Many indirect loan products require that fees be paid to the firm that originates the loanan auto dealer for example. Many institutions amortize these fees using a straightline method over a period of months approximately equal to the estimated life of the loan. For optimizing the performance of a loan portfolio, it is important to understand how the costs associated with these loans and how the upfront fees affect the effective yield on a loan; the straightline method isn't very good at this.
In some cases, institutions must amortize these fees in a way that satisfies SFAS 91, Accounting for Nonrefundable Fees and Costs Associated with Originating or Acquiring Loans and Initial Direct Costs of Leases. The discussion that follows is designed to provide a way to calculate fee amortizations that will work for loan portfolio optimization calculations. It may (or may not) be helpful in calculating amortizations for SFAS 91; you should discuss this with your accountant.
Using this method to calculate fee amortizations for loan portfolio pricing does not require that an institution use this method for financial accounting.
The calculation is easiest to describe with an example loan:
Principal  $10,000 
Fee paid  $1,000 
Interest Rate  7% 
Term  60 months 
Payment  $198 
Since levelyield calculations treat the unamortized fee as part of the loan balance, let's treat the fee amortization just like another payment with the same term and interest rate:
Fee Interest Rate  7% 
Term  60 months 
Fee pseudo payment  $19.80 
With this basic information, it is now time to calculate the amortization for a few periods, as shown in Table 1. The columns in coral show the calculation of the monthly principal portion of the monthly payment, with monthly principal of $139.89, $140.49 and $141.31.
Similarly, the cyan columns show the calculation of the monthly fee "principal" amortization, with fee amortization of $13.97, $14.05 and $14.13 respectively.
The light grey columns show the calculation of the level yield as the interest ($58.33 for period 0) divided by the level yield asset ($11,000) multiplied by 12 periods to annualize the result, which gives 6.36%. Repeating this for the other periods confirms that the yield on the combined asset is the same for each period.
What happens to the $5.83 "pseudo interest" in the amortization calculation. If we divide this by the the level yield asset balance ($11,000) and multiply by 12 to annualize it, we get 0.64%the difference between the contracted 7% interest rate and the effective yield after fee amortization.
Level Yield Amortization Detailed Calculation  Level Yield  Level Yield Simplified Calculation  

Period  Principal  Payment  Interest  Applied Principal  Fee Balance  Fee Pseudo Payment  Fee Pseudo Interest  Applied Fee Principal Amortization Expense  Level Yield Asset  Yield After Fee Amortization  Amortization Expense Reduction to Contract Yield  Simplified Calculation of Amortization Expense Reduction to Contract Yield  Simplified Calculation of Amortization Expense 
0  $10,000.00  $198.01  $58.33  $139.68  $1,000.00  $19.80  $5.83  $13.97  $11,000.00  6.36  0.64  0.64  $13.97 
1  $9,860.32  $198.01  $57.52  $140.49  $986.03  $19.80  $5.75  $14.05  $10,846.35  6.36  0.64  0.64  $14.05 
2  $9,719.83  $198.01  $56.70  $141.31  $971.98  $19.80  $5.67  $14.13  $10,691.81  6.36  0.64  0.64  $14.13 
This approach to calculating the fee amortization works fine until an asset prepays. For full prepayment, this is easythe entire remaining balance is amortized all at oncebut how do you calculate the fee amortization for a partial prepayment?
To do this, first we should look for an easier way to calculate the monthly fee amortization amount in a way that doesn't require calculating both the pseudo payment and pseudo interest for the fee. Notice that the fee pseudo payment is proportional to the fee balance divided by the principal balance$1,000/$10,000 or 0.1 in this case. Similarly, the applied principal, $139.68 is proportional to the fee amortization, $13.97.
From this we can calculate the monthly fee amortization as
To calculate the prepayment of an unusual amountperhaps a double payment in month 0we would just take the principal applied, and use the formula above to calculate the fee amortization:
The example also shows how this would be implemented in practice. For loan pricing optimization, the effective yield is needed for each loan type, term and credit gradeincluding prepayments. Calculating a pseudo payment for each loan and determining the fee amortization by month would be programmatically painful and inefficient. Since the principal portion of the payment would be present in most accounting systems at the loan level, this becomes an easy way to retroactively calculate the fee amortization for effective yield. This is also a calculation that is necessary if the institution decides to convert from one amortization method to a level yield method.
A complete example of this approach in an Excel spreadsheet can be downloaded here.
The formula displays in this example are formatted using MathJax.
{calltoaction} ]]>At the Independent Bankers Association of Texas (IBAT) Lending Compliance Summit in April, 2014 and at the Southwest Graduate School of Banking (SWGSB) Alumni program in May, there was much discussion about the regulatory focus on Fair Lending in general and the statistical analysis that is being done to identify disparate treatment. The article that follows is the first in a series of three that discuss how banks can prepare for an examination and minimize the likelihood of problems, how a bank might proceed with an inhouse study to identify and fix any disparate treatment problems and finally, how some statistical examples to help explain several questions that came up at the IBAT and SWGSB gatherings. For additional reading, you may wish to look at How a Bank Can Get in Trouble with Fair Lending Statistical Analysis and Doing Your Own Fair Lending Statistical Analysis.
The discussion of preparing for a disparate treatment statistical analysis is divided into the following sections:
When I worked in IBM’s Global Business Intelligence Systems datamining group, we had a saying:
There are customers that know they have a data quality problem, and there are customers that don’t know that they have a data quality problem.
A dataset can be pristine and balance to the penny from an accounting perspective, and yet be a nightmare from the viewpoint of performing any statistical analysis. If a regulatory statistical analyst receives a poorly prepared dataset, the analyst will will spend so much time cleaning up data that little time will be available to distinquish between unusual datapoints that can be discarded as mistakes and others that contain important information and must be included.
The FDIC Compliance Manual  January 2014 describes risk factors for discrimination to be used in planning an examination on page IV1.6:
C2. Prohibited basis monitoring information required by applicable laws and regulations is nonexistent or incomplete.
C3. Data and/or recordkeeping problems compromised reliability of previous examination reviews.
Don’t send a poorly prepared dataset for statistical analysis. As a banker, you are much better off if the analyst has more time and spends more time looking for data elements to explain racial/ethnic/gender patterns in your dataset. If the analyst spends hours cleaning up a poorly prepared dataset, expect to have examination problems.
All of these data quality analysis steps can be performed in Excel, though the corrections should be done on the source system so that you don’t have to repeat the cleanup process every year. Most IT personnel would probably choose to use a programming or scripting language that allows regular expressions and other features that make data manipulation easier.
All returned mail identifies an address problemeither an old address, an incorrect one, or one that is entered so badly that even the U.S. Post Office can’t figure out what it isand I am amazed at what the Post Office can deliver correctly. Before you do a data pull for any type of statistical analysis, make absolutely sure that you are caught up on fixing returned mail.
The statement mailing firm that you use probably does address standardization as part of the service that they provide, but the standardized addresses probably don't make it back to your core system. Investigate ways to get the standardized addresses into your core system.
If you don’t use address standardization software to identify and correct spelling, format and abbreviation problems in addresses, at least do a pull and get a count of addresses by city and state. Sort the list by the cities with only one accountthese are probably misspellings. If you don’t have address standardization software, you will be amazed at how many ways people can spell "Dallas" and "Houston." The Post Office correctly delivers a lot of mail that is badly misspelled. Make sure that all of the states abbreviations are valid.
If you don't have standardization software, you can use a geocoder to attempt to find the latitude and longitude of the address; if the geocoder can't figure out the latitude and longitude, it is either a Post Office Box, a Military address, or an invalid address. The next article in this series, Doing Your Own Fair Lending Statistical Analysis, has a significant discussion about geocoders and geocoding.
Most core systems do a very good job of preventing bogus dates from being entered, but you should check to make sureespecially for ancillary systems and datasets provided from third party vendors. At a minimum, check the following:
If you do indirect lending, make sure to include the name of the dealer or originator of the indirect loans, and that the loan type and originator are coded correctly and consistently.
Take an extract of your historical rate sheets, merge the rate sheet with your loan data by time of loan origination, calculate the difference between the rate sheet for the time period of loan and then rank by absolute value of the difference. Look at the extreme valuesthese are probably mistakes. Investigate the reason for the largest differences and add a code or comment to explain why these particular loans have unusual deviations from the rate sheet. If they are mistakes, work with the borrower to correct the loan.
Make sure that all loan modifications and rework of loans that were messed up somewhere along the line are coded in a way that they can be easily identified and understood. It should be easy for an analyst to figure out that a goofed up loan entry that was corrected and reissued under another number can be legitimately excluded as an outlier.
In the core systems, numbers can be stored in a variety of wayssome quantities are stored as floating point, some as decimal, some as integers, and occasionally as characters. Each of these data types works differently for rounding and in some cases may just truncate everything to the right of the decimal point. If you extract using a data type that truncates or take a number with 5 decimal places and round it to 2 decimal places, you can introduce some unusual patterns in your dataset.
Always export in the data type that is used to store an element, and always export the number of digits that are stored without rounding wherever possible.
Perhaps the biggest problem that you may encounter in a Fair Lending statistical analysis will be loan decisions that are based upon information that is present on a textbased credit report. If you calculate loan to value, debt to equity, or medical bill chargeoffs to total chargeoffs from a credit report, but don’t include that in the extract, you will almost certainly have problems during an examination. If these ratios have a strong statistical relationship with race/ethnicity/gender (likely, since income has a strong relationship), race/ethnicity/gender will show as a statistically significant, and you will have have to spend a lot of time and money providing a corrected extract plus the aggravation of dealing with examiners over Fair Lending disparate treatment issues.
If you include the additional credit worthinessrelated variables that you used in the underwriting process, race/ethnicity/gender will probably not show up as statistically significant, and your Fair Lending examination will probably go as smoothly as Fair Lending examinations can go.
If your origination system does not calculate all of the ratios that you use, pressure them to add the additional ratios so that it is easy to extract them. This isn’t so much to make Fair Lending examinations easier, as it is to make fraud and abuse analysis easier for you to do. You should use the Fair Lending dataset for a fraud and abuse analysis; you will probably quickly recover the cost of preparing the data set and will start using your fraud and abuse dataset as the one you submit for Fair Lending analysis.
If you have an indirect auto loan program, this is an area where race/ethnic/gender discrimination may be occurring without your knowledge or control. It is also an area where there is significant opportunity for fraud and abuse by an auto dealer, or specific employees at an auto dealer. The analysis that you do for indirect lending should be at least quarterly, as salespeople move from one dealership to another fequentlya dealer that has demonstrated exemplary performance for years can go south quickly when a new sales person comes onto the floor.
The discussion that follows is really oriented toward dealerlevel fraud and abuse problems rather than Fair Lending, but if a dealer or an employee at a dealer is willing to commit fraud or abuse, discrimination based upon race/ethnicity/gender would not be a far stretch and vice versa. To get to this point, you will have put in a fair amount of work; you should reap the benefit of that labor, and a simple fraud and abuse analysis is the way to do it. For regulatory purposes, this analysis may or may not constitute a review of Fair Lending practices that would require you to correct any problems found; that is a question for your attorney.
For a simple fraud and abuse analysis that can be done in Excel, calculate and rank dealers by the following quantities:
For a dealer that ranks at the top of each list, investigate individual loans that have defaulted or are delinquent. It is likely that this work will be financially rewarding to the bank.
