Application of Fuzzy Logic to debt appraisal

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Application of Fuzzy Logic to

Individual Debt Appraisal and

Analysis

Dissertation

Submitted in partial fulfillment of the requirements for

the degree of

Bachelor of Technology

By

Aman Bafna

Entry No: 2011EE10440

Vivek Ranjan Maitrey

Entry No: 2011EE10494

under the guidance of

Prof. SMK Rahman

Department of Electrical Engineering

Indian Institute of Technology, Delhi2014


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Dissertation Approval Certificate

Department of Electrical Engineering

Indian Institute of Technology, Delhi

The dissertation entitled Application of Fuzzy Logic to Individual Debt

Appraisal and Analysis, submitted by Aman Bafna (Entry No:

2011EE10440) and Vivek Ranjan Maitrey (Entry No:2011EE10494) is

approved for the award of B. Tech in Electrical Engineering from

Indian Institute of Technology, Delhi.

Signature: ....

Professor S.M.K. Rahman


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Declaration

I declare that this written submission represents my ideas in my own

words and where others ideas or words have been included, I have

adequately cited and referenced the original sources. I also declare that I

have adhered to all principles of academic honesty and integrity and have

not misrepresented or fabricated or falsified any idea/data/fact/source in

my submission. I understand that any violation of the above will be cause

for disciplinary action by the Institute and can also evoke penal action

from the sources which have thus not been properly cited or from whom

proper permission has not been taken when needed.

Signature:

Name:Aman Bafna

Roll No: 2011EE10440

Signature:

Name: Vivek Maitrey

Roll No: 2011EE10494

Date:


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Abstract

Due to increasing uncertainty in financial markets and risks because of

greater interconnectivity of the world, analyzing credit worthiness of a

company/individual has become very important. In India specially, the

NPAs of major banks has been steadily growing. Hence it is important to

have a sound mathematical model which can calculate the risk associated

with a particular loan. This paper explores the afore-mentioned problem

using Fuzzy Logic and Fuzzy Interface System.


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Acknowledgements

We would like to thank our guide Prof. SMK Rahman for his constant

guidance and support. His knowledge and eye for detail have helped us to

learn and produce more in the given time duration


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Contents

1 Introduction ............................................................................................................... 8

1.1 Problem Definition .......................................................................................... 9

1.2 Organization of the Report ........................................................................... 9

2 Literature Review ................................................................................................. 10

2.1 Artificial Neural Networks ........................................................................ 10

2.2 Regression Analysis............................................................. 10

2.3 Fuzzy Logic............................................................................................. 11

3 Methodology ........................................................................................................... 12

3.1 Identification of Crisp Inputs................................................................. 12

3.1.1 Debt Ratio .................................................................................................. 13

3.1.2 Loan To Value Ratio............................................................. 13

3.1.3 Debt Coverage Ratio.... 13

3.1.4 Priority Sector + Prior Bank Customer.. 14

3.1.5 Online Retail Default .... 15

3.1.6 Bill Payment Default .... 15

3.1.7 Bank Transaction Default.. 15

3.2 Mamdani System ........................................................................................... 25

4 Data and Results .................................................................................................... 28

4.1 Working of Credit Score............................................................................... 26

5 Conclusions .............................................................................................................. 28


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List of Figures and Tables

Figure 1: Fuzzy Logic Flow Chart .20 Figure 2: Fuzzy Interface System ..20Figure 3: Rule Editor for Fuzzy Interface System....21

Figure 4: Debt Ratio Fuzzy Set ...22

Figure 5: Loan To Value Ratio Fuzzy ..22 Figure 6: Debt Coverage Ratio Fuzzy Set .23

Figure 7: Priority Sector +Prior Bank Customer Fuzzy Set .23

Figure 8: Online Retail Default ..23

Figure 9: Bill Payment Default ..........23

Figure 10:Bank Defaults ... .24

Figure 11: Output Finction ......24

Table1: Fuzzy Inputs.22Table 2: Credit Score For different individuals30


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Chapter 1

1 Introduction

Banking like any business is not without its risks. The whole banking

system is based on the premise of extending credit to those who need it

and in turn get interest on the amount disbursed. In this era of

globalization financial systems all around the world have become

interconnected. No nation can remain insulated from developments

taking place even on the other side of globe. The most recent example of

this was the Sub Prime crisis in the United States, which brought about a

global economic meltdown.

The Sub Prime crisis was called so because banks extended loans to even

hose customers which did not have the financial soundness to repay the

loan. The banks started getting accumulated with mortgaged properties.

The sudden increase in properties in the open market further drove down

the prices prompting more customers to default on their loans. This

vicious cycle continued and the major financial giants crashed.

Banks are the backbone of the current financial system. They are the

gateway to the complex world of credit. It is imperative that banks remain

in proper financial health for the smooth functioning of the economy.

Banks are becoming increasingly vigilant and keep constant check on bad

loans after it became abundantly clear that the recent 2008 recession was

caused by aggressive lending by leading banks.

The key to check the rise of bad loans is to differentiate between a prime

customer and a sub-prime customer. Often banks treat prime and sub-

prime customers differently. Prime Lending Rate significantly lower than


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the normal lending rate of banks as there is lower risk of default. It

becomes imperative to make this distinction.

The best way to avoid a bad loan is to not provide loan to unworthy

debtor in the first place. Hence banks spend a lot of resources on loan

analysis. Current methods involve long questionnaires and

comprehensive background checks. Interviews of applicants are

conducted during the process. However these methods have certain

inherent problems. Certain terms are vague and subjective in nature. The

process is also prone to personal and political influences. Hence an

objective scheme is desired that is free from these drawbacks.

