What Bank Lenders Need To Know About Time and Credit Risk

Cumulative Bank Loan Default Probabilities

Chances are if you are like most banks you might price a 3, 5 or 10-year loan at the same spread.  If it is a fixed rate loan, maybe you price it off the appropriate Treasury, swap or FHLB index, but that only takes into account interest rate risk. As can be seen in the accompanying graph, based off community bank loan historic performance, credit risk starts off very low the first couple years of a loan, only to ramp sharply up before it starts to plateau around year seven.


Banks use two methodologies for pricing credit risk, either they utilize annual  probabilities of default or cumulative probabilities of defaults. Both are good approximations as long as your one-year annual probability of default is the average over the given time frame of the loan. For example*, the average annual 1-year default rate for a 5-year community bank commercial real estate loan (middle, blue line) is approximately 1.65%, or about 33bp per year. However, if it is a 10-year loan, then the cumulative default rate is 9.34%, or approximately 93bp per annum. That is almost three times the credit risk of a five-year loan.


Looking at it another way, if you needed to achieve a 15% ROE on that loan (about a 1% ROA), then that 5-year loan needs to be priced at a minimum of Libor + 1.97%, while that 10-year loan needs to be at Libor + 2.05% to achieve the same return.


If you think that pricing different doesn’t sound like much, then it is worth noting what is going on if you really hope to drive profitability at your bank. The 10-year loan gives a greater stream of cash flows, so return is greater all other factors held constant. While it is true the cumulative credit risk goes up, the rate of change peaks in about year 6, before starting to reduce. Thus, annual default risk starts to trail down after year 6 for the average CRE loan.


For lower risk  loans, the incremental spread on  10-year term  can actually be made at a lower spread then on a 5-year term to achieve the same return, as the additional cumulative credit risk of the loan is more than offset by each additional year of cash flow. Conversely, for riskier loans (red line in the graph), the opposite is true and the pricing difference would have to be much greater to compensate the greater possibility of loss.   


Finally, keep in mind that the analysis above, just takes into account pure credit risk.  Once you include interest rate-related credit risk, the pricing difference needs to be greater still.  Not only do things like, cash flow problems and tenant vacancies happen at a greater frequency over time, but rising rates further hurt debt service coverage on shorter loans causing an even greater cumulative loss rate.  In our example,  instead of a 2.05% spread to achieve a 15% ROE, if the loan is structured as a floater, that spread would need to be closer to 2.25% to offset the risk that comes as a result of more visibility on  rent stream, but rising debt expense.


Bankers need to be aware of how time interacts with credit and interest rates risk particularly in times of compressed margins.  Smart bankers that understand at least the forces at play will have a competitive advantage against banks that treat all credit risk the same and use the same spread for a 3-year loan as they do for a 10-year loan.  The important aspect to keep in mind is that lower risk loans need to be priced differently through the term structure (where longer term may actually decrease the needed spread) then higher risk loans (where longer term may require higher spread).


*We assume a 70% efficiency ratio, a 45bp cost of funds, a $3mm loan amount, 25-year amortization, a 1.35x debt service coverage and a 70% loan-to-value. 


Cumulative CRE Default Probabilities