UNIVERSITY OF REGINAUNIVERSITY OF REGINAFACULTY OF ENGINEERINGFACULTY OF ENGINEERINGMaster of Applied Science Master of Applied Science In Industrial EngineeringIn Industrial Engineering “AN INFERENCE SYSTEM APPROACH TO FINANCIAL MODELING”Maria M. Ortiz Maria M. Ortiz LermaLermaDr. Rene V. MayorgaDr. Rene V. MayorgaFall 2003Fall 20031 1Contents 1.Thesis Objective 2.Introduction 3.Technical Analysis4.Scenario Analysis5.Portfolio Selection6.Conclusion2 2Thesis 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.3 3Proposed MethodologyHere, 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:4 4IntroductionNon-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 ModelAsymmetric 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)5 5IntroductionFinancial markets: Reasons of uncertainty Expansive fluctuations in prices over short and long termsEach model in portfolio selection has its own advantages and disadvantagesMarket risk cannot be avoided with diversificationLarge number of deals produced by agents that act independently from each otherThe effective operation of the portfolio selection in practice requires an integrated decision support framework6 6Framework General StructureInputs (ti)Outputs (ti+6)OutputsScenario (ti+6)InputsInputsMarket indicator(ti+6)Market indicator(ti+6)Market indicator(ti+6)Price(ti+6)Market indicator(ti)Market indicator(ti)Market indicator(ti)Price(ti) Very Optimistic Optimistic Very Pessimistic Pessimistic Weakly Pessimistic Medium Pessimistic Hold Weakly Optimistic Medium Optimistic7 7Technical Analysis: Stage IInputs (ti)Outputs (ti+6)OutputsScenario (ti+6)InputsInputsMarket indicator(ti+6)Market indicator(ti+6)Market indicator(ti+6)Price(ti+6)Market indicator(ti)Market indicator(ti)Market indicator(ti)Price(ti) Very Optimistic Optimistic Very Pessimistic Pessimistic Weakly Pessimistic Medium Pessimistic Hold Weakly Optimistic Medium OptimisticHistorical data from January 1st, 1993 to August 29th, 20038 8Market indicatorsa)a) Monetary, Monetary, b)b) Sentiment, Sentiment, c)c) Momentum Momentum PricesPrices Rate of ChangeRate of Change Stochastic %KStochastic %K Stochastic %DStochastic %D9 9Indexes .Dow Jones Average (DOW) DJ 65 Composite Average : DJANew York Stock Exchange (NYSE) NYSE Financial : FNANational Association of Securities Dealers Automated Quotation System (NASDAQ) 259 Telecommunications: IXUTU.S. Treasury securities (Yieldx10) 30 year bond : TYX1010ANFIS Process Time Series : Mackey-Glass Differential Delay Equation Multidimensional input-output highly non-linear mapping y = f (x). nThe quantity of nodes, linear and non-linear parameters in the hidden layers is the same for each index1111ANFIS Structure Information DJADJANFANFAIXUTIXUTTYXTYXNumber of NodesNumber of Nodes193193193193193193193193Number of linear parametersNumber of linear parameters405405405405405405405405Number of non-linear Number of non-linear parametersparameters3636363636363636Total number of parametersTotal number of parameters441441441441441441441441Number of training data pairsNumber of training data pairs10001000100010001000100010001000Number of checking data Number of checking data pairspairs10001000100010001000100010001000Number of fuzzy rulesNumber of fuzzy rules81818181818181811212ANFIS Process for Prices and Rate of Change ANFIS Process for Prices and Rate of Change in one index in one index R(nT)Y(nT)R(nT)Y(nT)x(t-18), x(t-12), x(t-6), and x(t) to predict x(t+6).Inputs (ti)Outputs (ti+6)Hidden Layers 1 2 3 1313ANFIS Modeling Results: NYSE Financial FNAModeling algorithmNFACLOSING PRICELineal RegressionANFIS(Experiments 1)ANFIS(Experiments 2)Numberofdata200010002000Inputpartition4x4x4x44x4x4x4Numberofepochs20002000TrainingRMSE2.45630.45630.0013CheckingRMSE4.54510.38760.0045Trainingtime1430s2210s1414NYSE Financial FNA:Price and Rate of Change modeling 1515NYSE Financial FNA:Stochastic %K and %D modeling 1616MARKET INDICATORDJAOutput 6 days after .NFA Output 6 days after.IXUT Output 6 days after.TYXOutput6 days after.PriceY1(nT)$2751.72,695.1593.6584.56160.2156.335.45.22RateofChangeY2(nT)-0.692.51-0.3712.12-0.326.98-1.33-0.57Stochastic%KY3(nT)52.0433.986.3085.732.9170.0118.8531.71Stochastic%DY4(nT)49.9833.485.7284.732.80140.0121.1834.25ANFIS modeling results for Market Indicators and Price in ti+61717Scenario Analysis: Stage IIInputs (ti)OutputsScenario (ti+6)InputsInputsMarket indicator(ti+6)Market indicator(ti+6)Market indicator(ti+6)Market indicator(ti+6)Market indicator(ti)Market indicator(ti)Market