1.1 Problem Definition

To build a model based on fuzzy logic that will help in debt appraisal. The

model will provide a fuzzy score to every individual assesse based upon

which banks will decide to approve the debt or not.

1.2 Organization of the Report

The organization of this report is as follows. Chapter 2 provides the

literature review. Theory necessary to proceed for this study has been

summarized. Methodology and work flow of the simulation has been

discussed in chapter 3. The detailed results of the experiments have been

presented in chapter 4. Chapter 5 contains conclusions of this study.


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Chapter 2

Literature Review

Several strategies are available for mathematical modeling of systems

ranging in complexity and scale. Some of the most popular schemes

employed for financial modeling are :

2.1 Artificial Neural Networks (ANNs)

A neural network is a system composed of many simple processing elements

operating in parallel whose function is determined by network structure,

connection strengths, and the processing performed at computing elements

or nodes [1]

Artificial neural networks are highly adaptive non-linear computational

models that successfully discover complex relationships between the inputs

and output. However the major disadvantages of ANNs are their

computational intensive nature and the opaque nature of the model which

makes calibration difficult. They are usually avoided in favor of simpler,

faster models.

2.2 Regression Analysis

Regression analysis may be employed to find out the relationship between

two more variables. Regression analysis is especially useful when we have to

determine one quantitative which is a function of two or more independent

variables. [2]

For example a multivariate regression would relate credit worthiness of anindividual in the following manner

Y = a+ bX1+cX2+dX3 (1)

Where Y is some variable to measure the credit worth of an individual;X1,X2

andX3are variables representing common financial ratios such as Loan to

Value Ratio or Debt Service Coverage Ratio; and a,b,cand d are constants.

However regression analysis suffers from one major limitation that is the

assumption of linearity between the input variables and the output which

may not always be the case, which makes it unsuitable for the complexities of

financial world.


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2.3 Fuzzy Logic

Fuzzy set theory is widely used to model inaccuracy and uncertainty of real

world. Fuzzy logic is a form of many-valued logic; it deals with reasoning

that is approximate rather than fixed and exact. Compared to traditional

binary sets (where variables may take on true or false values), fuzzy logic

variables may have a truth value that ranges in degree between 0 and 1.

Fuzzy logic has been extended to handle the concept of partial truth, where

the truth value may range between completely true and completely false.[2]

Fuzzy logic is well suited for the purpose of loan assessment because it

closely resembles the discourse of loan appraisal. The fuzzy approach uses

fuzzy sets to model the linguistic description of the financial conditions.

The process to construct a fuzzy model consists of three steps:1. Fuzzification

2. Construction of rule base

3. Defuzzification

Fuzzification: Every fuzzy variable in the model is associated with a linguistic

description. The variables which take on a numerical value are assigned a

linguistic variable. This step essentially converts the raw financial statistics

into a linguistic assessment. It involves mapping the crisp input variable onto

a membership function which maps it onto fuzzy sets. Every fuzzy variable is

classified into Very Bad, Bad, Normal, Goodand Very Good.

Construction of rule base: The rule base consists of IF-THEN rules. The

structure of the rule base is founded upon the requirements of the bank.

The former evaluates the extent to which the objects satisfy the

requirements, and the later represents the response of the system.

Defuzzification is the last process of the model. The contribution from each of

the IF THEN rules is compressed into a single variable. There are several

methods for defuzzification, the most commonly ones used being the

weighted average and centroid location.

Advantages of using a Fuzzy approach to credit appraisal:

1. Subjective nature of inputs: The 5 Cs of credit Capacity, Capital,

Collateral, Conditions and Character are the inputs for making the

decision of loan approval. Loan officers try to capture as much

information about the customer from his balance sheet, income

declaration and banking records to evaluate the degree of potential

risk. These inputs have to be identified in ambiguous terms like good,


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above, below etc. Any decision that involves such ill defined terms

will be prone to error of judgment. The strength of the fuzzy approach

lies in its ability to capture this approximate reasoning through its use

of fuzzy sets.

2. Imperfect Data: In the real world, the data is never well defined. Oftensome of the data is missing or changing too often to be used for a

mathematical model. When the variables are themselves ill defined,

there is scope for misinterpretation. The variables may vary in scale

from customer to customer.

3. Adaptability: The fuzzy approach relies on the definition of

membership functions for the crisp variables. For example, the loan to

value ratio is considered to be good in the range 40%-60% but if

credit is available freely, banks may simply move this window to

45%-60%. This adaptability makes it ideal for the ever changing

world of finance. The rules base itself can be modified from time to

time.


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Chapter 3

3 Methodology

Identification of Crisp Inputs:

The first step in construction of a fuzzy model is the identification of crisp

inputs. There are several financial ratios that have are widely used for the

assessment of financial soundness. It is time tested method of financial

analysis. The most important advantage of using financial ratio is that

they neither sophisticated nor difficult to follow. Financial ratios are

simple comparisons between two figures gathered from the income

statement of an individual. Since these are ratios from the statistics of the

same individual, they allow for comparison between different applicants

based on their financial health even if there is huge disparity in the

amount of credit solicited.

Capacity, Capital, Collateral, Conditions and Character are considered to

be the 5 Cs of credit analysis. We will try to capture these variables for

our assessment. Since none of these variables are directly measurable,

certain financial variables will be used as proxies. These variables

however do not hold equal weightage. The most commonly used financial

ratios to evaluate the above are the following:

1. Debt Ratio : It is the ratio of total debt to total assets of an individual

expressed as a percentage. Itcan be interpreted as the proportion of a

customers assets that are financed by debt. [4] If the debt ratio of a

customer is too high, he will most probably be denied credit. Most

banks have a ceiling on the debt ratio and sometimes it is also set by

the central banks. Too high a debt ratio reduces the capacity of a

customer to borrow more. Generally 42% is upper limit on the debt

ratio. Debt ratio in the range 21%-42% is considered worrisome. Debt

ratio in the range 16%-19% is considered moderate, in the range 6%-


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16% it is considered favourable. Anything less than 6% is a very good

debt ratio and qualifies you to get more credit.

