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**Neural Networks in Financial Analysis**

By Rajesh Amradi( ) Nikhil Prakash ( ) Under the guidance of Prof. Pushpak Bhattacharya

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**Outline Introduction to Neural Networks Neural Networks in Finance**

Time Series Analysis Stock Market Analysis Capital Budgeting and Risk NN Model for Bankruptcy Variables Model Bond Credit Rating Problem Statement Variables and Models Comparative Study Modifications in Neural Networks Wavelet Neural Networks Fuzzy Wavelet Neural Networks

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**What are Neural Networks?**

Neural networks mimic the role and capacity of human brain to process information It maps some type of input stream of information to output stream of data Consists of ways to connect data/information to produce output that it consistent with the processes May seem simple, but far from trivial

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**What are Neural Networks?(Contd.)**

Neural network is computer science phenomenon which use Processing Elements High Degree of Interconnectivity Dependence of Variables Input to Output ratio not 1 to 1 Many interactions between inputs and backward linkages from output to inputs

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**Neural Networks and similarities with working of human brain**

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**Why use Neural Networks?**

Interest in Neural Networks stems primarily from its nonlinear models that can be trained to map past and future values of input output relationship Capability to recognize pattern and speed of its techniques to accurately solve complex processes in many applications Help to charactize relationships via a nonlinear non-parametric inference technique

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**Why use Neural Networks(Contd.)**

Usage of these networks distinguished by four types of applications Classification of Input Stream Association of output given sectors of input grouping Codification of input by producing output within a reduced dimensional subspace Simulation of output from input relationships and interconnections Added advantage of being able to establish a 'training phase' Can generalize results and lead to logical and unforeseen conclusions through the model

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**Neural Networks in Finance**

NNs are trained without restriction of a model to deprive parameters and discover relationships Driven and shaped solely by the nature of the data Has profound implications and applicability to the finance field

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Time Series Analysis Special form of data where past values influence future values Understanding time series can predict the functionality of financial markets Equation of the random model, used to model market prices p(t) = p(t-1) + u Where p represents market prices, t index of time, u stochastic variable u ≈ (0,c) Neural networks are an appropriate model to analyze financial time series

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Stock Market Analysis Stock pricing is an important aspect of financial economics Dividend Discount Model(DDM) applied to neural networks in order to verify if the entities are relatively stable Also to verify if prices are efficient and fair for stocks DDM assumes that the value of a share of common stock is the present value of all future dividends

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**Capital Budgeting and Risk**

One of the most important functions of financial management Planning expenditures on assets whose cash flows are expected to extend beyond one year Involves stock values and forecasting mechanisms, because of the presence of large values of money and financing to be planned in advance Hence, neural networks come into play

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**Neural Network Model for Bankruptcy Prediction**

Multivariate statistical analysis technique called Discriminant Analysis – widely used model in bankruptcy prediction Ratios used in discriminant analysis : X1 – Working Capital/Total Assets X2 – Retained Earnings/Total Assets X3 – Earnings before Interest and Taxes/Total Assets X4 – Market Value of Equity /Total Debt X5 – Sales/Total Assests

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**NN Model for Bankruptcy Prediction**

Consists of an input layer, hidden layer and an output layer Input layer consists of 5 nodes, one for each ratio Hidden layer consists of 5 nodes Output layer consists of only one neuron, with a response of 0(bankrupt) and 1(nonbankrupt) The network was presented with the ratios of the firms Firms with output>0.5, nonbankrupt and <0.5, bankrupt

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**NN Model for bankruptcy prediction**

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**NN model for bankruptcy prediction**

Uses backpropogation rule neural network One problem with the backpropogation model is the number of iterations needed to learn the data After training for 24 hours, and 191,400 iterations with the subsample of the training data of various firms with correct output of each data Correctly identified 36 firms in the test data as non bankrupt and 38 firms as bankrupt Much more promising when compared to Discriminant Risk Analysis

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**Bond Credit Rating: Assessing Credit Risk of a Corporation using Artificial Neural Networks**

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**Neural Networks Two Domains :**

Recognition Problem Generalization Problem Both Problems use a trained Neural Network for data set of Input/output Pairs Recognition : Problem of Recognizing output OJ corresponding to input IJ which can be a Noise Corrupted Input. Generalization: Given n pairs of I/O, predicting On+1 for corresponding In+1.

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Bond Credit Rating Grade given to Bonds that indicates their credit quality Rating given to financial strength of a bond issues or its ability to pay a bond’s principal and interest in a given time. The Process of Bond Credit Rating is a non- conservative domain and highly non linear, but is of enormous importance in real world of finance. Given by Standard Independent Rating Services such as Standard and Poor, Moody’s,Fitch’s,etc.

