS 2/12/2000 50 $ 5.63 DAB 2/12/2000 47 $ 7.88 HBNK 2/12/2000 -60 $ 16.13 FLSC 2/19/2000 210 $ 1.88 IT 5/7/2000 -37 $ 13.44 SHN 5/7/2000 -846 $ 0.81 IT 5/14/2000 37 $ 12.13 SHN 5/14/2000 846 $ 0.63 IT 7/14/2000 -37 $ 13.31 FLSC 7/14/2000 -210 $ 2.38 GPS 7/15/2000 22 $ 38.19

160 Appendix B: Portfolio History

9.2 Transactions by High Risk Investor Ticker Date Amount Price

MSFT 5/15/1999 126 $ 76.88 AOL 5/15/1999 1 $125.25 INTC 5/23/1999 2 $ 57.00 MSFT 5/23/1999 -9 $ 77.56 AAPL 5/23/1999 6 $ 43.94 AOL 5/23/1999 2 $126.44 BS 5/23/1999 18 $ 9.00 MSFT 5/30/1999 -2 $ 80.69 AOL 5/30/1999 1 $119.25 INTC 6/12/1999 42 $ 54.44 MSFT 6/12/1999 -100 $ 78.13 AAPL 6/12/1999 -4 $ 46.44 AOL 6/12/1999 55 $ 99.50 BS 6/12/1999 18 $ 7.56 INTC 6/19/1999 12 $ 54.94 MSFT 6/19/1999 6 $ 85.00 AOL 6/19/1999 -17 $112.00 CSCO 6/19/1999 3 $119.38 MSFT 7/3/1999 6 $ 90.19 AOL 7/3/1999 -3 $110.00 DELL 7/10/1999 24 $ 42.81 INTC 7/10/1999 4 $ 66.25 AAPL 7/10/1999 9 $ 55.63 AOL 7/10/1999 -23 $128.25 BS 7/10/1999 90 $ 8.06 CSCO 7/10/1999 9 $ 67.06 MSFT 7/17/1999 3 $ 99.44 BS 7/17/1999 -60 $ 8.13 IBM 7/24/1999 5 $124.81 BS 7/24/1999 -46 $ 8.06 IBM 7/31/1999 -2 $125.69

10 Appendix C: Screen Shots

The Task Agent

An E-Mail Recommendation


The Administration Tool

The “New Task” Dialog

163

The Investor List

General Investor Information

The Graphical Portfolio History


The Investor Transactions

The Current Investor Portfolio

The Return on Investment

165

The Stock List

General Stock Information


The Graph of the Stock Price

The Correlation between Stocks

11 Appendix D: Conceptual Data Model

12 Appendix E: Stocks Tracked in the

Simulation

3 Com COMS ACE*COMM Corp. ACEC Actrade International, Ltd. ACRT ADC, Inc. ADCT Air Express International AEIC Air Transportation Holding AIRT Airborne Freight Corp. ABF AirNet Systems, Inc. ANS AK Steel Holdings AKS Allied Irish Banks, p.l.c AIB Alterra Healthcare Corp. ALI America Online AOL American Express AXP American Home Products AHP AMRESCO, Inc. AMMB ANGEION Corp. ANGN Apple Computer AAPL Applied Materials, Inc. AMAT Archer Daniels Midland Co ADM Argentaria, Caja Postal y AGR ARV Assisted Living, Inc. SRS AT&T T Australia and New Zealand ANZ Autodesk ADSK Avon AVP Banco Comercial Portugues BPC Banco Santander Central STD Bank of Montreal BMO Bank of Tokyo-Mitsubishi MBK Barclays PLC BCS Bausch + Lomb BOL Bell Industries BI Bestfoods BFO Bethlehem Steel BS