2. Loan to Value Ratio: It is another very important financial ratio in risk

assessment. It the ratio of the principal of the debt being solicited to

the value of the collateral submitted to the bank. The collateral is the

final assurance of the bank for the repayment of debt. In case of failure

by the customer to service his debt, the banks take custody of the

collateral and auction it in the open market to recover their debt. If the

market value of the collateral is high, you are entitled to larger credit.

Higher loan to value ratios translate into greater risk for the bank

because they will need to sell the collateral at a higher price to recover

their debt. While if the loan to value ratio is less, the customer is more

likely to ensure repayment of debt.

In our analysis, we have taken the housing sector as the example.

Since residential properties are appreciating assets, banks allow loans

up to 80% of the market value of the collateral.

3. Debt Service Coverage Ratio: It is the ratio of cash available to the

principal and interest liabilities of the customer. It is an indispensable

component of risk assessment because it is the income through whichthe debt will be serviced. Ideally any ratio greater than should be

acceptable to the banks because the customer can meet his payments,

but is never the case. This is because the debt service coverage ratio

only measures the capacity of a customer to earn its debt service not

the amount of cash available to meet his obligations. The customer

may divert his/her earnings for other enterprises, tax liabilities or to

support his/her lifestyle. Acceptable industry norm for a debt service

coverage ratio is between 1.5 to 2.[5]

The above financial ratios are used to estimate the first three Cs namely

Capacity, Capital and Collateral. The remaining two Cs have to estimated

by other means.

Conditions also influence the terms of the loan. Conditions describe the

purpose of the loan whether it is capacity addition, business expansion or

personal consumption. They also include specific directions by RBI and

the government regarding engagement with certain sectors. For example,


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if the purpose of the loan is buying gold, the banks may issue loan only

upto 65% of the amount in the transaction. This is intentionally done to

keep people away from consuming gold which burns into the nations

foreign exchange reserves. At the same time, loans for agricultural

activities like buying seeds, fertilizers and farming equipment may be

granted loan up to 100% of the transaction amount. This has been done to

encourage farmers to adopt modern agricultural practices and save them

from local loan sharks. The most important conditions influencing the

loan approval processes are:

1. Purpose of Loan/Priority Sector Lending: Even within the priority

sector lending scheme, there are two categories of assistance. Direct

and Indirect Finance. Direct Finance is to help the small and

marginalized farmers directly by providing cheap and timely credit

assistance. Bigger loans to business majors for agricultural purposes

are considered as Indirect Assistance because they create employment

opportunities for rural work force. If the purpose of loan falls under

Direct Assistance Category, it gets a +2 score on a scale of 1 to 5. Loans

falling under Indirect Assistance get a +1 on their Conditions score.

2. Prior Bank Records: Banks usually reward loyal customers by easilyapproving their loans. A bank record of 5-10 years will get a +1 on

their conditions score, 10-15 years will get a+2 and anything above 15

years will fetch a +3.

The fifth C, the Character of the consumer is the most difficult to quantify.

It is very important to differentiate between responsible, reasonable

customers and irresponsible borrowers. During the classification of the

customers into responsible and irresponsible customers, there may be

errors of the following types.Type I error occurs when a worthy applicant

is flagged as unworthy debtor. In this this case the interest which could

have been made on a loan is lost. Type II error occurs when an unworthy

applicant is flagged as worthy debtor. In this case even the principal along

with the interest is at risk. Misclassification cost of a Type II error is

usually much greater than that for a Type I error. Any model for

assessment must be not prone to Type II errors.

To assess whether a customer is responsible customer or not we will use

the following indicators:


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1. Online retail default rate: With the increase in popularity of e-

commerce in India, there is an increase in the data available for

behavioral analysis of the customer. The recent growth in electronic

transactions has facilitated accumulation of user data which may bemined for critical insights into the spending habits of the customer. In

India, on the other hand, cash on delivery is the payment method for

up to eight in 10 transactions. We can use this data to differentiate

between responsible and irresponsible customers. A responsible

customer would order what he/she needs and honor the cash

commitment when the item is delivered. On the other hand, an

irresponsible customer is likely to order without giving much thought

and change his/her mind partly because there is no upfront

commitment to pay. The average default rate on Cash On Delivery

(COD) payments is quite high in India at the moment (35-45%).

2. Bill payment default rate: Invariably all people use public utility

systems, be it electricity, water, broadband, mobile or piped gas. Once

again, a reliable customer is more likely pay his utility bills regularly

and on time. Consumer behavior reports generated from these

payment patterns are closer to reality because there is no immediate

penalty for late submission of bills and there is no fear of supervision.

3. Bank credit default rate: With the increasing popularity of electronic

transactions, credit cards/debit cards are readily being adopted by the

Indian populace. These cards permit you to spend more than the cash

available with you. However, you have to pay the overdraft within a

stipulated amount of time, lest you incur penalty in form of interest.

Responsible customers pay their dues in time and are particularly

careful about deadlines. Such customers are likely to meet their

liabilities regularly. Bank credit default rates are around 4% and

anyone around this rate is a safe bet. [6]

After identifying the variables that will act as the crisp inputs, we need to

define the membership functions that govern the rule base. A number will

be produced based upon evaluation according to the rules base. Decision

would be made according to this score.


