In previous article, Fair Isaac has discussed this concept in terms of the "efficient frontier." In essence, it's the idea that by calculating expected losses, volume and profit at every operating point, a portfolio manager can examine trade-offs between different objectives and set cutoffs that advance the organization's goals (see Figure 1).

This profitability analysis plots the expected losses and profits by portfolio volume; each point on the curve represents a score cutoff. This helps clients reach an "efficient frontier" where, by examining trade-offs, they can set cutoffs to advance specific goals.

I'd like to address this topic further from a practical perspective. Using examples from a current financial services client project, I'll address some of the more difficult questions in the efficient frontier methodology, such as: What data do you need to collect? What are the difficulties in defining revenue and expenses? And how do you overcome these challenges to put the methodology into practice?

How to calculate revenue, expenses

Profit, in its most basic form, is revenue less costs. It's important to discuss how to accurately forecast these metrics, before I tackle the specifics of the efficient frontier methodology.

Revenue
Revenue for loans can be broken into two basic categories: 1) interest earned and 2) fees.

Interest revenue is the average daily balance multiplied by the interest rate for that day; for ease of analysis, we use a monthly average. By looking at the loan balance by score for every applicant in a large sample over 60 months, you can come up with an average monthly balance forecast. This would be true for both revolving and installment loans.

Clearly, there are challenges in calculating interest revenue:

1. We cannot use the payment pattern that the loan was amortized for on loans that are paid off early (prepayment).
2. We cannot observe payment and balance information on accounts that were rejected (declined or uncashed).
3. Many of the deals are censored; that is, there are accounts on which performance has yet to be observed.

Fees are collected in several ways on loans, such as for late payments, returned payments and extensions. Many fees would occur more often with high-risk rather than low-risk accounts.

Expenses
As with revenue, expenses can be broken into two basic categories-those that: 1) vary by risk (e.g., credit loss, collections) and 2) are fixed (e.g., acquisition costs). Institutions that have done activity-based costing within their operation units are at a distinct advantage here.

Since credit losses are directly associated with the risk measured by the scorecard, we can leverage this information; we know expected negative performance by score. Still, challenges exist:

1. Scorecards traditionally have been designed to predict a negative performance measurement (e.g., 1 x 60 days or worse delinquent), not loss in dollar amount.
2. With a declining balance product, it's critical to know when losses occur in order to define the loss value.
3. We cannot observe the occurrence of loss on accounts that were declined.
4. Many of the deals will be censored.

Do points #3 and #4 sound familiar? These are points #2 and #3 in the revenue challenges.

With expenses, a lot of attention is often spent on credit loss, but you'll also need to determine costs from acquisition marketing, collections and cost of funding.

A practical client example

Looking at the above challenges — and this is by no means an exhaustive list — the main issue is determining the balance of accounts at the end of each month, over 60 months, at all score levels, regardless of whether they are observed, censored or rejected.

A recent Fair Isaac client project demonstrates one approach to this challenge. The goal of the project was to provide the present value of profit by score for input into the client's cutoff setting process and business strategy planning.

For this project, we analyzed the client's installment loan portfolio over a time period of 60 months. All accounts were scored on a custom score built by Fair Isaac.

We began by taking all observed data to create a curve that defines the balance hazard rate. This rate represents the probability of an account having a zero balance at time t, given that it survived to time t. This zero balance could be due to natural pay-down, prepayment or charge-off (see Figure 2).

For a client's profitability analysis, Fair Isaac used observed data to calculate a balance hazard rate — the probability of an account having a zero balance at time t, given that it survived to time t. This zero balance could be due to natural pay-down, prepayment or charge-off. Using these results, we could then simulate results for censored and rejected accounts.

We derived the balance hazard from the observed data to 48 months and extrapolated the line out to 60 months. Applying this curve to the censored data allowed us to estimate a balance in any given month. Once we had a balance for each month, we derived a loss amount from scorecard and collections performance.

So we had all the necessary monthly financial data on all observed and censored accounts. Only the rejects held us back from a full population base.

The basic assumption for rejected accounts is that they will perform similarly to those with the same credit score. So we took the observed and censored data at the same score-band level, and fit a curve to the rejected accounts for revenue. For losses on these accounts, we used the loan amount, and the data calculated from the observed and censored accounts.

At this point, we had all the basic components in place. We had the financial information needed to create a present value of revenue and loss. Next, we used similar techniques to add other fees and costs that vary by score. Fixed costs and fees were calculated at the end.

Finally, we had values for volume (using existing volume per score distribution), profit and loss — the three components of the efficient frontier. For this client's portfolio, we discovered that maximum profits occurred at a cutoff of 181 on the Fair Isaac custom model (see Figure 3). Since the client had been using a higher cutoff score, it now had the opportunity to lower cutoffs in order to make more money.

This efficient frontier graphic shows the maximum profitability for the client's portfolio at a cutoff of 181 on its custom model. Since the client had been using a higher cutoff score, it now had the opportunity to lower cutoffs in order to increase profits.

In general, our clients are finding significant value in knowing whether their current cutoff strategies are generating a maximum level of profit. Even better, the process provides a method and dataset to allow for further analysis.

Explore alternate cutoff strategies

These efficient frontier results would hold true as long as you don't change your basic business in any significant way — not very likely. However, the strength of the methodology is the way in which the components come together. It allows you to alter the inputs in order to test typical scenarios that you might face.

In fact, most scenarios you dream up can be pushed through this type of model. For example, if you wish to test various pricing strategies for programs or the portfolio, you can modify the inputs into the calculation. Often, as in financial analysis, you must make assumptions to get there, but this allows you to explore the sensitivity of the metrics.

The types of scenarios you can test include:

• Changes to pricing, including risk-based pricing, simple increases or decreases, and adverse selection.
• Economic downturn, including shifts in the amount and frequency of loss.
• Changes in operational costs or overhead.

The approach described in this article is relatively straightforward, once the data has been organized — clearly no small feat for most organizations. I'm not saying that the methodology is not complex, but it makes logical financial sense, once all the components are built.

Darryl Knopp heads a consulting group within Fair Isaac's Global Custom Analytics. His group conducts the profitability analyses discussed in the article, among other types of analytic consulting. Knopp has ten years of experience in the banking industry, seven of them in risk management.

For more information on profitability analyses or other analytic consulting projects, contact Darryl Knopp at darrylknopp@fairisaac.com.