Loan fees examined mathematically

Banks demand different types of fees for giving loans. As to why, theories abound. Our mathematical economists examined these theories and created a new model to calculate the actual costs of a loan.

magnifying glass and money

One can imagine from the book-length contracts that loans are a highly complex business, but what is behind the various fees that borrowers have to pay? Many economists suppose that banks not only want to make money by demanding fees but also want to influence the behaviour of their customers.

When a loan is given not by a bank to an individual person but by a consortium of banks to a firm, it drastically complicates the arrangement of the fees. Most of these so-called “syndicated loans” contain a range of different fees that are put together differently depending on the loan type. Scientists suppose that borrowers pursue two objectives by doing so. On the one hand, the price of a loan is controlled to influence the likelihood of drawing it down. On the other hand, banks are gaining information about the potential borrowers through the fees by calculating how likely it is that companies actually use particular options in their loan agreement.

Tobias Berg from the Hausdorff Center jointly with colleagues from Berlin and New York mathematically analyzed whether these hypotheses about fees for loans are correct. The team examined all syndicated loans in the USA in the period from 1986 to 2011. For each loan, the researchers wrote down the loan size and every option determined in the contract together with the fees demanded for it. Furthermore, they recorded whether the approved amount was used by the firm, and researched the creditworthiness of the firm. Then, they evaluated the collected data statistically with a special computer program. In this way, they were able to calculate if the single parameters had an influence on each other, and, if so, how strong that influence was.

The results were unique. Fees are indeed a good measure to evaluate potential borrowers in advance. The data show that firms that conclude an agreement with low spreads but with high fees actually draw down their credit line. “Firms that prefer entering into contracts with high spreads and low fees seldom use the entire loan size”, Tobias Berg summarizes the analysis. In contrast, the scientists were able to show that loan fees serve less to have an influence on the price of the loan than to compensate for the banks’ risks. Banks, for instance, lose money in form of spreads, if the borrowers make use of a clause that permits an early redemption. Therefore, firms whose future development is highly uncertain have to accept higher fees for the possibility of an early redemption or not drawing down the credit line. In such cases, the chances are higher that they will not need the full approved amount or will repay it earlier, decreasing the bank’s profits.

The mathematical economists did not stop their work there. On the basis of their calculations, they identified the criteria that have the strongest influence on the actual overall costs of a loan. The criteria were applied to a new model with which it is now possible to calculate these actual costs individually for each loan. The scientists now hope that their research contributes to greater transparency in the maze of loans.

Original paper

TOBIAS BERG, ANTHONY SAUNDERS, SASCHA STEFFEN (2015): The Total Cost of Corporate Borrowing in the Loan Market: Don't Ignore the Fees. The Journal of Finance, DOI: 10.1111/jofi.12281.