169

Beverly Enterprises, Inc. BEV Black + Decker BDK Blonder Tongue Laboratories BDR Boca Research, Inc. BOCI Boeing BA Boston Communications Group BCGI Campbell Soup Company CPB Caterpillar CAT Celadon Group, Inc. CLDN Centigram Communications CGRM Chase Manhattan Bank CMB Checkpoint Software CHKP Chevron CHV Circle International Group CRCL Cirrus Technology CRUS Cisco CSCO Citigroup C Citrix CTXS CAN Financial Corp. CNA Coca-Cola COKE Colgate-Palmolive CL Compaq Computers CPQ Computer Associates CA ConAgra, Inc. CAG Converse Inc. CVE C-Phone Corp. CFON Cutter + Buck Inc. CBUK Cymer, Inc. CYMI Data Broadcasting Corp. DBCC Dave & Buster's Inc. DAB Deere + Co. DE Delhaize America Inc. DZB Dell Computers DELL Delta Airlines DAL Dexter Corp. DEX Dole Food Company, Inc. DOL Dow Chemicals DOW Eagle USA Airfreight, Inc. EUSA Eastman Kodak EK EIS International, Inc. EISI Emeritus Assisted Living ESC Ennis Business Forms, Inc. EBF EXECUTONE ELOT

170 Appendix E: Stocks Tracked in the Simulation

Expeditors International EXPD Exxon XOM FDX Corp. FDX First Albany Companies Inc. FACT Florsheim Group Inc. FLSC Fonix Corp. FONX Ford Motors F Fresh America Corp. FRES Fritz Companies, Inc. FRTZ Fruit of the Loom FTL Gartner Group IT General Electric GE General Mills, Inc. GIS General Motors GM Genesis Health Ventures GHV Great Atlantic and Pacific Tea Co. GAP Greenbriar Corp. GBR Gucci Group N.V GUC H.D. Vest, Inc. HDVS H.J. Heinz Company HNZ Harvey Entertainment HRVY HCC Insurance Holdings HCC Healthsouth Corp. HRC Henry Schein Inc. HSIC Hewlett Packard HWP Highland BanCorp. Inc. HBNK Hoenig Group Inc. HOEN Hollywood Park Inc. HPK Hub Group, Inc. HUBG HUMANA Inc. HUM IBM IBM Imperial Credit Industries ICII Intel Corp. INTC InterVoice-Brite Inc. INTV Jaclyn, Inc. JLN Justin Industries, Inc. JSTN Kellogg Company K Kenneth Cole Productions KCP K-Swiss Inc. KSWS LaCrosse Footwear, Inc. BOOT LandAir Corp. LAND Leather Factory, Inc. TLF Lifeline Systems, Inc. LIFE

171

LSI Logic LSI Lucent Technology LU M. H. Meyerson & Co., Inc. MHMY Madge Networks MADGF Manor Care, Inc. HCR Maytag Corp. MYG Mediaone Group Inc. UMG Metretek Technologies MTEK Microlog Corp. MLOG Micron Technology MU Microsoft Corp. MSFT MTI Technology Corp. MTIC Nabisco Holdings Corp. NA Nabors Industries Inc. NBR National Australia Bank NAB National Discount Brokers NDB National HealthCare Corp. NHC National Semiconductor NSM National Westminster Bank NW Natural MicroSystems Corp. NMSS Nexus Telecomm Sys Ltd. NXUSF Nike NKE Nobel Drilling Corp. NE NUWAVE Technologies, Inc. WAVE Oracle ORCL Orange Telephone PLC ORNGY Pepsi Co. PEP Pfitzer PFE Pittston BAX Group PZX Professional BanCorp., Inc. MDB Quaker Oats Company OAT Ralston Purina Company RAL RCM Technologies, Inc. RCMT Reebok International Ltd. RBK Res-Care, Inc. RSCR Research Partners Int’l RPII Response USA, Inc. RSPN Rite Aid Corp. RAD Rockwell International ROK Ross Stores ROST Royal Bank of Canada RY Salton, Inc. SFP Sara Lee Corp. SLE

