Agents: Definition, Classification and Structure

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UNIVERSITY OF REGINA FACULTY OF
ENGINEERING Master of Applied Science In
Industrial Engineering AN INFERENCE
SYSTEM APPROACH TO FINANCIAL MODELING Maria M.
Ortiz Lerma Dr. Rene V. Mayorga Fall 2003
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Contents

• Thesis Objective
• Introduction
• Technical Analysis
• Scenario Analysis
• Portfolio Selection
• Conclusion

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Thesis Objective

• The use of Intelligent Systems methodologies for
  the modeling of some systems behaviours
  characterized by highly non-linear relationships
  and having a high degree of uncertainty.
• In particular, the implementation of
  Artificial/Computational Intelligence and Soft
  Computing techniques in some Financial
  Engineering (closely related to Operations
  Research) problems.

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Proposed Methodology

• Here, it is proposed a novel Framework to use
• Adaptive Neuro-Fuzzy Inference System (ANFIS)
  and Fuzzy Inference Systems (FIS) for market
  indicators and prices modeling, and Optimization
  tools based on Mean-Variance method for
  portfolio (short term estimation) selection.
  
• In this framework it is necessary to consider
  three main components

Technical Analysis Adaptive Neuro-Fuzzy
Inference System
Scenario Analysis Fuzzy Inference System
Portfolio Selection Optimization tool
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Introduction

• Non-conventional Techniques
• Increasing literature on Fuzzy Inference Systems
  (FIS) and their use in Financial Engineering
• Many of these examples are related to stock
  market trading, Deboeck (1994), and recently
  Tseng et al. (2001) integrate Fuzzy and ARIMA
  models to forecast the Taiwan/US exchange rate.
• Artificial Neural Networks has been used as a
  tool for forecasting financial markets
• Peray (1999) determines an opportunity for equity
  fund investments using market fundamentals.

• Conventional techniques
• Optimization and Mean-Variance Model
• Asymmetric risk measures for portfolio
  optimization under uncertainty (King, 1993), and
  the arithmetic mean and the standard deviation of
  the different financial assets (Markowitz,
  1952,1987. Levy, 1970)

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Introduction

• Financial markets Reasons of uncertainty
• Expansive fluctuations in prices over short and
  long terms
• Each model in portfolio selection has its own
  advantages and disadvantages
• Market risk cannot be avoided with
  diversification
• Large number of deals produced by agents that act
  independently from each other
• The effective operation of the portfolio
  selection in practice requires an integrated
  decision support framework

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Framework General Structure
TECHNICAL ANALYSIS STAGE I
SCENARIO ANALYSIS STAGE II
PORTFOLIO SELECTION STAGE III
Outputs Scenario (ti6)
Inputs (ti)
Outputs (ti6)

• Very
• Pessimistic

ANFIS
PRE -ANA L YS I S
Price (ti6)
Price (ti)
FUZZY INFERENCE SYSTEM
OPTIMIZA-TION

• Pessimistic

• Medium
• Pessimistic

ANFIS
Market indicator (ti6)
Market indicator (ti)

• Weakly
• Pessimistic

• Hold

ANFIS
Market indicator (ti6)
Market indicator (ti)

• Weakly
• Optimistic

• Medium
• Optimistic

ANFIS
Market indicator (ti6)
Market indicator (ti)

• Optimistic

• Very
• Optimistic

Inputs
Inputs
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Technical Analysis Stage I
Historical data from January 1st, 1993 to August
29th, 2003
TECHNICAL ANALYSIS STAGE I
SCENARIO ANALYSIS STAGE II
PORTFOLIO SELECTION STAGE III
Outputs Scenario (ti6)
Inputs (ti)
Outputs (ti6)

• Very
• Pessimistic

ANFIS
PRE -ANA L YS I S
Price (ti6)
Price (ti)
FUZZY INFERENCE SYSTEM
OPTIMIZA-TION

• Pessimistic

• Medium
• Pessimistic

ANFIS
Market indicator (ti6)
Market indicator (ti)

• Weakly
• Pessimistic

• Hold

ANFIS
Market indicator (ti6)
Market indicator (ti)

• Weakly
• Optimistic

• Medium
• Optimistic

ANFIS
Market indicator (ti6)
Market indicator (ti)

• Optimistic

• Very
• Optimistic

Inputs
Inputs
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Market indicators

• a) Monetary,
• b) Sentiment,
• c) Momentum
• Prices
• Rate of Change
• Stochastic K
• Stochastic D

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Indexes

• Dow Jones Average (DOW)
• DJ 65 Composite Average DJA
• New York Stock Exchange (NYSE)
• NYSE Financial FNA
• National Association of Securities Dealers
  Automated Quotation System (NASDAQ)
• 259 Telecommunications IXUT
• U.S. Treasury securities (Yieldx10)
• 30 year bond TYX

.
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ANFIS Process

• Multidimensional input-output highly non-linear
  mapping

y f (x).

