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Opinions and analysis of Marketplace Lending, Online Lending, and Peer to Peer Lending.

Lending Club Portfolio Analysis: Updated for Trading Notes

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Credit Scoring and Models: Decision Trees

Posted by Anil Gupta | Thursday October 2, 2014, 11:35 pm | Categories: PeerCube

This series of blog posts tries to cover the theory behind credit scoring and models typically used in consumer lending domain. While anyone can perform statistics gymnastics given the historical loan data from Lending Club and Prosper, I believe, understanding the theory behind consumer credit behavior, scoring and lending decision making is important to profit from the opportunities in the marketplace lending. Listed at the bottom of the post are a few references that I have been using to deepen my own knowledge of credit scoring and modeling and are the reference materials for this series of posts.

The consumer credit has been the driving force behind the economies of leading nations. It has been responsible for growth in consumer spending in last 50 years. According to Federal Reserve Bank of New York’s Quarterly Report on Household Debt and Credit Report, August 2014, the total consumer indebtedness stands at $11.63 trillion with 74% in mortgage and home equity line of credit, 10% in student loans, 8% in auto loans, and 6% in credit card debt. The demand for consumer credit is growing at extremely high rate creating opportunity for automated risk assessment systems.

Credit Scoring

Credit scoring was a risk assessment approach introduced in 1950s. Credit scoring began with the application of statistical methods of classification in classifying good and bad loans. Credit scoring initially focused on whether one should grant credit to a new applicant, later come to known as applicant scoring. Credit scoring has been successful because of this singular objective.

It assumed that factors implying credit worthiness were relatively stable over a few years and assessed the chance of an applicant going 90 days overdue on their payment in next 12 months. The cut-off score at which applicants are accepted is made using the marginal good:bad odds at that score - ratio of additional goods to the additional bads that would be accepted if score was dropped.

Data on those who applied for credit 1 or 2 years ago, together with their subsequent credit history, was used to build the application scoring model that would be used to determine for the next 2 years or so which credit applicants to accept.

Behavioral scoring, as an extension to applicant scoring, uses information on payment and purchase behavior in the past year. This data is used to forecast the default risk over the next 12 months and typically updated monthly. The recent performance and current credit information is more powerful than just the initial application data.

Lenders are now focused on lending strategies that meet their profitability objectives rather than just default risk. They can choose the loan amount, interest rate, and other terms to maximize profitability. The techniques that support profitability based decision are called profit scoring.

Unlike applicant scoring that can use static credit models, behavioral and profit scoring models require dynamic credit models that consider past behavior. Traditionally, credit modeling has modeled each loan individually. However, the importance of the money lent will be lost because borrower default (credit risk) from a portfolio of loans has increased. There is currently no widely-accepted model of the credit risk for loan portfolio.

You can measure a credit scoring model by its discriminating ability between good and bad loans, by the accuracy of its probability predictions and by the correctness of its categorical forecasts.

Lending Decision Modeling

The main objective for a lender is to maximize profit on its loan portfolio. On an individual loan basis, the lender needs to do this by considering the return on amount lent. A loan with a profit of $10 when $100 is lent to a borrower is not as good when $3 is achieved on a loan of $25.

There is a risk that one of the borrowers will not repay the loan, in which case lending leads to substantial losses. Risk might be quantified by the default rate expected in the portfolio or the losses these defaults leads to. An alternate objective for the lender may be to keep the risk and return profiles within pre-defined limits.

Lending to a borrower is a based on a series of decisions: what information would be useful in making a decision, what is the chain of events that could occur during and after the decision process and the possible outcomes of the decision.

Influence Diagrams

Influence diagrams help one to visualize graphically how the decisions, the uncertainties, the information, and the outcomes are interrelated.

The Influence diagrams identify the important aspects of the decision, what data is relevant to the decisions and to what aspect of the decision making it is related. It consists of a graph with three types of nodes: decisions (rectangular nodes), uncertain events (circular nodes), and outcomes (diamond nodes) connected by arrows. The Figure 1 shows the influence diagram from a perspective of lender on marketplace lending platform.

Figure 1: Influence diagram for a lender on marketplace lending platform

In Figure 1, first there is a lender’s forecast of whether the borrower’s performance will be good or bad. The forecast is a random event in that the lender cannot decide what the forecast will say about a borrower. It will influence both the Invest in Loan or not decision and whether the borrower will subsequently be good or bad. Second, the platform may decide to issue the loan or not. It is a random event for lender. Lender has no influence or participation in decision making process to issue the loan except when not enough lenders decide to fund the loan. Once loan has been issued, lender can update the forecast based on whether income verification was performed and with any changes in FICO score and payment history. Depending on updated forecast, lender can decide to sell the loan or not on FOLIOfn secondary platform. Similarly, another lender may decide to purchase loan on secondary platform based on this updated forecast. These events affect the profitability of loan to the lender.

Decision Trees

Decision trees identify what are the optimal decisions and explain the sequence in which decisions have to be made and the sequence in which the information becomes available during the decision process.

Now consider how a decision tree model can be built of the decision structure visualized in the influence diagram. The decision trees are similar structure to influence diagrams. The outcomes are now represented by pay-off events represented by numerical values. Each path from a chance node (uncertain event) is given a weight representing the probability of outcome listed on that path to occur.

By starting at the end of each of the outcome branches and working backward in time through all the decision and chance event nodes, expected monetary value (EMV) can be calculated for each outcome.

Figure 2 shows the decision tree for a very simple lending decision. There is an initial decision by the lender of whether to invest in loan or not. If lender doesn’t invest in the loan, the pay-off to lender is 0. If lender invests in the loan, there is a chance event which is whether borrowers repayments are good or bad (defaults).

Figure 2: Decision tree of a lending decision

Consider the situation where the profit to lender if a borrower repays is 10 while the loss is 100 if borrower defaults. If chance of default is 5%, the expected profit from the borrower, if lender invests, is

0.95 x 10 + 0.05 x (-100) = 4.5

while if lender doesn’t invest the profit is 0. So the decision tree suggests that the lender should invest in the loan. If the probability of default increases to 10%, the expected profit from the borrower is

0.90 x 10 + 0.10 x (-100) = -1

So the decision tree now suggests that the lender shouldn’t invest in the loan.

Generalizing the above, if g is the profit made by lender from repaying borrower, l is the loss lender suffers because of borrower default, and p is the probability of borrower being good, under the EMV criterion, lender should invest in loan when pg - (1-p)l > 0.

Equation 1: good:bad odds

p/(1-p), the chance of being good divided by the chance of being bad is also called the good:bad odds.

A decision tree model that tries to cover all aspects of lending decision can become very unwieldy. However, the exercise of drawing decision tree helps understand the decision making process.

In the next post in this series, I will discuss probabilities and odds concepts and apply them to real historical data from Lending Club.

Reference Materials:

Comments: (1)

Raz | Wednesday October 15, 2014, 4:22 am

Excellent Intro Anil!

Infact, some iteration of machine learning we are using on our own platform and modeling risk.

Will eagerly follow this series. Keep it up.

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