172 Appendix E: Stocks Tracked in the Simulation

Saucony, Inc. SCNYA Sawtek Inc. SAWS Schering Plough Corp. SGP Shoney's, Inc. SHN Smithfield Foods Inc. SFD Southwest Securities Group SWS Spiegel Corp. SPGLA Starbucks Coffee SBUX Stifel Financial Corp. SF Stride Rite Corp. SRR Sun Microsystems SUNW Sunrise Assisted Living SNRZ Swank, Inc. SNKI Tandy Brands Accessories TBAC Texas Instruments TXN Textron Inc. TXT The Gap GPS Time Warner TWX Toronto-Dominion Bank TD Total Oil Co. TOT Track Data Corp. TRAC Unilever N.V. UN Unilever PLC UL United Airlines UAL United Shipping USHP Value City Department Stores VCD Vans, Inc. VANS Veritas DGC Inc. VTS Verity Inc. VRTY Vicon Industries, Inc. VII VISX, Inc. VISX Vodafone Airtouch VOD VTEL Corp. VTEL Wal-Mart WMT Wendt-Bristol Health Services WMD Westpac Banking Corp. WBK Xerox XRX

13 Appendix F: Bibliography

(1) Ambachtsheer, Keith, The Economics of Pension Fund Management, Financial Analysts Journal, Nov.-Dec. 1994, p.21-31.

(2) Anderson, The Box-Jenkins Approach, Butterworths, 1976.

(3) Aoki, Masanao Notes on Economic Time Series Analysis: System Theoretic Perspectives, Springer Verlag, 1983.

(4) Arthur, W.B., J. H. Holland, B. LeBaron and P. Tayler, Asset Pricing under Endogenous Expectations in an Artificial Stock Market, SFI Studies in the Sciences of Complexity, Vol. XXVII, Addision Wesley, 1997.

(5) Baldi, Pierre and Yves Chauvin, Smooth On-Line Learing Algorithms for Hidden Markov Models, Technical Paper of the Jet Propulsion Laboratory, 1993.

(6) Baldi, P., et al, Hidden Markov Models in molecular biology: New algorithms and applications, Advances in Neural Information Processing Systems, volume 5, Morgan Kaufmann, San Mateo, 1993.

(7) Barber, Brad M., Terrance Odean, The Courage of Misguided Convictions: The Trading Behavior of Individual Investors, Technical Report of the Graduate School of Management, UC Davis, Davis, California, 1999.

(8) Barnsley, Michael F. Factals Everywhere, 2. Edition, Academic Press Professional, 1993.

(9) Baum, L. E., T. Petrie, G. Soules and N. Weiss, A Maximization Technique Occuring in the Statistical


Analysis of Probabilistic Functions of Markov Chains, Ann. Math. Stat. 41(1): 164-171, 1970.

(10) Berenson, Mark L. and David M. Levine, Statistics for Business & Economics, Prentice Hall, 1990.

(11) Bhattacharyya, M. N. Comparison of Box-Jenkins and Bonn Monetary Model Prediction Performance, Lecture Notes in Economics and Mathematical System, Springer Verlag, 1980.

(12) Bishop, George W., Jr., Charles Dow and the Dow Theory, Appleton, Century Crofts, Inc., New York, 1960.

(13) Boldt, B. and H. Arbit, Efficient markets and the professional investor, Financial Analysts Journal, 40, July-August 1984, 22–34.

(14) Bookstaber, Richard, The Complete Investment Book, Scott, Foresman and Company, 1985.

(15) Borscheid, Peter Vom verdienten zum erzwungenen Ruhestand. Wirtschaftliche Entwicklung und der Ausbau des Sozialstaates, Digitale Bibliothek der Friedrich Ebert Stifung, 1999.

(16) Box, George E. P. and Gwilym M. Jenkins, Time Series Analysis, 2nd Edition, Holden-Day, 1976.

(17) Braun, Susanne, Neuronale Netze in der Aktienprognose, article contributed to “Neuronale Netze in der Ökonomie” Eds. Heinz Rehkugler and Hans Georg Zimmermann, Verlag Vahlen, 1994.

(18) Brockwell, Peter J. and Richard A. Davis, Time Series: Theory and Methods, Springer Verlag, 2nd Edition, 1986.

(19) Casdagli, Martin Nonlinear Prediction of Chaotic Time Series, Physica D35 (1989), 335-356.