Rank the loans by dealer participation for each dealer, and for all dealers. For the highest participations, are there any patterns? A high dealer participation could be an indicator for negative equity rolled into a deal for benign reasons, it could be negative equity rolled into a deal in anticipation of bankruptcy, it could be good negotiating on the part of the dealer, or it could be the result of discrimination based upon race/ethnicity/gender.
If you have an indirect lending program, negative equity rolled into a deal is a strong predictor of a lot interesting behavior. Estimating negative equity is painful if not impossible, as vehicles rarely sell for the Manufacturer’s Suggested Retail Price (MSRP) and there really isn’t a good way to capture the "value" of the vehicle. If you do capture MSRP and Kelly Blue Book (KBB) or a similar metric, it is worth calculating the difference between the purchase price and the MSRP/KBB as a proxy for negative equity.
Try to figure out a way to estimate the negative equity rolled into a loan. The dealer knows this exactly, but most lending systems don’t really have a way to record it. If high dealer participations are due to negative equity, you have a credit risk problem to monitor; if high dealer participations are not due to negative equity rolled into a deal, you absolutely have a customer satisfaction problem (the painfully high loan rate that gives the dealer the room to roll in negative equity or over charge has your name on it each monthnot the auto dealer’s name) and you may have a Fair Lending problem.
Although this article is about preparing for a Fair Lending examination statistical analysis, there is little in the steps to this point that is directly related to Fair Lendingmost of this preparation is related to general data quality and to simple fraud and abuse analysis. Everything in this article can be done using Excel, though there are other tools that your IS staff may have that are better suited to the task.
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At the IBAT Lending Compliance Summit in April, 2014 and at the SWGSB Alumni program in May, there was much discussion about the regulatory focus on Fair Lending in general and the statistical analysis that is being done to identify disparate treatment. This is the second in a series of articles that discuss statistical analysis as it can be used for Fair Lending analysis. The first article in the series, Preparing for a Fair Lending Examination Statistical Analysis, discusses how to collect and prepare a dataset that a regulatory agency will use for Fair Lending analysis. The steps described in the article that follows involve analysis doing your own Fair Lending compliance analysis to anticipate problems that might come up during an examination. Fortunately, there are now open source statistical tools to do very sophisticated analysis, though these tools may require skills that the bank may not have inhouse.
The article assumes that you have already cleaned up and prepared your dataset as described in Preparing for a Fair Lending Examination Statistical Analysis. The article is divided into the following sections:
The first step in almost any customeroriented analysis is to geocode the customer's address. Geocoding is the process of converting a street address into latitude and longitude coordinates that can be plotted on a map, used to merge address data with census data, used to calculate a drive time between two locations or used in calculating the Manhattan or the straightline distances between two points. It is very useful in a variety of banking analysis problems, not the least of which is address cleanup; if an address won’t geocode and isn’t a P.O. Box, it probably has some problems that need to be fixed. Ten years ago, geocoding was difficult and expensive. Today, there are a variety of applications to do this in volumes that are reasonable for small banks:
Since no one collects information on race and ethnicity in loan applications, in doing its Fair Lending analysis, the regulatory agencies must come up with some way to estimate the race, ethnicity and gender of a borrower. All of the ways to do this are errorprone to one degree or another, but that discussion is beyond the scope of this article. Use one of the alternatives below to come up with an estimate for the race, gender and ethnicity of each borrower, and then create an array of variables to use in the analysis.
Once you have geocoded all of your loans, join it with Census data, and add census variables for race, and ethnicity of the surrounding block group to your dataset. You'll end up with a number of
An online research publication, Using the Census Bureau’s surname list to improve estimates of race/ethnicity and associated disparities provides a description of a methodology for estimating the race/ethnicity for a person using Census surname data and the geocoded block group; the method described has a correlation of 0.76 when compared to selfreported race/ethnicity at a health insurance provider. The surname frequency and race/ethnicity probability can be downloaded from http://www.census.gov/genealogy/www/data/2000surnames/index.html.
Acxiom and a number of data brokers routinely provide estimated race and ethnicity data in demographic data sets. If this is available to you, merge this data with your loan data. Although you may not do business directly with Acxiom or the other major data brokers, many MCIF vendors offer demographic data enhancement services that resell Acxiom’s services. You can probably get this service through your MCIF vendor.
For each race, ethnicity and gender, create a variable with a probability that the person fits in to each category. You should develop two sets; one with all of the census detail, and a second where all of the unprotected groups (talk to your Compliance Officer on this) are merged. For each set create a variable that is the best estimate of race and ethnicity. You will use the second set of variables to determine whether or not you have a Fair Lending compliance problem, and the first set to diagnose and refine your understanding should you identify a Fair Lending compliance problem.
Since you have the latitude and longitude for each borrower, go ahead and calculate the Manhattan distance (distance North/South + distance East/West) between the borrower and your nearest branch and between the borrower and the nearest competitor’s branch. Distance to a branch is a strong predictor for a variety of consumer financial behaviors, so it is worth having it available for analysis. The Manhattan distance is easy to compute and doesn't require expensive software.
The time it takes to drive from the customer's address to the branch is a much better predictor than distance, but it is difficult to calculate. The easiest is a commercial package called Arcview Business Analyst and the related Arcview Network Analyst products from ESRI. They aren't cheap, so you might want to contract with ESRI to do this part of the work. There may be other alternatives within the Google Maps API or other navigation web services.
One of the most important tests is to look at deviations from published rate sheets (See FDIC Compliance ManualJanuary 2014 page IV1.8 section P2). To do this you will need to join your historical rate sheets with the loan data for corresponding dates and then calculate the deviation from the rate sheet.
Now that you have cleaned up all of your data as described in Preparing for a Fair Lending Examination Statistical Analysis, and done all of the estimates for the borrower’s race/ethnicity/gender, combine everything into a single dataset to be used for analysis. For codes that are numbers, make sure to identify them as factor or ordered factor data types rather than real valued numbers. Now is the time to start duplicating items with common data transformations to normalize values on a 0 to 1 scale, or take the log of a variable where the values are orders of magnitude different. This step is the first that must be done in a statistical tool, as databases and flat files don't support the concepts of "factor" and "ordered factor."
You should also create training and test datasets, to determine whether or not the models that you generate are overfitted. If protected groups (or unprotected groups) are very infrequent in your dataset, you should consider repeating some of these lowfrequency observations in the training data set. If they are very infrequent, they may be ignored, and a pattern could be present, but not recognized, in which case you could get a rude awakening during the examination.
There are several approaches to look for disparate treatment under the Fair Lending regulations. Since we are interested in screening for problems rather than proving a problem, it is appropriate to use that an approach that casts a wide net and identifies issues that might not rise to the level of statistical significance, financial materiality, frequency, or causation that may cause problems. These terms are mine and don't appear in any regulation or compliance manual that I've seen. I use them because most of the discussions that I've heard combine all of these concepts into the term “significant” and aren't all that precise.
The statistical approach that follows is hopefully not the procedure used used by regulators. The predictive modeling approach that I discuss below will probably indicate patterns where race/ethnicity/gender are useful in predicting price where hypothesis testing approaches might not identify race/ethnicity/gender as statistically significant. Remember that in this analysis, we want to cast a broad net to find anything that might be remotely problematic.
Once all of the data preparation is done, you can begin to look at the data and identify any race/ethnicity/gender patterns that exist. Broadly speaking, you will need to look at interest rates on loans that were approved, including both loans that closed and loans that did not close. You will also need to look at loan approvals.
Because we are screening for problems, we don't want to spend a lot of time if we can help it. The approaches below are by no means exhaustive, but instead are intended to be a laborefficient approach to screening for problems. The section is divided into the following steps:
Before doing any statistical tests on the dataset, it is usually helpful to look at some simple visualizations. A few possibilities are listed below:
lattice
package.There are many ways that you can look for disparate treatment in pricing in approved loans, but the fastest way to get an understanding of the data would be to do a stepwise regression to predict the interest rate on the loan using all of the creditworthiness metrics available plus race/ethnicity/gender. If the race/ethnicity/gender variable shows up as significant in the stepwise regression model, you either have disparate treatment in pricing, you have been making credit decisions on creditworthiness variables that are not included in your dataset, or you need to do further analysis to find a model that better explains the patterns present in the data. Stepwise regression gives good models quickly, but there may well be a model that better explains the patterns present in the data that the stepwise automation didn’t find.
At a minimum, you should do the following:
In all cases, make sure to check the residual plots for the various regression models.
Although it won't tell you anything directly, looking at the closing rates for each racial and ethnic group as shown in Table 1 can point you to further investigation; if there are statistically significant differences, you will probably want to expend more effort in the later steps.
Approved  Closed  Close Rate  Pvalue That Group Has Same Average as NonHispanic White 

NonHispanic White  100  50  0.50  
Ethnic Group 1  100  40  0.40  
Ethnic Group 2  100  60  0.60  
Ethnic Group 3  100  45  0.45  
All Groups  400  195  0.4875 
To look for disparate treatment in underwriting, you will need to look at both approvals and denials. To get a quick understanding, do a stepwise logistic regression to predict loan approval.
In all cases, make sure to check the residual plots for the various regression models.
Finally, we need to look at product selection to make sure that qualified borrowers aren't steered into more expensive subprime products when they qualify for a prime product. For this analysis, we will generate a matrix like the one shown in Table 2 below for each racial/ethnic group:
Qualified for Prime 
Not Qualified for Prime 

Sold Prime  100  
Sold SubPrime  100 
In this table, everyone should be on the northwest to southeast diagonal. If you have nonzero entries on the southwest to northeast diagonal for any of the racial or ethnic groups, you will need to perform a chisquared test (Χ^{2}) to determine if the groups are treated differently from a steering perspective.
If you come up with models that include race/ethnicity/gender as significant predictors even when all other creditworthiness variables are available to the stepwise regression, make sure to run them against the test data set. If the model continues to predict well, you are missing a creditworthiness variable with strong race/ethnicity/gender patterns, you have a lot of work ahead to find a manually constructed model that performs better or you have a disparate treatment problem that needs to be addressed.
The analysis described above will help you to identify whether you have disparate treatment patterns that could appear in a Fair Lending examination statistical analysis. Since the exact procedures that the regulatory agencies use are not public, it is not a guarantee that issues won’t come up.
]]>Many types of loans–mortgages in particular–allow a borrower to pay discount points at loan origination as a way to reduce the interest rate of a loan. For financial accounting and reporting purposes these discount points are treated as a prepaid interest asset that is expensed over the life of the loan, but the expense is negativeit is income to the loan. For purposes of setting prices, it is critical that upfront discount points be applied to income in a way that allows managers to compare product yields in a realistic way. The article that follows describes how to do this calculation. The procedure is analogous to the procedure for upfront fee expenses described in Effective Interest (Yield) Loan Fee Amortization, but the sign for the prepaid interest asset is negative instead of positive; this causes the the asset to be amortized to income rather than expense. This approach it makes it possible to use the same fee amortization code needed for Effective Interest (Yield) Loan Fee Amortization without modification; this makes it much easier to maintain reporting and analysis applications.