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Crisp Inputs

Fuzzifcation

Rule Base

Evaluation

Defuzzication(obtaining the credit score)

Decision

Figure 1: Flow chart of fuzzy logic

Working of the Credit Score

A credit score is a numerical expression based on a level analysis of a

person's credit files, to represent the creditworthiness of that person.[1]

Credit scores find utility in the evaluation of potential risk in lending to

customers. Using the credit scores banks are able to predict how likely is it

for a customer to repay his debt or service his obligations.

Credit scores were developed in an attempt to evaluate the credit worth of an

individual in a fair and objective manner. Since credit worth is highly

subjective in nature and thus prone to variation in analyses by different

individuals.

Credit scores reflect your current financial soundness, ability to meet your

obligations, how faithfully youve paid your bills and anything that somehow

may affect your credit worth. All that information and more can be captured

in a three digit number.

The credit score produced by our fuzzy model is after all a score. It doesnt

decide whether the loan is going to be approved or not. However, a good

score on the model clearly enhance the chances of the debt getting approved.

The credit score in our model varies from 0-320, with 320 being the bestpossible credit score. The credit score serves he following purposes:

Figure 1


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1. Uniform parameters to assess all individuals: By using the same

methodology on all potential customers, banks can differentiate prime

customers with the sub-prime customers.

2. Credit pricing: Since a lower credit score on the model indicates more risk

of default, banks can set the price of credit different for different customers.

Prime Lending Rate, the rate at which prime customers are granted loans is

50 to 100 basis points lower than the general lending rate. Banks can thus

balance their risk with more profit. This scheme is generally employed to

reward loyal customers and dissuade customers from defaulting.

3. Managing their credit portfolios: Banking laws in India have been made to

cater to the specific economic and social profile of Indian customers. Priority

Sector Lending is scheme has been implemented to benefit those people who

are the fringes of the market economy. According to the scheme 18 per cent

of the total credit disbursed by the banks has to go to specific sections of the

society like people engaged in agriculture and allied activities, fisheries, self-

help groups, food processing etc. If they fail to do, banks have to deposit an

amount equal to the shortfall in their lending quota with the NABARD

(National Bank for Agricultural and Rural Development). For customers

belonging to these sections can set a different qualifying score in order to

meet their targets.

4. Managing equity : Sometimes banks borrow from the market when credit

is freely available for example the easy money policy of the Federal reserve.

During times like this credit is in abundant supply hence it makes economic

sense to expand their customer base by simplifying the requirements for the

qualification of loan. If credit supply decreases and cash with the bank dries

up, bars can be set up higher.

5. Managing Economic cycles: All economies undergo boom/recession cycles.

During economic boom, banks lend credit aggressively as economic activity

is at its maximum level. Business expansion takes place at a rapid pace and

all sectors of the economy do well. However during such times, asset bubbles

might be created. Investors in speculation of rising prices of assets, invest

into them by borrowing from banks. Banks relying on the increasing value of

the collateral issue credit easily. When these asset bubbles burst, prices go

spiraling down, prompting others debtors to default on their loans. Banks arethen flooded with mortgaged assets which are not readily sold on the market.


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Cash with the bank dries up and its non-performing assets increase sharply.

As the financial health of banks deteriorates, all other sectors of the economy

are also affected. This is exactly what happened in 2008 Sub-prime crisis, the

effects of which are still being experienced. During boom period of the

economic cycle, banks can use higher benchmarks for approval of loans toprevent the creation of asset bubbles.


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Fuzzy Model- Mamdani Fuzzy Logic Controller-

The most commonly used fuzzy inference technique is the Mamdani method

which was proposed by Mamdani and Assilian[9] to control a steam engine

and boiler combination by synthesizing a set of linguistic control rules

obtained from human operators of the machine. In Mamdanis model the

fuzzy implication is modeled using the minimum operator of Mamdani, min

is the conjunction operator, t-norm for composition is min and max operator

is used for aggregation. We have used the Mamdani system because of its

simplicity. The other technique is the sugeno method.

Advantages of Mamdani system over Sugeno method-

It has widespread acceptance.

It is more intuitive.

It is more robust in the presence of noisy input data.

It is less sensitive to significant imprecision in the inputs than Sugeno.

This happens when the fuzzy sets overlap.

It has less processing time as compared to Sugeno.

Fuzzy Interface System-

Matlab has a very good Fuzzy Interface System, which makes modelling of a

fuzzy system very easy.

Figure 2- Fuzzy Interference System


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Working of the Mamdani Model [2]-

Step 1 Fuzzification-

The crisp inputs are taken and the degree to which they belong to the

appropriate fuzzy sets is calculated.

Step 2 Rules evaluation-The fuzzified inputs are then applied to the antecedents of the fuzzy rules. If

a given fuzzy rule has multiple antecedents, the fuzzy operator (AND or OR)

is used to obtain a single number that represents the result of the antecedent

evaluation. To evaluate the disjunction of the rule antecedents, one uses the

OR fuzzy operation. Typically, the classical fuzzy operation union is used:

AB(x) = max {A(x), B(x)}.

Similarly, in order to evaluate the conjunction of the rule antecedents, the

AND fuzzy operation intersection is applied:

AB(x) = min {A(x), B(x)}.

Now the result of the antecedent evaluation can be applied to the

membership function of the consequent.

Step 3: Aggregation of the rule outputs

The membership functions of all rule consequents previously clipped or

scaled are combined into a single fuzzy set

Step 4: Defuzzification

The most popular defuzzification method is the centroid technique. It finds a

Figure 3 Rules for the FIS


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point representing the center of gravity (COG) of the aggregated fuzzy set A,

on the interval [a, b]. A reasonable estimate can be obtained by calculating it

over a sample of points.