(20) Chen, Shu-Heng, Chia-Hsuan Yeh and Chung-Chih Liao, Testing for Granger Causality in the Stock Price-Volume Relation: A Perspective from the Agent-Based Model of

175

Stock Markets, Proceedings of the Fifth Joint Conference on Information Science, Volume II, Atlantic City, New Jersey, USA, 2000.

(21) Day, Shawn P. and Michael R. Davenport, Continuous-Time Temporal Back-Propagation with Adaptable Time Delays, submitted to IEEE Transactions on Neural Networks, 1992.

(22) de Groot and D. Würtz, Analysis of univariate time series with connectionist nets: A case study of two classical examples, Neurocomputing 2, Elsevier, 1990/91, 177 - 192.

(23) de Jong, Eelke Exchange Rate Determination and Optimal Economic Policy Under Various Exchange Rate Regimes, Lecture Notes in Economics and Mathematical System, (1991).

(24) Deppisch, Hierarchical training of neural networks and prediction of chaotic time series, Physics Letters A 158 (1991), 57-62.

(25) Dihardjo, Herlina and Clarence Tan, Moving Average As Technical Indicators And Artificial Neural Network Model – Trading System for Australian Dollar Market, Proceedings of the Conference on Advanced Investment Technology, Bond University, Australia, 1999.

(26) Dobbins, Richard and Stephen F. Witt, Portfolio Theory & Investment Management, Martin Robinson, Oxford, 1983.

(27) Doya, Kenji Bifurcations in the Learning of Recurrent Neural Networks, Proceedings of 1992 IEEE International Symposium on Circuits and Systems, 2777-2780.

(28) Doya, Kenji Bifurcations of Recurrent Neural Networks in Gradient Descent Learing, submitted to IEEE Transactions on Neural Networks, 1993.


(29) Elsner, Prediction time series using a neural network as a method of distinguisching chaos from noise, Journal of Physics A 25 (1992), 843-850.

(30) Fahlman, S. E. and C. Lebiere, The cascade-correlation learning architecture, Advances in neural information processing systems 2, D. S. Touretzky (Eds.) pp. 524-532, 1990.

(31) Farmer, J. Doyne, Andrew W. Lo, Frontiers of Finance: Evolution and Efficient Markets, Frontiers of Science, 1998.

(32) Financial Training Company, The, Finance for Non-Financial Manager, Course Training Materials, 1998.

(33) Frankel, J. and K. Froot, Understanding the U.S. Dollar in the Eighties: The Expectations of Chartists and Fundamentalists, The Economic Record, vol.62, pp.24-38, 1986.

(34) Fraser, Andrew M. and Alexis Dimitriadis, Forecasting Probability Densities by Using Hidden Markov Models with Mixed States, article contributed to “Time Series Prediction: Forecasting the Future and Understanding the Past”, Eds. Andreas S. Weigend and Neil A. Gershenfeld, Santa Fe Institute Studies in the Sciences of Complexity, Proc. Vol. XV, Addison-Wesley, 1993.

(35) Goh, TH; Wang, PZ; Lui, HC, Learning Algorithm for the Enhanced Fuzzy Perceptron, Institute of Systems Science, Technical Report presented at the National University of Singapore, 1991.

(36) Granger, C. W. J., Economic processes involving feedback, Information and Control, 6(1): 28-48, March 1963.

(37) Granger, C. W. J. Modeling Economic Series, Clarendon Press, 1990.

177

(38) Hastings, Harold M. and George Sugihara, Fractals - A Users’s Guide for the Natural Sciences, Oxford Science Publications, 1993.

(39) Heller, Robert, Business Masterminds: Warren Buffet, Dorling Kindersley, 2000.

(40) Hertz, John et al, Introduction to the Theory of Neural Computation, Santa Fe Institute Studies in the Sciences of Complexity, Addison-Wesley Publishing Company, 1992.

(41) Hsieh, David, Chaos and Nonlinear Dynamics: Application to Financial Markets, Technical Report presented at the Fuqua School of Business, Duke University, Durham, North Carolina, 1990.

