We talk to many bank executives and many bank lenders. We have been stumped by a conundrum until a few days ago. We estimate that approximately 80% of bank executives that we talk to insist that their banks are not being challenged to make long-term fixed-rate loans (five years and out). This has been true across many states and different bank sizes. On the other hand we estimate that approximately 90% of the lenders we talk to indicate that most of their term borrowers are looking for the longest fixed term possible. We are referencing lenders and executives at the same bank and within a close time period, so we have eliminated sample and time series bias.

We finally got our answer when we came across a game theory puzzle. We had to choose the correct answer from the following multiple choices:

- 4π sq inches
- 8π sq inches
- 16 sq inches
- 16π sq inches
- 32π sq inches

One problem is that we did not have the question, but we were told that the problem was a GMAT question. We immediately eliminated answer c) because it is the odd answer. It is so different from the others because it does not contain π that a tester would not present the correct answer without a close contrast. Now which of a) b) d) or e) is the answer?

By using game theory, we put ourselves in the shoes of the question writer. The writer wants people who understand the problem to get the right answer and those who do not, to get it wrong. The wrong answer has to be enticing to the test taker who doesn’t quite understand the material. Out of the remaining four possible answers, there is only one answer where the other three are enticing enough to a test taker. We concluded that the answer is d). If 16π sq inches is the answer, then how is the test writer trying to entice the test taker to choose the wrong answer?

Well, the area of a circle is πR^{2} so if R = 4 that would lead to answer d). Answer a) would be chosen if R = 4 and the test taker mistakenly believed that the formula for the area of a circle is πR. Answer b) would be chosen if R = 4 and the test taker mistakenly used the circumference formula of 2πR to calculate area of a circle. Answer e) would be chosen if R = 4 and the test taker mistakenly believed that the formula for the area of a circle is 2πR^{2}. Only answer d) presents a straight forward to a common GMAT-type question. In fact, d) is the right answer and the question was in fact, what is the area of a circle with a radius of 4 inches?

**Back to Banking**

To understand why lenders and executives have such a different perspective on the type of loan structure demanded in the market, we need to put ourselves in the shoes of the lender who has direct contact with the borrower and then work our way backward.

First, lenders try to serve two masters – the borrower and the bank. The bank may want a floating rate asset, and the borrower may want a 15-year fixed, so a 5-year fixed seems to present a perfect compromise. In many instances that is what the lender presents to the bank and borrower as the optimized solution.

Second, lenders want to minimize resistance to deal making – after all lenders are paid to consummate deals. A lender who proposes a fixed term that is longer than the bank is willing to accommodate is often rebuked. That lender is unlikely to relay future borrowers’ requests without some censorship.

Third, it is difficult to successfully sell provisional products. Unless a product is well defined, consistently positioned and marketed, it is typically not successful. We often hear from bank executives that they will create a special bucket for fixed-rate loans, only to find that lenders cannot fill it. When banks do not have a long-term fixed rate program, lenders are often stumped on how to market and position the product. The prepayment provision is uncompetitive, the pricing is incoherent and lenders are not motivated to propose the product to customers. Also, products that are used defensively are brought out only in dire circumstances – when a relationship is about to leave and, therefore, to win the business the proposal must be equally dire (lower priced or poorly structure). No wonder the fixed-rate loan bucket goes unfilled.

Reasoning backwards from the borrower’s and lender’s perspective can help management understand some of the “irrational” behavior we see in the market.

Submitted by Chris Nichols on October 01, 2014