indicator(ti)Market indicator(ti) Very Optimistic Optimistic Very Pessimistic Pessimistic Weakly Pessimistic Medium Pessimistic Hold Weakly Optimistic Medium OptimisticInputs (ti+6)1818Fuzzy Inference System 18 fuzzy rules in the system Reasoning used to develop these fuzzy rules are statements such as:ScenarioIf the rate of change is large, (+) Optimisticthen the price is likely to move higherIf the stochastic %K is low, (-) Pessimisticthen the price is likely to move lower10.501919Fuzzy Inference SystemFuzzy Inference System OUTPUTS SCENARIO (ti+6)INPUTS (ti+6)1. Very Pessimistic 2. Pessimistic3. Medium Pessimistic4. Weakly Pessimistic5. Hold6. Weakly Optimistic7. Medium Optimistic8. Optimistic9. Very OptimisticRate of ChangeStochastic %KStochastic %DClosing pricesRate of ChangeStochastic %KStochastic %DClosing pricesRate of ChangeStochastic %KStochastic %DClosing pricesRate of ChangeStochastic %KStochastic %DClosing prices1. Very low2. Low3. Medium low4. Weakly low 5. Stable6. Weakly large7. Medium Large8. Large9. Very large Classification 2020InvestmentScenarioInvestmentScenario Investment Scenario Interval Values (Z)Very pessimistic (vp) do not invest 0 Z = 11.11Pessimistic (p) do not invest 11.11 Z = 22.22Medium pessimistic (mp) do not invest 22.22 Z = 33.33Weakly pessimistic (wp) do not invest 33.33 Z = 44.44Hold (h) 44.44 Z = 55.55Weakly optimistic (wo) do invest 55.55 Z = 66.66Medium optimistic (mo) do invest 66.66 Z = 77.77Optimistic (o) do invest 77.77 Z = 88.88Very optimistic (vo) do invest 88.88 Z = 1002121Deffuzification for NFA Defuzzification system for NFA index: inputs rules and output scenario0 100ScenarioValue = 62.82222Investment Scenario for NFAWeakly Optimistic scenarioNFA weakly optimistic scenario surface2323Portfolio Selection: Stage IIIInputs (ti)Outputs (ti+6)OutputsScenario (ti+6)InputsInputMarket indicator(ti+6)Market indicator(ti+6)Market indicator(ti+6)Market indicator(ti+6)Market indicator(ti)Market indicator(ti)Market indicator(ti)Market indicator(ti) Very Optimistic Optimistic Very Pessimistic Pessimistic Weakly Pessimistic Medium Pessimistic Hold Weakly Optimistic Medium Optimistic2424Securities from NYSE Financial NameNumber of SecuritiesInsurance (accident and Health)80Consumer Financial Services 56Regional Banks40Savings Banks70Miscellaneous Financial Services60Money Center Banks84Insurance Prop. And Casualty40Total4302525Mean-Variance CriterionGeneral 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.nMarkowitz (1959)nThe return estimate is represented by the mean and asset risk is represented by the standard deviation2626Portfolio SelectionPortfolio SelectionSubject toObjective functionnThe monthly return rates and risk are calculated for each one of the 430 assets in accordance with the Mean-Variance modelMonthly data from January 2nd 1997 to September 2nd, 20032727Returns and Standard Deviations of the Optimal Interval for the Portfolio SelectionNumberofSecurityNumberofSecurity(S)(S)OptimalIntervalOptimalIntervalReturnsReturnsMinimumRiskMinimumRisk(Standarddeviation)(Standarddeviation)1 12 23 34 45 56 67 78 89 910101111121213131414151516161717181819192020212122222323242410.0310.0310.0610.0610.0710.0710.0810.0810.0910.0910.1110.1110.1510.1510.1810.1810.1810.1810.2110.2110.2110.2110.2310.2310.2510.2510.2710.2710.2710.2710.3110.3110.3210.3210.3710.3710.410.410.4710.4710.4810.4810.4910.4910.5110.5110.5310.532.452.452.462.462.482.482.492.492.492.492.52.52.52.52.512.512.512.512.522.522.522.522.532.532.532.532.532.532.542.542.542.542.552.552.552.552.572.572.582.582.592.592.592.592.612.612.612.612828Optimal Portfolio Selection2929ConclusionsuuThis is an innovative methodology, This is an innovative methodology, principalyprincipaly, , because of the use of Soft Computer because of the use of Soft Computer technologies such as, Fuzzy Inference technologies such as, Fuzzy Inference Systems (FIS), and Adaptive Systems (FIS), and Adaptive NeuroNeuro-Fuzzy -Fuzzy Inference Systems (ANFIS). Inference Systems (ANFIS). uuIn addition, the originality of this work In addition, the originality of this work consists in the application of the simulated consists in the application of the simulated framework where before solving financial framework where before solving financial problems based on future security values in problems based on future security values in the short term, we construct a good the short term, we construct a good representation of this future. representation of this future. 3030Thank you3131