# Patent

## Title
Computer-implemented risk evaluation systems and methods

## Abstract

Computer-implemented systems and methods are disclosed herein that relate to processes, which construct an empirically derived and statistically based risk evaluation and policy formulation system. For example, a process can be configured so as to accept as input an information base in computer readable form and produce either a single or multistage system composed of alternative decision making strategies.

## Background
CROSS-REFERENCE TO RELATED APPLICATIONS
This application claims priority to and is a continuation-in-part of U.S. Provisional Application Ser. No. 60/757,648, (entitled “Computer-Implemented Risk Evaluation Systems And Methods” and filed on Jan. 10, 2006) and U.S. application Ser. No. 11/651,914, (entitled “Computer-Implemented Risk Evaluation Systems And Methods” and filed on Jan. 10, 2007) now U.S. Pat. No. 7,610,257, and claims priority to U.S. Provisional Application Ser. No. 60/991,050 (entitled “Computer-Implemented Risk Evaluation Systems And Methods” and filed on Nov. 29, 2007), of which the entire disclosures (including any and all figures) of these documents are incorporated herein by reference.


BACKGROUND AND SUMMARY
The approval and pricing process for loans and insurance has evolved into a complicated decision making process. The scope of loans covered could include, but is not be limited to, credit card, overdraft checking protection, term loans, revolving credit lines, automobile loans (both direct and indirect), mortgages, and small business loans, Types of insurance policies include, but are not restricted to, automobile, renters hazard and theft, homeowners, income continuation, life, accident, and umbrella coverage. Many variables have to be considered when making an approval and/or pricing decision, or in negotiating terms and conditions. To assist in these approvals and pricing/negotiation processes, many different approaches have been used. For example, a technique known as dynamic programming can be used which solves the problem of analyzing multiple relationships by dividing the problem into “decision stages,” working backwards from the stated objectives, solving the simplest stages first, and assembling the individual stages into a complete system only after independently solving all of the intermediate stages.
Within this disclosure, computer-implemented systems and methods are disclosed that relate to processes, which construct an empirically derived and statistically based risk evaluation and policy formulation system. For example, a process can be configured so as to accept as input an information base in computer readable form and produce either a single or multistage system composed of alternative decision making strategies. For purposes of illustration, loan approval is used as the primary example. The same methodology applies also to insurance underwriting, loan and insurance policy pricing. The methodology also allows for different approval and pricing strategies based on variations in loan or insurance policy terms and conditions. In the case of loans, this would involve factors such as loan amount tier, the term of the contract, pre-payment penalty, income documentation requirements, etc. On the insurance side, such factors as policy deductible amount, scope of coverage, valuation method for reimbursement on loss of covered items, maximum amount of payout, etc.
As another example, a system and method can be configured to evaluate risks associated with alternative strategies for assessing an entity with respect to a predetermined objective. The system and method can include an action table containing a plurality of possible actions that can be taken with respect to the predetermined objective for various entity profiles. The action table contains an action (e.g., decision) for each entity profile. One or more statistical data stores are configured to contain risk amounts associated with each entity profile and to contain inferred percentage distribution of applicants associated with each entity profile. A profile identification data store contains entity identification information for use in determining an action for the entity. An action is determined for the entity by comparing characteristics associated with the entity with characteristics associated with the entity profiles contained in the action table. An improvement data store provides an indication in the improvement in risk based upon a change in one or more characteristics for an entity profile.
As yet another example, a system and method can be configured to also include a protected class data store that provides an indication of the impact of a policy change on a particular protected class, both with respect to the approval, collection, or promotion decision and relative to one or more characteristics, or combinations of characteristics, for an entity profile.



BRIEF DESCRIPTION OF THE DRAWINGS
FIGS. 1 and 2 are diagrams of computer-implemented systems to evaluate risks associated with alternative strategies for assessing an entity with respect to a predetermined objective.
FIG. 3 illustrates a two-stage system with first and second stage action tables.
FIGS. 4-11 illustrate an example of software modules operating within a credit approval risk evaluation system.
FIGS. 12-13 illustrate systems that modify criteria for factors of the first stage if the system of FIG. 3.
FIG. 14 illustrates a system providing a software module to allow for judgmental factors to be “instilled” into a model.
FIG. 15 illustrates a two-stage action table to handle small business loans.
FIG. 16 illustrates a system that accommodates changes in policy that result in a loosening or tightening of credit.
FIGS. 17 and 18 illustrate different systems configured to include a credit adjustment process.
FIG. 19 illustrates a system that performs analyses to assess model reasonableness and gauge performance.
FIG. 20 illustrates a software module that can help examine certain statistical characteristics of cells.
FIG. 21 illustrates a software module that can examine the residual values in each cell.



DETAILED DESCRIPTION
FIG. 1 depicts at 20 a computer-implemented system to evaluate risks associated with alternative strategies for assessing an entity 80 (e.g., an individual, organization, company, etc.) with respect to a predetermined objective. More specifically, the risk evaluation system allows a decision maker 30 to select from among a number of different strategies 40 in order to arrive at a policy which is aimed at achieving a specific objective.
Each policy is specified in the form of a single, or multistage, action table 50 which functions to enumerate all possible states-of-nature (profiles) 70 along with their associated actions. In addition, the action table 50 can assign a unique reference number to every state (or profile) for cross-referencing purposes. Such cross-referencing via action table reference number(s) can have different uses depending upon the application at hand, such as being used to:
A) allow for tracking of overrides originating from declined profiles
B) alleviate the need for sampling during a system update
C) allow for special reports such as delinquency by profile
D) provide information for other marketing activities

    
    
        a) direct response promotions
        b) credit control research
        c) automated collection efforts
    
    


Accompanying the action table 50 is a set of statistical tables 60 which specify the amount of risk associated with each individual profile or cell in the action table 50. Use of these tables 60 enables the decision maker 30 to alter any given policy with a minimum of difficulty.
As depicted in FIG. 2, the risk evaluation system 20 also can provide one or more tables 90 giving the maximum improvement in risk attained by a change in a single factor for every profile corresponding to a high risk cell in the action table 50. In each case a certain number of factors (e.g., the four most significant factors) are ranked in order of importance and the resulting net gain in reduction of risk is indicated for each factor. Also indicated are the new actions which would result in each instance.
Based upon the sampled data, the risk evaluation system 20 provides a forecast 92 of how the total population will be distributed with respect to the various components which make up the total profile on any given entity. Also provided are forecasted acceptance rates by profile components and combinations thereof, as well as percentage distributions of the new acceptee population by their profile components.
A decision maker 30 follows the recommendations stated explicitly in the action table 50 (which she selects based upon the level of risk she is willing to operate at). The risk evaluation system 20 can allow the decision maker 30 to track the system's performance, as well as to alter a current policy.
The risk evaluation system 20 can be applied in many different risk-related situations, such as to analyze risk associated with credit approval, direct response promotions, credit collection, insurance underwriting, etc. As an example, consider the application of a risk evaluation system 20 to construct a credit approval system. In such a case if we had a one-step system, then the entries of the action table 50 would state “accept” or “decline” based upon the credit applicant's profile as specified by the action table 50. Two alternative policies corresponding to different action tables might be (1) minimize the credit granting institution's exposure to risk while maintaining the current acceptance rate, or (2) maximize the acceptance rate while maintaining the current bad debt rate.
If a multi-stage action situation arises in a credit approval context, then a two-stage system can be constructed as illustrated at 100 in FIG. 3 where the second stage action table 120 includes credit bureau classifications, and the first stage action table 110 would have as entries “approval”, “decline” or “investigate” (where investigate implies call the credit bureau and run a check). For those investigated, the second state action table 120 would determine the final outcome of “approve” or “decline”.
“N” stages (e.g., “N” stage 130) can be constructed. As an illustration, for a three stage system those declined at one stage proceed to the next stage until they reach the third stage for a final decision. Each credit application could be classified in all stages so as to have “N” ordered action table reference numbers associated with it. This can be used for system updating and could be done regardless of the stage at which the application is actually approved.
FIGS. 4-11 provide an example of software modules operating within a credit approval risk evaluation system. Also below is an explanation of how a risk evaluation system may be modified so as to permit the construction of multistage systems comprised of several action tables which are referenced in sequence in order to arrive at a final decision for a given situation.
With reference to the processing 200 shown on FIG. 4, module IDP-X tallies the sample population of good, bad and declined credit applicants with respect to one dimension one at a time. Input consists of one record per sampled applicant read in at a time into an integer vector, whose elements serve as pointers. The coded data base which is input to the risk evaluation system could be created in the following way:

    
    
        A) Detailed and explicit definitions are generated which serve to categorize the client's customers as being either creditworthy or non-creditworthy (i.e. good or bad) as determined by their past performance in paying their bills in a timely manner. Acceptance rates and rates for the occurrence of non-creditworthy customers can also be provided.
        B) A population performance audit is run on the client's customer master file in order to determine historical bad rates and identify and flag the good and bad risks as determined by the definitions. In cases where manual transcription of data from hardcopy loan files is required, sampling quotas are established for a statistical sampling plan and a randomized sample candidate selection process is invoked on the flagged master file yielding a specific list of accounts to be sampled. In cases where the data is available electronically, an extraction and pre-processing program is developed to gather all of the data for the time period in question and sampling is not necessary.
        C) Next, the actual sampling, or automated extraction, process is conducted, which consists of the gathering of all documents, or electronic information, pertaining to the client's current and past policies which constitute the focus of the study. This includes data from individual credit applications, credit bureau reports, corporate credit policy manuals, etc.
        D) The sampled data are reviewed clerically and then transcribed into a coded data base as specified in an accompanying set of coding instructions that have been approved by the client's credit underwriters and operations staff. If the data are already in electronic form, then the review step is all that is required to ensure the integrity of the information collected.
    
    


This input can be one record per sampled applicant are read in one at a time into an integer vector, whose elements serve as pointers. The pointers for module are used as addresses in other arrays, one for each dimension which vary in size according to the number of strata present in each. Let the integer vector be denoted as IVEC. Let the separately dimensional array for the first item in the sampled record read in be denoted as TI(5). We have that T1 corresponds to a dimension having five stratum, which are mutually exclusive and exhaustive. Hence, when a record is read in, the program tallies the proper stratum for the first item in the equation:

TI(IVEC(1))=TI(IVEC(1))+1

The other dimensions are tallied in a similar fashion.

The output from this module is in the form of a separate frequency distribution for each dimension for each behavior group. The between group variation for good and bad behavior is calculated as described in an article by Richard Light and Barry Margolin entitled, “An Analysis of Variance for Categorical Data”, which appeared in the Journal of the American Statistical Association, September 1971, Vol. 66, page 535, equation (3.4). The Kullback divergence statistic is also calculated for the good versus bad and known versus unknown groups as detailed in a book by Matthew Goldstein and William Dillon entitled Discrete Discriminant Analysis, Copyright 1978 by John Wiley & Sons, Chapter 4, Section 4.3.3, page 76, equation (4.3-13).
Example data is given throughout the discussion of FIGS. 4-11 for the various analyses produced by the modules. They are based on a fictitious client—XYZ Department Store.
A portion of the example output for this module is as follows:

    
    
        Client: XYZ Department Store
        Type of System: Credit Approval
        Month/Year: February YYYY
        Production Module: IDP-X
    
    


Characteristic Analysis by Behavior Group

















Good
Bad
Log
Known
Unknown
Log

















Dept. Store Ref.
Count
PCNT
Count
PCNT
Odds
Count 
PCNT
Count
PCNT
Odds




















NONE
337
45.6
406
55.8
−0.20
783
50.4
440
65.0
−0.25


ONE or MORE
449
54.4
322
44.2
0.21
771
49.6
264
35.0
0.35









Between Group Variation for Good and Bad Behavior . . . 3.95

Kullback Divergence Statistic Good vs. Bad 0.041 Known vs. Unknown 0.088


















Good
Bad
Log
Known
Unknown
Log

















Bank Ref.
Count
PCNT
Count
PCNT
Odds
Count
PCNT
Count
PCNT
Odds




















NONE
67
8.1
171
23.5
−1.06
238
15.3
189
25.1
−0.49


SAVINGS
92
11.1
156
21.4
−0.65
248
16.0
119
15.8
0.01


CHECKING
219
26.5
163
22.4
0.17
382
24.6
165
21.9
0.12


BOTH
448
54.2
238
32.7
0.51
686
44.1
281
37.3
0.17









Between Group Variation for Good and Bad Behavior . . . 32.07

Kullback Divergence Statistic Good vs. Bad 0.347 Known vs. Unknown 0.063

The columns entitled “LOG ODDS” were calculated by taking the natural logarithms of the quotient of the first and second figures in the corresponding “PCNT” (percent) columns. The statistical measures described help the analyst to do a quick “eyeball estimation” of the predictive content of each characteristic. This report provides a check on down stream processing which should be fairly consistent with these results. However, IDP-X gives a one dimensional look at the sampled data and hence interdependencies cannot be taken into account by this analysis. It represents a first look at the data.