The article is divided into the following sections:
Although this type of upfront discount points can occur on many loan and lease types, the most common are mortgage loans. For our example, a mortgage loan will be used:
Principal  $100,000 
Interest Rate  3.5% 
Term  360 months 
Payment  $449.04 
Note that the normal loan payment has a negative sign for cash flow and the discount points payment has a positive sign for the cash flowin this case the loan payment reduces the principal balance and the amortization payment increases the principal balance. The “discount points” payment can be thought of as a regular prepayment to principal, but since it is contractually used to buy down the interest rate, we need to amortize this principal reduction over the life of the loan. To do that, we will treat the discount points payment as a type of loan and then calculate a payment to get the principal and income that must be amortized:
Discount points paid  $2,000 
Discount points Interest Rate  3.5% 
Term  360 months 
Discount points amortization payment  $8.98 
With this basic information, it is now time to calculate the discount points amortization to income for a few periods, as shown in Table 1. The columns in coral show the calculation of the monthly principal portion of the monthly payment, with monthly principal of $157.38, $157.84 and $158.30 respectively.
Similarly, the cyan columns show the calculation of the monthly discount points "principal" amortization to principal, with discount points amortization of $3.15, $3.16 and $3.17 respectively. The discount points are subtracted from the principal balance in period 0, and then the “principal” portion of the “amortization payment” is amortized back into the loan principal as the loan pays down. The signs for discount points amortization are the opposite of the signs for fee amortization; the fee amortization is a positive expense while the discount points amortization is a negative expense– income for all intents and purposes.
The light grey columns show the calculation of the level yield as the interest ($291.67 for period 0) divided by the level yield asset ($98,000) multiplied by 12 periods to annualize the result, which gives 3.57%. Repeating this for the other periods confirms that the yield on the combined asset is the same for each period.
What happens to the $5.83 "pseudo interest" in the amortization calculation. If we divide this by the the level yield asset balance ($98,000) and multiply by 12 to annualize it, we get 0.07%the difference between the contracted 3.5% interest rate and the effective yield after discount points amortization.
It may seem counterintuitive to reduce the principal by the amount of the discount points, but it may help to think of it in terms of net cash flows: the bank’s net disbursement is $98,000 but the bank gets paid interest on $100,000, just as in the upfront fee case the bank would have a net disbursement of $102,000 but would get interest on only $100,000.
Monthly Principal and Interest  Level Yield Discount Points Amortization Detailed Calculation  Level Yield  Level Yield Simplified Calculation  

Period  Principal  Payment  Interest  Applied Principal  Discount points Balance  Discount points Pseudo Payment  Discount points Pseudo Interest  Applied Discount points Principal Amortization Expense  Level Yield Asset  Yield After Discount points Amortization  Amortization Income Increase to Contract Yield  Simplified Calculation of Amortization Income Increase to Contract Yield  Simplified Calculation of Amortization Expense 
0  $100,000.00  $449.04  $291.67  $157.38  $2,000.00  $8.98  $5.83  $3.15  $98,000.00  3.57  0.07  0.07  $3.15 
1  $98,842  $449.04  $291.21  $157.84  $1996.85  $8.98  $5.82  $3.16  $97,845.77  3.57  0.07  0.07  $3.16 
2  $98,684  $449.04  $291.21  $158.30  $1993.70  $8.98  $5.81  $3.17  $97,691.09  3.57  0.07  0.07  $3.17 
In this amortization case, the discount points asset is subtracted from the loan principal rather than added to the loan principal for purposes of yield calculation, which seems backward.
This approach to calculating the discount points amortization works fine until an asset prepays. For full prepayment, this is easythe entire remaining balance is amortized all at oncebut how do you calculate the discount points amortization for a partial prepayment?
To do this, first we should look for an easier way to calculate the monthly discount points amortization amount in a way that doesn't require calculating both the pseudo payment and pseudo interest for the fee. Notice that the discount points pseudo payment is proportional to the fee balance divided by the principal balance$2,000/$100,000 or 0.02 in this case. Similarly, the applied principal, $157.38 is proportional to the discount points amortization, $3.15.
From this we can calculate the monthly discount points amortization as
To calculate the prepayment of an unusual amountperhaps a double payment in month 0we would just take the principal applied, and use the formula above to calculate the discount points amortization:
The example above shows how this would be implemented in practice. For loan pricing optimization, the effective yield is needed for each loan type, term and credit gradeincluding prepayments. Calculating a pseudo payment for each loan and determining the discount points amortization by month would be programmatically painful and inefficient. Since the principal portion of the payment would be present in most accounting systems at the loan level, this becomes an easy way to retroactively calculate the discount points amortization for effective yield. This is also a calculation that is necessary if the institution decides to convert from one amortization method to a level yield method.
A complete example of this approach in an Excel spreadsheet can be downloaded here. The spreadsheet also contains a tab with an alternate calculation approach that may be appropriate for uses other than pricing use, but it would not reuse the code from fee amortization.
Writing a program to calculate the level yield discount points amortization schedule is very simple, but writing the code to extract the necessary information from loan systemsand put the calculated values back into the loan systemcan be quite involved. If you can implement this as an extractcalculatereport capability through a data warehouse or data mart, implementing this is fairly straightforward. If you need to put values back into your loan system, you should first work with your loan system vendor to find out if they can implement the capability as a new feature or as an addon. If that is not possible, plan to spend a significant amount of time with your Information Technology staff working out how the calculated values will be put back into the loan system.
In either case, you will need to work out a way to handle loan modifications. If the modified loan is handled systematically as a new loan, you will need to figure out a way to calculate the remaining discount point balance and transfer that to the modified loan record.
The formula displays in this example are formatted using MathJax. If the formulas do not display in a recognizable way, you should check your browser to make sure that JavaScript is enabled; MathJax requires JavaScript to render the equations. If you want to copy the math displays, right click on the equation and you will get a menu of options. MathML can be imported into many versions of Microsoft Word by copying the MathML to the clipboard and pasting it into Word using the "Keep Text Only" paste option. It can also by copied and pasted in LaTeX format.
]]>At the Independent Bankers Association of Texas (IBAT) Lending Compliance Summit in April, 2014 and at a lecture on compliance at the Southwest Graduate School of Banking (SWGSB) alumni program in May, there was a great deal of discussion about the statistical analysis that the FDIC is doing to test for disparate treatment under the Fair Lending (Reg Z) laws. One participant said incredulously "we do 80% of our loans to Hispanic borrowers, and they [FDIC] are telling us that we're discriminating against Hispanic borrowers." She assumed that because her bank does a large number of loans to Hispanic borrowers, that it is impossible that the bank could have disparate treatment. I'll use an example to show that the participant's assumption is wronga bank can have disparate treatment even though the bank does a majority of its lending to Hispanic borrowers. It can actually be easier to have disparate treatment problems when most of a bank's loans are to a protected group and a minority of the bank's loans are to nonHispanic whites.
Another person told of an encounter with a regulator where the regulator stated that if the bank were engaging in disparate treatment that the regulators would find and punish it. I would not have that much confidence; disparate treatment can exist but not rise to a level where it will be identified by statistical methods; this can be easily demonstrated.
Another person described a bank officer who was so appalled and stressed that his bank was being cited for disparate treatment, that he had a heart attackhe felt that he was being accused of being racist. It is possibleeven probablethat a bank can have a very real disparate treatment problem without anyone on the staff being remotely racist. I'll describe a scenario where the cause is not remotely racist, but where the pricing is undeniably disparate and unfair.
A fourth discussion cited an instance where a bank was cited for disparate treatment, but the penalty was approximately $1,000 to cover a large number of Hispanic borrowers. It is possible to have statistically significant disparate treatment that is not financially material. The examples in the article that follows will illustrate financial materiality and illustrate different ways to determine whether or not a pricing difference is material.
Finally, it struck me as unusual that all of the disparate treatment questions discussed involved Hispanic borrowers and that none involved blacks (the Census term). The method that is presumed to be used by the FDIC for identifying a borrower’s race/ethnicity is more accurate at identifying Hispanic borrowers than nonHispanic whites or blacks; the variability that this introduces makes it less likely that disparate treatment would be identified for a black population. This will be illustrated with an example.
The same inaccuracy in racial/ethnic identification that make a finding of disparate treatment for blacks unlikely also makes it makes it possible that a bank could be subject to a finding of disparate treatment of Hispanic borrowers when perfect racial/ethnic identification would not trigger a finding of disparate treatment. This will be illustrated with an example.
The article is a grossly simplified and contrived series of examples that are intended to illustrate both the power and weakness of statistical analysis for disparate treatment in fair lending. It will hopefully allow bankers and regulatorsneither of whom commonly have statistical trainingto have more useful discussions about the statistics involved in a finding of disparate treatment.
The article touches on many controversial subjects; if you don't like controversy, stop reading now. To make the discussion easier to follow and more precise in conjunction with other publications, I identify racial groups by the terms used in the Census, rather than terms which may be more common in current journalism style sheets. The examples are contrived but hopefully illustrate what may be a common scenario in banking and society that can be understood and discussed. The examples are constructed to illustrate how statistics can and cannot be applied to the analysis of disparate treatment. There is some discussion of the statistical use of the term significant and the popular use of the term “significant” which more commonly is used with the meaning of the accounting term material or the common word “frequent.” A bank can have disparate treatment that is statistically significant while at the same time such treatment is neither financially material nor frequent.
This article is the second in a series on Fair Lending disparate treatment analysis. You should also read Preparing for a Fair Lending Examination Statistical Analysis. The article is divided into the following sections:
The loan portfolio for these examples has 1000 borrowers, of whom 80 percent are Hispanic borrowers and 20 percent are nonHispanic white borrowers. To take out all of the complications of differences in credit scores and other creditworthiness metrics, we assume that all borrowers’ creditworthiness is absolutely the same in all respects. The only difference is that some are Hispanic and some are nonHispanic white. The interest rates are assigned to the whole population using a random number generator with a normal distribution of specified mean and standard deviation that differs from example to example.
For the first example, we start out with a loan portfolio where the average interest rate is 15.00% for both Hispanic borrowers and nonHispanic whites. In this bank, there is a lot of negotiation on loan rates, and thus a lot of variability. We will assume that one loan officer is nonHispanic white and goes to a church that is overwhelmingly nonHispanic white. Since many churches are very closely tied to ethnic groupsGreek and Russian Orthodox congregants are predominately of Greek and Russian descent, Lutherans are predominately of German or Scandinavian descent, Presbyterians are predominately of Scottish or ScotsIrish descent, Episcopals are predominately of British descent, African Methodist Episcopal church members are predominately African Americanit is reasonable to assume that the vast majority of the congregants at the loan officer’s church are similarly nonHispanic white.
The loan officer knows several congregants well and knows far more about how they spend (or don't spend) money than one could ever tell from a loan application. He feels that they are unusually good credit risks. He knows that some of them struggled for several years but managed to pay off substantial medical bills. If this loan officer were to give a preferential interest rate to these congregants1.50% betterhow many preferential loans would he have to make before the bank has a disparate treatment problem that is identifiable through statistics or in the language of statistics, is “statistically significant.”
The first figure below shows the the distribution of interest rates from the loan portfolio before we apply the preferential interest rates, with the Hispanic distribution on the left and nonHispanic white distribution on the right. The second figure shows the distribution after the loan officer gives enough preferential loans to detect it using a statistical test at the 0.01 level. This means that the probability is less than 0.01 (1%) that the Hispanic and nonHispanic white groups are getting the same interest rate. It doesn't look a lot different, but you can find the differences if you study it for a moment.
