Auto Loan Severity of Loss and the CPI for Used Cars and Trucks
Institutions typically use their own experience to estimate recoveries and thus the severity of loss for auto loan defaults. The Consumer Price Index for Used Cars and Trucks (CPI-UCT) can be helpful in determining whether changes in recoveries and severity of loss are due to declining credit quality or changes in the used car and truck market. When used car prices fall and thus the CPI-UCT falls, auction prices are lower and the recoveries on repossessed vehicles are lower, leading to a higher severity of loss. When the CPI rises, auction prices are higher, recoveries are higher and the severity of loss is lower. The discussion that follows will illustrate how changes in the CPI-UCT and the averaging period used for pricing-related loss rate forecasting can help in understanding changes in severity of loss for auto loan portfolios.
The CPI-UCT has stabilized since mid-2011 as shown in Figure 1. This will change the severity of loss behavior of most auto loan portfolios, causing losses to be higher than expected for institutions that price loans using an estimate for the severity of loss using a rolling average with a period of more than two years.
Figure 1 shows the dramatic drop in the CPI-UCT during the early part of the recession in 2008-2009, followed by a dramatic rebound due to the reduced new-car manufacturing capacity that resulted from bankruptcies and restructuring in the auto industry. The rebound largely ended in the summer of 2011. The CPI-UCT is currently dominated by seasonal used-auto purchase demand; it is high in the Spring and low in the Winter.
For institutions that use a rolling average to estimate future severity of loss for new and used auto loans, the changes in the used car market reflected in the CPI-UCT will affect the actual severity of loss compared to the severity of loss estimate used to price loans at the time of origination. Institutions that use a rolling average of more than 5 years have experienced lower than expected severity of loss, and thus higher than expected net interest income. This better than expected performance is about to end for these institutions, not because loans are performing better or worse, but because the 2008-2009 crash in the used car market is about to roll out of the data set used to calculate the rolling average that was used in pricing the loans.
Figure 2 shows the 5-year rolling average for CPI-UCT and has a clearly rising value that will cause losses to be lower then originally estimated. For example, loans that originated in January of 2012 (rolling average of 138 used for pricing) and defaulted in January of 2013 (actual value of 147 at time of default) saw a 6% higher recovery than expected. The better than expected performance will decline as the 2008-2009 crash numbers continue to drop out of a 5-year rolling average in the coming months.
This affect would be greatest for loans originated in October, November or December of 2009 when the 5-year rolling average hit a minimum of slightly more than 135. Loans originated at the bottom would experience an approximately 8.5% better than expected recovery in the event of default.
Institutions that use shorter rolling averages have already begun to see the 2008-2009 crash values and the subsequent rebound begin to drop out. For example, using a 3-year rolling average for pricing purpose as shown in Figure 3, the same January 2012 loan would have been priced with a estimated recovery value of 140, with an actual recovery value of 147 at time of default for a 5% higher than expected recovery.
The three-year rolling average is more volatile than the 5-year; the minimum would have been 132, for an approximately 11.4% better than expected recovery in January, 2013. This benefit will rapidly go away as the values from the crash continue to drop out of the rolling average used for pricing.
Using the 2-year rolling average shown in Figure 4, the recovery estimate used for pricing would be about 146, for a less than 1% better than expected recovery in January of 2013; institutions using this shorter rolling average have already seen the affects of the crash period dropping out of the average.
Although a 6% better than expected recovery may not sound like much, it can translate into a disproportionately large change in the severity of loss. 6% on a $10,000 vehicle would be $600. If the outstanding loan is $12,000, when the 6% better than expected recovery goes away, the severity of loss goes from $1,400 ($12,000 - $10,600), to $2,000--a change of 43%.
The CPI-UCT is helpful in determining whether changes in recoveries are due to credit problems, or used car market problems. The crash in used car and truck prices that occurred in 2008-2009 was a very unusual event, and will cause some unusual and perhaps negative changes in the severity of loss in car loan portfolios.