Term 1(very

bad)

2(bad) 3(normal) 4(good) 5(very

good)

Debt Ratio >0.42 0.21-0.42 0.16-0.20 0.06-0.15 0-0.06

Loan to Value

ratio

>0.90 0.80-0.90 0.60-0.80 0.40-0.60 0.5 0.4-0.5 0.2-0.4 0.1-0.2 0-0.1

Bill payment

default

>0.3 0.2-0.3 0.1-0.2 0.05-0.1 0-0.05

Bank default >0.2 0.15-0.2 0.11-0.15 0.04-0.11 0-0.04

Table 1: Fuzzy Inputs

Following are the fuzzy sets assigned to the inputs-

1. Debt Ratio

2. Loan to value Ratio

Figure 4

Figure 5


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3. Debt Coverage Ratio

4. Priority Sector+ prior bank history

5. Online retail default

6. Bill payment default

Figure 6

Figure 7

Figure 8

Figure 9


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7. Bank default

Output Function

The output function is divided in 16 membership functions that denote different

credit ratings from the worst (D) to the best (AAA).

RULES-

We have used 172 rules to make the system as robust as possible and to

account for all the variations in the input variables. The rules are in the code

below in the form-

1 1 1 1 1 1 1, 1 (1) : 1

This means if (Debt ratio is very bad(1)) and (loan to value ratio is very

bad(1)) and (Debt coverage ratio is very bad(1)) and (priority sector+ prior

bank customer is very bad(1)) and (online retail default is very bad(1)) and

(bill payment default is very bad(1)) and (bank default is very bad(1) then

output is D (i.e. the worst credit rating).

Figure 10

Figure 11


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Defuzzification

We get the final credit score using defuzzification on the output fuzzy set by

Centroid method. Centroid defuzzification returns the center of area underthe curve. If you think of the area as a plate of equal density, the centroid is

the point along the x axis about which this shape would balance. The credit

score will lie in the range of 0-320.

Decision making: The number obtained from this model is a customers

credit score. It does not automatically decide whether someones loan will be

approved or not. However a good score will greatly enhance the odds of

getting the loan approved. Thw working of the credit score has already been

explained in Chapter 3.


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Fuzzy Inference System File Code

[System]Name='btp'Type='mamdani'Version=2.0

NumInputs=7NumOutputs=1NumRules=172AndMethod='min'OrMethod='max'ImpMethod='min'AggMethod='sum'DefuzzMethod='centroid'

[Input1]Name='Debt_ratio'Range=[0 50]NumMFs=5

MF1='very_bad':'trapmf',[4045 60 100]MF2='bad':'trimf',[17 31 45]MF3='normal':'trapmf',[10 1719 25]MF4='good':'trimf',[3 10 17]MF5='very_good':'trapmf',[-58.6 -9.32 4 10]

[Input2]Name='loan-to-value_ratio'Range=[0 150]NumMFs=5

MF1='very_bad':'trapmf',[85100 180 300]MF2='bad':'trimf',[70 85100]MF3='normal':'trapmf',[50 6575 85]MF4='good':'trimf',[30 5070]MF5='very_good':'trapmf',[-176 -27.9 29.960317460317550.6]

[Input3]

Name='Debt_coverage_ratio'Range=[0 5]NumMFs=5MF1='very_bad':'trapmf',[-5.865 -0.9325 1.2 1.25]MF2='bad':'trimf',[1.1 1.251.4]MF3='normal':'trapmf',[1.251.35 1.45 1.55]MF4='good':'trimf',[1.4 1.752.05]MF5='very_good':'trapmf',[1.75 2.1 6 10]

[Input4]

Name='priority_sector +prior bank customer'Range=[0 5]NumMFs=5

MF1='very_bad':'trapmf',[-5.865 -0.9325 1 2]MF2='bad':'trimf',[1 2 3]MF3='normal':'trapmf',[2 2.53.5 4]MF4='good':'trimf',[3.5 44.5]MF5='very_good':'trapmf',[44.5 6 10]

[Input5]Name='online_retail_default'Range=[0 1]

NumMFs=5MF1='very_bad':'trapmf',[0.50.6 1.1 1.9]MF2='bad':'trimf',[0.3 0.450.6]MF3='normal':'trapmf',[0.150.2 0.4 0.5]MF4='good':'trimf',[0.080.15 0.3]MF5='very_good':'trapmf',[-0.36 -0.04 0.08 0.15]

[Input6]

Name='bill_payment_default'Range=[0 1]NumMFs=5MF1='very_bad':'trapmf',[0.25 0.3 1.1 1.9]MF2='bad':'trimf',[0.15 0.250.35]MF3='normal':'trapmf',[0.0750.1 0.2 0.25]MF4='good':'trimf',[0.040.075 0.15]MF5='very_good':'trapmf',[-0.36 -0.04 0.05 0.1]

[Input7]Name='bank_default'Range=[0 1]NumMFs=5MF1='very_bad':'trapmf',[0.18 0.3 1.1 1.9]MF2='bad':'trimf',[0.14 0.180.3]MF3='normal':'trapmf',[0.080.11 0.15 0.18]MF4='good':'trimf',[0.020.08 0.14]

MF5='very_good':'trapmf',[-0.36 -0.04 0.04 0.08]


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[Output1]Name='output1'Range=[0 320]NumMFs=16MF1='D':'gauss2mf',[41.3 -9.47 9.59 2.0564168656584]MF2='C-':'gaussmf',[4.3529.3731310942578]MF3='C':'gaussmf',[4.7649.4665222101842]MF4='C+':'gaussmf',[4.07214376489123 69.8]MF5='Ca':'gaussmf',[4.3287.7731310942579]MF6='Caa':'gaussmf',[4.35108.266522210184]MF7='b-':'gaussmf',[3.93

