Three Things People Get Wrong About Loss Curves

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1. Multiplying an annualized loss rate


Under the current ALLL guidance, a common approach is to calculate a loss rate as the total loss over n months divided by the average portfolio balance across those months. This rate is often annualized to reflect expected losses over one year (e.g. if n=24, the rate would be divided by 2, if n=36, the rate is divided by 3, etc.). Of course, when CECL comes to town, it will be required to calculate expected losses over the lifetime of the loan rather than just over a single year. Well, that’s easy, just multiply the annual loss rate by the number of years remaining in the life of the loan. Right? WRONG. Doing so would assume that the expected loss for a single loan would remain constant over the loan’s life, and this is simply not true. Rather, a more accurate shape of the lifetime loss curve is something like the below.

loss curve shape.jpg

2. Using the wrong balance in the rate

Now that we have you convinced of the sinful nature of multiplying an annualized loss rate, we can talk about the actual CECL loss curve creation. It might seem natural to calculate a loss curve by considering a pool of loans (let’s arbitrarily say all auto loans originated in 2010), and calculating yearly loss rates for this pool. You might be tempted to calculate the rates as follows (building the curve based only on loans of the 2010 vintage):

 

  • Year 1 rate = (total year 1 losses)/(average year 1 balance)
  • Year 2 rate = (total year 2 losses)/(average year 2 balance)
  • Year 3 rate = (total year 3 losses)/(average year 3 balance)
  • Etc.

 

Let’s think about what we want to do with the rates in the curve. We want a rate that we can multiply by a current balance to obtain an expected loss. Consider an active loan that originated last year (2016), so it is currently in its second year. To obtain expected second year loss for this loan, we’d want to multiply current balance by a rate that is of the form (year 2 loss)/(year 2 balance). This aligns well with the rates defined above. But what if we want expected third year loss for this loan? If we want to multiply a rate by the current (year 2) balance, the desired rate should look like this: (year 3 loss)/(year 2 balance). See the problem? The loss rates defined in the bulleted list do not accomplish this. Thus, if you are going to take a loss curve approach for CECL, you need to make sure that the denominators in your rates are compatible with the balance by which you multiply the rates.

3. Using one curve for all active vintages

This one is really just an extension of number 2, but it’s a subtle little guy, so we gave it its own number (also you can’t have a list with just 2 items). Let’s say you build a curve using the following rates (again, only using loans originating in 2010):

  • Year 1 rate = (total year 1 losses)/(average year 1 balance)
  • Year 2 rate = (total year 2 losses)/(average year 1 balance)
  • Year 3 rate = (total year 3 losses)/(average year 1 balance)
  • Etc.

Notice that it is perfectly acceptable to apply this curve to all active loans that originated this year (2017, so in their first year). However, since the denominators are based on year 1 balances, this curve should not be applied to active loans in their second year, or third year, and so on. So, as much as we’d all like the simplicity of a “one size fits all” loss curve, multiple curves are likely the way to go (unless you have 30+ years of data on losses and balances, but that’s another topic for another day).

mistake.jpg


Rachel Messick

Product Manager/Data Scientist at Visible Equity


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