(42) Hsieh, David, Implications of Nonlinear Dynamics for Financial Risk Management, Journal of Financial and Quantitative Analysis, March 1993.

(43) Hutchinson, James M., A Radial Basis Function Approach to Financial Time Series Analysis, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, 1994.

(44) Ivarsson, Per H Weak-Form Efficient Market Hypothesis in the Interbank Foreign Exchange Market, Technical Report, Institute of Theoretical Physics, December 16, 1997.

(45) Jensen, Michael C, The Performance of Mutual Funds in the Period 1945-64, Journal of Finance 23, 389-416, 1968.

(46) Joshi, S. and M. A. Bedau, An Explanation of Generic Behavior in an Evolving Financial Market. In R. Standish, B. Henry, S. Watt, R. Marks, R. Stocker, D. Green, S. Keen, T. Bossomaier, eds., Complex Systems '98--Complexity Between the Ecos: From Ecology to


Economics, Complexity Online Network; Sydney, pp. 327-335, 1998.

(47) Kahneman, Daniel and Amos Tversky, Prospect Theory: An Analysis of Decision Making under Risk, Econometrica, 1979.

(48) Karpoff, J.M. The Relation between Price Changes and Trading Volume: A Survey, Journal of Financial and Quantitative Analysis, Vol. 22, No. 1, pp. 109-126, 1987.

(49) Kerr, Edward Financial Management Study Notes, University of Hertfordshire, Business School, Lecture Notes, March 1997.

(50) Kosko, Bart Neural Networks and Fuzzy Systems, Prentice-Hall International Editions, 1992.

(51) Kumar, Kuldeep, Clarence Tan and Ranadhir Ghosh, Using Chaotic Component and ANN for Forecasting Exchange Rates in Foreign Currency Market, Proceedings of the Conference on Advanced Investment Technology, Bond University, Australia, 1999.

(52) Kurumatani, Koichi, Yuhsuke Koyama, Takao Terano, Hajime Kita, Akira Namatame, Hiroshi Deguchi, Yochinori Shiozawa and Hitoshi Matsubara, Vsmart: A Virtual Stock Market as a Forum for Market Structure Analysis and Engineering, Proceedings of the Fifth Joint Conference on Information Science, Volume II, Atlantic City, New Jersey, USA, 2000.

(53) Langer, Mariensen, Quinke, Simulationsexperimente mit ökonomischen Makromodellen, GMD, R. Oldenbourg Verlag, 1984.

(54) LeBaron, Blake, Experiments in evolutionary finance, Working Paper, Department of Economics, University of Wisconsin-Madison, November 1995.

(55) Lewis, Michael Liar’s Poker, Hodder and Stoughton, page 38, 1989.

179

(56) Le Cun, J. S. Denker and S. A. Solla, Optimal Brain Damage, Advances in Neural Information Processing Systems 2, Morgan Kaufmann Publishers, 1990.

(57) Lequarré, Jean Y., Foreign Currency Dealing: A Brief Introduction (Data Set C), article contributed to “Time Series Prediction: Forecasting the Future and Understanding the Past”, Eds. Andreas S. Weigend and Neil A. Gershenfeld, Santa Fe Institute Studies in the Sciences of Complexity, Proc. Vol. XV, Addison-Wesley, 1993.

(58) Looman, Volker, Die Höhe der Alterversorgung ist eine Frage der Selbstdiziplin, Frankfurter Allgemeine Zeitung, Seite 26, Nr. 128, 3. Juni 2000.

(59) Naylor, Thomas H., Computer Simulation Experiments with Models of Economic Systems, John Wiley & Sons, Inc., 1971.

(60) Markowitz, Harry M., Portfolio Selection, Journal of Finance, Vol. VII No. 1, 1952.

(61) Markowitz, Harry M., Portfolio Selection: Efficient Diversification of Investments, John Wiley and Sons, 1959.

(62) Mâlâroiu, Simona, Kimmo Kiviluoto and Erkki Oja, Time Series Prediction with Independent Component Analysis, Proceedings of the Conference on Advanced Investment Technology, Bond University, Australia, 1999.

