Bank Loan Portfolio Equilibruim Mix: A Markov Chain Approach

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Managing credit risk (loan) has been the priority of almost all Financial Institutions in recent years. The interest lies as to whether the financial institution will be able to meet the demands of their potential clients whereas clients are expected to meet their short term or long term loan obligation. In view of this an optimal loan allocation mix policy from the steady State distribution of loan disbursement process is presented in this study. The objectives of the study are to (i) obtain an optimal loan allocation mix policy (ii) to estimate the transition matrix using time series data on loans. Monthly data on actual loan Disbursement of four loan types for a period of twenty-four months is analyzed. An estimated Transition probability matrix of the movement of one loan type to another is obtained using an optimization technique. It is from this transition probability matrix that the steady state distribution of loan disbursement process is obtained. Opportunity International Savings and Loans in Ghana was used as our case study. Among the loan types offered are Agricultural, Susu, Small and Medium Enterprise (SME) and Salary loans. The estimated transition matrix showed that the probability of loan switching from Agricultural to SME is the highest (0.54) while loan switching from Salary to Agric is the lowest (0.034). Probability of no loan switching for Susu is (0.380), Probability of no loan switching for SME is (0.52), and whiles that of Salary is (0.044). From the estimated probability transition matrix, the steady state distribution indicated that in the long run, SME loan constitutes 52.36% of the total funds allocated for loans. This is followed by Agricultural loan 38.17%, salary loan 4.95% and Susu loan 3.76%, of the total loan amount.
A thesis submitted to the Board of Graduate Studies, Kwame Nkrumah University of Science and Technology, Kumasi in partial fulfillment of the requirements for the degree of Mphil Applied Mathematics,