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Due to high unemployment rate in the country most Zimbabweans are living below the poverty line and this made people to move from formal to informal businesses. Most of the business being informal do not have proper records which shows cash flows which includes past, present and future expected and hence they do no longer meet the minimum requirements for qualify for a bank loan. This has led to the growth of micro finance industries as their requirements differ from one institution to another for loan facilities. Micro finance institutions have become major players of providing financial services to both formal and informal sectors. Through micro finance, governments have designed a way to provide the poor, with better access to financial services. Robinson (2001) defined micro finance as small-scale financial services provided to people into petty businesses in both rural and urban communities. He also indicated that micro finance institutions are primarily established to provide business and consumer credit services to poor and vulnerable groups in society with a major goal of eradicating poverty. However, many micro finance institutions are failing to survive in the industry due to loan default(s). According to Balogun and Alimi (1990), loan default can be defined as the inability of a borrower to fulfil his/her loan obligation when due. High default rates in small and medium enterprises (SMEs) lending are of major concern because of its negative effects on SMEs financing. Micro finance institutions around the world are facing the challenge of loan default. This situation has been of much concern to the extent that some financial institutions have implemented eccentric methods of trying to retrieve these loans. The sustainability of micro finance institutions depends largely on their ability to collect their loans as efficiently and effectively as possible. In other words, to be financially viable, micro finance institutions must ensure high collection rate based on 100% repayment, or at worst low default rate, cost recovery and efficient lending.
While a credit facility institution can fail due to many reasons like high operation cost, liquidity crisis, poor management and many others, the major of all is loan default which makes it not viable for the business to keep running if it is not dealt with in order to minimize or eliminate it. The major cause of loan default is poor risk management. This research will help identify major causes of loan default and came up with a mathematical model which can helps reduce it. Literature on loan default discusses about several methods which can be used to reduce or eliminate high default rate but mathematical models are not usually put into consideration and practice as a way to reduce or eliminate it since there are many causes which differs from one client to another which leads to defaulting and usually solutions to each case differs depending with the reasons for defaulting.
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The aim of the research is to build a calculator which calculates the risk of a client defaulting on a loan and implement binary logistic regression methods for prediction of the possibility of a client to default on a loan applied.
• To identify the variables that contribute more on loan default.
• To fit a model that gives reliable estimations of predicting the probability of a client to default.
• Determine variables which influence loan default at a micro finance institution.
• To come up with better loan terms that minimize the risk of defaulting.
The study aims to address the following questions:
• How the logistic regression model can help reduce risk of loan default?
• Identify variables with better predicting power on the client’s probability to default?
• What are the pros and cons of the model developed?
• How the model can be used in the institutions?
The study will help in the Finance industry as it can be referred to in future studies. It also serves in the industry as new players can use the final model to determine the risk of defaulting on their clients. In the long run a company can see the trend based on their clients to determine the factors which influence the defaulting and they can revisit their terms and fine tune them according to their client base so as to reduce the risk of defaulting and also not to loss clients.
The methodology that will be used will make use of quantitative and qualitative variables in
Logistic Regression. The data to be used will be secondary data collected from a micro finance institution. The dependent variable in logistic regression is known as DICHOTOMOUS as it does not give only a value but the value determines the class to which it belongs since it is a binary variable.
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Assumptions of Logistic Regression
• It does not require a linear relationship between the dependent and independent variables.
• The error terms do not need to be normally distributed.
• Observations are independent of each other.
• There should be little or no multicollinearity among the independent variables
• Sample size is large and a minimum of 10 cases with the least frequent outcome for each independent variable.
• The resources and time to gather data from a number of institutions in the country by the researcher.
The results of the study obtained may not apply to other micro finance institutions because the industry is still growing in Zimbabwe hence requirements for one to qualify for loan at a micro finance differs from one institution to another which means the variables used might not apply to another institution.
The instruments for this study include a computer, software such as SPSS, Microsoft Excel, R, calculator, pen/pencil and paper.
The data to be used will be secondary data collected from a micro finance institution. The data has already been captured by the institution for their records so this will include all the loans both paid up and defaulted from 2018 June to 2019 march. Due to privacy policy of the institution some information will not be available on the data only useful to the research will be presented to the researcher.
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The study will use logistic regression model which based on binomial probability theory. It is a mathematical modelling approach used in describing the relationship of several independent variables to a dichotomous dependent variable. The logit function will be used because the dependent variable “default” is dichotomous, whereas the proposed covariates will be mixture of continuous and random variables. Therefore, the model has been chosen over others due to the data structure and purpose. The logit model is a derivative of the odds function. The odd of a function is the ratio of the probability of success to that of failure.
Thus odds
( Y = 1) =
P ( Y = 1 | X = x )
P ( Y = 0 | X = x )
(1)
Where ( Y = 1) is the odds of default and ( Y = 1) is the probability that default occurs given a set of explanatory variables and (Y = 0) is the probability of non-default given set of explanatory variables. If the odds of default are greater than one it means there is a higher probability of default compared to that of non-default. A value less than one indicates a higher probability of non-default than that of default. Given the binary response variable (default or non-default), the probability distribution of the number of defaults in a given loan portfolio size, for given values of explanatory variables is binomial. Thus, the probability that the number of default of a given portfolio size n is exactly equal to size x is given by
P ( X = x ) = n
∗ p x ∗ q n − x where q = P( non − def ault ) , P(Y=0) x
Y = n
1 ,Def ault
0 ,N on − Def ault
Let us consider a number of independent variables n. Where n =1, 2, 3, 4, 5, 6. . . 20 that means our equation will be as follows:
E ( Y x
1
, x
2
, x
3
, x
4
, x
5
, . . . . . . x
20
) = e
( β
0
+ β
1 x
1
+ β
2 x
2
+ β
3 x
3
+ ......