Processing 250 involving module VSP-X is next performed for this example as shown in FIG. 5. (A program flow for this module can be constructed as discussed in the aforementioned U.S. Provisional Application Ser. No. 60/757,648.) Module VSP-X is a stepwise variable selection procedure that is not restricted to dichotomous responses and that has the desirable property of deleting a variable, once selected, at a later stage. The method is due to J. M. Lachin [1973] “On a stepwise procedure for two population Bayes decision rules using discrete variables,” Biometrics, 29, pages 551-564. Also refer to discussion in Goldstein and Dillon (previously cited on page 22) Chapter 4, Section 4.3.2, pages 73-75 and Chapter 6, Section 6.6, pages 153-168.
Processing 400 involving module PEP-X is next performed for this example as shown in FIG. 7. The computer module PEP-X derives maximum likelihood estimates for the parameters in a given model. The current version accomplishes the task in up to four dimensions and requires 752K bytes of core memory to execute. In addition, standardized parameter estimates and variances are calculated for main, first and second order effects. Reference: article by Leo A. Goodman in Technometrics, Volume 13, Number 1, February 1971, page 38, equation (11).
A portion of the report generated by PEP-X would look as follows:
Behavior Group Bad
Number of Dimensions 6
Number of Strata within each dimension 2 2 2 2 3 4 0
Number of Cells in the 6 dimensional table 192












No.
Dimension Name
Strata Labels




















1
DEPT. STR
NONE
ONE-UP




2
OIL CO.
NONE
ONE-UP




3
MAJOR CC
NO
YES




4
HOUSING
RENT/OTH
OWN/BUY




5
MO. INC.
$0-900
901-1499
$1500-UP



6
BANK REF
NONE
SAVE
CHECK
BOTH









The Grand Mean Effect is 0.903501











MAIN EFFECT TERMS











MODEL 




PARAMETER 



DIMENSION
VALUES





RAW
1
0.038270-0.038270


ASYMPTOTIC VARIANCE
1
0.002840 0.002840


STANDARDIZED
1
0.718164-0.718164



















THIRD ORDER INTERACTION TERMS














TERM
I
J
K
L
PARAMETER


















1234
1
1
1
1
0.010614




1
2
1
1
−0.010615




2
1
1
1
−0.010621




2
2
1
1
0.010612






.








.








.





3456
1 
1 
1 
1 
−0.093943




1
1
2
1
0.039539




1 
1 
3 
1 
0.040584




1
2
1
1
0.093937




1
2
2
1
−0.067981




1 
2 
3 
1
−0.040585






.








.








.










Processing 300, 500, and 600 involving module MEP-X is next performed for this example as shown in FIGS. 6-8. MEP-X sequentially evaluates alternative hierarchical log-linear models for a given set of data. It utilizes an iterative procedure to obtain maximum likelihood estimates of the theoretical values postulated by a given model. This procedure is carried out subject to possible user-specified constraints that certain fixed margins be preserved in the final solution. Two different tests for checking the goodness-of-fit of a particular model are employed. The first is the simple generalization of the Pearson chi-square test statistic, and the second is the likelihood ratio chi-square test statistic. Both have the same asymptotic chi-square distribution. The likelihood-ratio test statistic is also used in the process of selecting a suitable model, via the technique of partitioning.
In addition to providing the fitted cell estimates, the module can also be configured to supply the corresponding standardized residuals as an aid to subsequent analysis. Also a numerical subroutine can be used to compute the chi-square probabilities of the goodness-of-fit statistics, thus alleviating the user of the necessity of making repeated table look-ups for these values.
In the event the user seeks to evaluate a model or data exhibiting structural rather than sampling zeros, he or she may do so by supplying a preliminary fit for it. Tests of various hypotheses, including those of quasi-independence, are performed on such incomplete designs. The program can compute and print any of the various marginal frequencies that the user might find desirable.
In the case where sampling zeros do occur in large numbers, the user may wish to make use of a “built-in” pseudo-Bayes estimation procedure which is superior to the generally accepted practice of adding 1⁄2 to the count in each cell of a sparse matrix. This method provides for the selection of a prior array of probabilities which are derived from the observed data. It gives the user an all-purpose method for removing the zeros in an observed frequency distribution.
This module is used to construct structural models for the populations of interest, namely the good, bad and unknown groups. These models specify the final estimated counts as functions of a set of parameters which correspond to the various individual predictor dimensions (called main effects) as well as the multi-way interactions among the predictor dimensions. Consider a one-stage system having six dimensions. Let the indices 1, 2, 3, 4, 5, and 6 correspond to these dimensions and let θ (theta) represent the index set which is comprised of just these indices. Let P (θ) denote the power set of θ (for an explanation of this terminology refer to Paul Halmos, Naïve Set Theory, ©1960, Section 5, pp. 19-20). Let M1θ, M2θ, and M3θ denote, respectively, the final estimated cell counts for the (i, j, k, l, m, n) cell for the good, bad and unknown behavior groups, respectively. Then the structural models previously referred to are of the form:




  
    
      M
      
        1
        ⁢
        
          (
          θ
          )
        
      
    
    =
    
      exp
      ⁡
      
        [
        
          
            μ
            1
          
          +
          
            
              ∑
              
                i
                ⁢
                
                  
                
                ∈
                
                  
                
                ⁢
                I
              
            
            ⁢
            
              
            
            ⁢
            
              
                u
                
                  1
                  ⁢
                  i
                
              
              ⁡
              
                (
                θ
                )
              
            
          
        
        ]
      
    
  
  ,
  
    I
    ⊆
    
      P
      ⁡
      
        (
        θ
        )
      
    
  




(wherein “I” is a subset of the power set of “θ”)




  
    
      
        M
        
          2
          ⁢
          
            (
            θ
            )
          
        
      
      =
      
        exp
        ⁡
        
          [
          
            
              μ
              2
            
            +
            
              
                ∑
                
                  j
                  ⁢
                  
                    
                  
                  ∈
                  
                    
                  
                  ⁢
                  J
                
              
              ⁢
              
                
              
              ⁢
              
                
                  u
                  
                    2
                    ⁢
                    j
                  
                
                ⁡
                
                  (
                  θ
                  )
                
              
            
          
          ]
        
      
    
    ,
    
      J
      ⊆
      
        P
        ⁡
        
          (
          θ
          )
        
      
    
  




  
    
      
        M
        
          3
          ⁢
          
            (
            θ
            )
          
        
      
      =
      
        exp
        ⁡
        
          [
          
            
              μ
              3
            
            +
            
              
                ∑
                
                  k
                  ⁢
                  
                    
                  
                  ∈
                  
                    
                  
                  ⁢
                  K
                
              
              ⁢
              
                
              
              ⁢
              
                
                  u
                  
                    3
                    ⁢
                    k
                  
                
                ⁡
                
                  (
                  θ
                  )
                
              
            
          
          ]
        
      
    
    ,
    
      K
      ⊆
      
        P
        ⁡
        
          (
          θ
          )
        
      
    
  



Where μ1, μ2, μ3 are the grand mean effects.

A specific example of one such structural model for, say, the unknown group (XYZ Dept. Store Project) is given by the following parametric equation:




  
    m
    
      3
      ⁢
      
        (
        θ
        )
      
    
  
  =
  
    
      μ
      3
    
    +
    
      
        u
        1
        
          (
          3
          )
        
      
      ⁡
      
        (
        θ
        )
      
    
    +
    
      
        u
        2
        
          (
          3
          )
        
      
      ⁡
      
        (
        θ
        )
      
    
    +
    
      
        u
        3
        
          (
          3
          )
        
      
      ⁡
      
        (
        θ
        )
      
    
    +
    
      
        u
        4
        
          (
          3
          )
        
      
      ⁡
      
        (
        θ
        )
      
    
    +
    
      
        u
        5
        
          (
          3
          )
        
      
      ⁡
      
        (
        θ
        )
      
    
    +
    
      
        u
        6
        
          (
          3
          )
        
      
      ⁡
      
        (
        θ
        )
      
    
    +
    
      
        u
        13
        
          (
          3
          )
        
      
      ⁡
      
        (
        θ
        )
      
    
    +
    
      
        u
        16
        
          (
          3
          )
        
      
      ⁡
      
        (
        θ
        )
      
    
    +
    
      
        u
        23
        
          (
          3
          )
        
      
      ⁡
      
        (
        θ
        )
      
    
    +
    
      
        u
        24
        
          (
          3
          )
        
      
      ⁡
      
        (
        θ
        )
      
    
    +
    
      
        u
        26
        
          (
          3
          )
        
      
      ⁡
      
        (
        θ
        )
      
    
    +
    
      
        u
        35
        
          (
          3
          )
        
      
      ⁡
      
        (
        θ
        )
      
    
  




where the superscripts are used to indicate the behavior group in order to avoid confusion with the subscripted dimension indices.

The decision procedure used to determine which parameters to include in the model is as follows:
1) Sampling zeros are eliminated from the sampled data via a pseudo-Bayes estimation procedure in MEP-X if necessary.
2) Parameter estimates and their standardized values are derived for the saturated model in PEP-X.
3) An analysis of the standardized parameter values and parameter estimates from module PEP-X is carried out in order to identify the statistically significant effects in the saturated model (saturated refers to all effects assumed present). For example, a seven-dimensional model with all four-way effects present would be comprised of:




  
    
      ∑
      
        i
        =
        0
      
      4
    
    ⁢
    
      
    
    ⁢
    
      
        (
        
          
            
              7
            
          
          
            
              i
            
          
        
        )
      
      ⁢
      
        5
        i
      
    
  
  =
  
    
      35
      +
      35
      +
      21
      +
      7
      +
      1
    
    =
    
      89
      ⁢
      
        
      
      ⁢
      parameters
    
  




Assuming five categories within each dimension, the number of parameter estimates printed would be:





  
    
      
        ∑
        
          i
          =
          0
        
        4
      
      ⁢
      
        
      
      ⁢
      
        
          (
          
            
              
                7
              
            
            
              
                i
              
            
          
          )
        
        ⁢
        
          5
          i
        
      
    
    =
    
      
        
          
            35
            *
          
          ⁢
          
            5
            4
          
        
        +
        
          
            35
            *
          
          ⁢
          
            5
            3
          
        
        +
        
          
            21
            *
          
          ⁢
          
            5
            2
          
        
        +
        
          
            7
            *
          
          ⁢
          5
        
        +
        1
      
      ⁢
      
        

      
      ⁢
      
        
      
      =
      21
    
  
  ,
  
    
      875
      +
      
        
          4,375
        
        +
        525
      
      +
      35
      +
      1
    
    ⁢
    
      

    
    ⁢
    
      
    
    =
    
      26,811
    
  




4) Using a model which is comprised of only the significant effects found in step (3) as a starting solution, i.e., a basic feasible solution, MEP-X is used to examine, test and compare all adjacent models (i.e., all models differing by just one term) in order to arrive at the optimal one. The procedure is stepwise, starting with the basic feasible solution, and eliminating one term at a time (this is known as backwards elimination as opposed to forward selection). (Refer to Bishop, Fienberg and Holland, Discrete Multivariate Analysis Theory and Practice, Copyright 1975 by MIT, Section 4.5, pp. 155-168. Backwards elimination discussed, p. 166 Steps (1) and (2) discussed p. 156—Strategy 1).
In order to decide if multiple systems are indicated, a detailed analysis of the results from PEP-X is carried out. It may happen that significant parameter values occur for different subpopulations, for example, consider:


























Standardized

STD

STD

STD

STD


TERM
I
J
K
Estimate
IJK
EST
IJK
EST
IJK
EST
IJK
EST



























136
1
1
1
1.53
112
0.28
113
−1.93
114
−1.91
121
−1.59



1
2
2
−0.68
123
1.25
124
−0.51
211
−1.51
212
−0.68



2
1
3
1.24
214
−0.50
221
1.82
222
0.28
223
−1.93



2
2
4
−1.91









We find significant interaction of variables (dimensions) 1, 3 and 6 for the third and fourth levels of dimension 6 when dimensions 1 and 3 are both on the same level (i.e. 1 or 2).