Statistics by itself only gives the probability that the two groups are getting the same interest rate; I've arbitrarily chosen to say that 0.01 (1%) is improbable enough that I will accept that the two groups are being treated differently. 0.01 (1%) is a stringent threshold for accepting or rejecting that two groups are different. For some types of analysis where the stakes are lowlike a marketing direct mail response modelstatisticians might use 0.10 (10%) probability of random occurrence (pvalue) as the threshold while for medical drug efficacy it might be a much more stringent threshold of 0.02 (2%) or 0.01 (1%).
The third figure shows how the probability drops as the number of preferential loans increases. 57 preferential loans would be statistically significant at the 0.01 level. This is useful in understanding that although findings of disparate treatment are pass/fail, regulators will almost certainly notice when a bank’s loan portfolio comes back with a pvalue of 0.10 or 0.05. From a regulatory point of view, it would be efficient to use this information to allocate more resources to fair lending examinations for banks that scored a pvalue that was near the level of enforcement on previous examinations.
The fourth figure shows how the average interest rate for nonHispanic whites drops as the number of preferential loans increases. In this example, it drops to 25 basis points to 14.75% at about 40 loansthe point where the preferential treatment becomes statistically significant at the 0.01 level.
In this example, we know that all of the preferential loans indicate disparate treatment, but the threshold that I've chosen doesn't kick in until I've give preferential rates to 57 of the 200 nonHispanic whites in the loan portfolio. With 0.01 as the standard of significance, a bank with only 55 preferential loans would get a pass, while one with 57 preferential loans would get a fail.
This example illustrates two points:
In the scenario that I've described, the bank is clearly giving preferential treatment to the nonHispanic white group that is statistically significant, but I don't think that anyone would describe the cause of preferential rates to longknown friends as intentionally racistjust grossly unfair to people who don't attend his church. Statistically significant has special meaning in statistical terminologybut is this case also “significant” as we use the term “significant” in everyday speech? More precisely, is this financially material?
Let's assume that these are unsecured term loans for $1000.00 with a term of 12 months, and calculate the difference in interest paid between the normal and the preferential rate in a simplified estimate using just the average interest rate of the Hispanic borrowers and the average interest rate of the preferential loans as shown in Table 1. To simplify the example analysis, the time value of money will be ignored in estimating the value of the preferential pricing.
Loan Amount  $1000.00 
Loan Term  12.00 months 
Normal Rate  15.00% 
Preferential Rate  13.50% 
Average nonHispanic white Int Rate  14.73% 
Normal Cumulative Interest  $83.10 
Preferential Cumulative Interest  $74.62 
Individual Preference Value  $8.48 
Total Preference Value Given  $483.10 
Average Preference Value for nonHispanic white Population  $2.42 
Average Preference Value as a Percent of Cumulative Interest  2.91% 
Total Preference Spread Across Hispanic Population  $0.60 
Total Preference Value if preferential rate extended to all Hispanic borrowers  $6780.34 
Number of Preferential Loans  57 
As shown in Table 1, the preference value is $8.48 per loan, for a total value of the preference given of $483.10 . If this $483.10 were apportioned to all 800 Hispanic borrowers, they would each receive $0.60. If the preferential rate were extended to all 800 Hispanic borrowers, the value would be $6780.34. Since all 1000 peopleincluding 800 Hispanic borrowershave exactly the same creditworthiness, if any of the nonHispanic white borrowers were eligible for the 13.50% rate, then all borrowers should be eligible for the 13.50% rate.
At what point does the individual preference value become material? This is a subject for much discussion and debate. To provide context, most financial statements are in units of $1,000, so $1,000 will appear as a change on a financial statement. At most institutions, the staff would work for a considerable time before closing a teller workstation with a $1,000 discrepancy. If we take this as an arbitrary standard for the lowest amount that is financially material for a bank, how would this translate to a household? A $500 million bank generates $5,000,000 in income for a 1% ROAwhat would this look like scaled to a household income? Figure 5 shows how a $1,000 discrepancy at a $500 million institution would scale to modest household incomes. By this measure, $10 would be material for a household with an income of $50,000 per year, and $5 would be material for a household income of $25,000 per year.
A colleague who is black reviewed this article and said, "it's not just that [bank loan prices]. It's everything." This conversation inspired another approach to determining whether or not a preference could be considered material. Out of this conversation came an approach to materiality that looks at the value of the preference as a percentage of the transaction, which is 2.91% in this case. If all purchases by a protected group were at a 2% higher price, what would be the aggregate affectwould 2% be material in the aggregate? Figure 6 shows 2% of incomean amount that is clearly material for all income levels.
In any case, annecdotes suggest that the FDIC has chosen an average rate difference of 0.25% as the threshold enforcement.
Example 1 is clearly statistically significant, but with an average preference value of $2.42 for nonHispanic whites that is below the range of being financially material even after scaling for a lowincome household as estimated in Figure 5, it is hard to describe this case as material either from the perspective of the bank or the borrower. Anecdotal evidence indicates that the FDIC could well consider this case to be disparate treatment that rises to the level of action. This suggests that frequency of occurrence is as important or more important than whether the preference is financial material.
In a population where everyone is exactly equally creditworthy, 57 preferential loans out of 200 loans to nonHispanic whites should reasonably be considered frequent enough to justify action.
Anecdotal evidence suggests that the FDIC is using a 0.25% unexplained difference in interest rates between Hispanic and nonHispanic whites as a threshold for action. The variability and size of preference in Example 1 were carefully chosen so that the probability of random occurrence reached 0.01 at the same time that the average interest rate difference reached 0.25%. 57 nonHispanic whites received the preferential rate in this case. What happens when the amount of preference is lowered? Example 2 keeps the same variability but changes the preference from 1.5% to 0.65%. Figures 7, 8, 9 and 10 illustrate what happens when the amount of the preference is lowered.
As shown in Figure 8, this requires 131 preferential loans for this random portfolio before reaching the threshold of 0.01 probability of random occurrence compared to 57 preferential loans when the preference was larger. Lowering the preference further would result in a higher number of preferential loans. Table 2 shows that the materiality calculations don't really change from Example 1, but almost 50% of the nonHispanic whites received the preferential ratea number that is certainly frequent.
This example is equally as statistically significant, is also not individually financially material, but it is clearly much more frequent.
This example illustrates the point that the frequency of preference given is perhaps a more useful measure than the amount of the financial preference.
Loan Amount  $1000.00 
Loan Term  12.00 months 
Normal Rate  15.00% 
Preferential Rate  14.35% 
Average nonHispanic white Int Rate  14.74% 
Normal Cumulative Interest  $83.10 
Preferential Cumulative Interest  $79.42 
Individual Preference Value  $3.68 
Total Preference Value Given  $481.71 
Average Preference Value for nonHispanic white Population  $2.41 
Average Preference Value as a Percent of Cumulative Interest  2.90% 
Total Preference Spread Across Hispanic Population  $0.60 
Total Preference Value if preferential rate extended to all Hispanic borrowers  $2941.73 
Number of Preferential Loans  131 
Examples 1 and 2 show that if there is a lot of variability in the interest rates that borrowers negotiate, it can take a relatively large number of preferential loans before there is a statistically significant disparate treatment at the 0.01 level28.50% and 65.50% of the nonHispanic white borrowers received preferential loans. How are things different when the bank tightens up it pricing so that there is no variability in pricing?
For this example, we will start with the same portfolio of 800 loans to Hispanic borrowers, and 200 loans to nonHispanic whites. All of the borrowers have exactly the same creditworthiness. All loans will have exactly the same interest rate. How many preferentially priced loans (interest rate is 1.50% better) would be necessary to have disparate treatment that is significant at the 0.01 level?
Figure 11 shows the distribution of interest rates before giving preferential rates, while Figure 12 shows the distributions when the probability that the preferential loans occurred randomly is less than 0.01 (1%). Figure 13 shows the probability that they occurred randomly as the number of preferential loans increases. Instead of 57 preferential loans, it now only takes 2 preferential loans to cross the threshold of statistical significance. The second bar at 13.50% in the nonHispanic white side of Figure 12 is so small that it is very hard to see and it may not show up if you print this article.
Although this case is equally as statistically significant as the case in Example 1, the calculations in Table 3 show that the value given for the preference is substantially less than in Example 1, with a total preference value of $16.95 compared to $483.10 . The preference extended to all Hispanic borrowers is the same at $6780.34, even though only 2 preferential loans were given instead of 57 . The comparison of Examples 1 and 2 with Example 3 show that the determination of materiality must be part of the analysis, and is probably the reason that anectdotal evidence suggests that the FDIC uses both a pvalue of 0.01 and an average difference of 0.25% in making enforcement determinations.
You can have statistically identifiable disparate treatment without the disparate treatment being financially material. Although equally statistically significant when compared to Example 1, the average nonHispanic white preference value of $0.08 does not rise to any reasonable level of being financially material at the household level. With an average interest rate difference between Hispanic borrowers and nonHispanic whites of 0.02% this probably would not rise the level of FDIC action during an examination.
This example illustrates the point that statistical significance and financial materialilty are not related.
Loan Amount  $1000.00 
Loan Term  12.00 months 
Normal Rate  15.00% 
Preferential Rate  13.50% 
Average nonHispanic white Int Rate  14.98% 
Normal Cumulative Interest  $83.10 
Preferential Cumulative Interest  $74.62 
Individual Preference Value  $8.48 
Total Preference Value Given  $16.95 
Average Preference Value for nonHispanic white Population  $0.08 
Average Preference Value as a Percent of Cumulative Interest  0.10% 
Total Preference Spread Across Hispanic Population  $0.02 
Total Preference Value if preferential rate extended to all Hispanic borrowers  $6780.34 
Number of Preferential Loans  2 
To fully understand the difference between statistical significance and financial materiality, let’s look at another example where all loans are priced exactly equally and the preferential rate is 0.05% betterinstead of 15.00%, the preferential rate is 14.95%. Figures 15, 16, 17 and 18 look almost identical to their counterparts in Example 3with the perfect pricing (in statistical terms a standard deviation of 0), the tiny preferential rate is just as statistically significant as the large preferential rate.
How do the two cases differ in financial materiality? Table 4 shows the estimate of the value of the preference given is $0.57 and the value of the preference extended to all Hispanic borrowers is $226.48. This is a clear case where the disparate treatment is statistically significant but not financially material nor frequent.
Loan Amount  $1000.00 
Loan Term  12.00 months 
Normal Rate  15.00% 
Preferential Rate  14.95% 
Average nonHispanic white Int Rate  15.00% 
Normal Cumulative Interest  $83.10 
Preferential Cumulative Interest  $82.82 
Individual Preference Value  $0.28 
Total Preference Value Given  $0.57 
Average Preference Value for nonHispanic white Population  $0.00 
Average Preference Value as a Percent of Cumulative Interest  2.91% 
Total Preference Spread Across Hispanic Population  $0.00 
Total Preference Value if preferential rate extended to all Hispanic borrowers  $226.48 
Number of Preferential Loans  2 
The anecdotal FDIC enforcement triggers of a 0.01 level of significance and a 0.25% difference in the interest rate between protected groups and nonHispanic whites makes it possible to develop a chart estimating how many preferential loans of a particular size are likely to trigger an enforcement action. The FDIC has not made public statements of these triggers, so these assumptions are just thatassumptions. Do not depend upon the accuracy and correctness of this curve, as these assumptions could be completely wrong, and this simulation is a contrived twogroup population rather than the complex populations that occur in real life. To the extent that the various assumptions are reasonable, Figures 19 and 20 give an estimate of the zone where banks are in danger of triggering an enforcement action. Above the curve enforcement action would be likely under these assumptions, while enforcement action is less likely as a portfolio moves farther below the curve. This isn't a hard linethis curve assumes the variability used in Examples 1 and 2 (in statistical terms, the standard deviation is 1.25%); with higher variability the curve will move up while with lower variability the curve will move down. Figure 19 shows all of the data points from 20 simulations; think of this as doing this test with portfolios from 20 different banks. Figure 20 is from the same data, but is drawn to show the 95% confidence interval for the enforcement boundary.
