Loan Portfolio Optimization using Genetic Algorithm

N. Metawa, M. Elhoseny, M. K. Hassan and A. E. Hassanien, "Loan portfolio optimization using Genetic Algorithm: A case of credit constraints," 2016 12th International Computer Engineering Conference (ICENCO), Cairo, 2016, pp. 59-64. (doi: 10.1109/ICENCO.2016.7856446)

Loan Portfolio Optimization using Genetic Algorithm: A case of credit constraints Noura Metawal, Mohamed Elhoseny2, M. Kabir Hassan3, and Aboul Ella Hassanien4 1,3 College of Business Administration, University of New Orleans, USA 2 Faculty of Computers and Information, Mansoura University, Egypt 4 Faculty of Computers and Information, Cairo University, Egypt 2,4The Scientific Research group in Egypt [email protected], [email protected], [email protected], [email protected]

Abstract-With the increasing impact of capital regulation on banks financial decisions especially in competing environment with credit constraints, it comes the urge to set an optimal mechanism of bank lending decisions that will maximize the bank profit in a timely manner. In this context, we propose a self-organizing method for dynamically organizing bank lending decision using Genetic Algorithm (GA). Our proposed GA based model provides a framework to optimize bank objective when constructing the loan portfolio, which maximize the bank profit and minimize the probability of bank default in a search for an optimal, dynamic lending decision. Multiple factors related to loan characteristics, creditor ratings are integrated to GA chromosomes and validation is performed to ensure the optimal decision. GA uses random search to suggest the best appropriate design. We use this algorithm in order to obtain the most efficient lending decision. The reason for choosing GA is its convergence and its flexibility in solving multi-objective optimization problems such as credit assessment,

portfolio optimization and bank

lending decision.

Keywords- Bank Lending, Genetic Algorithm, Credit Con­ straints, Bank Profit I.

INTRODUCTION

The nature of the recent financial crisis in US has brought to the fore concerns regarding banks ability to continue with its traditional bank lending strategies. The main channel through which a banking crisis affect the real economy relates to the ability of the private sector to access the credit needed to fund investment and consumption, meanwhile the ability of banking system to provide the credit needed given credit constraints imposed on them. Hence, a key question at the heart of the any financial crisis is whether and how did the banking sector managed to distribute the limited credit available in a way that maximize their profits in the time of crisis. The leading reasons behind a sudden limited banking loan activity varies between an unexpected decline in the value of the collateral used by the banks to secure the loans; an exogenous change in monetary conditions (e.g. unexpected rise in reserve requirements or applying a new regulatory constraint that limits the lending process); the direct credit controls imposed by the government on the banking system; or an the increased perception of risk regarding the solvency of other banks [12]. The Inability of banks to manage loan portfolio efficiently may result in a

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credit crunch. A credit crunch is often caused by a sustained period of careless and inappropriate lending, resulting in losses for lending institutions and investors in debt when the loans turn sour and the full extent of bad debts becomes known. Eventually financial institutions tend to reduce the availability of credit, and mostly increase the cost of accessing credit by raising interest rates. The liquidity crisis is triggered when business finds itself temporarily incapable of accessing the bridge finance it needs to expand its business or smooth its cash flow payments. In this case, accessing additional credit lines and "trading through" the crisis can allow the business to navigate its way through the problem and ensure its continued solvency and viability. It is often difficult to know, in the midst of a crisis, whether distressed businesses are experiencing a crisis of solvency or a temporary liquidity crisis [11]. The main contribution of this paper is the creation of a GA model that facilitates how banks would make an efficient decision in case of a cut back on lending supply when faced with a negative liquidity shock, while staying focus on the main objective of bank profit maximization. The main focus of the GA model is two-fold: to stabilize systemically banks while achieving maximum profit, and to establish the capital base so that banks would increase lending efficiently. The GA model takes into account the margins along which banks adjust their loan portfolios in response to the crisis, either through imposing credit supply contractions across all types of borrowers, or disproportionally cut back credit for some specific types of loans. The remaining of this paper is organized as the following: Section 11 discuss the related work of the bank lending decision problem. Section 111 describes the proposed method and the GA data representation. Then, section IV discuss the experimental results. Finally, section V concIudes the paper. 11. LITERATURE REVIEW