In this example, the dimensions are:

















No.
Name
Strata
1
2
3
4







1
DEPT. STR.

NONE
ONE-UP




3
MAJOR CC

NO
YES




6
BANK REF

NONE
SAVE
CHECK
BOTH









The interpretation is as follows: There is a significant interaction between the 1st, 3rd and 6th dimensions for the cases when either:

A) No department store or major credit card references are given and the applicant has either a checking account or both a checking and savings account, or
B) Both department store and major credit card references are given and the applicant has either a checking account or both a checking and savings account.
Thus we may wish to split the data base on the dimensions “Bank REF” building a separate system for those with no references or just a savings account and one for those having a checking account or both a checking and savings account. Another possible split would be to combine the department store and major credit card references into one 4-level variable and split on those who have either both or neither references and those who have at least one but only one of the two. A final possibility would be to combine all three dimensions and build separate systems for the derived groups of sub-classifications. The first and second alternatives would result in 2 systems. The third could result in 16 systems.
In the case of loans covered under Regulation C, Home Mortgage Disclosure Act (1975), the protected class status relative to race/ethnicity and gender are available. Hence it is possible to perform analysis and fit log-linear models to specific protected class and control group populations, such as Hispanic, African-American, Asian-American, Native-American, White Non-Hispanic, female, and male classifications. In this way, distinct risk models can be developed for different groups based upon protected class status, e.g. by race/ethnicity for accept, reject, good and bad populations. This information details explicit relationships that can be used to derive equally predictive credit approval models, while treating a protected class more favorably. The same can be done relative to loan pricing, marketing, or product selection.
Processing 700 involving module RCP-X is next performed for this example as shown in FIG. 10. Four top-levels steps are performed involving module RCP-X. With respect to these top-level steps, the logical flow and calculations in module RCP-X are as follows:
1. Input optimal cell estimates for known population from disk storage.
2. Convert raw counts to percentages separately for the two behavior groups (good and bad).
3. Calculate the odds ratio based on good/bad percentages for every cell along with its logarithm base e.
4. Output table of cell risk estimates and un-scaled indices.
5. Input the acceptance rate and bad rate for the known population.
6. Calculate the expected number of sampled goods and bads in the unknown population as follows:
Let TL(I)=risk estimate for the Ith cell

    
    
        TU(I)=unknown count for the Ith cell
        B1=known bad rate
        B(I)=number of expected goods in the unknown population for Ith cell.
        G(I)=number of expected bads in the unknown population for Ith cell.
    
    


Then,

B(I)=(1.0/(1.0+TL(I)*((1.0−B1)/B1)))*TU(I)

G(I)=TU(I)−B(I)

7. Calculate the population odds as follows:
Let B2=bad rate for the unknown population

    
    
        SUMB=total number of inferred bads in the unknown population
        SUMU=total number of sampled unknowns
        FB=overall fraction of bads
        A=acceptance rate
    
    


Then,

B2=SUMB/SUMU 

FB=A*B1+(1.0−A)*B2

And the population odds=P=(1.0−FB)/FB
8. Output the table of inferred cell estimates, e.g.






















OIL CO.
NONE
NONE
ONE-UP
ONE-UP


BANK REF
MO. Inc.
HOUSING
MAJOR CC
DEPT. STR
NONE
ONE-UP
NONE
ONE-UP







NONE
$0-900
RENT/OTH
NO
UNKNOWN
20.2709
9.2697
2.1231
0.9709






EXPT. BDS
9-3802
3.3723
0.4849
0.1514






EXPT GDS
10.8907
5.8974
1.0383
0.8195









9. Scale counts for each population, so as to arrive at a model based on 10,000 applicants.
10. Calculate scaled risk indices by cell.
After step 9 summary statistics are printed as follows:
Minimum unsealed index was −2.97786
Maximum unsealed index was 2.84800
The average index was 0.02411
Acceptance Rate 0.5500
Bad Rate for the knowns 0.0420
Bad Rate for the unknowns 0.1162
Number of unknown bads 88
Number of unknowns 754
The Population Odds 12.3/1.0
Known Goods 5269
Inferred Goods 3977
Total Goods 9246
Known Bads 231
Inferred Bads 523
Total Bads 754
11. Output table giving good and bad risk distributions by cell (scaled to 10,000 applicants), applicant percentages by cell and risk index by cell, e.g.:






















OIL CO.
NONE
NONE
ONE-UP
ONE-UP


BANK REF
MO. Inc.
HOUSING
MAJOR CC
DEPT. STR
NONE
ONE-UP
NONE
ONE-UP























NONE
$0-900
RENT/OTH
NO
Goods
71
43
17
16






Bads
61
24
5
3






% Applicant
1.32
0.67
0.21
0.19






Index
203.
211.
224.
234.









12. Print Applicant Population Distributions for Stability Analyses, e.g.:















APPLICANT





DEPT. STR
FORECAST
DEPT. STR.









NONE

54.38



ONE-UP

45.42






















APPLICANT
FORECAST
DEPT. STR BY MAJOR CC BY HOUSING











HOUSING
MAJOR CC
DEPT. STR.
NONE
ONE-UP














RENT/OTH
NO

17.64
12.36


RENT/OTH
YES

12.82
12.42


OWN/BUY
NO

12.76
9.62


OWN/BUY
YES

11.35
11.02




.






.






.









13. Output to disk overall percentages by cell and risk indices by cell.
Processing 800 involving the fifth top-level step of module RCP-X is next performed for this example as shown in FIG. 11. The logical flow is as follows:
1. Read in input description card, scores and percentages.
2. Sort the array of risk indices via pointer indices in a dummy vector.
3. Consolidate and sort good, bad and applicant percentages based on risk indices.
4. Sort cell addresses for each risk level in place in an array.
5. Print linear cell addresses for every risk index. This reference will be helpful in determining exactly the profile of those groups to be affected by a particular cutoff strategy.
6. Compute counts and odds by cell. Counts for each strata are scaled so as to arrive at 10,000 applicants. Print the risk index density functions, e.g.
















RISK
GOOD
BAD
TOTAL




















INDEX
NBR

PCNT
NMBR
PCNT
NMBR
PCNT

ODDS
CELLS




















203
71

0.8
61
8.1
132
1.3

1.2
1


209
50

0.5
32
4.2
82
0.8

1.6
1


211
114

1.2
66
8.8
181
1.8

1.7
2









7. Compute Ascending Cumulative Risk Index Distribution Functions and print them, e.g.




















203
71
0.8
61
8.1
132
1.3
1.2
1


209
121
1.3
93
12.3
214
2.1
1.3
2


211
235
2.5
159
21.1
394
3.9
1.5
4









8. Compute Descending Cumulative Risk Index Distribution Functions and print them, e.g.
















RISK
GOOD
BAD
TOTAL




















INDEX
NBR

PCNT
NMBR
PCNT
NMBR
PCNT

ODDS
CELLS




















259
5356

57.9
95
12.6
5454
54.5

56.2 
106


258
5370

58.1
96
12.7
5466
54.7

55.9
107


257
5620

60.8
110
14.6
5731
57.3

50.9
113









(above is an excerpt from the printout centered about the current acceptance rate of 55% ̃54.7 at risk level 258 which corresponds to maintenance of the current acceptance rate.)

An example of the printout from Step (5) is:

Reference Table Enumerating all Cells which Correspond to each Risk Level:















Index
Number
Corresponding
Cell
Addresses (sorted into Increasing Order)























203
1
1








209
1
9








211
2
2
17







215
1
10








218
2
18
25







220
1
33









.










.










.









257
6
29
54
68
69
70
178



258
1
87








259
2
56
179







260
7
23
71
88
116
148
154
155


261
1
108









.










.










.









315
1
189








317
1
192








320
1
190









The subroutine calling sequence is shown in FIG. 12.

Processing 800 involving the sixth top-level step of module RCP-X is next performed for this example as shown in FIG. 11. The logical flow is as follows:
1. Input control information, scores, and percentages.
2. Read in current policy cutoff to maintain acceptance (or bad) rate along with the dimension of the array which is to hold all marginal tables.
3. Build the Action Table.
4. Create array of percentages for acceptee population.
5. Output the decision table, e.g.

    
    
        XYZ Department Store Action Table for Granting Credit Accounts Developed By STATCOMP. Effective Date: February YYYY
        
            Strategy: Maintain Current Acceptance Rate
        
        
    
    
























OIL CO.
NONE
NONE
ONE-UP
ONE-UP


BANK REF
MO. Inc.
HOUSING
MAJOR CC
DEPT. STR
NONE
ONE-UP
NONE
ONE-UP







NONE
 $0-900
RENT/OTH
NO
CELL NO.
 1
 2
 3
 4






ACTION
Decline 
Decline
Decline
Decline





.










.










.







NONE
$901-1499
OWN/BUY
YES
CELL NO.
29
30
31
32






ACTION
Decline
Decline
Approve
Approve





.










.










.









(6) Print Decline Analysis, e.g.

The following table gives the maximum improvement in risk level to be achieved by a change in any one of the four most important factors indicated for all applicant profiles corresponding to decline cells in the action table. Also, included in the table are the new actions which would result if each of the four possible changes were to have occurred individually.














ACTION
FACTOR 1
FACTOR 2
FACTOR 3
FACTOR 4


TABLE
NET GAIN
NET GAIN
NET GAIN
NET GAIN


REF. NO.
RESULT
RESULT
RESULT
RESULT







 1
MAJOR CC
BANK REF
OIL CO.
MO. INC.



47
30
21
18



DECLINE
DECLINE
DECLINE
DECLINE


 2
MAJOR CC
BANK REF
OIL CO.
MO. INC.



40
34
23
16



DECLINE
DECLINE
DECLINE
DECLINE


 3
MAJOR CC
BANK REF
MO. INC.
DEPT. STR.



28
19
19
 9



DECLINE
DECLINE
DECLINE
DECLINE


.






.






.






 15
BANK REF
MO. INC.
DEPT. STR.
OIL. CO.



40
21
 1
 0



APPROVE
APPROVE
DECLINE
DECLINE


.






.






.






169
MAJOR CC
OIL CO.
DEPT. STR.
MO. INC.



49
16
12
10



APPROVE
APPROVE
APPROVE
APPROVE


.






.






.






178
MAJOR CC
HOUSING
OIL CO.
DEPT. STR.



46
20
16
 0



APPROVE
APPROVE
APPROVE
DECLINE









(7) Print Multidimensional Acceptee Regulation Forecasts, i.e.
















ACCEPTEE





DEPT. STR.
POPULATION
DEPT. STR.









NONE

45.79



ONE-UP

54.21




.





.





.






















ACCEPTEE
POPULATION
DEPT. STR. BY OIL CO. BY MO. INC.











MO. INC.
OIL. CO.
DEPT. STR.
NONE
ONE-UP














  $0-900
NONE

7.94
9.00


  $0-900
ONE-UP

4.15
6.91


 901-1499
NONE

7.56
9.66


 901-1499
ONE-UP

5.39
7.50


$1500-UP
NONE

14.06
12.31


$1500-UP
ONE-UP

6.69
8.77



.






.






.









(8) Print Multidimensional Acceptance Rates, i.e.













ACCEPTANCE RATES: DEPT. STR










DEPT. STR.








NONE
45.85



ONE-UP
65.24



.




.




.











ACCEPTANCE RATES: MAJOR CC BY HOUSING












HOUSING
MAJOR CC
NO
YES







RENT/OTH

7.60
82.18



OWN/BUY

47.59
93.78



.






.






.










Note that the applicant forecast for DEPT. STR is:

















NONE
54.38



ONE-UP
45.42










From above we have the acceptee percentage split is:

















NONE
45.79



ONE-UP
54.21










And the acceptance rates are:

















NONE
45.85



ONE-UP
65.24










Recall that the overall acceptance rate is 55%. Hence, based on 10,000 applicants we have:

NONE 5438X(0.4585)/5,500=45% of acceptees ✓

ONE-UP 4542X(0.6524)/5,500=54% of acceptees ✓ and the forecasts are consistent.

Steps (2)-(8) are repeated for the strategy which maintains the current bad debt rate.