127.879739978332]MF8='b':'gaussmf',[4.17147.919826652221]MF9='b+':'gaussmf',[4.63169.733477789816]MF10='ba':'gaussmf',[4.87190.320260021669]MF11='baa':'gaussmf',[3.89208.926868905742]MF12='a-':'gaussmf',[5.42227.466955579632]MF13='a':'gaussmf',[4.59167473828521 250]

MF14='a+':'gaussmf',[3.32183282669534 270]MF15='aa':'gaussmf',[4.99655186951675 290]MF16='Aaa':'gaussmf',[8318.5]

[Rules]1 1 1 1 1 1 1, 1 (1) : 13 3 3 3 3 3 3, 11 (1) : 15 5 5 5 5 5 5, 16 (1) : 12 2 2 2 2 2 2, 6 (1) : 14 4 4 4 4 4 4, 14 (1) : 1

2 2 2 2 2 3 3, 9 (1) : 12 2 2 2 3 2 3, 9 (1) : 12 2 2 2 3 3 2, 9 (1) : 12 2 2 2 3 3 3, 9 (1) : 12 2 2 3 2 3 3, 9 (1) : 12 2 2 3 3 2 3, 9 (1) : 12 2 2 3 3 3 2, 9 (1) : 12 2 2 3 3 3 3, 9 (1) : 12 2 3 3 2 3 3, 9 (1) : 12 2 3 3 3 2 3, 9 (1) : 12 2 3 3 3 3 2, 9 (1) : 12 2 3 3 3 3 3, 9 (1) : 12 3 2 3 3 3 3, 9 (1) : 1

2 3 3 2 3 3 3, 9 (1) : 12 3 3 3 2 3 3, 9 (1) : 12 3 3 3 3 2 3, 9 (1) : 1

2 3 3 3 3 3 2, 9 (1) : 13 2 3 3 3 3 2, 9 (1) : 13 3 2 3 3 3 2, 9 (1) : 13 3 3 2 3 3 2, 9 (1) : 11 1 1 1 1 2 2, 4 (1) : 11 1 1 1 2 1 2, 4 (1) : 1

1 1 1 1 2 2 1, 4 (1) : 11 1 1 1 2 2 2, 4 (1) : 11 1 1 2 1 2 2, 4 (1) : 11 1 1 2 2 1 2, 4 (1) : 11 1 1 2 2 2 1, 4 (1) : 11 1 1 2 2 2 2, 4 (1) : 11 1 2 1 2 2 2, 4 (1) : 11 1 2 2 1 2 2, 4 (1) : 11 1 2 2 2 1 2, 4 (1) : 11 1 2 2 2 2 1, 4 (1) : 11 1 2 2 2 2 2, 4 (1) : 11 2 1 2 2 2 2, 4 (1) : 11 2 2 1 2 2 2, 4 (1) : 1

1 2 2 2 1 2 2, 4 (1) : 11 2 2 2 2 1 2, 4 (1) : 11 2 2 2 2 2 1, 4 (1) : 12 1 2 2 2 2 1, 4 (1) : 12 2 1 2 2 2 1, 4 (1) : 12 2 2 1 2 2 1, 4 (1) : 12 2 2 2 1 2 1, 4 (1) : 12 2 2 2 2 1 1, 4 (1) : 15 5 5 5 5 4 4, 15 (1) : 15 5 5 5 4 5 4, 15 (1) : 15 5 5 5 4 4 5, 15 (1) : 15 5 5 5 4 4 4, 15 (1) : 15 5 5 4 5 4 4, 15 (1) : 1

5 5 5 4 4 5 4, 15 (1) : 15 5 5 4 4 4 5, 15 (1) : 15 5 5 4 4 4 4, 15 (1) : 15 5 4 5 4 4 4, 15 (1) : 15 5 4 4 5 4 4, 15 (1) : 15 5 4 4 4 5 4, 15 (1) : 15 5 4 4 4 4 5, 15 (1) : 15 5 4 4 4 4 4, 15 (1) : 15 4 5 4 4 4 4, 15 (1) : 15 4 4 5 4 4 4, 15 (1) : 15 4 4 4 5 4 4, 15 (1) : 15 4 4 4 4 5 4, 15 (1) : 15 4 4 4 4 4 5, 15 (1) : 14 5 4 4 4 4 5, 15 (1) : 14 4 5 4 4 4 5, 15 (1) : 14 4 4 5 4 4 5, 15 (1) : 14 4 4 4 5 4 5, 15 (1) : 14 4 4 4 4 5 5, 15 (1) : 13 3 4 3 4 4 4, 13 (1) : 13 3 4 4 3 4 4, 13 (1) : 13 3 4 4 4 3 4, 13 (1) : 13 3 4 4 4 4 3, 13 (1) : 13 3 4 4 4 4 4, 13 (1) : 13 4 3 4 4 4 4, 13 (1) : 13 4 4 3 4 4 4, 13 (1) : 13 4 4 4 3 4 4, 13 (1) : 13 4 4 4 4 3 4, 13 (1) : 13 4 4 4 4 4 3, 13 (1) : 13 4 4 4 4 4 4, 13 (1) : 1


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4 3 4 4 4 4 4, 13 (1) : 14 4 3 4 4 4 4, 13 (1) : 14 4 4 3 4 4 4, 13 (1) : 14 4 4 4 3 4 4, 13 (1) : 14 4 4 4 4 3 4, 13 (1) : 14 4 4 4 4 4 3, 13 (1) : 1