+ β
20 x
20
)
1 + e ( β
0
+ β
1 x
1
+ β
2 x
2
+ β
3 x
3
+ ......
+ β
20 x
20
) where, β
0
, β
1
, β
2
, β
3
, ......β
20
, are the estimated logistic coefficients. The logistic regression slope will have the usual interpretation, except that it will be in probability terms: for every 1 unit change in a given independent variable there will be a change in probability of being in a category.
In this research the categories are default and non-default. The predicted probability for each case can be derived from the log odds and consequently the residual can be calculated. Unlike multiple linear regression models, logistic regression does not assume linearity of relationship between dependent and independent variables. Also, the error term ( ) is not normally distributed since
Y takes only values 0 and 1. In addition, the probability of occurrence of the event Y lies between
0 and 1; that is 0 ≤ P ( Y ) ≤ 1. The logistic regression was used to calculate the probability of success over the probability of failure; the results of the analysis were in the form of an odds ratio and will help in the prediction of group.
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A loan is said to be in default when a payment is late (CGAP, 1999). A loan is said to be defaulted loan when the chances of recovery it becomes minimal. There are three broad types of default indicators: collection rates, arrears rates, and portfolio at risk rates. Default occurs when a debtor has not met his or her legal obligations according to the debt contract. For example, a debtor has not made a scheduled payment (Ameyaw-Amankwah, 2011). A default is the failure to pay back a loan. Default may occur if the borrower is either not willing or not able to pay their debt. A loan default occurs when the borrower does not make required payments or follow the terms of a loan.
Lack of willingness to pay loan, diversion of funds by borrowers, deliberate negligence and improper assessment by loan officers are causes of loan default according to Ahmad, (1997).
Hurt and Fesolvalyi (1998), found that, commercial loan default increases as real gross domestic product decline, and that the exchange rate decrease directly affects the repayment ability of borrowers. Balogun and Alimi (1988) also identified the major causes of loan default as loan shortages, delay in time of loan delivery, high interest rate, age of borrowers, poor supervision, non-profitability of business enterprises. Berger and De Young (1995) identified the main causes of default of loans as poor analysis of project viability, lack of collateral security/sensible mortgage against loans, unrealistic terms and schedule of repayment, lack of follow up measures and default due to natural calamities. Inadequate financial analysis according to Sheila (2011) is another cause of loan default. This is when in the loan officer(s) do not carefully analyses the applicants to ensure that (s)he has a stable financial base such that the risk of loss is mitigated in case of default. Other causes include disappearance of loan clients and poor business practice.
Kasozi (1998) said, there are weaknesses of the borrower over which the lender has little control.
Business management is also an important part that requires to be emphasized. You find that many borrowers lack the business ethics like keeping records and checking on the business performance until they have to pay back the loan. This is usually hard because they never invest back the profits leading to loan default in the long run. According to the study by Nguta, and
Guya (2013) showed that one of the major reasons for loan default is the characteristic of the business which are industry of the business, period the business has been operational, location of the business and monthly profit range of the business.
Kohansal and Mansoori (2009) said that, lenders devise various institutional mechanisms aimed at reducing the risk of loan default. These include pledging of collateral, third-party credit guarantee, use of credit rating and collection agencies, etc. according to Kay Associates Limited
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(2005), bad loans can be minimized by ensuring that loans are made available only to clients who have high chance of repaying. Loan assessment of potential clients should be carried out in order to judge the loan risk with the client and to have a lending decision. Loan repayments should be monitored and whenever a customer defaults action should be taken. Therefore, microfinance institution should avoid loans to risky customers, monitor loan repayments and renegotiate loan conditions when customers get into difficulties (Ameyaw-Amankwah, 2011). Microfinance institution need a monitoring system that highlights repayment problems clearly and quickly, so that loan officers and their supervisors can focus on defaults before it gets out of hand (Warue, 2012).
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Ameyaw-Amankwah, I.(2011). Causes and effects of loan defaults on the profitability of Okomfo
Anokye Rural Bank. Thesis, unpublished. KNUST.
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Bichanga, W. O., and Aseya, L. (2013). Causes of loan default within Microfinance institutions in Kenya. Economics of Transition0, 8:401 – 420, 2000
CGAP, (1999).
Measuring microcredit delinquency: Occasional paper no.
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Dinh, T., Kleimeier, S. (2007). A Credit Scoring Model for Vietnam’s Retail Banking Market, .International Review of Financial Analysis, Vol.16, Issue 5, p.571-495.
Kohansal, M.R. and Mansoori, H. (2009). Factors Affecting on Loan Repayment Performance of
Farmers in Khorasan-Razavi Province of Iran, Conference on International Research on Food Security, Natural Resource Management and Rural Development, University of Hamburg, Germany
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In 16th Mathematical Conference of Bangladesh Mathematical Society, Dhaka, Bangladesh, Dec
2009.
Robinson. (2001). The microfinance revolution. Washington DC: World Bank Publications
Sheila Arishaba L.(2011).Lending Methodologies and loan losses and default in a Microfinance deposit-taking institutions in Uganda. A case study of Finca Uganda Kabala Branch(MDI).Researh
report presented to Makerere University, Uganda
T.R. Bielecki and M. Rutkowski. Credit Risk: Modelling, Valuation and Hedging. Springer,
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Warue, B.N., (2012). Factors affecting loan delinquency in Microfinance in Kenya. International Journal of Management Sciences and Business Resea
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