A program flow for these steps can be constructed as discussed in the aforementioned U.S. Provisional Application Ser. No. 60/757,648. As an example, the module can invoke another subroutine or module to provide the following operations:

(1) An array of action table cell reference numbers (addresses) is passed to it from the main program (these correspond to decline cells) along with the total number of decline cells.
(2) An n-tuple is calculated for each address passed.
(3) Next, a search is made over a set of generated n-tuples differing only in one coordinate from the address being examined.
(4) Differences in risk indices are calculated over the generated set of n-tuples to determine the maximum improvement in risk by a change in any one coordinate.
(5) Finally, the decline factors are rank ordered and the four most significant ones are output.
From item (8) and item (10), we project that a reduction in bads of [(231.96)/231]=58.4% can be achieved while maintaining the current acceptance rate.
The math is: 58.4%=[(0.0420)−(96/5466)]/(0.0420) (row with Risk Index=258: Bad NMBR/Total NMBR)=(96/5466) and, the bad rate for the knowns=0.0420. If you divide the numbers, you get 58.18, which is not exactly equal to 58.4. That is because the risk index cut-off of 258 corresponds to a 54.7% acceptance rate, not a 55% acceptance rate. For setting cut-offs, this is an acceptable approximation.
Following is an assessment of this policy's effect on the known sampled applicants:
Under the Maintain Current Acceptance Rate Strategy:













DECLINES












BANK REF
BAD
GOOD
NUMBER 
SAMPLED














NONE
157
39
GOOD
826


SAVINGS
125
51
BAD
728










CHECKING
107
48
NO. GOODS TURNED DOWN = 208


BOTH
148
70
NO. BADS ACCEPTED = 728 − 537 = 191



537
208









Comparison of Rates of Error:














For Good Group
208/826 = 25%


For Bad Group
191/728 = 26%


For Known Group
(208 + 191)/(826 + 728) = 399/1554 = 26%









Thus, 74% of the original population is distinguishable by the system using this strategy. Now, the 26% error rate computed for bads implies we should be able to cut the bad rate by 74% while the table shows only a 58% reduction. The reasons for this are:

1) The declines assigned caused more overlap among the good and bad populations, i.e., made them less distinguishable, and
2) Here we are working off the sampled counts rather than the final estimates.
Multistage Sequential Credit Approval System Development Example
Benefits of this approach:
1) Smaller development sample size required, although all of the data should be utilized when readily electronically available
2) Increased accuracy in risk estimation with respect to the structural modeling aspect. Analogous to multiple system development.
Instead of having just one action table, the risk evaluation and policy formulation system would be comprised of two or possibly three action tables (or more). The dimensions of the first action table would be the most significant characteristic in terms of their predictive power (additional consideration may be given to characteristics which are also the least objectionable from a legal standpoint and the easiest to use to classify credit applicants). For example, whether or not the applicant has a checking account should have significant predictive power while being most acceptable from an ECOA standpoint (anyone can open a checking account regardless of economic status) and it is easy to determine as opposed to calculating a debt ratio or classifying an employer or occupational title. The first action table would typically be made up of from four to seven variables (possibly more, especially if there are more dichotomous variables which would mitigate the problem of generating too large a profile set. E.g. ten dichotomous variables would result in 1,024 distinct profiles, or action table cells, which is identical to that which would result from having only five variables, where each of the five individual variables can take on any one of four possible values.). The number of variables in the first action table would depend upon the number of predictor variables available, and their nature with respect to the above criteria. The second action table would consist of another set of predictors which may be required to compensate for any weaknesses among the stage one variables, or are a bit more difficult to classify (e.g. debt ratio, occupation, etc.), or less desirable from an ECOA compliance standpoint, e.g., occupation, number of dependents, age, etc. Again, the same reasoning would apply to the third stage. Credit bureau predictors may comprise a separate stage, or be intermixed with applicant-supplied information in any stage.
How the Multistage System would operate: If the application cannot be either declined or approved (i.e. some final or definitive action taken) at the first stage, it proceeds to the next stage for further classification, and possible final action, and so on.
A decision model such as this is more complicated than the single action table system in several respects. Following is an enumeration of the added difficulties and their proposed solutions:
7) Effect on Structural Model:
For the first action table we have




  
    
      M
      θ
      
        (
        1
        )
      
    
    =
    
      exp
      ⁡
      
        [
        
          
            μ
            1
            
              (
              1
              )
            
          
          +
          
            
              ∑
              
                i
                ⁢
                
                  
                
                ⁢
                ε
                ⁢
                
                  
                
                ⁢
                I
              
            
            ⁢
            
              
            
            ⁢
            
              
                u
                i
                
                  (
                  1
                  )
                
              
              ⁡
              
                (
                θ
                )
              
            
          
        
        ]
      
    
  
  ,
  
    I
    ⊆
    
      P
      ⁡
      
        (
        θ
        )
      
    
  




(for the good behavior group, denoted by superscript “(1)”.)





  
    
      M
      θ
      
        (
        2
        )
      
    
    =
    
      exp
      ⁡
      
        [
        
          
            μ
            1
            
              (
              2
              )
            
          
          +
          
            
              ∑
              
                j
                ⁢
                
                  
                
                ⁢
                ε
                ⁢
                
                  
                
                ⁢
                J
              
            
            ⁢
            
              
            
            ⁢
            
              
                u
                i
                
                  (
                  2
                  )
                
              
              ⁡
              
                (
                θ
                )
              
            
          
        
        ]
      
    
  
  ,
  
    J
    ⊆
    
      P
      ⁡
      
        (
        θ
        )
      
    
  




(for the bad behavior group, denoted by superscript “(2)”.)

Similarly, for the second action table we have





  
    
      M
      ξ
      
        (
        1
        )
      
    
    =
    
      exp
      ⁡
      
        [
        
          
            μ
            2
            
              (
              1
              )
            
          
          +
          
            
              ∑
              
                k
                ⁢
                
                  
                
                ⁢
                ε
                ⁢
                
                  
                
                ⁢
                K
              
            
            ⁢
            
              
            
            ⁢
            
              
                u
                k
                
                  (
                  1
                  )
                
              
              ⁡
              
                (
                ξ
                )
              
            
          
        
        ]
      
    
  
  ,
  
    K
    ⊆
    
      P
      ⁡
      
        (
        ξ
        )
      
    
  




and





  
    
      M
      ξ
      
        (
        2
        )
      
    
    =
    
      exp
      ⁡
      
        [
        
          
            μ
            2
            
              (
              2
              )
            
          
          +
          
            
              ∑
              
                l
                ⁢
                
                  
                
                ⁢
                ε
                ⁢
                
                  
                
                ⁢
                L
              
            
            ⁢
            
              
            
            ⁢
            
              
                u
                l
                
                  (
                  2
                  )
                
              
              ⁡
              
                (
                ξ
                )
              
            
          
        
        ]
      
    
  
  ,
  
    L
    ⊆
    
      P
      ⁡
      
        (
        ξ
        )
      
    
  




The combined model is of the form:





  
    M
    ψ
    
      (
      1
      )
    
  
  =
  
    
      exp
      ⁡
      
        [
        
          
            μ
            1
            
              (
              1
              )
            
          
          +
          
            
              ∑
              
                i
                ⁢
                
                  
                
                ⁢
                ε
                ⁢
                
                  
                
                ⁢
                I
              
            
            ⁢
            
              
            
            ⁢
            
              
                u
                i
                
                  (
                  1
                  )
                
              
              ⁡
              
                (
                θ
                )
              
            
          
        
        ]
      
    
    *
    
      exp
      ⁢
      
        
      
      [
      
        
          μ
          2
          
            (
            1
            )
          
        
        +
        
          
            ∑
            
              k
              ⁢
              
                
              
              ⁢
              ε
              ⁢
              
                
              
              ⁢
              K
            
          
          ⁢
          
            
          
          ⁢
          
            
              u
              k
              
                (
                1
                )
              
            
            ⁡
            
              (
              ξ
              )
            
          
        
      
      ]
    
  




and





  
    M
    ψ
    
      (
      2
      )
    
  
  =
  
    
      exp
      ⁡
      
        [
        
          
            μ
            1
            
              (
              2
              )
            
          
          +
          
            
              ∑
              
                j
                ⁢
                
                  
                
                ⁢
                ε
                ⁢
                
                  
                
                ⁢
                J
              
            
            ⁢
            
              
            
            ⁢
            
              
                u
                j
                
                  (
                  2
                  )
                
              
              ⁡
              
                (
                θ
                )
              
            
          
        
        ]
      
    
    *
    
      exp
      ⁢
      
        
      
      [
      
        
          μ
          2
          
            (
            2
            )
          
        
        +
        
          
            ∑
            
              l
              ⁢
              
                
              
              ⁢
              ε
              ⁢
              
                
              
              ⁢
              L
            
          
          ⁢
          
            
          
          ⁢
          
            
              u
              l
              
                (
                2
                )
              
            
            ⁡
            
              (
              ξ
              )
            
          
        
      
      ]
    
  




where ψ={θ∪ξ}. If we denote the odds quote in a cell of the two-stage action table by





  
    ω
    ψ
  
  =
  
    
      M
      ψ
      
        (
        1
        )
      
    
    
      M
      ψ
      
        (
        2
        )
      
    
  




then we have ωψ=ψθ*ψξ, i.e., a direct product of the one stage structural model with the second stage structural model.

With the one stage system the cell odds estimate is ωθ, so that ωψ, ωθ=ωξ amounts to a refinement of the stage one estimate. Note the assumption of independence here. The justification for this assumption is two-fold:
A) Independence need not hold for the group of applicants approved at the first stage since their odds estimate is never refined further;
B) Any approximations derived without the assumption would be less accurate since abandonment at the assumption would entail the calculation of a matrix of conditional probabilities at the form P(ωξ|θ) which represents n×m terms (where n, m are the number of cells in action tables one and two respectively) and, in many instances, the data are too sparse for these calculations to be meaningful.
The multi-stage approach is not dependent upon this assumption of independence, and alternative dynamic conditional estimates can be used in place of the cell odds that are calculated as a direct product as described previously. In this case, the two-stage cell odds relationship would be represented as: ωψ≈θ(x11, x12, x13, . . . , x1n; x21, x22, x23, . . . , x2m), where ƒ is a function whose domain of values are the combined values of the variables that comprise the union of the two sets of “n” variables for stage one and “m” variables for stage two, and whose range is a real number interval that is bounded above and below. The form of this function ƒ(.) may be specified by a pooled set of conditional equations based on estimated linkages and multi-dimensional interactions between the factors appearing in the two stages. This result generalizes directly to cases where there are three or more action table stages present.
We cannot use the entire population to estimate ωξ since those approved in stage one are no longer to be considered in the decision process. Thus, the stage one action table induces a partition on the development sample. It will, however, be desirable to include some sample points having profiles with associated risk indices close to the cutoff, but on the approved side, in the second stage development sample. This is because there may be changed in the acceptance policy by a client and in the event the stage one approval policy were made tighter, we would want the second stage risk estimates to be valid for those new profiles being judged for the first time by the second stage action table. On the other hand, this precaution may not be necessary, provided that the Client regulate the approval rate by adjusting the second stage of the system only. We may describe the portion of the original development sample used for the stage two development sample as follows:

















I.:
Stage 1 approvals.






II.:
Marginal above 


Total




cutoff approvals


Applicants 




(perhaps 10% of the 

Risk
(Cumulative




overall applicants)

Index
%)



III.:
Declines from stage 1
I
350
2.0






349
4.0






.







.







.







275
43.0





II
274
45.0






273
47.0






272
49.0






271
51.0






270
53.0





III
269
55.0
cutoff 





268

for no





.

change in





.

acceptance





.

policy









Hence, the development sample of stage two for this example would consist of all sample points whose profiles have corresponding stage one risk indices in groups II and III. This would comprise approximately 10%+45%=55% of the original development sample.
We would proceed with the development of the second stage of the system, recalculating the percentage of good and bad risks by cell for the known groups at the beginning of Module RCP-X using data from II and III for the good and bad behavior groups to get new risk estimates ωξ.
As for the unknown or declined behavior group, we would use data only from III for the unknown counts in RCP-X.
Now we have that:




  
    ω
    ψ
  
  =
  
    {
    
      
        
          
            
              
                ω
                θ
              
              ,
              
                
                  if
                  ⁢
                  
                    
                  
                  ⁢
                  θ
                
                ∈
                
                  I
                  ⁢
                  
                    
                  
                  ⁢
                  or
                  ⁢
                  
                    
                  
                  ⁢
                  θ
                
                ⁢
                
                  
                
                ∈
                II
              
            
            ⁢
            
              
            
          
        
      
      
        
          
            
              
                ω
                θ
              
              ·
              
                ω
                ξ
              
            
            ,
            
              
                if
                ⁢
                
                  
                
                ⁢
                θ
              
              ⁢
              
                
              
              ∈
              
                
              
              ⁢
              III
            
          
        
      
    
  




Selected Topics Concerning the Multistage Approach.