The key lesson from this analysis is that a small number of big “sweetheart deals” in a small pool of nonHispanic white borrowers may be enough to cause significant problems for a bank during a Fair Lending examination.
All of the previous examples assumed that the identification of Hispanic and white nonHispanic borrowers was perfect. In reality, we know that this is not perfect. The paper thought to describe the FDIC approach to estimating a borrower’s race and ethnicity is described in Using the Census Bureau’s Surname List to Improve Estimates of Race/ethnicity and Associated Disparities. The paper lists correlations of 0.7 for identification of black borrowers, 0.76 for nonHispanic white/other and 0.82 for Hispanic borrowers which corresponds roughly to accuracy of 49%, 58% and 67% respectively. If through identification errors, nonHispanic whites (some of whom have preferential loan rates) are mixed in with blacks or Hispanic borrowers who do not have preferential loan rates, how does this alter the number of preferential loans needed to reach a pvalue of 0.01 and an average rate difference of 0.25%?
Figures 21 and 22 show the region where enforcement action is likely for four scenarios where the fraction of Hispanic correctly identified is varied from 100% to 70% and the fraction of white nonHispanic borrowers is varied from 100% to 60%. Generally, as accuracy decreases the likely enforcement region relaxes upward and to the right.
Although this simulation is a binary example between two populations, it illustrates a possible cause for the anecdotal observation that there are few enforcement actions involving disparate pricing for blacks; the lower accuracy of the the racial/ethnic identification of blacks relaxes the enforcement region significantly to the right. From high to low, the relative accuracy of identification is Hispanic, nonHispanic white and black. This makes it more likely that enforcement will occur for disparate pricing to a Hispanic population than to a black population.
The simulation was run 20 times with a different random number seed each timethink of this as running the simulation using portfolios from many banks. The discontinuities in the various curves (especially the 70%/60% curve) are due to the variability of the data. In a single bank, a small number of loans could move the bank from the nonenforcement region into the enforcement region.
Table 5 shows the number of portfolios from this simulation where the 70%/60% curve crosses below the 100%/100% curve; these a particular portfolios where an enforcement action might occur when perfect race/ethnicity identification would not cause it to occur. The inaccuracy in race/ethnicity assignment makes it much less likely that most banks would face enforcement, but for a small number of banks, enforcement could occur when it would not occur with perfect race/ethnicity identification.
Total Simulations  20 
Simulations where 70%/60% Identification Curve More Strict than Perfect 100%/100% Identification Curve  0 
Percent Simulations with 70%/60% Identification Curve More Strict than Perfect 100%/100% Identification Curve  0% 
The differences in Figures 23/24 and 25/26 illustrate the variability introduced by having a small nonHispanic white population and a large Hispanic population. Figure 24 (varying correct identification of the Hispanic population) shows curves that are not smooth and which have some discontinuities, while Figure 26 (varying correct identification of nonwhite Hispanic population) shows curves that are very smooth. Incorrectly identifying a few Hispanic borrowers as nonHispanic white results in significant changes in the interest rate distribution of the small nonHispanic white population, while incorrectly identifying a nonHispanic white as Hispanic does not significantly alter the interest rate distribution of the Hispanic population. The differences in these two figures emphasizes how a small number of preferential loans in a small nonHispanic white population can quickly move a bank from the nonenforcement region to the likely enforcement region.
The examples in this article are grossly simplified from a real case in a few ways:
Figure 7 shows that if the preference is small, disparate treatment could occur frequently (though not necessarily materially) without rising to the level of enforcement using what is currently understood to be the FDIC threshold for enforcement. When this characteristic is combined with the inaccuracy of race/ethnicity identification for some groups, disparate treatment could be pervasive for some groups without rising to the level of enforcement.
Figures 7, 8, 9 and 10 show that there is no difference between a small but widespread preference and a large but unusual preference. Most people would view these cases very differently; most would agree that widespread small preference is probably more worthy of enforcement than infrequent large preference; in the latter case, the vast majority of nonHispanic whites who didn't get the preferential rate will be just as angry as Hispanic borrowers that did not get the preferential rate.
It is clear in Figures 21 and 22 that the inaccuracy in race/ethnicity identification relaxes the enforcement region for most banks, but that it can lead to a small number of scenarios where enforcement could occur when perfect identification would not cause enforcement.
Figures 22 and 26 show that when the accuracy of identification is higher for Hispanic borrowers than nonHispanic whites, there is a wide degree of overlap in the 95% confidence intervals for the perfect identification scenario and for the 70%/60% correct identification scenario. In Figures 21/22 and 25/26, it is clear that for some portfolios, enforcement would occur due to errors in identification when enforcement would not occur with perfect identification.
If this is the procedure used for race/ethnicity identification, then enforcement actions could occur in some circumstances where they should not occur. For banks that are aggressive in working to identify problems before an examination, this presents further frustration. The easiest way to estimate race/ethnicity is to purchase data from a third party provider. Since some third party data includes selfreported race and ethnicity, it is likely more accurate than the procedure thought to be used by the FDIC. With the more accurate identification, the bank's work might not find disparate treatment when the FDIC ends up finding disparate treatment due inaccuracy of the race and ethnicity estimation.
The inaccuracy in the identification of blacks makes it unlikely that even widespread disparate treatment would rise to the level of enforcement. Blacks who are descended from slaves frequently have the same surname as the nonHispanic white slaveholder; surnames do not provide useful information for race/ethnicity identification in this case, resulting in some number of black borrowers being misidentified as nonHispanic white borrowers. This makes it unlikely that pervasive disparate treatment of black borrowers would be identified.
Given that churches, synagogues, mosques and many other religious and social institutions have very strong immigration histories and resulting race and ethnicity patterns, if a bank's workforce is disproportionately nonHispanic white and the bank allows relationshipbased price negotiation, the bank can unintentionally have a disparate treatment pricing problem that is statistically significant. If a bank’s workforce is predominately nonHispanic white and the borrower pool for a product is predominately Hispanic, the bank is a higher risk for an unintentional disparate treatment problem. There are a couple of actions that a bank can take to avoid problems:
If your bank is subject to a finding of disparate treatment there are a few things from an analytical standpoint that you should do in response:
There is the old saying “there are lies, damned lies and statistical lies;” in discussions of regulatory use of statistics in Fair Lending analysis, bankers who avoid learning statistical terminology do themselves, their bank and their customers a disservice. A banker that ignores the issues of workforce racial and ethnic composition in a racially and ethnically selfsegregated community does the bank and the bank’s customers a disservice. When a regulator uses inaccurate borrower race/ethnicity identification and arrives at a finding of statistically significant disparate treatment, the regulator should take steps to confirm that enforcement would not occur with perfect race/ethnicity identification.
The simulations discussed in this article show that it is disturbingly easy to have a statistically significant disparate treatment problem that is not material and that the enforcement region is very nebulous and can vary by a factor of 2 due to the misidentification errors in the procedures used to estimate race and ethnicity.
Deriving a closedform equation to estimate the probability of enforcement when perfect race/ethnicity identification would not cause enforcement would be useful, as would graphical models to illustrate the characteristics of more racially complex populations than were considered here.
The charts in this article were prepared using R, RStudio and the knitr package to integrate text and statistical analysis. The charts use the ggplot2 package. Multicore parallel processing for the simulations uses the doMC package.
Run Time:
print(proc.time()  startTime)
## user system elapsed ## 11545.773 215.456 2250.363
Whether your institution sets pricing by a variation of cost of funds plus target, or by demandbased optimization, it is important to use the correct cost of funds in the calculation–a single cost of funds cannot be used for all loan products. A 30year mortgage and a 5year auto loan have very different interest rate risk characteristics, just as they have very different credit risk characteristics. The cost of hedging interest rate risk must be included in the cost of funds in order to accurately compare the profitability of different loan types in the same way that cost of hedging credit risk is included in the loan price.
The article that follows describes how to calculate a cost of funds for a loan product that includes the cost of hedging interest rate risk. The article is divided into the following sections:
Hedging interest rate risk requires either funding the loan with deposits that will mature on the same schedule that the loan will pay down or purchasing an interest rate swap or some other instrument to hedge the interest rate risk. Performing the calculation with the funding approach is much easier; in this approach the interest rate risk weighted cost of funds is the average of the deposit yield curve weighted by the the principal payment schedule for the loan product. A better name might be the “paydown weighted cost of funds.”
Unfortunately, even this approach requires some knowledge of a derivative call an interest rate swap; swaps are perhaps the best publicly available estimate for the top of the certificate of deposit market, and are thus the easiest way to come up with a deposit yield curve. Swap rates are very useful in transfer pricing and interest rate risk calculations, so it is important to understand how they work.
In an interest rate swap, two parties enter into a contract to pay one another the interest on a fixed balance: party A pays party B the current floating market interest rate, usually London Interbank Overnight Rate (LIBOR) while party B pays party A a fixed interest rate negotiated at the start of the contract. The two institutions “swap” their interest rates to hedge their respective interest rate risks. If party A has a term CD deposit, but a floating rate loan, party A will lose money in a falling rate environment. With a swap, as rates fall, party A will pay less but continue to receive the fixed rate on the swap which will offset the loss in margin on the loan. Similarly, if party B has floating rate deposits and fixed rate loans, party B will lose money as rates rise. With a swap, party B will receive more from the swap as rates rise which will offset the losses on the fixedrate loan.
If implemented correctly, swaps can be an effective tool in hedging interest rate risk. Implemented incorrectly or when used speculatively, they can bankrupt an institution.
Because swap contracts are readily available and have an established market, it is rare that an institution would pay significantly more than the market swap rate on CD products as part of a funding program. Small institutions may pay about 40 basis points over swap rates in various fees to wholesale providers, but it is unusual for an institution to go any higher in pricing CDs. Swap rates are the best rate to use for transfer prices and interest rate hedging calculations because a bank can both buy and sell funds at this price. The remaining calculations use swap rates to calculate the interest rate risk weighted cost of funds.
The first step in calculating the interest rate risk weighted cost of funds is determining the risk weights–the principal payment schedule for a loan portfolio over the period when the portfolio pays down. It is important to use actual data in this calculation and to include prepayments (and chargeoffs) in the estimate. Figure 1 shows the paydown schedule for a loan pool with no prepayments, with 10% per year in prepayments and for balloon loan (50% of principal in final period) with no prepayments. For shortterm loans, estimating prepayments is not critical, but this estimate becomes more important as the length of the loan product increases.
Figure 2 shows the perperiod principal paydown up to the final period where the scale of the $20,000 balloon distorts the scale. The principal paydown amounts are the weights that will be used for the weightedaverage cost of funds.
It is important to note that the prepayment rate can change dramatically as economic conditions change; in a declining economy, prepayments due to chargeoffs increase due to job losses, and prepayments due to refinancing increase as interest rates decline. You should work to estimate prepayments as accurately as possible, but how to do that is beyond the scope of this article.