(63) Motamen, Homa Economic Modelling in the OECD Countries, Chapman and Hall, 1987.

(64) Mozer, Michael C., Neural Net Architectures for Temporal sequence Processing, article contributed to “Time Series Prediction: Forecasting the Future and Understanding the Past”, Eds. Andreas S. Weigend and Neil A. Gershenfeld, Santa Fe Institute Studies in the Sciences of Complexity, Proc. Vol. XV, Addison-Wesley, 1993.


(65) Murata, Noboru et al, Network Information Criterion - Determining the Number of Hidden Units for an Artificial Neural Network Model, Department of Mathematical Engineering and Information Physics, University of Tokio, 1992.

(66) Niarchos, Nikitas A. Christos A. Alexakis, Stock market prices, causality and efficiency: evidence from the Athens stock exchange, Applied Financial Economics, Volume 8, Issue 2, pp 167 – 174

(67) Nienstedt, Heinz-Werner Ein Verfahren zur Kurzfristprognose - Die Integration von Methoden der Zeitreihenanalyse in ein ökonometrisches Modell, Dissertation zum Erlangen des Grades eines Doktors der Wirtschaftswissenschaften eingereicht am Fachbereich Informatik der Technischen Universität Berlin, 1984.

(68) Ofer, Aharon R. and Arie Melnick, Price Deregulation in the Brokerage Industry: An Empirical Analysis, pp. 633-641, The RAND Journal of Economics, Volume 9, No. 2, Autumn 1978.

(69) Paaß, Gerhard Prognose und Asymptotik Bayesscher Modelle, GMD, R. Oldenbourg Verlag, 1984.

(70) Packard, H. et al, Geometry from a Time Series, Physical Review Letters, Vol 45, Number 9, (1980), 712-716.

(71) Parkinson, Alan, Financial Time Series Prediction using Neural Networks: Approaches to Data Pre-Processing, Proceedings of the Conference on Advanced Investment Technology, 1999.

(72) Poritz, A.B., Hidden Markov Models: A guided Tour, IEEE International Conference on Acoustic Speech Signal Proceedings, volume 198-8, 1988.

(73) Rabiner, L.R., A Tutorial on Hidden Markov Models and Selected Application in Speech Recognition, Proceedings of the IEEE, volume 77-2, 1989.

181

(74) Rehkugler, Heinz und T. Poddig, Statistische Methoden versus Künstliche Neuronale Netzwerke zur Aktienkursprognose, Nr. 73/1990, T.U. Bamberg.

(75) Rehkugler, Heinz und Hans Georg Zimmermann, Neuronale Netze in der Ökonomie, Verlag Vahlen, 1994.

(76) Reitz, Ulrich Marktprofil: Joachim Goldberg, Welt am Sonntag, 6. Februar 2000.

(77) Renals, Steve Chaos in Neural Networks, Lecture Notes in Computer Science, 90 - 99 (1990).

(78) Robinson, David M., Steven Zigomanis, Chartists, Fundamentalists and Nonlinear Dependence, Proceedings of the Conference on Advanced Investment Technology, Bond University, Australia, 1999.

(79) Rössler, O.E. Chaos and Order, Physics Letters, A57, 397-402, (1976).

(80) Rohwer, Richard, The “Moving Targets“ Training Algorithm, Lecture Notes in Computer Science, 100-109 (1990).

(81) Rojas, Raul, Theorie der neuronalen Netze. Eine systematische Einführung, Springer-Verlag, 1993.

(82) Rudzio, Koija, Verflixte Psyche, Die Zeit, Nr. 41, 7. Oktober 1999.

(83) Rüegg-Stürm, Controlling für Manager, Campus Verlag, 1997.

(84) Samuelson, Paul, Proof that Properly Anticipated Prices Fluctuate Randomly, 1965.

(85) Sauer, Tim, Time Series Prediction by Using Delay Coordinate Embedding, article contributed to “Time Series Prediction: Forecasting the Future and Understanding the Past”, Eds. Andreas S. Weigend and Neil A. Gershenfeld, Santa Fe Institute Studies in the


Sciences of Complexity, Proc. Vol. XV, Addison-Wesley, 1993.