According to [7] banks have private information that leads to higher levels of illiquidity for their loans, as they optimize their loan portfolio based on loan returns coverage to its risk exposure which eventually decreases these capital constrained

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banks willingness to make new loans. During recession and financial crisis era, credit becomes less available for borrowers as banks tend to adapt strategies of credit rationing focusing on optimizing their loan portfolio. On this matter, [5] find that typical us commercial banks reduced their business lending during the financial crisis, this decline was due to increased risk overhang effect (related to higher levels of illiquidity), and increased levels of credit rationing, which is consistent with the higher lender risk aversion. Targeting loan portfolio optimization focusing on the goal of loan default and bad loans elimination, [3] used goal programming technique to determine the boundaries of loan portfolio decisions that would reduce loan default rate in Nigeria banks. Focusing on Italian banks, [4] used importance sampling technique for loan portfolio optimization problem, the IS technique objective is minimizing loan portfolio volatil­ ity in 23 Italian banks during risky and uncertain economic conditions. Using value at risk technique (VAR), [8] mea­ sure uncertain environments of loan portfolio when all the loan rates are subject to uncertain changes. They designed uncertain simulations to test VAR technique solutions for loan optimization and explained the cases where VAR can be used to maximize loan portfolio returns in dynamic environment. [10] presented the application of a multi-objective optimization GA model addressing the problem of the risk-return tradeoff in bank loan portfolio. The authors obtained an approximation to the set of Pareto-optimal solutions which increases the decision ?exibility available to the bank manager and provides a visualization tool for one of the tradeoffs involved. The paper did not consider interest rate risks as a factor in the trade off of loan portfolio optimization. On the same sequence, [1] applied genetic algorithm model of loan portfolio multiple constrains optimization of banks risk-return. The article built portfolio with mean-variance dominating for both AAA rating and AA rating and calculating for the loan portfolio risk and return. Their GA technique is applied to a leading bank of India and designed as per Indian Banking Regulations has been outperformed the current portfolio of the bank. III.

METHODOLOG Y

This paper proposes an efficient, GA-based model to maximize bank profit in lending decision. In our proposed method, the lending decision is dynamically decided based on customers loan characteristics. With the assumption that all customers are applicable (good) to get the required loan, GA is employed to search for the most suitable customers depending on a set of factors such as loan age, loan size, loan interest rate, loan type, and borrower credit rating. A set of other depending variables, i.e., expected loss on the loan, are considered as weil. Using the chosen customers, the optimum bank lending decision and the loans details are determined. This paper assumes that each customer has a set of predefined loan characteristics. These characteristics represent the variables of the proposed model. Before discussing the working steps of our proposed GA method, we listed here the different variables that are represented in our GA-based model to determine which customer is selected to take the loan.

The first variable is the Loan Age which is divided into four categories depending on its expected period time. In our model, the value of the loan age is ::::; 20 years. The second variable in our problem is the Credit Limit which represents the maximum loan amount that can be given to the customer based on his income and occupation. The credit limit is used to determine the third variable, Loan Size, in each case which is also categorized in micro, small, medium and large credit limits. In addition, the Loan Type is another variable in our model. There are three types of loans: Mortgage (M), Personal (P), and Auto (A). In future, we are planning to add corporate loans as the fourth type. It is not allowed for customer to request a personal or an auto loan with more than 10 years of loan age which can be represented as a mathematical constraint in our model. Another variable in our model is the Loan Interest Rate which is determined based on the values of the loan type and the loan age. In our model the loan interest rate is classified into three different categories and its value is determined according to the average loan rates of the largest US banks, i.e., Chase, and Capital One. Moreover, the Expected Loan Loss and Borrow Credit Rating is significant variable to determine the bank lending decision. Borrow Credit Rating is used to measure the range of the expected loan loss. Good creditor customers are divided into five credit ratings ranges which are AAA, AA, A, BBB, and BB. In our GA-based method, a GA chromosome is a set of parameters or factors that determine a proposed solution to the intended problem, which is the lending decision. For that, we make each gene in the chromosome indicates to a candidate customer. The value of a gene can be either 1 or 0, where 1 indicates that the corresponding customer is elected to get the loan and 0 indicates a non-selected customer. Figure 1 depicts a chromosome for a field with 25 customers. The GAs fitness function (Fx ) simply consists loan revenue (19), loans cost (/-l), total transaction cost (IV), and cost of demand deposit (ß). The main objective is to maximize F(x). The value of (19) is calculated depending on the values of the Loan Interest Rate, the Loan Size, and the Expected Loan Loss. In addition, the loan cost /-l is determined based on the Loan size and a predetermined institutional cost for each loan size. The total transaction cost of the expected lending decision IV is determined by the institutional transaction cost and the customer transaction rate rT. Moreover, The value of the institutional transaction cost can be obtained as defined at Eq. 1 where K is the required reserved ratio of the financial institutions deposit D. In addition, rT is deterrnined based on the banks deposit interest rate rD. However, in this paper we assume that the customer transaction rate rT 0.01 in all our experiments. =