I. Effect on Acceptance Rate Calculation

Make the first action table account for say 1⁄4-1⁄2 of the approvals. So, if we are aiming for a 55% acceptance rate, have 15-25% of the population approved at stage one (actually this will partially be dictated by a comparison of the individual risk levels with the overall portfolio adds and partially will be a function of the sampled data. We want to make the cutoff odds high enough to ensure significant use of stage two).
Fine tuning could be done on the stage two table(s), i.e., the strategy should be enforced there. Stage one should be set for the life of the system (possibly within 10% bounds, i.e., only individual profiles from group II would be permitted to into group III). Hence, there should be no completely specified strategy associated with the stage one action table. Both of the specified policies will be carried out in the second stage giving two alternative stage two action tables, or sets of stage two action tables, with the same stage one action table in both cases.
II. Applicant Profile Distributions and Acceptee Population Forecasts
For tables accompanying the stage one action table, calculations will be based on data from I, II and III. For those accompanying the second stage action table, calculations will be based on data from III only. Acceptance rates will be calculated accordingly.
III. Applicant Profile Analysis
The scheme previously described for a one stage system discussed above is modified as follows:
Tally the reference numbers for the two-stage system action tables in ordered pairs or in an n×m table (where n, m are the total number of cells in the first and second action tables, respectively) as follows:











Action Table 1
Action Table 2 Reference No.














Reference No.
1
2
3

m-1
m
Total





1
X11
X12
X13
. . .
X13m-1
X1m
X1.


2
X21
X22
X23
. . .
X21-1
X2m
X2.


3
X31
X32
X33
. . .
X31m-1
X3m
X3.


.
.
.
.
.
.
.
.


.
.
.
.
.
.
.
.


.
.
.
.
.
.
.
.


n-1
Xn-1, 1
Xn-1, 2
Xn-1, 3
. . .
Xn-1, m-1
Xn-1, m
Xn-1.


n
Xn1
Xn2
Xn3
. . .
Xn, m-1
Xnm
Xn.


Total
X.1
X.2
X.3
. . .
X.m-1
X.m
X..









Where Xij's=tallied counts,





  
    
      X
      
        i
        ⁢
        
          
        
        ⁢
        •
      
    
    =
    
      
        ∑
        
          j
          =
          1
        
        m
      
      ⁢
      
        
      
      ⁢
      
        X
        ij
      
    
  
  ,
  
    
      X
      
        •
        ⁢
        
          
        
        ⁢
        j
      
    
    =
    
      
        ∑
        
          i
          =
          1
        
        n
      
      ⁢
      
        
      
      ⁢
      
        X
        ij
      
    
  




Recognizing that Xij=constant for all profiles “ι” εI, we have that part of the tally sheet can be blacked out (entries can be made in the row total (marginal) column).

IV. System Update

A system may have all action table reference numbers stored in the master file regardless of the stage one profile classification. This would allow for system updates where predictors could switch stages in the updated version. If the Client cannot be convinced to store all reference numbers in the master file for model updating, then one may be stored along with a designation as to the action table stage to which it refers. In the event that a single action table reference number is stored and it refers to the very last stage, then a full system update can be performed in the sense that all cell risk indices can be re-estimated. However, in this case, the form of the model remains the same, i.e., the two action tables describes, or represents, the same profiles as before.
Sample Size Determination
If we assume that the data exhibits no severe pathologies, e.g. extreme asymmetry, high percentage of zero cells, etc., then we require only that the expected cell counts be non-zero. It would be desirable to have expected counts of at least two in every cell. For sample sizes of 800 or less, we restrict our selection of multi-way tables to those having 400 or fewer cells. The table below lists the number of distinct consumer profiles, or cells, in a multi-way table given the number of dimensions and the number of strata within each dimension.
There are other considerations aside from the number of cells in the table. These include:
1) Number and type of predictor candidate variables appearing on the application form,
2) Rejection and Bad Rates, plus monthly volume,
3) Client preferences for particular emphasis on specific variables, i.e. many strata,
4) Individual sample sizes among stratified groups,










Number of Strata within each of the Dimensions

















Number of










Number of
Distinct










Dimensions
Profiles
1
2
3
4
5
6
7
8



















8
384
2
2
2
2
2
2
2
3



256
2
2
2
2
2
2
2
2


7
320
2
2
2
2
2
2
5




288
2
2
2
2
2
3
3




256
2
2
2
2
2
2
4




192
2
2
2
2
2
2
3




128
2
2
2
2
2
2
2



6
288
2
2
2
3
3
4





256
2
2
2
2
4
4





216
2
2
2
3
3
3





192
2
2
2
2
3
4





144
2
2
2
2
3
3





128
2
2
2
2
2
4





96
2
2
2
2
2
3





64
2
2
2
2
2
2




5
256
2
2
4
4
4






243
3
3
3
3
3






216
2
3
3
3
4






192
2
2
3
4
4






162
2
3
3
3
3






144
2
2
3
3
4






128
2
2
2
4
4






108
2
2
3
3
3






96
2
2
2
3
4






72
2
2
2
3
3






64
2
2
2
2
4






48
2
2
2
2
3






32
2
2
2
2
2





4
288
2
3
8
6







288
3
4
4
6







256
4
4
4
4







256
2
2
8
8







240
3
4
4
5







216
2
3
6
6







200
2
4
5
5







192
3
4
4
4







192
2
4
4
6







160
2
4
4
5







144
3
3
4
4







128
2
4
4
4







108
3
3
3
4







96
2
3
4
4







81
3
3
3
4







72
2
3
3
4







64
2
2
4
4







54
2
3
3
3







48
2
2
3
4







36
2
2
3
3







32
2
2
2
4







24
2
2
2
3







16
2
2
2
2









5) Ease and availability of documents for sampling and coding (plus associated costs and time),
6) Level of significance desired α,
7) Sampling design,
8) Non-centrality parameter (X) under likely alternatives H1,

    
    
        Non-centrality parameter (X) for development sample when considering update sample size,
    
    


9) Degrees of freedom associated with the model,
10) Desired power (1-β),
11) The nature and degree of high order interactions in the data (not known a priori—except in the case of update),
12) The number of stages,
13) The number of systems under development.
Item (13) is determined after initial sampling, so that additional sampling may be required.
(When high numbers of sampling zeros do occur, the method discussed with respect to pseudo-Bayes estimation, is used. The algorithm is based on formulas given in Bishop, Frenberg and Holland's Discrete Multivariate Analysis, Theory and Practice, ©1975 MIT Press, pp. 401-402.)
Algorithm for Eliminating Sampling Zeros.
1) Use module MEP-X to fit a model “loosely” to the data.
2) Use the fitted values obtained in step 1) i.e. {yijkl} (in the five dimensional case for example) to estimate the prior probabilities {λijklm} via the equation λijklm=(yijklm/n) where n=sample size. [In order to make the discussion more general, let “θ” denote a subscript set of arbitrary size—in this example so far θ={I, j, l, m}]
3) Compute the weighting factor:




  
    k
    ^
  
  =
  
    
      
        n
        2
      
      -
      
        
          ∑
          θ
        
        ⁢
        
          
        
        ⁢
        
          X
          θ
          2
        
      
    
    
      
        ∑
        θ
      
      ⁢
      
        
      
      ⁢
      
        
          (
          
            
              X
              θ
            
            -
            
              n
              ⁢
              
                
              
              ⁢
              
                λ
                θ
              
            
          
          )
        
        2
      
    
  




(Xθ's are the observed counts)

4) Compute the cell estimates:




  
    m
    θ
    *
  
  =
  
    
      np
      θ
      *
    
    =
    
      
        n
        
          n
          +
          
            k
            ^
          
        
      
      ⁢
      
        (
        
          
            X
            θ
          
          +
          
            
              k
              ^
            
            ⁢
            
              λ
              θ
            
          
        
        )
      
    
  




5) Output estimated frequencies as well as cell counts, i.e. both pθ*&mθ*.
ECOA Compliance Re: Development-Time Validation
Procedure can be as follows:
1) Split development sample of known behavior groups by application date. The most recent 150 (this number may vary depending upon particular circumstances discussed in the previous section on sample size determination) in each behavior group will constitute the hold out sample.
2) System construction proceeds with the balance of the development sample.
3) Validation is assessed on the hold out sample and total development sample.
4) Development-time system update is performed.
5) Corrected system's performance is assessed on 1) hold out sample, 2) balance development sample, and 3) total or combined development sample.
Via this method, there is no need for additional sampling and ECOA requirements are met.
Classification of a Non-Response to a Question
Procedure is as follows:
1) Data is captured as a separate non-response category.
2) If a significantly large enough group it is retained, unless the client requires that all applications be complete in which case all non-responses are dropped from the analysis (by consequence of the fact that the client sends back incomplete apps, there should be an insignificant number of these).
3) If the non-response group is small, then we combine it with one of:

    
    
        A) Worst Group (intuitively appealing)
        B) Group it behaves the most like (statistically appealing)
        C) Neutral Group (perhaps legally appealing with respect to ECOA), or
        D) Drop from the analysis if client requires complete applications.
    
    


A problem may be encountered here if the client has used non-response in the decision process previously, or ignored the issue, but no longer wishes to continue this policy in the future. In such a case we cannot simply drop non-response from the analysis because a large fraction of the development sample may consist of apps. with one or more questions left unanswered. Hence, the system can infer how the applicant would have answered, given their behavior group and other answers. (This is the reverse of the reject inference problem). To solve the problem, we opt for solution 3B) above via characteristic analysis in one dimension along with a check of the parametric form in “N” dimensions to search for the most “similar” response group for the particular question left unanswered. By “similar” we mean similar in terms of behavior or performance, i.e. similar log odds with respect to characteristic analysis and similar interaction parameters as determined by module PEP-X discussed previously.
Credit Approval Example
As another example of a credit approval application, there are two ways in which a system's effectiveness can diminish. Either the distribution of applicants corresponding to specific profiles changes, or the risk associated with specific profiles changes. In both cases, application of the proper system maintenance techniques will uncover these shifts so that fluctuations in the system's performance can be anticipated, understood. and corrected. A risk evaluation system can provide within such a credit approval application context such advantages as:

    1) Specifying interrelationships among variables.
    2) Facilitating comparisons of different populations.
    3) Increasing the credibility of sample results.


A) Achieves reductions in sampling variances
B) Bias reduction.

    4) Individual components may be tested for significance.
    5) Facilitating model validation and tests of complicated hypotheses at prescribed confidence levels.
    6) Having intuitive appeal and being easy to explain to the layperson.
    7) Allowing for a statistical assessment of the impact of model predictions on a protected class of individuals (Effects Test).


In this credit approval application, a risk evaluation and policy formulation system allows for the identification of optimal strategies for effectively handling various types of delinquent accounts. Each policy is specified in the form of an action table which functions to enumerate all possible performance profiles along with their associated actions. In addition, the action table assigns a unique reference number to every performance profile for cross-referencing purposes. It is imperative that this number be included in the client's master record for system performance monitoring and updating for a period of four months.
The system uses socio-economic information and individual account purchase and payment history to compute an index indicating the probability that an account will pay its obligations satisfactorily over a given period of time (four months for accounts eight or more months old and three months for recently acquired accounts). Every month at billing time, each account is classified according to a previously determined scheme which associates a percentage likelihood of credit redemption for the particular account's performance profile. All such profiles are identified via their action table reference numbers. This index can be used by a collector in planning his collection approach to an account, by credit personnel in evaluating a credit authorization request or setting credit limits, and by account evaluation programs at renewal time.
The following are examples of performance strata that can be used in this example:
1) current accounts which are over their limit,
2) accounts thirty days past due,
3) accounts sixty days past due,
4) accounts ninety days past due,
5) accounts one hundred twenty or more days part due.
The following are examples of performance descriptor variables:
1) application risk index or credit score,
2) amount over limit,
3) previous high delinquency during the last eight months,
4) number of months current during the last might months,
5) amount of last payment,
6) number of times thirty days past due,
7) number of times sixty days past due,
8) number of times ninety days past due,
9) number of times one hundred twenty or more days past due,
10) percent of balance due to current month's purchases,
11) number of times previously over limit,
12) previous month's status,
13) number of months with zero balance,
14) average balance over the last eight months,
15) average balance over the last four months,
16) amount of average purchase this month,
17) amount of average purchase last month,
18) amount of average purchase during the last eight months,
19) average balance as a percentage of limit,
20) amount of this month's payment,
21) amount of last month's payment,
22) average payment during the last four months,
23) average payment during the last eight months,
24) average payment as a percentage of balance,
25) number of times paid in full,
26) account age in months,
27) maximum previous balance.
For accounts which are eight months or older, the following monthly monitoring report can be produced for each performance stratum beginning four months after system installation:

















ACTION
NUMBER
PERCENT
ACCOUNTS
PERFORMANCE INDEX
DIFFERENCE
STD
AT


TABLE
OF
ACCOUNTS
REDEEMED
AND STD. ERROR AT
INDEX MINUS
NML
ALPHA

















REF. NO.
ACCOUNTS
ACT.
EST..
NMBR
PCT
ALPHA =
.05 LEVEL
PCT REDEEMED
Z
LEVEL





xxx
xxxx
xx.x
xx.x
xxxx
xx
xx
xx.x
xx.x
x.xx
.xxx









The same report can be produced for recently established accounts beginning three months after system installation.