(86) Schöneburg, Stock price prediction using neural networks: A project report, Neurocomputing 2, Elsevier, 1990/91, 17 - 27.

(87) Schwerk, Thomas Künstliche Neuronale Netze zur Beurteilung von Marktgrößen, Diplomarbeit, TU Berlin, 1994.

(88) Schwerk, Thomas, Forecasting of Time Series with Neural Networks, Proceedings of The Third International Congress on Industrial and Applied Mathematics, Hamburg, Germany, 1995.

(89) Schwerk, Thomas, Portfolio Recommendations Based on Non-Linear Models, Proceedings of the Conference on Advanced Investment Technlogy, Bon University, Gold Coast, Australia, 1999.

(90) Schwerk, Thomas, Using Non-Linear Mathematical Models for Stock Portfolio Management, Proceedings of the Fifth Joint Conference on Information Science, Volume II, Atlantic City, New Jersey, USA, 2000.

(91) Schwert, G. William, The Capital Asset Pricing Model: Theory, Tests and Extensions, William E. Simon Graduate School of Business Administration, Lecture Notes, 1997.

(92) Silva, Fernando M. and Luis B. Almeida, Acceleration Techniques for the Backpropagation Algorithm, Lecture Notes in Computer Science, 100 - 119 (1990).

(93) Trippi, Robert R. and Efraim Turban, Neural Networks in Finance and Investing, Probus Publishing Company, 1993.

(94) Utans, Joachim and John Moody, Selecting Neural Network Architectures via the Prediction Risk: Application to Corporate Bond Rating Prediction, submitted to First

183

Internation Conference on Artificial Intelligence Applications on Wall Street, IEEE Computer Society Press, 1991.

(95) Wan, Eric, Time Series Prediction by Using a Connectionist Network with Internal Delay Lines, article contributed to “Time Series Prediction: Forecasting the Future and Understanding the Past”, Eds. Andreas S. Weigend and Neil A. Gershenfeld, Santa Fe Institute Studies in the Sciences of Complexity, Proc. Vol. XV, Addison-Wesley, 1993.

(96) Weymann, Peter Kalman-Filter und -Glättung und deren Anwendung auf Erwartungsbildungsmechanismen, Dissertation an der Universität Fridericiana Karlsruhe, 1987.

(97) White, Halbert Economic prediction using neural networks: the case IBM daily stock returns, Proceedings of the IEEE International Conference on Neural Networks, San Diego, 1989, II-451 - II-459.

(98) Wong, S. and Pan Yong Tan, Neural Networks And Genetic Algorithm For Economic Forecasting, submitted to AI in economics and business administration, 1990.

(99) Wong, S. Time series forecasting using backpropagation neural networks, Neurocomputing 2, Elsevier, 1990/91, 147 - 159.

(100) Wong, S. and P.Z. Wang, A stock selection strategy using fuzzy neural networks, Neurocomputing 2, Elsevier, 1990/91, 233 - 242.

(101) Weigend, Andreas S. and Neil A. Gershenfeld, Time Series Prediction: Forecasting the Future and Understanding the Past, Santa Fe Institute Studies in the Sciences of Complexity, Proc. Vol. XV, Addison-Wesley, 1993.


(102) Weigend, Andreas S. and David. A. Nix, Predictions with Confidence Intervals (Local Error Bars), working paper of the Sonderforschungsbereich 373 at the Humboldt-Universität zu Berlin, 1994.

(103) Woodwell, Donald R., Automating your Financial Portfolio, Dow Jones-Irwin, 1983.

(104) Zappa, Frank, Joe’s Garage: Packard Goose, Munchkin Music, 1979.

(105) Zimmermann, Hans Georg, Neuronale Netze als Entscheidungskalkül, article contributed to “Neuronale Netze in der Ökonomie” Eds. Heinz Rehkugler and Hans Georg Zimmermann, Verlag Vahlen, 1994

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