Pricing Bank Loans For Default Volatility

Controlling Lending Risk

If you got past the title it is likely that you care about the accuracy of your loan pricing more than the average banker. Banks have long ignored the variability around default risk and it is starting to be a problem, as with tighter spreads, there is now less room for error. While bankers solve for credit risk through taking loan loss reserves and through pricing, it is rare that a community banks takes into account default variability. Many large banks do and this article shows how community banks can gain about 80% accuracy through a simple methodology. For those that are mathematically inclined, the post-conclusion section of this piece will further elaborate a more refined methodology.


An Example


Let’s take an example – you have a choice to make a multifamily loan or an owner-occupied commercial real estate (CRE) loan. Which do you choose? If you chose the owner-occupied loan because the relationship is multiple times more profitable, you are right, but that is not the topic for today. Let’s say it is just a loan with no other cross or up sell possibilities for the loan’s life. Then what do you choose? Most bankers would choose the multi-family loan with the thought being that it is cheaper to make and contains less risk.


Our 10-year projected loss rates for major lending lines at banks are below. As can be seen, the loss rates for multifamily and owner-occupied commercial real estate (CRE) are about the same at approximately 0.37%. However, because of the greater liquidity, the multitenant nature of the product and the easier underwriting (easier to understand apartment rental than it is to ascertain the credit risk of a rubber manufacturer purchasing their warehouse), pricing is tighter on the multifamily product.

The average price for quality owner-occupied (credit grade 3/1.5x debt service coverage or better) for April was a credit spread of approximately 2.46% compared to 2.35% for similar credit quality multifamily. If you run both through a pricing model and adjust for cost of acquisition, maintenance, credit, interest rate and liquidity, you get about a 14% risk-adjusted return for both.


After looking at this data, many bankers might be indifferent. 


10 Year Projected Loss Rates For Bank Loans


However, that is only part of the story.


Default Volatility


Without getting too deep in the weeds (read below if you want to), most banks, including many of the top 50, use a 1-factor pricing model which is a linear interpretation of risk. That is, all risk along the pricing spectrum is about equal, is static and only moves along one dimension – credit. This is most of the risk, so in our industry’s defense, using a simple pricing model gets banks in the right ballpark.  However, not all risk is the same.


Despite having the same 10-year expected default rates (they also coincidentally have the same historic default rates) the volatility around owner-occupied CRE is much lower, by about 37%. We can look at the variability around the default rates and then take the standard deviation or measure of variance for each quarter and now get a measure for how much defaults jump around. We can see the volatility of the major lines in the below graph.

10 Year Default Volatility Graph


It turns out that the variability around owner-occupied CRE is much less with a standard deviation of 0.31% compared to 0.49% for owner-occupied CRE. Another way to say this is that within a probability of 68.2% (one standard deviation), the default rate around owner-occupied CRE is going to go up or down about 31 basis points. Thus, in all likelihood the 10-year default rate will be between 0.06% and 0.68%.


Multifamily lending, by contrast, has a range of -0.12% (negative because of recoveries) and 0.86%.


Solving For This Problem


While an over simplification, there are three main ways that banks can solve this problem. One is to get a more sophisticated model. This is expensive for any bank under $10B in total assets and complicated (see below). However, if you can afford it, this is the way to go since accurately pricing your credit is one of the most important things a bank can do since it is so highly leveraged as to its capital.


The second way to handle this issue is to stress test and then adjust pricing to compensate for your base stress scenario. While many banks do stress test on an individual basis, most do not adjust pricing based on the outcome. Here, you would want to take into account the base stress scenario and price to equate to the same risk-adjusted return on equity for the loan. This stressed pricing would then be weighted by expectation of that scenario occurring. Thus, you might weight this pricing scenario 10% during the start of the cycle, 50% halfway through and 80% nearing the end. We believe we are just a little more than halfway through the cycle, so we might suggest a 60% weighting right now as an example. 


The third way to handle this risk is to increase your reserves by half the amount of the standard deviation of defaults under the concept that you are just adjusting for the downside scenario. Thus, banks would increase their reserve and then adjust the reserves for this risk factor each period as the loan ages and the risk outlook changes. This is the most common way that banks proactively choose to handle this problem.




There is a fourth way which is the most common passive way to handle this issue and that is to ignore it and just hold more capital. If this is your path, at least acknowledge the risk and know that you are taking this potential variability to your earnings and to your capital in the future.


Further, it is helpful to understand the volatility of loss when making strategic decisions and allocating resources each year to different lending lines.


Post Script – You Should Stop Reading


If you made it this far, then it is likely that you are either a Fed researcher, a hotshot Phd. at some major bank, a student looking for a thesis subject or deep past the line of bank model geekdom. We tried hard to take a complex subject and simplify it for practical purposes and this section will likely make you feel overwhelmed to the point of not trying any of the above proposed methods to account for volatility risk. Thus, you should really stop reading unless you really care about the last mile of accuracy. 


Solving for default probability across different asset classes is actually a much more complicated calculation than it seems. Most research centers around price volatility associated with an options model such as Black-Scholes. The problem is that we are talking default volatility and a loan is not an option. While it does have some optionality, the option is inefficient at best. Further, most models available today can do well pricing a single asset class in an observable market such as equities but because of the wider variety of loans and structures, coupled with the fact that there is no observable market, most established framework is unusable.


To really solve the question of pricing for default volatility in loans one needs to adjust the capital asset pricing model to include a non-parametric measure of loan-wide volatility innovation within the bounds of a two or three factor model. By adding a negative risk premium as a state variable instead of just another statistical factor (which is the case for most models), banks can gain a high level of predictive power and accuracy.


If you are really interested in achieving this level of accuracy there are probably only five models in existence to do this, three of which are proprietary and two of which have price tags starting at $150k per year or more.