Data are from the CUSR0000SETA02 series available from the St. Louis Federal Reserve FRED2 system.
- Written by Bruce Moore
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Open Source Solver Resources
Solvers are the basis for all optimization modeling. There are four major types, according to the type of problem that the particular software can solve:
- Linear integer, otherwise known as "mixed integer"
- Non-linear integer
Most pricing problems in finance are either quadratic or nonlinear, so the non-linear solvers will be listed first.
- Ipopt is an open source solver designed for constrained non-linear problems. It was originally written by Andreas Wachter while at IBM, and is currently released under the Eclipse Public License. It is probably the most robust of the available open source solvers.
- Excel has a built-in non-linear integer solver, but it is limited to 300 variables; since some of these are used for internal variables that are not present in the spreadsheet as cells, the problems that it can handle are really pretty small, but it can be useful if your problem fits into 300 variables.
Linear, Integer and Quadratic
- Clp is a linear solver that was written by John Forrest while at IBM, and is currently released under the Eclipse Public License. It is has a reputation as the most robust of the available open source solvers, and is considered to be competitive with commercial solvers for all but very large problems. It is unusual among open source linear solvers in that it can handle quadratic objective functions.
- Cbc is a mixed integer solver that was written by John Forrest while at IBM, and is currently released under the Eclipse Public License. It is has a reputation as the most robust of the available open source solvers, and is considered to be competitive with commercial solvers for all but very large problems.
- GLPK is a mixed integer solver written by Andrew O. Makhorin (Андрей Олегович Махорин) while at the Moscow Aviation Institute. It is widely used due to the inclusion of the GNU Linear Programming Language that is essentially a subset of the commercially available AMPL language. The modeling language is much slower than AMPL and does not allow order sets (among many other things), but it can be useful when you don't have an AMPL license available. It is significantly slower than commercial solvers, especially on integer programs.
- lp_solve is a linear solver that was probably the first widely used open source solver and which has a reputation as being useful for problems larger than GLPK can handle, but smaller than Clp can handle.
- Written by Bruce Moore
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R - Open Source Statistical Software
While working on my praxis during my Doctor of Engineering program, I tried to do a multiple linear regression in Excel--and discovered Excel's limitations. Since I didn't have budget money for SAS and couldn't move the data to the university's computers for confidentiality reasons. I started frantically surfing the web: "open source" "free" "statistics" "linear" "regression".
I downloaded several programs, most of which had even more problems than Excel. I finally downloaded a program called "R" and was able to install it, load my data, and run my regression in less than an hour. Although the language was very different from all of the languages that I knew (or for that matter know), it worked reliably, and did what I needed.
More than 12 years later, I am still an R user and have attended the UseR! conferences in Ames (2007), Dortmund (2008), Rennes (2009), Coventry (2011) and Albacete (2013). The links that follow provide a few resources for this great statistical package. R is now used in a number of Fortune 500 firms, including Google (which does its own internal distribution) and a number of pharmaceutical companies.
- R project web site Provides links to mirrors for downloading.
- Revolution Analytics is a commercial vendor that distributes a supported version of R and it's related packages. The Revolution Analytics interpreter has some proprietary features that are of use for parallel computing and large datasets.
- RStudio offers a wonderful free integrated development environment for R, and various educational offerings. Hadley Wickham is one of the most prolific and respected package writers.
- RMetrics is a project to develop R packages for the financial engineering. This user group has its own conference, and most of the finance crowd goes to this conference rather than the general UseR! conference.
- RGeo is a project to develop geospatial analysis packages for R.
- BioConductor is a very large project to develop software for genomic and pharmalogical research. Pharmaceutical firms were among the first to adopt R.
Important Blogs for R
R User Groups
- Dallas Ft. Worth R User Group
- Houston R User Group
- Austin R User Group
- San Antonio R User Group
- Atlanta R User Group
- Burlington R User Group
- List of world-wide R user groups
- Written by Bruce Moore
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