T

= (1- K)D -

L

(1)

Finally, the cost of demand deposit ß is simply defined at Eq. 2. (2)

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GA Chromosome

lIil Va l u e Customers Characteristics loan

Age

loan

Size

Not Selected

Selected

Fig. 1. Chromosome Representation for 25 customers.

Where rD is given by a weighted average of all different deposits rates based on deposit type (checking, saving) and based on deposit age ranging from (3 months till 10 years). In the GA model we left this rate to vary randomly for each bank. And for the fitness function calculation we used average rate of 0.9% for the return on deposit. Dependently, the GAs fitness function is hence defined as Eq. 3 with the aim of profit maximization.

Fx

=

73

+

n w

-ß-

2::>, i=O

(3)

A. Genetic Algorithm Operations and Lending Decision Val­ idation

To be self-content, we briefly review the main operations of GAs [2], [9]. GA is adaptive search method that simu­ lates some of the natural processes: selection, information, inheritance, random mutation and population dynamics [1], [2], [6]. A GA starts with a population of strings and thereafter generates successive populations of strings. A simple GA consists of three operators [3]: •

Reproduction: is the process of keeping the same chromosome without changes and transfer it to the next generation. The input and the output of this process is the same chromosome.

select (Ps) for each chromosome (e). While Eq. 5 calculates the expected count of select (n), and the actual count of select for each chromosome as the following:

. Ps(z) n

=

fx(e) L�=o fx(i)

(4)

=".::-,,-fx( e) � -:[L�=l f-:-x(i) / n]

(5)

=

Where n is the number of the chromosomes in the popula­ tion. A new generation of the GA begins with reproduction. We select the mating pool of the next generation by spinning the weighted roulette wheel six times. So, the best chromo­ some representation get more copies, the average stay even, and the worst die off and will be excluded for further process­ ing. The proposed model develops a GA validation algorithm which used to validate each new generated chromosome before adding it to the GA population. The validation algorithm calculates the total loan amount of the expected lending decision to make sure that its value is not exceed the required reserved ratio of the bank deposit. The validated chromosome is then added to the population. If the chromosome violates the validation condition, a new randomly generated chromosome is created and the process will be repeated until the number of validated chromosome is equal to the population size. B. Pseudo Code of the Proposed Model

•

Crossover: is the process of concatenating two chromosomes to generate a new two chromosomes by switching genes. The input of this process is two chromosomes while its output is two different chromosomes.

As we mentioned before, our proposed model uses a binary chromosome to specify the selected customer in the lending decision, in which a digit one represents an elected customer and a zero represents a customer that is not eligible. Algorithm 1 presents the pseudo code of the proposed model. In this algorithm, q E Q] denotes the number of generations, and the population size is P. The pool of chromosome, denoted by U, is initialized with randomly generated indlviduals. An intermediate pool of chromosomes, denoted by U, is used to hold the individuals created in a generation, and depending on the needs user can specify any intermediate population size that is greater than the initial population size P. In crossover operation, two chromosomes are randomly selected from U and, according to the crossover probability; two new chromosomes are created by switching consecutive genes. In mutation operations, the value of a randomly picked gene is altered between 0 and 1 according to the mutation probability m.

