Behavior Model to Capture Bank Charge-off Risk for Next Periods Working Paper

Transcription

1 1 Behavior Model to Capture Bank Charge-off Risk for Next Periods Working Paper Spring 2007 Juan R. Castro * School of Business LeTourneau University 2100 Mobberly Ave. Longview, Texas Keywords: charge-offs, bank delinquencies, financial risk, credit scoring. JEL Classification: Corresponding author: Tel: , Fax: [email protected] (Juan Castro)

2 2 Behavior Model to Capture Bank Charge-off Risk for Next Periods Abstract One of the major tasks for any financial institution in any country is to capture the population risk for the next period. Capturing the risk for next months or quarters make the financial institution to change their interest rates and reserve requirements appropriately. Capturing the risk for the populations also helps them to price their products accordingly and put restrictions on their lending policies. Most financial institutions use credit scoring to measure the underlying risk for any application that has been approved. A cut-off score level is used to determine the acceptance/decline decision of any given loan. Most of the time this cut-off levels are fixed and only changed after some extended period when the cut-off has been proved wrong due to nonperforming loans or high levels of charge offs. This paper proposes a model that forecast if the risk of the population has changed in the last period and forecast what will be the risk for the next period. The model uses previous average scores and find what will be the weights for each previous period. Introduction and Rationale Credit scoring systems can be found in virtually all types of credit analysis, from consumer credit to commercial loans. The idea is to find and pre-identify certain factors that determine the probability of default for a given loan or credit by using quantitative scores. In some cases, the score can be interpreted as a probability of default. The score may also be used to classify or quantify the potential of default or to group a borrower into a good or bad category. Credit scoring systems are also known as behavioral scoring in which the score tries to predict behavioral trends in the customers. Credit scoring applies logic to behavioral results and provides warning reports to portfolio management personnel on credits possessing undesirable behavioral attributes deemed to be associated with greater potential loss. Attributes of credit scoring systems may include, but not limited to, updates of loan accounting system information, updates of loan deposit information, and information from personal and/or business credit bureau files. With a credit scoring system, accounts can be queued to portfolio management personnel for risk grade

3 3 establishment and exposure assessment. Without proper data mining capabilities, lenders cannot effectively understand the impact of scoring models and other credit underwriting modifications. Further, in the face of credit compliance audits, banks lacking quality portfolio reporting cannot effectively evidence the performance trends of their portfolios or the soundness of specific practices. Further, the lack of dynamic portfolio data prevents business lenders from detecting early indications of economic cycle changes as well as market specific risks such as fraud patterns. While credit scoring is used within the small business lending industry, it is still a relatively new process. Due to the emergence of small business credit scoring, the question of how to conduct a scorecard validation has become a concern for many lenders. The need to forecast credit losses in the lender s lending portfolio has become crucial for the economy as a whole. There is a significant risk of error inherent in any credit loss forecast due to its vulnerability to shifts in the industry, population, and the economy. The need to have a robust loss forecasting model requires a sufficient number of charge off accounts to establish a relatively precise relationship between predictive account behavior characteristics and account charge-offs. This paper investigates a forecasting technique to measure future changes in the population risk and intends to capture the charge-off risks for next periods. The Model Let Y t-1 be the principal amount in dollars lent to an applicant at t-1. Let AP t be the amount in dollars paid out to the principal at time t. Then, in case of default, the charge - off amount, CO t at time t, is given by: CO t = Y t-1 AP t (1) Where, Y t-1 = y i = sum of future payments. The risk of a given account to charge off is given by : S t = t CO t (2) Where S t is the risk measure or credit score that the loan application received when it was accepted by the lender, and t measures the probability of charge-off. Notice that the credit score for a loan was given at S t-1 at the same time the loan was approved, i.e. Y t-1.

4 4 The risk of individual loan application is measured through credit scoring. Every loan application get a score S k, at the time the borrower submit his application, that is at time t-1. S k measures or indicates the risk of the loan application. S k,t-1 = k,t-1 ( Z k,t-1, X k,t-1, U k,t-1, V k,t-1, ) Where, Z k, X k, U k, V k, represents predictive variables such as maximum potential exposure (MPE), expected revenues, personal bureau credit risk, commercial bureau credit risk, and so on. The individual loan applicant is going to be accepted or decline depending of its position with respect to a cut-off value, S co. If S k is lower than S co, then the loan is expected to be rejected, if S k is greater than S co, then the loan is expected to be accepted. Loan applications that have a score below S co have a higher probability to become delinquent and charge off. We are assuming that the credit score for each individual application is the same for the duration of the loan. S t-1 = S t = S t+1 = S t+2 = S t+3 (3) This implies that the credit scoring is done once. So, even if the account becomes delinquent or charge-off, the score given when the loan application was approved will remain the same throughout the life of the account. The probability that a borrower is going payback or not the whole amount is given by PB t such that: PB t = 1 Y t-1 + (1-1 ) CO t (4) Where, PB t is the payback amount at certain point. Notice that if 1 is equal to 1, then the amount is going to be paid in full, that is, PB t = Y t-1. (5) Now, if 1 = 0, then, the amount is application is going to charge-off, that is, PB t = CO t. (6) For example, if 1 = 0.5, implies that there is chance of the loan to be paid and default respectively. So, the lower the values for 1 the higher the possibility that the application will charge off.

5 5 If we concentrate only in the charge off side of equation (4), then we can get that (1-1 ) CO t or CO t = 1 CO t, or CO t = 1 CO t CO t CO t CO CO N CO Nco + t (7) Where, CO t = CO i / N co, and (8) i = 1 N co, is the number of individual charge-offs in a given period t. i = 1, and CO t are charge off for different periods. In the case that i = 1, the total sum of the charge off will be equal to the total payment of the loan or principal. The error term, t, provides the unexpected loan risk of the charge-off that could be not known to the lender when the loan was approved. This error term also measures hidden information not given by the borrower, or any other market risk which information was not available when the loan was processed. If the lender would have known the information contained on t, the credit score given to that application would have been lower than the cut-off value, which in turn would have rejected the loan application. Using the estimates for s, we can then find the weights that can be assigned to the risks found in previous periods. So we can forecast the next period risk level by using the previous average weighted risk levels using the following equation. S t+1 = t S t + t-1 S t-1 + t-2 S t-2 + t-3 S t-i + r t + t (9) S t = S j / N s, (10) Where, j = 1 N s, is the number of individual scores in a given period t. And, N i co = N j s, which means that all charge-offs are scored. (11) The interest rate spread, r t measures the market expectation for the next period, r t = r t - r t-1, (12)

6 6 In order to capture the immediate effect on the market, a short-term rate, r t, should be used such as money market rates or ninety day treasury bill. If r t increases, it will imply that the market risk has increased, increasing the expected score for S t+1. The estimate error term, t, provides the information of the charge-offs accounts for which the scores did not capture the risk involved on the underlying accounts. Data Data from previous charge offs months from local financial institutions will be used to estimate the monthly weights. Scores from the charge off accounts from financial institutions will be used to find the average monthly scores. Methodology In order to find the weights for the forecast model, discriminate regression, logist regression, and possibly Monte Carlo simulation will be used. The charge-offs are run several times to get the estimations. These weights are the used to estimate the forecast model.