System updating (state transition update) focuses on a reassessment of the accuracy of the credit redemption index associated with each delinquent account profile enumerated in an action table. Thus, risk evaluation and policy formulation systems are not bound to a set of initial risk estimates derived during system construction. The time dynamic mechanisms used to interpret individual account behavior are themselves periodically reviewed to ensure acceptable levels of accuracy.
Direct Response Application Example
Situations involving a direct response application can include:
1) New Account Acquisition
2) Inactive Account Stimulation
3) Retail Outlet CO-OP Promotion
4) Solo Direct Mail Merchandising

    
    
        A) Loans
        B) Insurance
        C) Goods
        D) Services

Objective Functions that can be Used within the Risk Evaluation System can Include:

    
    


1) Response
2) Approved Response
3) Higher Purchase Activity
4) Profitability
5) Heighten Consumer Awareness
A single or multistage risk evaluation and policy formulation system is constructed for each type of promotion having a specified goal. Given a properly designed test structure, this system will enable the user to isolate specific profiles which characterize the type of individual who is the most desirable to promote. Here the term profile refers to a set of variables associated with an individual which specify all of the information pertinent to the selection process. This set usually includes socio-economic characteristics obtained from the mailing list along with design variables such as market area, advertising package type, incentive, list source, and so on.
Processing steps can include:

    
    
        1) Assess Predictive Content of Variables Via a Characteristic Analysis.
        2) Build Structural Models for the Populations of Interest.
        3) Calculate a Response Index for Each Profile.
        4) Profile Analysis of Mail File.
        5) Generate Statistical Tables Which Allow for the Formulation of Alternative Marketing Strategies as a Function of the Overall Level of Response to be Required.
        6) Build Action Tables.
        7) Forecast Response Rates for Population Strata.
        8) Generate Percentage Breakdowns of Respondents by Their Profile Components.

A Multistage System Example

    
    


In the application area of credit approval, an applicant who is declined at the first stage proceeds to the next stage for classification and so on. This forward selection process is due in part to the legal requirement that all of the pertinent information furnished by the applicant be considered prior to a decline decision. In contrast, the application area of direct response promotions provides systems which employ forward elimination. For those profiles which are ultimately selected, the decision is not made until the last stage.
Sequential Systems
In the case where we are dealing with multi-objective functions or have a controlled experiment, it will be necessary to develop multiple systems. Consider the following two examples.
EXAMPLE 1
New Account Acquisition
Two objective functions are specified, namely response and high purchase activity. The first system will isolate profiles corresponding to those individuals who are most likely to respond to the promotion. After a required period of time a second system is developed which will identify those respondents who are most likely to have high purchase activity. Each system associates a response index and activity index, respectively, with every profile. Selection for future mailouts is then based on a function of these two sets of indices.
EXAMPLE 2
Inactive Account Stimulation
A subset of inactive accounts is promoted. The balance of inactive accounts serve as a control group. Promoted activation is observed along with spontaneous reactivation in the control. First a respond/no respond system is built which isolates respondent profiles and provides their corresponding response indices. Next, using suitable data transformations and multivariate estimation techniques, the extent of spontaneous reactivation in the promoted group is inferred from the control group. A second system is then constructed which forecasts the net response due to the promotion.
Detailed Credit Approval Example
In this detailed credit approval example, a component of a risk evaluation system is an action table which assigns a specific action for each individual applicant profile. Let us consider a one stage, six characteristic system for granting credit at XYZ Department Store. An action table corresponding to one of eighty-four possible policies is shown in Charts I and II below. Accompanying an action table is an applicant profile identification manual which enables operations personnel to find the correct action table entry for an arbitrary credit applicant. (Refer to Charts III. and IV.)
When a credit application is declined, the system identifies and quantifies specific weaknesses in the application and indicates each factor's influence on the decision. (Refer to Charts V-VIII).
Chart IX displays the total percentage of applicants failing within each of eighty-four different risk levels. The column labeled “cells” gives the number of distinct profiles making up each of these eighty-four groups. By summing the table in Chart XIV from bottom-to-top we arrive at the table shown in Chart X.
The reader will note that Chart X is used in the formulation of policies whereby the applicants representing the lowest risk (starting with risk index 320) are taken for a given acceptance rate policy. Each of the eighty-four lines in this table correspond to a distinct action table.
For example, the action table in Charts I and II corresponds to a risk index cutoff of 258 with resulting acceptance rate of approximately fifty-five percent. In this hypothetical case, the credit grantor's previous delinquency experience with a fifty-five percent acceptance rate was a 4.2 percent bad rate. Since the table in Chart X is based on ten thousand applicants we note that the previous number of bad loans made was two hundred thirty-one and this most closely corresponds to a cutoff risk index of 245.
At a risk level of 245, the credit grantor would experience a seventy-five percent acceptance rate while taking the same number of bad loans as before. The action table corresponding to this latter acceptance policy appears in Charts XI and XII.
Assessment of the Impact of a Change in Policy
A risk evaluation and policy formulation system allows for immediate identification of individual profiles affected by a change in approval policy. A table specifying all profiles corresponding to each and every risk level is provided for this purpose, and is displayed in Chart XIII.
For example, a change in policy from risk level 261 to 262 would result in the elimination of one profile from the portfolio, identified by action table reference number 108. Referring to the action table in Chart XI, we see that profile 108 corresponds to an applicant with a checking account, in the low income range, who owns a home, has no major credit card, and has both department store and oil company references.
CHART I


    
    
        CLIENT NAME: XYZ DEPARTMENT STORE
        TYPE OF SYSTEM: CREDIT APPROVAL
        PRODUCTION MODULE: SCP-X STEP 6
        XYZ DEPARTMENT STORE ACTION TABLE FOR GRANTING CREDIT ACCOUNTS DEVELOPED BY STATCOMP
        STRATEGY: MAINTAIN CURRENT ACCEPTANCE RATE
    
    























MAJOR
OIL CO.
NONE
NONE
ONE-UP
ONE-UP


BANK REF
MO. INC.
HOUSING
CC
DEPT. STR
NONE
ONE-UP
NONE
ONE-UP







NONE
$0-900
RENT/OTH
NO
CELL NO.
 1.
 2.
 3.
 4.






ACTION
DECLINE
DECLINE
DECLINE
DECLINE


NONE
$0-900
RENT/OTH
YES
CELL NO.
 5.
 6.
 7.
 8.






ACTION
DECLINE
DECLINE
DECLINE
DECLINE


NONE
$0-900
OWN/BUY
NO
CELL NO.
 9.
10.
11.
12.






ACTION
DECLINE
DECLINE
DECLINE
DECLINE


NONE
$0-900
OWN/BUY
YES
CELL NO.
13.
14.
15.
16.






ACTION
DECLINE
DECLINE
DECLINE
DECLINE


NONE
901-1499
RENT/OTH
NO
CELL NO,
17.
18.
19.
20.






ACTION
DECLINE
DECLINE
DECLINE
DECLINE


NONE
901-1499
RENT/OTH
YES
CELL NO.
21.
22.
23.
24.






ACTION
DECLINE
DECLINE
APPROVE
APPROVE


NONE
901-1499
OWN/BUY
NO
CELL NO.
25.
26.
27.
28.






ACTION
DECLINE
DECLINE
DECLINE
DECLINE


NONE
901-1499
OWN/BUY
YES
CELL NO.
29.
30.
31.
32.






ACTION
DECLINE
DECLINE
APPROVE
APPROVE


NONE
$1500-UP
RENT/OTH
NO
CELL NO.
33.
34.
35.
36.






ACTION
DECLINE
DECLINE
DECLINE
DECLINE


NONE
$1500-UP
RENT/OTH
YES
CELL NO.
37.
38.
39.
40.






ACTION
APPROVE
APPROVE
APPROVE
APPROVE


NONE
$1500-UP
OWN/BUY
NO
CELL NO.
41.
42.
43.
44.






ACTION
DECLINE
DECLINE
DECLINE
DECLINE


NONE
$1500-UP
OWN/BUY
YES
CELL NO.
45.
46.
47.
48.






ACTION
APPROVE
APPROVE
APPROVE
APPROVE


SAVE
$0-900
RENT/OTH
NO
CELL NO.
49.
50.
51.
52.






ACTION
DECLINE
DECLINE
DECLINE
DECLINE


SAVE
$0-900
RENT/OTH
YES
CELL NO.
53.
54.
55.
56.






ACTION
DECLINE
DECLINE
DECLINE
APPROVE


SAVE
$0-900
OWN/BUY
NO
CELL NO.
57.
58.
59.
60.






ACTION
DECLINE
DECLINE
DECLINE
APPROVE


SAVE
$0-900
OWN/BUY
YES
CELL NO.
61.
62.
63.
64.






ACTION
APPROVE
APPROVE
APPROVE
APPROVE


SAVE
901-1499
RENT/OTH
NO
CELL NO.
65.
66.
67.
68.






ACTION
DECLINE
DECLINE
DECLINE
DECLINE


SAVE
901-1499
RENT/OTH
YES
CELL NO.
69.
70.
71.
71






ACTION
DECLINE
DECLINE
APPROVE
APPROVE


SAVE
901-1499
OWN/BUY
NO
CELL NO.
73.
74.
75.
76.






ACTION
DECLINE
DECLINE
APPROVE
APPROVE


SAVE
901-1499
OWN/BUY
YES
CELL NO.
77.
78.
79.
80.






ACTION
APPROVE
APPROVE
APPROVE
APPROVE


SAVE
$1500-UP
RENT/OTH
NO
CELL NO.
81.
82.
83.
84.






ACTION
DECLINE
DECLINE
DECLINE
DECLINE


SAVE
$1500-UP
RENT/OTH
YES
CELL NO.
85.
86.
87.
88.






ACTION
DECLINE
DECLINE
APPROVE
APPROVE


SAVE
$1500-UP
OWN/BUY
NO
CELL NO.
89.
90.
91.
92.






ACTION
DECLINE
DECLINE
APPROVE
APPROVE


SAVE
$1500-UP
OWN/BUY
YES
CELL NO.
93.
94.
95.
96.






ACTION
APPROVE
APPROVE
APPROVE
APPROVE









CHART II


    
    
        CLIENT NAME: XYZ DEPARTMENT STORE
        TYPE OF SYSTEM: CREDIT APPROVAL
        PRODUCTION MODULE: SCP-X STEP 6
        XYZ DEPARTMENT STORE ACTION TABLE FOR GRANTING CREDIT ACCOUNTS DEVELOPED BY STATCOMP
        STRATEGY: MAINTAIN CURRENT ACCEPTANCE RATE
    
    























MAJOR
OIL CO.
NONE
NONE
ONE-UP
ONE-UP


BANK REF
MO. INC.
HOUSING
CC
DEPT. STR
NONE
ONE-UP
NONE
ONE-UP







CHECK
$0-900
RENT/OTH
NO
CELL NO.
 97.
 98.
 99.
100.






ACTION
DECLINE
DECLINE
DECLINE
DECLINE


CHECK
$0-900
RENT/OTH
YES
CELL NO.
101.
102.
103.
104.






ACTION
APPROVE
APPROVE
APPROVE
APPROVE


CHECK
$0-900
OWN/BUY
NO
CELL NO.
105.
106.
107.
108.






ACTION
DECLINE
DECLINE
DECLINE
APPROVE


CHECK
$0-900
OWN/BUY
YES
CELL NO.
109.
110.
111.
112.






ACTION
APPROVE
APPROVE
APPROVE
APPROVE


CHECK
901-1499
RENT/OTH
NO
CELL NO.
113.
114.
115.
116.






ACTION
DECLINE
DECLINE
DECLINE
APPROVE


CHECK
901-1499
RENT/OTH
YES
CELL NO.
117.
118.
119.
120.






ACTION
APPROVE
APPROVE
APPROVE
APPROVE


CHECK
901-1499
OWN/BUY
NO
CELL NO.
121.
122.
123.
124.






ACTION
DECLINE
APPROVE
APPROVE
APPROVE


CHECK
901-1499
OWN/BUY
YES
CELL NO.
125.
126.
127.
128.