[1,

•

Mutation: is the process of randomly revers the value of one gene in a chromosome. So, the input is a single chromosome and the output is different one.

An example that clarifies the GA operations in our proposed model is shown at Figure 2. First, the GA creates the initial population by randomly generates a set of lending decisions. Then, each decision is evaluated using the proposed fitness function. The fitness functions value of a lending decision determines its probability to be selected as a chromosome at the new population for the next GA generation as shown at Eq. 4 and Eq. 5. Eq. 4 is used to calculate the probability of

61

Lending Decision 1

0100011010

Initial population

15%

Fitness Evaluation and Roulette Wheel Selection

!

Crossover Result

�

20%

34%

o 00 :1001

001

1!

0 0100 001

�

1100101:1 11 ,

110 1001001

I I 1001000000 I I 1100101001 I I 1110001001

IQ10 1 01001

I I 1011000000 I I 1100101001 I I 1110001101

:

Mutation Result

Lending Oecision 4

I I 1101001000 I I 0001001001 I I 1100101111 27 %

110 1001 00

Cut point and Crossover Selection

Lending Oecision 3

Lending Oecision 2

Lending Oecision 1

Lending Decision 2

Lending Decision 3

Lending Decision 4

Fig. 2. An example for the GA operations that are used in the proposed model

Aigorithm

1

Bank Lending Decision Algorithm

TABLE I

SET OF PARAMETERS TO CONTROL THE GA EV OLUTION PROCESS

1: Randommly generate a pool of S Lending Decisions X =

{Xl, X2, ""xs}.

2: Represent each decision in S by one chromosome to get a pool 3:

P of chromosomes U = {Ul,

'VUi

ters)

U2, . . . , up}.

4: Evaluate the fitness of each

Ui

5: forq=I,2,... ,Qdo 6: 7: 8:

(;

Objective

E U, Forming the Lending Decision According to Parame-

-{=

E U using

Raw Fitness

Fx.

0

tor p = 1,2,... , P do

ua, Ub E U (a =1= b) jeu): jeu) jeu) = L-c jeu)' Ua and Ub according to a:

Randomly select

based on the

Parameters

normalized fitness

9:

Cross over

C(ua, ubla:) 10:

11: 12: 13: 14:

Perform mutation on

u�

M(u�Iß)

=?

Evaluate

j(ua)

and

and

Ua,

=?

u�

Stopping Criteria

according to m

M(u�Iß)

=?

Ub.

j(Ub).

-{=

-{=

15: end for

16: Find the chromosome

u*

U* = argmax jeu), U 17: Return the lending decision

IV.

x*

+w

-ß -2:�=o .\.

- Population Size (n) - 60 - GA Generations (3() = 60 - Crossover ratio = 0.8 - mutation ratio = 0.006 - Reproduction ratio(n) = 0.194 - Basic selection method is spanning the weighted roulette wheel selection six times. -The evolution continues until: Fx (t) = R where t is the time interval

A. First Scenario: Simulated Data

The parameters that are used to generate the simulated data are shown at Table 11. This simulation assumes that rD=0.009 a weighted average of the deposit interest rates over short and long run. In addition, the institutional cost is 0.0025 in all cases based on the previous literature. TABLE II

that satisfies

u

Fx={}

u�, u�.

(; U {Ua, ud end for U {Ui;Ui E (; and j(Ui)} (;

- Make a bank lending decision that maximizes the bank profit. - Make a bank lending decision that minimizes the crediting cost.

SET OF VARIABLES TO GENERATE SIMULATED DATA. THE VA LUES OF D IS REPRESENTED IN MILLIONS.

E U

by mapping

u*

back

RESULTS AND DISCUSSION

First, all data are obtained from World Bank public database for year 2016. In our evaluation, the GA parameters used in our experiments are listed in Table I. The analysis of the results is conducted based on 10 experiments. To evaluate the proposed model, two scenarios are created to study the routine method performance in real and simu­ lated environments. In the simulation scenario, the proposed model randomly generates customer loans characteristics for a defined count of customers with different values and exports them to a database file. Then, GA starts its work using the generated data.