3 3 3 3 3 3 4, 12 (1) : 13 3 3 3 3 4 3, 12 (1) : 13 3 3 3 3 4 4, 12 (1) : 13 3 3 3 4 3 4, 12 (1) : 13 3 3 3 4 4 3, 12 (1) : 13 3 3 3 4 4 4, 12 (1) : 13 3 3 4 3 4 4, 12 (1) : 13 3 3 4 4 3 4, 12 (1) : 13 3 3 4 4 4 3, 12 (1) : 13 3 4 3 4 4 3, 12 (1) : 13 3 4 4 3 4 3, 12 (1) : 13 3 4 4 4 3 3, 12 (1) : 13 4 3 4 4 3 3, 12 (1) : 1

3 4 4 3 4 3 3, 12 (1) : 13 4 4 4 3 3 3, 12 (1) : 14 3 4 4 3 3 3, 12 (1) : 14 4 3 4 3 3 3, 12 (1) : 14 4 4 3 3 3 3, 12 (1) : 13 3 3 3 3 3 2, 10 (1) : 13 3 3 3 3 2 3, 10 (1) : 13 3 3 3 3 2 2, 10 (1) : 13 3 3 3 2 3 2, 10 (1) : 13 3 3 3 2 2 3, 10 (1) : 13 3 3 3 2 2 2, 10 (1) : 13 3 3 2 3 2 2, 10 (1) : 13 3 3 2 2 3 2, 10 (1) : 1

3 3 3 2 2 2 3, 10 (1) : 13 3 2 3 2 2 3, 10 (1) : 13 3 2 2 3 2 3, 10 (1) : 13 3 2 2 2 3 3, 10 (1) : 13 2 3 2 2 3 3, 10 (1) : 13 2 2 3 2 3 3, 10 (1) : 13 2 2 2 3 3 3, 10 (1) : 12 3 2 2 3 3 3, 10 (1) : 12 2 3 2 3 3 3, 10 (1) : 13 3 2 2 2 2 2, 7 (1) : 13 2 3 2 2 2 2, 7 (1) : 13 2 2 3 2 2 2, 7 (1) : 13 2 2 2 3 2 2, 7 (1) : 1

3 2 2 2 2 3 2, 7 (1) : 13 2 2 2 2 2 3, 7 (1) : 13 2 2 2 2 2 2, 7 (1) : 13 3 3 2 2 2 2, 8 (1) : 13 3 2 3 2 2 2, 8 (1) : 13 3 2 2 3 2 2, 8 (1) : 1

3 3 2 2 2 3 2, 8 (1) : 13 3 2 2 2 2 3, 8 (1) : 12 3 2 2 2 2 2, 8 (1) : 12 2 3 2 2 2 2, 8 (1) : 12 2 2 3 2 2 2, 8 (1) : 12 2 2 2 3 2 2, 8 (1) : 12 2 2 2 2 3 2, 8 (1) : 12 2 2 2 2 2 3, 8 (1) : 11 1 1 1 1 1 2, 2 (1) : 11 1 1 1 1 2 1, 2 (1) : 11 1 1 1 2 1 1, 2 (1) : 11 1 1 2 1 1 1, 2 (1) : 11 1 2 1 1 1 1, 2 (1) : 1

1 2 1 1 1 1 1, 2 (1) : 12 1 1 1 1 1 1, 2 (1) : 12 2 1 1 1 1 1, 2 (1) : 12 2 1 1 1 1 2, 2 (1) : 12 2 1 1 1 2 1, 2 (1) : 12 2 2 1 1 1 1, 2 (1) : 11 2 2 2 2 2 2, 5 (1) : 12 1 2 2 2 2 2, 5 (1) : 12 2 1 2 2 2 2, 5 (1) : 12 2 2 1 2 2 2, 5 (1) : 12 2 2 2 1 2 2, 5 (1) : 12 2 2 2 2 1 2, 5 (1) : 12 2 2 2 2 2 1, 5 (1) : 1

2 1 1 1 1 1 2, 3 (1) : 12 1 1 1 1 2 1, 3 (1) : 12 1 1 1 2 1 1, 3 (1) : 12 1 1 2 1 1 1, 3 (1) : 12 1 2 1 1 1 1, 3 (1) : 12 2 1 1 1 2 2, 3 (1) : 12 2 1 1 2 1 1, 3 (1) : 12 2 1 2 1 1 1, 3 (1) : 12 2 2 1 1 1 2, 3 (1) : 12 2 2 1 1 2 1, 3 (1) : 12 2 2 1 2 1 1, 3 (1) : 12 2 2 2 1 1 1, 3 (1) : 1


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Chapter 4

Data and Results

Due to lack of real life data for all our inputs, we applied our data analysis on

5 individuals, with a created financial history.

1. Individual A- With a good business, A has assets worth Rs 10 crore a

debt of Rs 30 lakhs. He has been buying a lot of things from online stores

and is quite a reliable customer, having refused or rejected items that he

ordered only twice in 40 transactions. He also pays his DTH, mobile and

electricity bill regularly on time, with a late payment or default rate of

only 2.5%. He has never had a case of a bounced check or non-payment of

credit card dues and always pays his EMIs on time. He wants to take aloan worth Rs 30 lakhs @ 14% interest rate from a bank to start a small

scale industry (which is a priority sector lending area as prescribed by

RBI). He has been a customer of that bank for the past 20 years. He is

ready to put up the property where he plans to open the industry and

which is worth Rs 1 crore as collateral for the loan. His annual income

comes out to be Rs 20 lakh. Based on this data, the 7 financial inputs of

our model for A comes out to be (0.03,0.30,3,5,0.05,0.025,0.05,313.932).His credit score comes out to be 313.356which is close to the best.

According to our model, the bank should definitely give him the loan.

2. Individual B- B wants to take a similar loan as A for the same purpose.But he has inferior assets valued at Rs 1 crore and a debt of Rs 29 lakhs.