ACTION
APPROVE
APPROVE
APPROVE
APPROVE


CHECK
$1500-UP
RENT/OTH
NO
CELL NO.
129.
130.
131.
132.






ACTION
DECLINE
DECLINE
DECLINE
APPROVE


CHECK
$1500-UP
RENT/OTH
YES
CELL NO.
133.
134.
135.
136.






ACTION
APPROVE
APPROVE
APPROVE
APPROVE


CHECK
$1500-UP
OWN/BUY
NO
CELL NO.
137.
138.
139.
140.






ACTION
APPROVE
APPROVE
APPROVE
APPROVE


CHECK
$1500-UP
OWN/BUY
YES
CELL NO.
141.
142.
143.
144.






ACTION
APPROVE
APPROVE
APPROVE
APPROVE


BOTH
$0-900
RENT/OTH
NO
CELL NO.
145.
146.
147.
148.






ACTION
DECLINE
DECLINE
DECLINE
APPROVE


BOTH
$0-900
RENT/OTH
YES
CELL NO.
149.
150.
151.
152.






ACTION
APPROVE
APPROVE
APPROVE
APPROVE


BOTH
$0-900
OWN/BUY
NO
CELL NO.
153.
154.
155.
156.






ACTION
DECLINE
APPROVE
APPROVE
APPROVE


BOTH
$0-900
OWN/BUY
YES
CELL NO.
157.
158.
159.
160.






ACTION
APPROVE
APPROVE
APPROVE
APPROVE


BOTH
901-1499
RENT/OTH
NO
CELL NO.
161.
162.
163.
164.






ACTION
DECLINE
DECLINE
DECLINE
APPROVE


BOTH
901-1499
RENT/OTH
YES
CELL NO.
165.
166.
167.
168.






ACTION
APPROVE
APPROVE
APPROVE
APPROVE


BOTH
901-1499
OWN/BUY
NO
CELL NO.
169.
170.
171.
172.






ACTION
DECLINE
APPROVE
APPROVE
APPROVE


BOTH
901-1499
OWN/BUY
YES
CELL NO.
173.
174.
175.
176.






ACTION
APPROVE
APPROVE
APPROVE
APPROVE


BOTH
$1500-UP
RENT/OTH
NO
CELL NO.
177.
178.
179.
180.






ACTION
DECLINE
DECLINE
APPROVE
APPROVE


BOTH
$1500-UP
RENT/OTH
YES
CELL NO.
181.
182.
183.
184.






ACTION
APPROVE
APPROVE
APPROVE
APPROVE


BOTH
$1500-UP
OWN/BUY
NO
CELL NO.
185.
186.
187.
188.






ACTION
APPROVE
APPROVE
APPROVE
APPROVE


BOTH
$1500-UP
OWN/BUY
YES
CELL NO.
189.
190.
191.
192.






ACTION
APPROVE
APPROVE
APPROVE
APPROVE









CHART III
XYZ DEPARTMENT STORE CREDIT APPROVAL SYSTEM
ACTION TABLE REFERENCE MANUAL
THIS MANUAL IS INTENDED TO SERVE AS A GUIDE TO THE IDENTIFICATION OF THE INDIVIDUAL APPLICANT'S CLASSIFICATION ACCORDING TO EACH CATEGORY MAKING UP THE ACTION TABLE. THE INSTRUCTIONS WHIM FOLLOW SHOULD BE SUFFICIENT TO ENABLE THE USER TO FIND THE CORRECT ACTION TABLE CELL CORRESPONDING TO ANY ARBITRARY CREDIT APPLICATION

Financial Institution Reference

A checking account may be with a bank, a savings and loan company, trust company, or credit union. It may be either a personal or joint account. Similarly, a savings account may be with a bank, savings and loan company, trust company, credit union, or finance company. Savings accounts include Certificates of Deposit and Christmas Clubs. The savings account is in the applicant's name or a joint account and is an open account. Checking and savings accounts need not be with′ the same financial institutions.

    
    
        NONE No checking account or savings account is Shown on the application.
        SAVE The applicant indicates that he/she has a savings account. No checking account is shown.
        CHECK The applicant indicates a checking account, but no savings account is listed.
        BOTH The applicant shows' both checking and savings accounts.

Monthly Income

This refers to the total gross monthly income of the family. This includes the applicant's salary, co-applicant's salary and all additional income received from part-time work, second jobs, rentals, social security, pensions, alimony, welfare, child support, etc.

If hourly, weekly, or yearly amounts are given, convert all income to a gross monthly amount as indicated below:

        If an hourly rate is given, multiply by 173 hours/month
        If a weekly rate is given, multiply by 4.3 weeks/month
        If a yearly rate is given, divide by 12 months/year
        If net income is given, multiply by 1.3 (income amounts are assumed to be gross unless stated to be net)
        $0-900 Refers to all applicants having a total gross monthly income of $900 or less.
        $901-1499 Refers to applicants having a total gross monthly income ranging from $901 to $1499.
        $1500-UP Refers those applicants having a total gross monthly income of $1500 or more.

Housing

Identify the applicant's current residential' status as shown on the application. If the applicant is renting at the present address, but owns elsewhere, classify him/her as a renter.

    
    


CHART IV


    
    
        OWN/BUY Refers to an applicant who owns or is buying the house or condominium shown as the current residence.
        RENT/OTH Refers to an applicant who rents the house, apartment, or condominium shown as the current residence. Also refers to an applicant whose residential status includes 1) living with parents or relatives, 2) students living in college housing, 3) military personnel living on base, 4) living quarters furnished by employer, 5) mobile homes.

Major Credit Card Reference

        NONE Refers to an applicant who fails to list any major credit card references in the credit reference section of the application.
        ONE-UP Refers to an applicant who gives one or more major credit card references in the credit reference section. Account numbers are listed in order for the reference to count. A partial list of some of the major credit cards currently in use is as follows: Access Card, Airline Credit Card, American Express Card, any Bank Credit Card, BankAmericard, Barclay Card, CAP Card, Carte Blanche Card, Chargex, Diners Club Card, Empire Card, Master Charge Card, NAC Card, TWA Getaway Card, Visa Card. Do not limit to this list.
    
    


Do not include telephone charge cards, car rental charge cards, oil company charge cards, or check guarantee cards.
Oil Company Reference


    
    
        NONE Refers to an applicant who fails to list any oil company accounts in the credit reference section of the application.
        ONE-UP Refers to an applicant who gives one or more oil company accounts in the credit reference section. Account numbers are supplied in order for the reference to count. A partial list of oil companies is as follows: American Oil (AMOCO), Ashland Petroleum, (APCO), Atlantic' Richfield (ARCO) Beacon Oil, Boron, British Petroleum, Chevron Oil, Cities Service (Citgo), Clark Oil, CONOCO, Continental Oil, Crown, ENCO, ESSO, EXXON, Getty Oil, Gulf Oil, Hancock, Hudson, Humble, Husky, Imperial, Mobil Oil, Mohawk, Phillips 66, Shamrock, Shell Oil, Sinclair, Shell Oil, Sohio, Standard Oil, Sun Oil (SUNOCO), Tenneco Oil, Texaco, Tidewater, Union Oil, Wilshire, Zephyr. Do not limit to this list. Also include oil company travel and entertainment cards such as Chevron Travel Card, Torch (Standard Oil of Indiana), etc.

Department Store Reference

        NONE No department store accounts listed in the credit reference section of the application.
        ONE-UP One or more department store accounts listed in the credit reference section. Account numbers are present in order for the reference to be valid. A list of department stores (alphabetically ordered) is attached. LIMIT TO THIS LIST.
    
    


CHART V


    
    
        CLIENT NAME: XYZ DEPARTMENT STORE
        TYPE OF SYSTEM: CREDIT APPROVAL
        PRODUCTION MODULE: RCP-X STEP 6

THE FOLLOWING TABLE GIVES THE MAXIMUM IMPROVEMENT IN RISK LEVEL TO BE ACHIEVED BY A CHANGE IN ANY ONE OF THE FOUR MOST IMPORTANT FACTORS INDICATED FOR ALL APPLICANT PROFILES CORRESPONDING TO DECLINE CELLS IN THE ACTION TABLE. ALSO INCLUDED IN THE TABLE ARE THE NEW ACTIONS WHICH WOULD RESULT IF EACH OF THE FOUR POSSIBLE CHANGES WERE TO HAVE OCCURRED INDIVIDUALLY.

    
    
















ACTION
FACTOR 1
FACTOR 2
FACTOR 3
FACTOR 4


TABLE
NET GAIN
NET GAIN
NET GAIN
NET GAIN


REF. NO.
RESULT
RESULT
RESULT
RESULT



















1
MAJOR CC
BANK REF
OIL CO.
MO. INC.



47.
30.
21.
18.



DECLINE
DECLINE
DECLINE
DECLINE


2
MAJOR CC
BANK REF
OIL CO.
MO. INC.



40.
34.
23.
16.



DECLINE
DECLINE
DECLINE
DECLINE


3
MAJOR CC
BANK REF
MO. INC.
DEPT. STR



28.
19.
19.
 9.



DECLINE
DECLINE
DECLINE
DECLINE


4
BANK REF
MAJOR CC
MO. INC.
HOUSING



26.
21.
18.
 4.



APPROVE
DECLINE
DECLINE
DECLINE


5
BANK REF
MO. INC.
OIL CO.
HOUSING



38.
13.
 3.
 2.



APPROVE
APPROVE
DECLINE
DECLINE




. . . .




145
MAJOR CC
HOUSING
DEPT. STR
OIL CO.



57.
17.
15
13.



APPROVE
DECLINE
DECLINE
DECLINE


146
MAJOR CC
HOUSING
OIL CO.
MO. INC.



51.
14.
14.
12.



APPROVE
APPROVE
APPROVE
DECLINE


147
MAJOR CC
HOUSING
DEPT. STR
MO. INC.



59.
16.
16.
15.



APPROVE
APPROVE
APPROVE
APPROVE


153
MAJOR CC
MO. INC.
OIL CO.
DEPT. STR



53.
19.
13.
13.



APPROVE
APPROVE
APPROVE
APPROVE


161
MAJOR CC
HOUSING
OIL CO.
DEPT. STR



54.
18
16.
14.



APPROVE
DECLINE
DECLINE
DECLINE


162
MAJOR CC
OIL CO.
HOUSING
MO. INC.



47.
17.
16.
 5.



APPROVE
APPROVE
APPROVE
DECLINE


163
MAJOR CC
HOUSING
DEPT. STR
MO. INC.



35.
18.
15.
 5.



APPROVE
APPROVE
APPROVE
APPROVE


169
MAJOR CC
OIL CO.
DEPT. STR
MO. INC.



49.
16.
12.
10.



APPROVE
APPROVE
APPROVE
APPROVE


177
MAJOR CC
HOUSING
OIL CO.
DEPT. STR



53.
22.
15.
14.



APPROVE
APPROVE
APPROVE
DECLINE


178
MAJOR CC
HOUSING
OIL CO.
DEPT. STR



46.
20.
16.
 0.



APPROVE
APPROVE
APPROVE
DECLINE









CHART IX


    
    
        CLIENT NAME: XYZ DEPARTMENT STORE
        TYPE OF SYSTEM: CREDIT APPROVAL
        PRODUCTION MODULE: RCP-X STEP 5
        XYZ DEPARTMENT STORE RISK EVALUATION SYSTEM RISK INDEX DENSITY FUNCTIONS
    
    

















RISK
GOOD
BAD
TOTAL

















INDEX
NUMBR
PCNT
NMBR 
PCNT
NMBR
PCNT
ODDS
CELLS


















203
71.
0.8
61.
8.1
132.
1.3
1.2
1


209
50.
0.5
32.
4.2
82.
0.8
1.6
1


211
114.
1.2
66.
8.8
181.
1.8
1.7
2


215
25.
0.3
13.
1.7
41.
0.4
2.1
1


218
91.
1.0
37.
4.9
128.
1.3
2.5
2


220
61.
0.7
22.
2.9
83.
0.8
2.8
1


222
68.
0.7
23.
3.1
91.
0.9
2.9
1


224
44.
0.5
13.
1.8
57.
0.6
3.3
2


226
106.
1.1
29.
3.8
135.
1.4
3.7
2


228
35.
0.4
9.
1.2
43.
0.4
4.0
1









CHART XI


    
    
        CLIENT NAME: XYZ DEPARTMENT STORE
        TYPE OF SYSTEM: CREDIT APPROVAL
        PRODUCTION MODULE: RCP-X STEP 6
        XYZ DEPARTMENT STORE ACTION TABLE FOR GRANTING CREDIT ACCOUNTS DEVELOPED BY STATCOMP
        STRATEGY: MAINTAIN CURRENT BAD DEBT RATE
    
    























MAJOR
OIL CO.
NONE
NONE
ONE-UP
ONE-UP


BANK REF
MO. INC.
HOUSING
CC
DEPT. STR
NONE
ONE-UP
NONE
ONE-UP







NONE
$0-900
RENT/OTH
NO
CELL NO.
 1.
 2.
 3.
 4.