The second step in calculating the interest rate risk weighted cost of funds is to obtain a yield curve for funding sources and then interpolate values for missing portions of the curve. We need to get estimates for rates at all points on the outstanding balance curve shown in Figure 1, but interest rates are routinely available only in 1year increments. Figure 3 shows the swap rates that are available on the St. Louis Federal Reserve Bank’s FRED 2 research system for December, 2004: overnight, 1, 2, 3, 4, 5, 7, 10 and 30year. An inspection of the data points in Figure 3 shows a relatively traditional yield curve increasing rapidly in the short term and then flattening out beyond 10 years. It is instructive that the most recent “normal” yield curve occurred 10 years ago.
The easiest way to interpolate the intermediate values is to use a regression model based upon the data points available. In most cases, using a straightline regression model will give a perfectly reasonable estimate of the intermediate values, but if you have five or more data points, a quadratic, cubic or especially a spline model may work somewhat better. The sections that follow show R code for each of the methods, while Figure 4 compares the fit of the various interpolation models. Whatever interpolation approach you take, make sure to include an interest rate at or beyond the length of the loan; interpolating between points is generally quite safe, but extrapolating beyond available data is generally perilous. If the 60month swap rate were taken out, it is likely that both interpolation methods would over estimate the 60month rate by about 0.5%–a big difference.
To do the interpolation, you will need to create a data set or in R a data frame that contains the period of the observation–in this case 0, 12, 24, 36, 48, 60, 84, 120 or 360 months (variable
is the FRED2 series and period
is the numerical value for the term) and the interest rate (the value
column). Depending upon what tools you have available for the curve fitting and interpolation, you may need to add columns for the square of the period (period2
in this example) and the cube of the period (period3
in this example):
summary(swpDf)
## dateVal variable value period period2 period3 ## Min. :20041201 MSWP30 :1 Min. :2.09 Min. : 0.0 Min. : 0 Min. : 0 ## 1st Qu.:20041201 MSWP10 :1 1st Qu.:3.38 1st Qu.: 24.0 1st Qu.: 576 1st Qu.: 13824 ## Median :20041201 MSWP7 :1 Median :3.81 Median : 48.0 Median : 2304 Median : 110592 ## Mean :20041201 MSWP5 :1 Mean :3.79 Mean : 82.7 Mean : 17664 Mean : 5485056 ## 3rd Qu.:20041201 MSWP4 :1 3rd Qu.:4.29 3rd Qu.: 84.0 3rd Qu.: 7056 3rd Qu.: 592704 ## Max. :20041201 MSWP3 :1 Max. :5.25 Max. :360.0 Max. :129600 Max. :46656000 ## (Other):3
The sections below describe four different ways to fit the yield curve so that you can interpolate intermediate values. The first three are readily possible in Excel, IBM’s DB2 database management system (DBMS), Oracle’s DBMS, MySQL and PostgreSQL, but the final–and best– will probably require R or some other statistical package. Some DBMS packages allow calls to R or other statistical packages via custom programming interfaces. The various methods are discussed in the following sections:
A simple linear regression is the easiest of the interpolation methods. The R call to do this and the regression coefficients are shown below:
# # Show the results of the linear interpolation # ycM < glm(value~period,data=swpDf) ycM
## ## Call: glm(formula = value ~ period, data = swpDf) ## ## Coefficients: ## (Intercept) period ## 3.22588 0.00677 ## ## Degrees of Freedom: 8 Total (i.e. Null); 7 Residual ## Null Deviance: 6.82 ## Residual Deviance: 2.36 AIC: 19.5
The regression line is of the form
\[ \begin{aligned} \text{interpolated rate}&=&\text{(intercept + coefficient*period)} \\ &=&3.226\text{ + }0.006765\text{*period} \end{aligned} \]Similarly, the quadratic regression just adds the square of the period to the formula for the call. The R call and coefficients are shown below:
# # Show the results of the quadratic interpolation # ycM < glm(value~period+period2,data=swpDf) ycM
## ## Call: glm(formula = value ~ period + period2, data = swpDf) ## ## Coefficients: ## (Intercept) period period2 ## 2.59e+00 2.49e02 4.88e05 ## ## Degrees of Freedom: 8 Total (i.e. Null); 6 Residual ## Null Deviance: 6.82 ## Residual Deviance: 0.445 AIC: 6.47
The quadratic regression curve is of the form
\[ \begin{aligned} \text{interpolated rate}&=&\text{intercept + coefficient1*period + coefficient2*period}^2 \\ &=&2.588 \text{ + }0.02492\text{*period + }4.885e05\text{*period}^2 \end{aligned} \]Similarly, the cubic regression just adds the square and cube of the period to the formula for the call:
# # Show the results of the cubic interpolation # ycM < glm(value~period+period2+period3,data=swpDf) ycM
## ## Call: glm(formula = value ~ period + period2 + period3, data = swpDf) ## ## Coefficients: ## (Intercept) period period2 period3 ## 2.32e+00 4.39e02 2.67e04 4.66e07 ## ## Degrees of Freedom: 8 Total (i.e. Null); 5 Residual ## Null Deviance: 6.82 ## Residual Deviance: 0.156 AIC: 0.947
The cubic regression curve is of the form
\[ \begin{aligned} \text{interpolated rate}&=&\text{intercept + coefficient1*period + coefficient2*period}^2 \text{ + coefficient3*period}^3 \\ &=&2.318 \text{ + }0.04389\text{*period + }0.0002671\text{*period}^2 \text{ + }4.661e07\text{*period}^3 \end{aligned} \]The spline method is somewhat more complex. A simple description is that it does a cubic regression over portions of the data points to achieve a near perfect fit for that segment of the data, and then does another cubic regression over the next portion of the data until it has fitted the entire range of data points. The R call and output are shown below:
# # Show the results of the spline interpolation # #ycM < interpSpline(value~period,swpDf) #ycM < bs(swpDf$value) ycM < smooth.spline(swpDf$period,swpDf$value) ycM
## Call: ## smooth.spline(x = swpDf$period, y = swpDf$value) ## ## Smoothing Parameter spar= 0.5829 lambda= 2.369e12 (22 iterations) ## Equivalent Degrees of Freedom (Df): 9 ## Penalized Criterion: 1.997e14 ## GCV: 1.707e+13
The spline curve uses a cubic fit for each point, so it has four terms for each data point. Spline curves generally provide the best interpolation, but it is important to test and visualize the fit as shown in Figure 4.
Figure 4 shows the actual and interpolated values for the various curve fitting methods. For fitting and interpolation over the region of 0 to 10 years, all of the methods do a reasonable job, but when you add the 30year swap rate, only the spline method works well. For yield curve data, the spline method will generally give the best results, but it is also the most difficult to implement, as it requires a true statistics language.
The final step is to apply the risk weights obtained from the paydown curve to the yield curve. This is just a weighted average:
\[ \begin{aligned} \text{interest rate risk weighted COF}&=&\frac{\sum_{i=0}^{n} \text{(period paydown)}_i\text{*(interpolated rate)}_i}{\sum_{i=0}^{n} \text{(period paydown)}_i} \end{aligned} \]For this example, with no prepayments, the interest rate risk weighted cost of funds is 3.417% while with prepayments it is 3.295%. The total interest cost difference is $111.09 compared to a total interest income of $7522.88 for the prepayment case. Not estimating prepayments in this case would result in an error on the order of 1.477%. A difference of 0.1216% doesn't sound like much until you compare it to the return on assets for an institution, where a 0.1% difference translates into the difference between a good year and bad year. Errors in estimates for prepayments can make a significant difference as the length of the loan increases or when comparing loans of very different durations.
The balloon loan has a cost of funds of 3.703%. Comparing the balloon loan to the normal loan gives a larger but still small difference: 0.2867% which results in an interest income difference of $445.54. Accurate prepayment rates are especially important for leases and for balloon loans.
The procedure for estimating an interest rate risk adjusted cost of funds is a relatively simple calculation; in practice, the only complexity is that you must do the calculation for each product in your portfolio. Until even a few years ago, the regression and interpolation steps in the process made this a difficult task, but with the statistical capabilities in R, Python and other languages, doing this calculation is now fairly simple to automate.
Although it is not a major issue for shortterm loans, estimating prepayments accurately becomes increasingly important as the term of a loan product increases. It is impossible to completely hedge interest rate risk due to uncertainty in prepayments, but getting a good estimate to start out can help significantly in hedging interest rate risk, and ensuring that this risk is priced into the loan product.
The charts in this article were prepared using R, RStudio and the knitr package to integrate text, calculated values and graphics. The charts use the ggplot2 package. Interest rates for the swap rate data on the St. Louis Federal Reserve Bank Fred2 system were obtained using the fredSeries command in the FinCal package.
The formula displays in this example are formatted using MathJax. If the formulas do not display in a recognizable way, you should check your browser to make sure that JavaScript is enabled; MathJax requires JavaScript to render the equations. If you want to copy the math displays, right click on the equation and you will get a menu of options. MathML can be imported into many versions of Microsoft Word by copying the MathML to the clipboard and pasting it into Word using the "Keep Text Only" paste option. It can also by copied and pasted in LaTeX format.
## user system elapsed ## 4.248 0.080 6.740
Good pricing and asset and liability management decisions require uptodate relevant economic information. The econometric charts that follow are generated automatically in R using data pulled from the FRED2 data repository of the St. Louis Federal Reserve. For authoritative data, please refer directly to the FRED2 system.
]]>A couple of weeks ago, the Independent Bankers Association of Texas (IBAT) asked members for stories on regulation problems that the Association’s leadership could use in lobbying efforts to support the passage of the TAILOR act and other efforts to roll back some of the provisions of DoddFrank. I decided to write an article on the subject rather than just a letter, to at least get some search engine optimization value for the time spent.
My primary product, a loan rate sheet profit optimization tool, has not sold. People with quantitative backgrounds are very excited about what I am doing, but bankers are not. The primary reason for this is my poor sales ability, but when I speak to bankers, they clearly understand what I am doing and then state “but that isn’t how we do business.” At the 2014 IBAT Convention, the exhibit hall was poorly arranged and few bankers were hanging out with the vendors who were exhibiting, so I had a chance to have some extended conversations with several accountants and other vendors with no bankers present. I got some disheartening, but ultimately very helpful comments:
How did this happen? In today’s banking world, you can still see the vestiges of the pre1980 era when interest rates were regulated and banks competed strictly on customer service and personal relationships; community bankers today overwhelming come up through the loan sales ranks rather than operational or financial career paths. The sales career path is how they do business. This vestige of the pre1980 era manifests itself with bankers who do not have strong quantitative skills by the standards of current business practice, and are less prepared to recognize, adapt or adopt new technologies than are managers in other industries. Until someone with a strong quantitative background gets to Clevel at a bank, the prospects are not good for quantitative approaches like mine. As one person said of my business prospects, “waiting for someone to die is not a good business strategy.”
After the passage of DoddFrank, Community Bankers have been overwhelmed with the volume of regulation and regulatory change. While I am not an expert on the specific changes, I have heard of numerous examples of regulations that clearly address abusive practices at highvolume toobigtofail banks, but which make no sense for lowvolume small banks where loan officers have very visible and personal responsibility for the loans they sell. I have commented that bankers are so consumed with regulatory change that the building could be burning down and they would not notice.