Count of Customers 200 400 600 800 1000 2000

D

K

5 5 10 10 15 100

0.00 0.00 0.00 0.00 0.15 0.20

Accepted Customers 77 82 153 124 246 1115

M(%)

p(%)

A(%)

31 41 32 41 32 27

38 37 35 39 36 41

31 22 33 20 32 32

As shown at Table 11, the loan lending decisions are distributed to the three types of loans. Although, there is no constraints for the ratio of each type, it seams that the GA balanced between them. Based on Table 11, Figure 3 shows the count of selected customer for each type of loan. We can say, the proposed method provides a great way to balance between all types of loans.

62

100 ---+--1\1: LOlns -+.--PLoans

80

�A Loans

70 60 ;0 40 30 '" 10

o �--�--�----� 600 400 o 100 100 300 ;00 700 800 900 1000 Total Count of Customers

Fig. 3. The count of selected customer for each type of loan

Efficiency is an important factor in real-world applications. Our experiments are conducted in a computer with Intel core i5 2.6 GHz CPU, 4GB memory, and Windows 8 operating system. The algorithms are implemented in C#. Table III lists the average time used to determine the lending decision in each case of run. The time reported is at the last GA generation. The number at the second raw is the standard deviation. In addition to first scenario that uses simulated data, we also experiment with the real data scenario keeping the same parameters. The average time used by the proposed model is comparable to the other methods. Note that the most time-consuming process in the proposed method is evaluating fitness, which can be implemented with parallel programming to improve efficiency in case of complicated multi-objective problems.

TABLE IV LENDING DECISION USING REAL DATA Applied Customers 500 1000 2000

Accepted Customers 205 395 871

Selected

Selected

40 33 50

31 28 22

M (%)

Selected A (%) 29 39 28

P (%)

Fx

ratio (%) 7.2 2.9 4.1

TABLE V

PROPOSED METHOD CONSISTENCY Loan Type Mean STD

M

0.43 0.011

P

0.32 0.021

A 0.25 0.064

TABLE III

PROPOSED METHOD EFFICIENCY Count of Customers Mean STD

V.

200

400

600

800

1000

2000

0.42 0.10

0.45 0.22

0.51 0.14

0.65 0.28

0.74 0.47

1.2 0.33

B. Second Scenario: Real Data

The second scenario aims to evaluate the system perfor­ mance using a pre-known solution for using real data collected from Jefferson Credit Union's bank. Compared to the tradi­ tional bank lending optimization methods, the proposed GA model greatly increases the bank profit using the suggested lending decision in case of using these real data as shown at Table IV. The last column of Table IV shows the increasing ratio in Fx that was achieved using the proposed method compared to the traditional method for each case. On the other hand, effective GA model must guarantee the results consistency. For that, we run the proposed model 10 tünes using the same real data and the same GA parameters. Table V lists the average of the selected loan type and its standard deviation at various run times. Small STDs indicate balanced ratio of a specific loan type.

C ONCLUSION AND FUTURE

W O RK

The nature of the recent financial crisis in US has brought to the fore concerns regarding banks ability to continue with its traditional bank lending strategies. The Inability of banks to manage loan portfolio efficiently may result in a credit crunch. The liquidity crisis is triggered when business finds itself temporarily incapable of accessing the bridge finance it needs to expand its business or smooth its cash flow payments. This paper proposes a GA model that facilitates how banks would make an efficient decision in case of a cut back on lending supply when faced with a negative liquidity shock, while staying focus on the main objective of bank profit maximization. The proposed model is tested using simulated and real data as weil. The results shows that the proposed GA model greatly increases the bank profit using the suggested lending decision in case of using the real data. For future research we suggest using this GA model for loan portfolio op­ timization using small and medium business customers instead of regular customers. Moreover, our GA model can be applied to optimize the investment portfolio using the behavioral factors [13] such as investor sentiment and overconfidence, in order to rationalize the investor decision on the stock market.

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