• The quantity of nodes, linear and non-linear
  parameters in the hidden layers is the same for
  each index

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ANFIS Structure Information
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ANFIS Process for Prices and Rate of Change in
one index
Hidden Layers 1 2
3
Inputs (ti)
Outputs (ti6)
R(nT)
N
x(t-18)
Y(nT)
1
R1(1)
N
x(t-12)
2
Price (ti) R1(nT)
R1(2)
Price (ti6) Y1(nT)
N
x(t-6)
?
3
R1(3)
N
x(t)
4
R1(4)
x(t6)
N
5
R(nT)
N
x(t-18)
Y(nT)
1
R2(1)
N
x(t-12)
2
Rate of Change (ti) R2(nT)
R2(2)
Rate of Change (ti6) Y2(nT)
N
x(t-6)
?
3
R2(3)
N
x(t)
4
R2(4)
x(t6)
N
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x(t-18), x(t-12), x(t-6), and x(t) to predict
x(t6).
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ANFIS Modeling Results NYSE Financial FNA
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NYSE Financial FNA Price and Rate of Change
modeling
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NYSE Financial FNA Stochastic K and D
modeling
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ANFIS modeling results for Market Indicators and
Price in ti6
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Scenario Analysis Stage II
PORTFOLIO SELECTION STAGE III
TECHNICAL ANALYSIS STAGE I
SCENARIO ANALYSIS STAGE II
Outputs Scenario (ti6)
Inputs (ti6)
Inputs (ti)

• Very
• Pessimistic

ANFIS
PRE -ANA L YS I S
Market indicator (ti6)
Market indicator (ti)
FUZZY INFERENCE SYSTEM
OPTIMIZA-TION

• Pessimistic

• Medium
• Pessimistic

ANFIS
Market indicator (ti6)
Market indicator (ti)

• Weakly
• Pessimistic

• Hold

ANFIS
Market indicator (ti6)
Market indicator (ti)

• Weakly
• Optimistic

• Medium
• Optimistic

ANFIS
Market indicator (ti6)
Market indicator (ti)

• Optimistic

• Very
• Optimistic

Inputs
Inputs
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Fuzzy Inference System

• 18 fuzzy rules in the system
• Reasoning used to develop these fuzzy rules are
  statements
• such as
• Scenario
• If the rate of change is large, ()
  Optimistic
• then the price is likely to move higher
• If the stochastic K is low, (-) Pessimistic
• then the price is likely to move lower

1 0.5 0
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Fuzzy Inference System
OUTPUTS SCENARIO (ti6)
INPUTS (ti6)
Classification
1. Very Pessimistic 2. Pessimistic 3. Medium
Pessimistic 4. Weakly Pessimistic 5.
Hold 6. Weakly Optimistic 7. Medium
Optimistic 8. Optimistic 9. Very Optimistic
FUZZY INFERENCE SYSTEM
1. Very low 2. Low 3. Medium low 4. Weakly
low 5. Stable 6. Weakly large 7. Medium
Large 8. Large 9. Very large
FUZZY INFERENCE SYSTEM
FUZZY INFERENCE SYSTEM
FUZZY INFERENCE SYSTEM
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Investment Scenario
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Deffuzification for NFA
Defuzzification system for NFA index inputs
rules and output scenario
0 100
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Investment Scenario for NFA
Weakly Optimistic scenario
NFA weakly optimistic scenario surface
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Portfolio Selection Stage III
SCENARIO ANALYSIS STAGE II
TECHNICAL ANALYSIS STAGE I
PORTFOLIO SELECTION STAGE III
Outputs Scenario (ti6)
Inputs (ti)
Outputs (ti6)

• Very
• Pessimistic

ANFIS
PRE -ANA L YS I S
Market indicator (ti6)
Market indicator (ti)
FUZZY INFERENCE SYSTEM
OPTIMIZA-TION

• Pessimistic

• Medium
• Pessimistic

ANFIS
Market indicator (ti6)
Market indicator (ti)

• Weakly
• Pessimistic

• Hold

ANFIS
Market indicator (ti6)
Market indicator (ti)

• Weakly
• Optimistic

• Medium
• Optimistic

ANFIS
Market indicator (ti6)
Market indicator (ti)

• Optimistic

• Very
• Optimistic

Inputs
Input
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Securities from NYSE Financial
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Mean-Variance Criterion

• Markowitz (1959)
• The return estimate is represented by the mean
  and asset risk is represented by the standard
  deviation

General Optimization Problem

• Optimal portfolio must meet the following
  constraints
• The sum of the portfolio weights must be equal to
  1.
• The weight of each asset must be greater than or
  equal to zero.

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Portfolio Selection
Objective function
Subject to

• The monthly return rates and risk are calculated
  for each one of the 430 assets
• in accordance with the Mean-Variance model
• Monthly data from January 2nd 1997 to September
  2nd, 2003

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Returns and Standard Deviations of the Optimal
Interval for the Portfolio Selection
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Optimal Portfolio Selection
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Conclusions

• This is an innovative methodology, principaly,
  because of the use of Soft Computer technologies
  such as, Fuzzy Inference Systems (FIS), and
  Adaptive Neuro-Fuzzy Inference Systems (ANFIS).
• In addition, the originality of this work
  consists in the application of the simulated
  framework where before solving financial problems
  based on future security values in the short
  term, we construct a good representation of this
  future.

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Thank you