The Short Answer: Historically, No, It’s the Other Way Around
The Long Answer: let’s look at scatter plots and correlations and see the two large problems with using it.
This is the third in a series of three posts.
Two Regimes
In our first post, Unemployment as a Commercial Loan Loss Predictor, we showed time-series graphs of the unemployment rate (U) and the C&I charge-off rates (CO) for all banks since 1985.1 Scatter plots—whether the pairs of observations are contemporaneous or one is lagged—are a great way to visualize and investigate the relationship between two variables independent of time…meaning not sequentially. Here are contemporaneous observations, where neither CO nor U lags or leads. We put the unemployment rate on the horizontal axis in the first graph (as that’s usually thought as the “driver,” and invert the relationship in the second graph of the slider.
Notice how the green points on the bottom and to the right form a very nice, increasing, convex function when U is on the horizontal axis, and when it’s flipped, there is a nice, increasing, concave relationship between C&I COs and U. Again, these are contemporaneous observations, and not the “best fit,” but they still look nice, and the two patterns are discernible.
So, it looks like there are two distinct regimes, which leads to two questions:
- Do the green points have anything in common, and
- Do the purple points have anything in common?
As it turns out, both subsets do. As illustrated below, the purple points are observations prior to 2010 and seem to have a roughly linear/slightly convex relationship, and the green points are from 2010 to 2019 and clearly have a convex relationship (with U on the horizontal axis).2
The next slider shows the scatter plots for 1985 – 2009, and with C&I CO on the horizontal axis, the linear (or nearly linear) relationship is easy to see. Its inverse is presented, too.
This slider shows the scatter plots for 2010 – 2019, and here we’re showing U on the horizontal axis, first. By the way, we’re not making any claim that our partition of pre-2010 and 2010-and-after is the ultimate one, and you might be able to do better, but it doesn’t change our point; clearly, different patterns exist at different points in time.
All else equal, this creates a dilemma when forecasting: which relationship should you use?
An ostrich-like developer, with his head buried in the sand (or somewhere else), might say that his bank’s data set only goes back to, say, 2007, so he can use the latter relationship. However, it’s clear that that relationship is not stationary (and is likely, already, obsolete in Q1 2020). Moreover, no developer who deserves to keep his or her job should dismiss data and relationships that negate what they hope to be the case—even if they call themselves “data scientists,” from these benchmark, industry-wide observations.
Leading from Behind?
As we discussed in our original post, since 1985, peaks in the unemployment rate have always been later than the associated peaks in the industry-wide charge-off rate. For the first two (of three) recessions since 1985, charge-offs peaked three quarters earlier than unemployment. Moreover, as we explained, on average, C&I defaults tend to occur more than a quarter before their associated charge-offs, especially for large borrowers. What does that mean? Well, at least for stress testing, where one is trying to forecast peak losses, the unemployment rate is a weak choice for an explanatory variable and, unless you’re Marty McFly or Dr. Emmett Brown, it’s definitely late when the goal is to use it as an (early) indicator for risk management.
Clearly, analyzing peaks is—by definition—an extreme argument, but why not use unemployment to forecast CECL, which is trying to forecast average or best-guess (or minimum mean-squared-error) losses?
Let’s look at the correlation between U and CO—with various lags or leads—to see if that captures more of that “average” relationship than do the peaks. Consider the entire sample history, 1985 – 2019, as well as our two regime periods: 1985 – 2009 and 2010 – 2019. Now, also consider three relationships: (1) the untransformed data—with an assumed linear relationship—and two convex functions, (2) CO = eU and (3) CO = U2. Click the graph to see correlations for the inverse relationships. (If you want, you can (i) think of the functions as transforming the raw data, and (ii) again, we’re not arguing that these are the ultimate fits or transformations but they serve our purpose to show the sloth of the unemployment rate.) We show the correlations for nine different time pairs. For example, if s = -4, then in the first table, U is leading CO by four quarters, and if s = 3, then U is lagging CO by three quarters.
Consistent with our observations of the peaks in the time-series graphs, and regardless of the functional form, the correlation is maximized with some lead of the charge-off rate to the unemployment rate. Again, that means that current charge-off rate may explain future unemployment rates, but the current unemployment rate best explains past charge-offs. not contemporaneous or future charge-offs. Of course, that doesn’t help much when forecasting losses. Remember, the point of the earlier post was that for C&I loans, the unemployment rate isn’t a predictor of charge-offs. There is a strong relationship, but C&I charge-offs (CO) lead the unemployment rate–both at the extremes and on “average.”
In the table with CO as the dependent variables, look at the third section that analyzes the most recent regime. Notice that correlations are highest when charge-off rates lead the unemployment rate by four quarters! And, again, unlike consumer loans, C&I defaults tend to lead charge-offs by a bit. All else equal, if you told me the unemployment rate, today, the best prediction of charge-offs I could make with it would be the first quarter, last year, but we already know that number.
Granted, all of this analysis involves the entire banking industry and all C&I loans. You may be thinking that, “well, our bank is different,” which you would have to prove, of course. Alternatively, you might be wondering, “maybe it works for certain C&I segments?” If that’s the question, then we’d encourage you to re-read our second post on the topic that discusses segmentation.
In our fourth post, we look at the relationship between the unemployment rate and CRE charge-off rates. Any guess at how that will turn out? We’ll also analyze consumer charge-offs, too.
P.S. We may add graphs of the lagged/led relationships as time permits.
- For CECL—by definition—we’re interested in expected losses, and, therefore, defaults, for any reasonable model that can also be used for risk management. However, the industry-wide charge-off rate for C&I loans is available for free from FRED and/or can be compiled for any subset of banks by downloading that data from the FDIC. Everything that we did with these seasonally-adjusted sequences, we did with non-seasonally-adjusted or raw series, too. ↩
- Three points here: (i) it’s possible to argue that the 1985-2009 relationship is slightly convex (concave); (ii) these are contemporaneous observations that don’t maximize correlations, but we’re showing them to avoid the problems from end of 2009/beginning of 2010 with lags or leads; and (iii) it seems like the latter regime won’t hold through this past quarter (Q1 2020) when the unemployment rate jumped but C&I charge-offs haven’t. ↩