Also, he can only provide a property worth Rs 60 lakh as collateral. Like A

he also pays his bills regularly and he has the same annual income as A.

but due to the inferior debt ratio and loan to value ratio his credit score

comes out to be 218.4. The difference in score between A and B is a lot,

because of the increased risk the bank has to undergo. In case Bs

industry does not work, due to lower value of collateral and assets, it will

be really difficult for the bank to recover its investments. Hence, giving

loan to B is a more risky proposition but bank should still consider giving

him the loan because his other credentials are quite good.

3. Individual C- C has assets worth Rs 1 crore and outstanding debt of 19

lakhs. He is an occasional defaulter in bill payments (15%). Sometimes,

he has also been late in his credit card and other bank payments (10%).

Similarly he has also not paid up once in a while on Cash-On-Delivery

payments while ordering from online retail websites. He wants to take a

loan of Rs 7 lakhs to buy a car (not a priority sector). He has Gold worth

Rs 10 lakhs which he can give as collateral. He earns around 12 lakhs peryear. According to his financial data, his credit score comes out to be 160.

His is a borderline case. The bank or NBFC can decide to give him the loan

or not.


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4. Individual D- D has assets worth Rs 50 lakhs and a debt of Rs 22.5 Lakhs.

He has quite a high defaulting rate in all his payments, be it credit card,

online retail, mobile or electricity payments. His annual salary is Rs 10

lakhs. He wants to take a loan of Rs 9.50 lakhs as a housing loan (not apriority sector). He has collateral worth Rs 10 lakhs to cover the loan. He

has been the customer of that bank for only 3 years. His credit scorecomes out to be 39.8403. The bank should not give a loan to this

individual. There is a very high risk of his defaulting and he does not have

enough assets for the bank to recover its loan.

Individuals Debt

ratio

Loan

to

Value

Ratio

Debt

Coverage

ratio

Priority

Sector+prior

bank history

Online

retail

default

Bill

Payment

default

Bank

Default

Credit

Score

1.A 0.03 0.30 3 5 0.05 0.025 0.05 313.3562.B 0.29 0.50 3 5 0.05 0.025 0.05 218.4

3.C 0.19 0.70 1.4 1 0.1 0.15 0.1 160

4.D 0.45 0.95 1 1 0.5 0.75 0.3 39.8403

5 0.19 0.70 1.4 2.5 0.3 0.15 0.1 182.7180

6 0.30 0.85 1.25 1.5 0.45 0.25 0.175 124.4528

7 0.03 0.30 3 5 0.15 0.075 0.1 290

Table 2: Credit Scores for different individuals


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Chapter 5

5 Conclusions

Fuzzy logic provides a natural means for handling the imprecise statements

and approximate reasoning articulated by commercial lending experts. In

summary, the application reported in this paper demonstrates how fuzzy

logic can be used to model the abilities of a commercial lending expert. Fuzzy

logic proves out to be much better than traditional approaches to calculate

the credit rating based on crisp value methods.[13]

The credit rating of an enterprise is frequently described as very good,

good, poor, very poor. It would be impossible to describe the rating as

good etc completely objectively. Although if large dataset is available, we

can make some good objective decisions. However the different grades

obtained with these objective results must constantly change with time, with

mindset etc. The fuzzy set represents linguistic or vague terms and hence it is

neither complex nor too simplified representation for the credit risk

evaluation. For such a subjective problem as loan assessment, fuzzy is one of

the most suitable mathematical model available.

In our analysis of an individuals credit worthiness, we have tried to take

advantage of the plethora of data available about an individual in todays

digital age. The online retail boom that India has seen in recent years,provides us with real data about an individuals honesty and seriousness of

commitment when faced with paying a bill of a few hundred rupees. Similarly

with the advent of credit cards, debit cards, NEFTs, RTS, net banking, mobile

banking etc. banks also have a huge amount of digital data, pertaining to each

of their customers. Also, telecom companies, DTH TV companies, public

utility providers like BSNL, Power Grid etc are also gradually dealing with

online payments, automatically creating a record book of their customers

timely or untimely payments. It is RBIs intention to combine and consolidate


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these various sources and make a digital repository of individuals payment

history. Hence, in the future all these parameters could be used to calculate

the credit worthiness of an individual. In that scenario, our model would not

only be viable, but also has the potential to become the standard model used

by commercial banks for loan appraisal.

A lot needs to be done in the development of the model. It requires data

related to all the inputs, to make the membership functions more suitable

and attuned to the market. It also requires some aspects of machine learning

so as to deliver optimum results. All that requires further research.


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Bibliography[1] Kar A. , Stock Prediction using Artificial Neural Networks,

retrieved April (2013) , Available FTP:

http://www.cs.berkeley.edu/~akar/EE671/report_stock.pdf

[2] Novk, V., Perfilieva, I. and Moko, J. (1999) Mathematical

principles of fuzzy logic Dodrecht: Kluwer Academic

[3] John O. Rawlings, Sastry G. Pantula and David A. Dickey,

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Applied_Regression_Analysis_A_Research_Tool.pdf

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013/news/31159922_1_online-retailers-online-transactions-cash

[8] Matt Robinson, Bloomberg News, 15/4/14 [Online] Available FTP:http://www.bloomberg.com/news/2014-04-15/consumer-default-

rates- drop-to-eight-year-low-s-p-experian-says.html

[9] Mamdani, E. H. & Assilian, S. (1975). An experiment in linguistic

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[10] Iancu, Ion. A Mamdani Type Fuzzy Logic Controller. Pg:325-339.

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[13] P Duchessi , J LEVY E MALLACH in A Fuzzy Logic Evaluation

System for Commercial Loan Analysis

Documents

Application of Fuzzy Logic to debt appraisal