Interest rate regulations from a generation ago did not require bankers with quantitative skills and have constrained the current pool of executives to those without strong quantitative backgrounds; current regulations, and regulatory churn require executives with legal and compliance skills but not the analytical and quantitative skills that are used by executives in virtually all other industries. Current regulations will constrain the executive pool for the next generation to executives with legal, but not quantitative skills. This will continue to make it difficult for banks to even think about the future even when forwardthinking leadership is in place. For vendors like me, this means that getting traction will be difficult until the succession of past regulatedrate era executives is complete and the analyticsera executives are not tied up with regulatory spaghetti.
In recent years, Fair Lending regulation has focused on disparate impact where a bank can be penalized for policies or procedures that have disparate impact for different racial and ethnic groups even when there was no intent to discriminate. While I have not met any bankers that I believe were racist, I think that unintentional racially disparate pricing is probably far more common than anyone would like to admit; read the discussion in How a Bank Can Get in Trouble with Fair Lending Statistical Analysis for an understanding of why price discrimination is probably common for minority borrowers even without intentional discrimination on the part of bankers.
Some bank lobbyists hope to require that regulators show that the bank intended to discriminate against minorities in order to trigger a Fair Lending violation. I think this approach is wrong and shortsighted. The problem with the current regulatory approach stems not from being laborious; the problem is that current methods will not readily identify banks that do have price discrimination problems and sometimes falsely identify a bank as having a Fair Lending problem. Changing the regulatory standards to require “intent” for a violation will not improve the accuracy of identifying instances where discrimination is occurring, nor will it reduce the labor required for analysis. Requiring intent for a violation would probably increase the labor required for both regulators and bankers without improving the situation for borrowers who have experienced racerelated price discrimination.
Banks will make much more progress in reducing the regulatory burden and the fights over regulation by admitting that minorities do face unintentional discriminatory pricing and then working to eliminate the causes of discriminatory pricing. About 20 years ago, the Wall Street Journal published an article about different approaches taken by medical professional societies to reducing malpractice insurance (if you do not have a WSJ subscription, How Anesthesiologists Reduced Medical Errors provides a summary). The association with the highest premiums, anesthesiologists, took the approach of studying anesthesiarelated deaths and changing practice to reduce deaths. All other associations took the approach of pursuing legal limits on malpractice insurance. Anesthesiologists ultimately ended up with the lowest insurance rates. Bankers should take the same approach; admit the problem and fix it.
The current approach depends upon an errorprone estimate of a borrower’s race and ethnicity; the current surname and geographic race estimation method is especially errorprone for blacks descended from slaves. The errors effectively hide discriminatory pricing when it occurs.
One possible approach would be to offer a safeharbor for loan products where no rate negotiation is allowed; compliance could then be measured by auditing applications for accurate pricing classification. When a pricing classification error is noted, two things would occur:
Banks need to recognize that there are problems and address them, or plan for additional generations of fighting related regulatory oversight.
Indirect lending is perhaps the highest risk area for Fair Lending violations, but it is one where current regulatory practices will not identify a dealer that is intentionally discriminating against minorities; a discriminatory dealer’s loans are diluted with loans from nondiscriminating dealers so that analysis at the bank level will not identify the problem dealer (unless the dealer decides to intentionally create problems for a bank). Analysis of loans at the dealer level must occur to fix this problem.
]]>US House Resolution 3072 would increase the minimum size of banks that are subject to direct examination by and reporting to the Consumer Financial Protection Bureau (CFPB) from $10 billion in assets to $50 billion in assets. As of June, 2017, this would exempt about 80 banks from the examination and reporting rules and leave about 40. I am opposed to this legislation for three reasons:
Although I am opposed to this legislation, I am not strongly opposed for the simple reason that most of the mischief during the financial crisis occurred at the “too big to fail” banks, and this does not exempt those banks from CFPB examination.
The current $10 billion threshold is about the 98th percentile in assets ($10.7 billion), while the proposed $50 billion threshold is above the 99th percentile ($30 billion). These are not small banks with a small staff. Figure 1 shows employment by bank as a function of asset value. There are few banks of $10 billion with fewer than 1,000 employees, so these banks already have fulltime compliance staff; this does not present the disproportional regulatory burden that it would for banks with less than 1,000 employees. Although this legislation would remove some oversight for some arguably large banks, it leaves in place oversight for the largest banks in a system that is badly skewed to very large banks. To understand the relative size of of banks in the US, Figure 2 shows the asset size distribution–even though it represents more than 5,800 banks the chart looks like an error due to the vast empty space in the right 90% of the histogram. Figure 3 shows only banks larger than $10 billion (about 120 of 5,800) and points out the dramatic skew in bank size.
When legislation is written with arbitrary dollar limits as this bill uses, it means that normal inflation will push banks (or taxpayers in the case of the Alternative Minimum Tax) over the threshold when nothing has changed in terms of bank operations. Inevitably, the legislature is slow to reset the threshold, and institutions and consumers struggle to deal with a regulation that was never intended to apply to them. This legislation perpetuates that problem. It guarantees business for lobbyists, but is not a good way to write laws.
For businesses serving the banking industry, regulatory instability is probably a bigger problem than regulatory burden. If regulation is stable, you can automate the solutions, and banks can buy an inexpensive solution. If regulation is unstable, it cannot be automated and the management burden at a bank prevents the bank from innovating any way; the focus is on how to stay in compliance in a changing compliance world. This type of regulatory threshold is ultimately unstable for a larger number of institutions than other approaches.
There are at least two better thresholdbased approaches:
Some banks just do not touch consumers, and examinations by the CFPB just do not make sense. Table 1 shows the banks that were above $10 billion at the end of June, 2017. There are clearly some banks in this list that have wholesale models where the word “consumer” just does not apply. Figuring out legislation that would take this approach is probably beyond the capability of any legislative body in the United States, so this is probably not a realistic approach, though it would be the best.
Table 1. List of Banks with Assets Greater than $10B  
Bank  City  State  Assets ($1K)  Deposits ($1K)  Employees  Web Site 

WELLS FARGO BANK, NATIONAL ASSOCIATION  SIOUX FALLS  SD  1,673,246,000  1,237,791,000  237,944  http://www.wellsfargo.com 
JPMORGAN CHASE BANK, NATIONAL ASSOCIATION  COLUMBUS  OH  1,631,896,000  1,270,117,000  189,315  http://www.jpmorganchase.com 
BANK OF AMERICA, NATIONAL ASSOCIATION  CHARLOTTE  NC  1,611,631,000  1,270,151,000  143,354  www.bankofamerica.com 
CITIBANK, N.A  SIOUX FALLS  SD  851,012,000  474,780,000  175,473  www.citibank.com 
U.S. BANK NATIONAL ASSOCIATION  CINCINNATI  OH  448,673,608  329,468,253  70,522  http://www.usbank.com 
PNC BANK, NATIONAL ASSOCIATION  WILMINGTON  DE  357,293,517  257,675,713  51,679  www.pnc.com 
CAPITAL ONE, NATIONAL ASSOCIATION  MC LEAN  VA  280,164,033  220,751,261  30,163  www.capitalone.com 
TD BANK, N.A  WILMINGTON  DE  268,184,699  227,051,124  25,096  www.tdbank.com 
BRANCH BANKING AND TRUST COMPANY  WINSTON SALEM  NC  215,064,000  163,093,000  35,503  www.BBT.com 
SUNTRUST BANK  ATLANTA  GA  202,481,382  162,671,910  22,464  http://WWW.SUNTRUST.COM 
HSBC BANK USA, NATIONAL ASSOCIATION  MC LEAN  VA  188,763,813  128,153,520  5,708  www.banking.us.hsbc.com 
BANK OF NEW YORK MELLON, THE  NEW YORK  NY  175,879,000  126,191,000  41,578  www.bnymellon.com 
CHARLES SCHWAB BANK  RENO  NV  175,657,000  162,367,000  612  www.schwabbank.com 
STATE STREET BANK AND TRUST COMPANY  BOSTON  MA  156,181,432  79,114,517  31,940  http://www.statestreet.com 
GOLDMAN SACHS BANK USA  NEW YORK  NY  151,219,000  105,886,000  992  www.gsbank.com 
FIFTH THIRD BANK  CINCINNATI  OH  138,297,752  104,809,057  17,695  https://www.53.com 
CHASE BANK USA, NATIONAL ASSOCIATION  WILMINGTON  DE  134,893,661  41,856,629  9,492  http://www.chase.com 