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**Type of Grades AAA and AA : High credit quality investment grade**

AA and BBB: Medium credit Quality Investment BB,B,CCC,CC,C:Low Quality or ‘Junk Bonds’ D: Bond in default for non-payment of principal and interest

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Problem Statement Let B represent the space of n bonds, B1, B2,…. Bn, and R be the set of possible m bond ratings, R1, R2,….. Rm . And Let F represent the k dimensional feature space ,F1, F2,…, Fk, describing each bonds then Each bond Bi can be considered as a k-tuple(F1Bi, F2Bi,.., F1Bi ) in the cartesian space F1 x F2 x … x Fk. And rating the bonds involves finding the one to one mapping function f such that: f : F1 x F2 x … x Fk R

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**Problem Statement (contd.)**

Precise Mathematical form of f is unknown Multivariate regression models have tried to approximate the function f . But success was Limited. Approximation for f is attempted using Neural Networks and they are proved to be better than the Classical Regression Methods.

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**Classical Regression Model**

Regression Models are Classical Models for predicting Bond Credit Rating Have Limitations because of having Standard Mathematical and Statistical Techniques

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Neural Network Model Multilayer network is used having simple processing elements called ‘units’. Each ‘unit’ interacts with other using weighted connections. A ‘state’ is assigned to each unit which is decided by the units in the layer below. Activation function used is Monotonic Nonlinear Function

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**Variables Selected for Predicting Bond Ratings**

Liability Debt Proportion Sales/Net Worth Profit Financial Strength Earning Past five-year revenue Growth Rate Projected next five year revenue growth Rate Working Capital Subjective prospect of company

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**Details of the Experiments**

All the Ten Variables were used to Predict Bond Ratings Two Configurations of Neural Networks were Experimented Two Layered and Three Layered Configurations

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**Correct Prediction(in percent) using Different Models **

By 10 Credit Rating Organizations Organization Linear Regression Two Layered Three Layered A 61.5 76.9 89.4 B 62.4 74.5 82.4 C 38.5 55.6 61.6 D 48.9 67.9 63.4 E 23.9 49.4 58.9 F 44.5 60.3 65.3 G 56.8 67.5 69.7 H 43.1 65.2 67.4 I 81.2 87.3 J 54.9 69.1

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Results Neural Network Model consistently outperforms Regression Model in predicting Bond Rating Increasing Number of layers was giving considerable difference in prediction rate except in some cases. Reasons for Better Performance is that Regression Models have Statistical and Mathematical Techniques while in neural networks , model improves itself after every iteration.

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**Modification in Neural Networks**

Wavelet Neural Networks Wavelets ,a technique used in multi-resolution analysis in signal processing, is used to overcome the limitations in Neural Networks Wavelet Neural Networks approximates a function f better than neural networks WNN has universal L2 approximation properties and is a consistent function estimator

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**A Wavelet Neural Network[6]**

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**Fuzzy Wavelet Neural Networks**

Fuzzy Wavelet Neural Networks improves function approximation accuracy and are used for modeling Nonlinear Dynamic Systems Set of Fuzzy Rules generalize the basis function of wavelets and thus approximates better

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**Fuzzy Wavelet Neural Network [3]**

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References [1]Martin P. Wallace. “Neural Networks and their application to finance”. Business Intelligence Journal, July 2008. [2]Marcus D.Odom, Ramesh Sharda. “A Neural Network Model for Bankruptcy Prediction”. IJCNN International Joint Conference on Neural Networks, 1990. [3]Daniel W. C. Ho, Ping-An Zhang, and Jinhua Xu. “Fuzzy Wavelet Networks for Function Learning”. IEEE TRANSACTIONS ON FUZZY SYSTEMS, VOL. 9, NO. 1, FEBRUARY 2001 [4] R. Campos, F. J. Ruiz, N. Agell & C. Angulo. “Financial credit risk measurement prediction using innovative soft-computing techniques” International Conference on Computational Finance & its Applications [5]Dr Clarence N W Tan, PhD. “An Artificial Neural Networks Primer with Financial Applications Examples in Financial Distress Predictions and Foreign Exchange Hybrid Trading System”. School of Information Technology, Bond University, Gold Coast, QLD 4229,Australia [6]Jun Zhang, Member, IEEE, Gilbert G. Walter, Yubo Miao, and Wan Ngai Wayne Lee, Member, IEEE “Wavelet Neural Networks for Function Learning” IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 43, NO. 6. JUNE 1995

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