KEYBANK NATIONAL ASSOCIATION  CLEVELAND  OH  133,501,414  105,344,214  19,017  www.key.com 
ALLY BANK  MIDVALE  UT  126,005,000  86,256,000  6,880  http://www.ALLY.com 
REGIONS BANK  BIRMINGHAM  AL  123,716,371  99,191,861  21,350  http://www.regions.com 
MANUFACTURERS AND TRADERS TRUST COMPANY  BUFFALO  NY  120,357,682  94,979,081  16,039  http://www.mtb.com 
CITIZENS BANK, NATIONAL ASSOCIATION  PROVIDENCE  RI  120,137,787  87,914,988  14,828  www.citizensbank.com 
MUFG UNION BANK, NATIONAL ASSOCIATION  SAN FRANCISCO  CA  116,550,535  86,832,006  12,221  www.unionbank.com 
MORGAN STANLEY BANK, N.A  SALT LAKE CITY  UT  116,382,000  100,032,000  344  NA 
CAPITAL ONE BANK (USA), NATIONAL ASSOCIATION  GLEN ALLEN  VA  107,203,368  66,210,077  22,446  www.capitalone.com 
BMO HARRIS BANK NATIONAL ASSOCIATION  CHICAGO  IL  106,192,025  76,880,136  12,277  http://www.bmoharris.com 
HUNTINGTON NATIONAL BANK, THE  COLUMBUS  OH  101,280,420  77,936,696  15,070  www.Huntington.com 
DISCOVER BANK  GREENWOOD  DE  92,584,050  55,200,692  12,353  www.discover.com 
NORTHERN TRUST COMPANY, THE  CHICAGO  IL  87,267,889  36,878,232  17,292  www.northerntrust.com 
BANK OF THE WEST  SAN FRANCISCO  CA  86,911,273  64,078,723  10,094  www.bankofthewest.com 
COMPASS BANK  BIRMINGHAM  AL  83,946,716  66,222,248  9,837  www.bbvacompass.com 
FIRST REPUBLIC BANK  SAN FRANCISCO  CA  80,978,231  63,293,706  3,881  www.firstrepublic.com 
USAA FEDERAL SAVINGS BANK  SAN ANTONIO  TX  80,557,577  72,000,203  7,295  www.usaa.com 
SANTANDER BANK, NATIONAL ASSOCIATION  WILMINGTON  DE  79,360,980  57,291,082  9,448  www.santander.com 
SYNCHRONY BANK  DRAPER  UT  73,668,489  56,205,604  9,897  WWW.SYNCHRONYFINANCIAL.COM 
COMERICA BANK  DALLAS  TX  70,917,599  57,342,295  7,305  www.comerica.com 
ZB, NATIONAL ASSOCIATION  SALT LAKE CITY  UT  65,276,867  52,785,401  10,007  http://www.zionsbank.com 
MORGAN STANLEY PRIVATE BANK, NATIONAL ASSOCIATION  PURCHASE  NY  60,560,000  49,564,000  610  NA 
UBS BANK USA  SALT LAKE CITY  UT  52,817,587  46,982,008  341  http://www.ubs.com/cefs/en/ubsbankusa/ubsbankusa.html 
AMERICAN EXPRESS BANK, FSB  SALT LAKE CITY  UT  49,860,950  40,485,436  106  http://www.americanexpress.com 
CITY NATIONAL BANK  LOS ANGELES  CA  46,210,687  40,770,707  4,305  http://www.cnb.com 
SILICON VALLEY BANK  SANTA CLARA  CA  46,102,989  39,843,834  2,310  www.svb.com 
E*TRADE BANK  ARLINGTON  VA  45,504,146  40,344,566  47  www.etrade.com 
NEW YORK COMMUNITY BANK  FLUSHING  NY  44,762,686  26,330,850  2,022  https://www.mynycb.com 
DEUTSCHE BANK TRUST COMPANY AMERICAS  NEW YORK  NY  44,195,000  32,634,000  585  http://www.db.com 
PEOPLE'S UNITED BANK, NATIONAL ASSOCIATION  BRIDGEPORT  CT  42,705,802  32,064,694  5,233  www.peoples.com 
CIT BANK, NATIONAL ASSOCIATION  PASADENA  CA  41,181,081  31,912,428  3,699  cit.com 
SIGNATURE BANK  NEW YORK  NY  40,718,610  33,173,195  1,251  http://www.signatureny.com 
AMERICAN EXPRESS CENTURION BANK  SALT LAKE CITY  UT  37,010,205  19,283,445  294  http://www.americanexpress.com 
CITIZENS BANK OF PENNSYLVANIA  PHILADELPHIA  PA  35,666,791  30,178,882  2,885  www.citizensbank.com 
FIRSTCITIZENS BANK & TRUST COMPANY  RALEIGH  NC  34,599,352  29,483,243  6,665  https://www.firstcitizens.com 
EAST WEST BANK  PASADENA  CA  34,024,016  29,489,477  2,872  http://www.eastwestbank.com 
TIAA, FSB  JACKSONVILLE  FL  32,773,078  23,115,407  3,300  www.everbank.com 
BOKF, NATIONAL ASSOCIATION  TULSA  OK  32,318,943  22,549,197  4,680  www.bokfinancial.com 
BANCO POPULAR DE PUERTO RICO  SAN JUAN  PR  31,585,000  26,777,000  6,539  http://www.popular.com 
BARCLAYS BANK DELAWARE  WILMINGTON  DE  30,811,587  21,369,027  3,387  www.barclaysus.com/deposits 
FIRST NATIONAL BANK OF PENNSYLVANIA  GREENVILLE  PA  30,561,411  21,229,104  4,321  www.fnbonline.com 
SYNOVUS BANK  COLUMBUS  GA  30,534,286  25,465,778  4,094  www.synovus.com 
FROST BANK  SAN ANTONIO  TX  30,227,278  25,665,873  4,253  http://www.frostbank.com 
ASSOCIATED BANK, NATIONAL ASSOCIATION  GREEN BAY  WI  29,703,427  21,867,226  4,365  www.associatedbank.com 
FIRST TENNESSEE BANK NATIONAL ASSOCIATION  MEMPHIS  TN  29,176,534  22,621,047  4,112  http://www.firsttennessee.com 
BANKUNITED, NATIONAL ASSOCIATION  MIAMI LAKES  FL  28,909,570  20,949,969  1,686  http://www.BankUnited.com 
WHITNEY BANK  GULFPORT  MS  26,539,923  21,526,679  4,076  www.hancockwhitney.com 
WEBSTER BANK, NATIONAL ASSOCIATION  WATERBURY  CT  26,167,932  20,554,212  3,256  http://www.websteronline.com 
UMPQUA BANK  ROSEBURG  OR  25,220,026  19,566,602  4,342  https://www.umpquabank.com/ 
COMMERCE BANK  KANSAS CITY  MO  24,970,053  20,955,595  4,705  www.commercebank.com 
INVESTORS BANK  SHORT HILLS  NJ  24,324,696  16,352,535  1,943  www.myinvestorsbank.com 
VALLEY NATIONAL BANK  PASSAIC  NJ  23,413,583  17,303,067  2,902  valleynationalbank.com 
BNY MELLON, NATIONAL ASSOCIATION  PITTSBURGH  PA  23,272,288  18,930,200  1,958  www.bnymellon.com 
TEXAS CAPITAL BANK, NATIONAL ASSOCIATION  DALLAS  TX  23,109,493  17,506,254  1,501  www.texascapitalbank.com 
PROSPERITY BANK  EL CAMPO  TX  22,286,297  17,101,925  3,037  http://www.prosperitybankusa.com 
PRIVATEBANK AND TRUST COMPANY, THE  CHICAGO  IL  22,284,353  19,255,774  1,358  www.theprivatebank.com 
PACIFIC WESTERN BANK  BEVERLY HILLS  CA  22,223,332  17,366,146  1,696  https://www.pacificwesternbank.com/ 
TD BANK USA, NATIONAL ASSOCIATION  WILMINGTON  DE  22,215,091  18,872,549  75  http://www.tdbank.com 
TCF NATIONAL BANK  SIOUX FALLS  SD  21,756,559  17,655,784  5,889  http://www.tcfbank.com 
IBERIABANK  LAFAYETTE  LA  21,713,975  17,738,360  2,941  http://www.iberiabank.com 
BANK OF AMERICA CALIFORNIA, NATIONAL ASSOCIATION  SAN FRANCISCO  CA  21,567,000  17,719,000  0  NA 
PINNACLE BANK  NASHVILLE  TN  20,765,252  15,800,346  2,263  http://www.pnfp.com 
RAYMOND JAMES BANK, NATIONAL ASSOCIATION  SAINT PETERSBURG  FL  20,101,873  17,418,199  212  www.raymondjamesbank.com 
UMB BANK, NATIONAL ASSOCIATION  KANSAS CITY  MO  20,081,185  16,240,966  2,787  www.umb.com 
BANK OF THE OZARKS  LITTLE ROCK  AR  20,068,595  16,241,570  2,395  http://www.bankozarks.com 
MB FINANCIAL BANK, NATIONAL ASSOCIATION  CHICAGO  IL  19,874,009  14,281,176  3,478  www.mbfinancial.com 
FIRST NATIONAL BANK OF OMAHA  OMAHA  NE  19,518,079  16,159,398  4,667  www.firstnational.com 
FIRST HAWAIIAN BANK  HONOLULU  HI  19,497,364  16,143,601  2,191  http://www.fhb.com 
SALLIE MAE BANK  SALT LAKE CITY  UT  19,335,095  14,307,988  1,485  www.salliemaebank.com 
WESTERN ALLIANCE BANK  PHOENIX  AZ  18,748,070  16,082,923  1,647  http://www.westernalliancebank.com 
CHEMICAL BANK  MIDLAND  MI  18,730,163  13,227,524  3,364  http://www.chemicalbank.com 
ARVEST BANK  FAYETTEVILLE  AR  17,298,302  14,984,820  5,820  www.arvest.com 
FIRSTBANK  LAKEWOOD  CO  17,274,585  15,619,162  2,413  http://www.efirstbank.com 
STATE FARM BANK, FSB  BLOOMINGTON  IL  17,203,912  11,507,096  2,390  www.statefarm.com/finances/banking 
SCOTTRADE BANK  TOWN AND COUNTRY  MO  17,008,138  15,592,844  143  www.scottrade.com 
BANK OF HAWAII  HONOLULU  HI  16,456,854  13,859,935  2,142  www.boh.com 
FLAGSTAR BANK, FSB  TROY  MI  15,890,503  9,023,774  3,432  www.flagstar.com 
STERLING NATIONAL BANK  MONTEBELLO  NY  15,344,598  10,567,551  997  www.snb.com 
WASHINGTON FEDERAL, NATIONAL ASSOCIATION  SEATTLE  WA  15,084,501  10,667,533  1,815  www.washingtonfederal.com 
OLD NATIONAL BANK  EVANSVILLE  IN  14,863,415  10,797,561  2,411  www.oldnational.com 
BANCORPSOUTH BANK  TUPELO  MS  14,848,975  11,932,560  3,989  www.bancorpsouth.com 
MIDFIRST BANK  OKLAHOMA CITY  OK  14,547,409  7,829,551  2,479  www.midfirst.com 
ASTORIA BANK  LONG ISLAND CITY  NY  14,068,775  9,078,423  1,364  www.astoriabank.com 
CATHAY BANK  LOS ANGELES  CA  13,933,869  11,235,245  1,127  www.cathaybank.com 
STIFEL BANK AND TRUST  SAINT LOUIS  MO  13,926,601  12,057,553  176  http://www.stifelbank.com 
TRUSTMARK NATIONAL BANK  JACKSON  MS  13,907,101  10,439,499  2,858  http://www.trustmark.com 
BANK OF HOPE  LOS ANGELES  CA  13,852,962  10,968,853  1,378  http://www.bankofhope.com 
FIRST MIDWEST BANK  ITASCA  IL  13,776,789  11,080,838  2,113  http://www.firstmidwest.com 
RABOBANK, NATIONAL ASSOCIATION  ROSEVILLE  CA  13,660,000  10,381,000  1,532  www.rabobankamerica.com 
THIRD FEDERAL SAVINGS & LOAN ASSOCIATION OF CLEVELAND  CLEVELAND  OH  13,488,146  8,264,611  1,030  http://www.thirdfederal.com 
UNITED BANK  FAIRFAX  VA  13,309,359  9,168,084  1,310  www.bankwithunited.com 
APPLE BANK FOR SAVINGS  MANHASSET  NY  12,850,974  11,662,658  847  www.theapplebank.com 
BREMER BANK, NATIONAL ASSOCIATION  SAINT PAUL  MN  11,786,183  9,709,206  1,692  http://www.bremer.com 
FIRSTBANK PUERTO RICO  SAN JUAN  PR  11,699,027  8,584,845  2,579  http://www.1firstbank.com 
COMENITY BANK  WILMINGTON  DE  11,625,835  4,258,173  571  www.comenity.net 
GREAT WESTERN BANK  SIOUX FALLS  SD  11,460,391  8,978,245  1,629  www.greatwesternbank.com 
FULTON BANK, NATIONAL ASSOCIATION  LANCASTER  PA  11,262,145  8,431,272  1,287  www.fultonbank.com 
SOUTH STATE BANK  COLUMBIA  SC  11,151,597  9,063,129  2,260  www.southstatebank.com 
CUSTOMERS BANK  PHOENIXVILLE  PA  10,864,677  7,538,543  781  www.customersbank.com 
CENTENNIAL BANK  CONWAY  AR  10,861,231  7,861,199  1,551  http://www.my100bank.com 
UNITED COMMUNITY BANK  BLAIRSVILLE  GA  10,817,173  8,820,998  1,922  www.ucbi.com 
COMMUNITY BANK, NATIONAL ASSOCIATION  CANTON  NY  10,643,289  8,703,618  2,087  www.communitybankna.com 
EASTERN BANK  BOSTON  MA  10,574,493  8,848,771  1,786  www.easternbank.com 
BANC OF CALIFORNIA, NATIONAL ASSOCIATION  SANTA ANA  CA  10,356,655  8,104,994  811  www.bancofcal.com 
CAPITAL BANK CORPORATION  RALEIGH  NC  10,101,534  8,164,389  1,691  WWW.CAPITALBANKUS.COM 