ACTION
DECLINE
DECLINE
DECLINE
DECLINE


NONE
$0-900
RENT/OTH
YES
CELL NO.
 5.
 6.
 7.
 8.






ACTION
APPROVE
APPROVE
APPROVE
APPROVE


NONE
$0-900
OWN/BUY
NO
CELL NO.
 9.
10.
11.
12.






ACTION
DECLINE
DECLINE
DECLINE
DECLINE


NONE
$0-900
OWN/BUY
YES
CELL NO.
13.
14.
15.
16.






ACTION
APPROVE
APPROVE
APPROVE
APPROVE


NONE
901-1499
RENT/OTH
NO
CELL NO.
17.
18.
19.
20.






ACTION
DECLINE
DECLINE
DECLINE
DECLINE


NONE
901-1499
RENT/OTH
YES
CELL NO.
21.
22.
23.
24.






ACTION
APPROVE
APPROVE
APPROVE
APPROVE


NONE
901-1499
OWN/BUY
NO
CELL NO.
25.
26.
27.
28.






ACTION
DECLINE
DECLINE
DECLINE
APPROVE


NONE
901-1499
OWN/BUY
YES
CELL NO.
29.
30.
31.
32.






ACTION
APPROVE
APPROVE
APPROVE
APPROVE


NONE
$1500-UP
RENT/OTH
NO
CELL NO.
33.
34.
35.
36.






ACTION
DECLINE
DECLINE
DECLINE
APPROVE









CHART XIII


    
    
        CLIENT NAME: XYZ DEPARTMENT STORE
        TYPE OF SYSTEM: CREDIT APPROVAL
        PRODUCTION MODULE: RCP-X STEP 5

REFERENCE TABLE ENUMERATING ALL CELLS WHICH CORRESPOND TO EACH RISK LEVEL

INDEX NUMBER CORRESPONDING CELL ADDRESSES (SORTED INTO INCREASING ORDER)

    
    






















203
1
1








209
1
9








211
2
2
17







215
1
10








218
2
15
25







220
1
33








222
1
49








224
2
3
26







226
2
65
81







228
1
34








230
2
11
30







231
1
145








232
2
41
97







233
1
82








234
2
4
66







235
2
19
37







237
1
42








238
3
12
99
161






240
1
113








241
3
51
58
73






242
1
27








243
1
95








244
5
20
35
129
147
177




245
2
39
105







246
2
74
145







247
2
83
133







248
2
67
115







249
1
25








250
5
3
52
90
100
114




251
4
6
13
14
107





252
4
7
36
131
162





254
7
15
21
39
106
121
130
163


255
7
3
16
22
43
53
84
85


256
4
30
55
86
169





257
6
29
54
68
69
70
178



258
1
57









While examples have been used to disclose the invention, including the best mode, and also to enable any person skilled in the art to make and use the invention, the patentable scope of the invention is defined by claims, and may include other examples that occur to those skilled in the art. For example, it should be understood that the steps and the order of the steps in the flowcharts and other process flows described herein may be altered, deleted, modified and/or augmented and still achieve the desired outcome.
As another example, the systems and methods disclosed herein may be configured in a number of different ways. As illustrations, a risk evaluation system can be configured to have one or more of the following characteristics:
1. Simplicity of the end product.
Action tables provide the approval decision without the need of adding up numbers as scoring system users are required to do. This results in one or more of the following benefits:
A) Lower operating costs due to more rapid processing;
B) Elimination of erroneous decisions due to arithmetic errors; and
C) Elimination of score fudging where, in a scoring system environment, scorers may tend to add a few points to the applicant's final score if he is close to the numerical cutoff in order to grant an approval when the scorer disagrees with the system.
2. Accuracy.
A) Unique risk equations are derived for every applicant profile (action table cell) which provides more accurate estimates of creditworthiness than those obtained using other methods.
B) The risk evaluation system allows for a more accurate comparison of sampled populations by viewing the discrimination problem within the context of multidimensional contingency-table analysis. Using this approach, entire distributions are compared simultaneously over a multidimensional lattice of applicant profiles rather than resorting to the use of (and relying upon) a measure of separation which amounts to no more than a simple algebraic function of a couple of parameters from each of the two distributions (e.g. Fair Isaac and Co. measures the distance between two-distributions by the formula:




  
    
      (
      
        
          μ
          G
        
        -
        
          μ
          B
        
      
      )
    
    2
  
  
    
      1
      2
    
    ⁢
    
      (
      
        
          σ
          G
        
        +
        
          σ
          B
        
      
      )
    
  




where μG and μB are the respective means of the score distribution for the good and bad risk groups and σG and σB are the corresponding standard deviations).

3. Elimination of normality assumption and equal variance assumption.
Scoring system developers ignore violation of these assumptions as they know of no good solution to these problems. Because the fundamental nature of the approach embodied in the risk evaluation system differs radically from other methods used by scoring system developers, these assumptions are not required. Hence, models formulated during the risk evaluation process do not suffer the adverse affects which are incumbent with violated assumptions.
4. Smaller sample sizes are required for system development under the risk evaluation system.
This fact is due both to the methods of estimation employed during the risk evaluation system as well as the multistage approach towards system construction.
5. The risk evaluation system produces multidimensional acceptance rates for an approval policy whereas scoring systems provide only one dimensional acceptance rates.
6. The risk evaluation system produces percentage distribution forecasts for the applicant population by their profile components, and all combinations thereof, while other processes produce only a single forecast of the applicant score distribution. Thus, the risk evaluation system provides more detailed and exact estimates of the distribution of applicants by each individual profile than a scoring system which maps many different profiles to the same score (when their risk levels are the same) so that all information leading back to specific profiles is lost.
7. The risk evaluation system also provides a multidimensional analysis of the acceptee population mix which is not possible when other development processes are used.
8. Credit system compliance with Regulation B of the Equal Credit Opportunity Act.
A) The risk evaluation system produces credit approval systems which possess a table which enumerates four decline reasons for all decline cells in the action table. For each cell, the four reasons are ranked in order of importance and both the change (improvement) in risk to be obtained by the last response in each category as well as the resulting new decision is given. Scoring system users cannot supply accurately specific reasons for decline as they resort to looking at point differences on the scorecard to approximate the reasons for an applicant not making the numerical cutoff.
B) Effects Test. A scorecard development process is vulnerable to bias. This is true because ECOA Section 202.2(p)(1) that provides the standard for an empirically derived, demonstrably statistically sound (EDDSS) scorecard does not delve into the level of specificity around scoring system development to adequately address choice of model variables Scoring system developers openly admit to multiple optimal scorecards. It follows that no two of them will leave the same protected class invariant when scored out, i.e., significantly different acceptance rates will result from two different scorecards for the protected class in question. It turns out that the order in which variables are allowed to come into the predictor set has a great deal to do with how much weight is put on each factor. Since different factors have a different impact on protected classes, this implies that scorecards suffer from two main fair treatment drawbacks associated with the path-dependency of their final point score values, namely:

    
    
        1. There are a large number of alternative scorecards that possess different characteristics which have equal good/bad predictive power, while treating the protected class more favorably than the scorecard adopted by the institution
        2. There exist alternative scorecards that possess identical characteristics as the scorecard currently in use by the institution, but which have different point values and different relative importance of the model factors, and which exhibit comparable good/bad predictive power, while treating the protected class more favorably than the scorecard adopted by the institution.

In contrast, the risk evaluation process constructs a risk evaluation and policy formulation system which affords a choice of a specific policy for approval which is stated explicitly and exhaustively via an action table. Thus, the impact of any specific approval policy on a protected class of individuals can be easily quantified and, if need be, corrected if the situation warrants such action. This task can be accomplished via a profile analysis of the protected sub-population, followed by an analysis of the decline factors associated with decline cells exhibiting high incidence among the sub-population of interest.

    
    


9. Better Public Relations due to logical approval criteria. The policy embodied in an action table is logically based on historical repayment rates for each individual profile. Scoring systems, on the other hand, often exhibit irrational looking point criteria which puts them in an unfavorable light with respect to the public who are judged by the illogical criteria.
10. The final product from the risk evaluation system allows for immediate identification of individual profiles affected by a change in approval policy. A table specifying all profiles corresponding to each and every risk level is provided for this purpose. Scoring systems, on the other hand, cannot identify specific profiles affected by a change in policy. Hence, when a scoring system user changes the numerical cutoff, he does not know which profiles he has affected.
11. Applicant Profile Analysis.
Significant shifts in the structure of the applicant population with respect to any individual profile or group of profiles can be detected early on via this analysis so that changes in the systems performance can be anticipated, understood, and corrected. All that is required is a tally of the number of applicants corresponding to each individual cell in the action table. The profiles are identified easily by their action table reference numbers. The new totals are added to the development sample (or census) counts in every cell and the percentage of applicants is re-calculated for every action table cell (distinct applicant profile). This technique is far more powerful than the corresponding early warning measures employed by scoring system users to explain shifts in score distribution as they relate to various sub-strata in the applicant population.
12. System Updating.
Systems developed by the risk evaluation process are easier to update than scoring systems. Because of estimation procedures used during the risk evaluation process, updates can also be made more frequently than for scoring systems.
System updating focuses on a re-examination of the degree of risk that the system associates with various applicant profiles specified in the action table. A performance audit is carried out on the client's customer master file for all accounts opened since the date of system installation. Provided that the appropriate action table reference numbers are maintained on this file, there is no need for re-sampling as is the case with scoring system validation studies. The number of good, bad, and indeterminate loans that fall outside of any exclusion criteria can simply be tallied for each action table reference number. Results from this audit are analyzed to determine whether or not the overall distribution of newly acquired good and bad customers is significantly different from that of the previously sampled good and bad customers. Finally, appropriate adjustments are made so as to ensure accurate risk estimates for those profiles which are affected. This final step is not possible with a scoring system, as point values on the scorecard cannot be updated. Hence, with a scoring system, if an update is indicated, the developer undertakes to reconstruct an entirely new scoring system at a substantial cost to the system user in terms of both time and money. Furthermore, scoring system developers re-sample because they cannot retrieve applicant profiles from the score on a customer master file as is possible with action table reference numbers.
13. The two previous items in this section (namely items 11 and 12) provide the means whereby a risk evaluation system can, with historical data used as a starting solution, adapt over time in a non-stationary environment. There are two ways that a system can diminish in effectiveness, namely: 1) the distribution of applicants corresponding to specific profiles changes, or 2) the risk associated with specific profile changes. By way of the above referred to items, these time varying parameters are adjusted as additional information becomes available. In contrast, scoring systems represent static models in a constantly changing environment. From the very time of scoring system installation, the signal to noise ratio decreases over time until the system finally self-destructs. Consequently, the accuracy of decisions made by a scoring system diminishes steadily over time. It should also be noted that both the applicant distribution and the degree of risk, relative to the cells in an action table, may alternatively be forecast using any method desired and the results can be incorporated into the action table to simulate the impact on individual risk profiles and to test different policy formulations in order to determine how to achieve any of a number of different stated objectives (e.g. maximize revenue, minimize credit losses, maintain an acceptance rate, increase overall market share by ten percent, increase a particular product's share by twenty percent, etc.) or to optimize profitable portfolio growth, or marketing campaigns, in general. Furthermore, the assumptions underlying a particular forecast may be linked directly, or indirectly, to a single, or multi-stage, action table by including the discrete analog (e.g. a variable based on specific ranges of values) of one or more forecasting model variables as one, or more, dimensions in the action table. In this way the action table may include cells that are based upon risk profiles determined by the individual applicant, borrower, or customer, and also by assumptions relative to one or more factors relative to corporate, economic, market, collateral, or other business-related conditions.
14. In a broader sense, the information components of an action table cell may be expanded to include all of the elements of a profit and loss statement, plus other operating statistics, for the associated segment of customers, borrowers, or applicants. Rate of attrition, propensity to buy, 30-60-90 day delinquency rates, average age of account, average remaining term on closed-end loan, average credit line utilization on an open-ended loan, gross credit loss rate, recovery rate, overlimit rate, single pay default rate, rate of fraudulent transactions, average annual fraud dollar charge-off, response rate to various types of promotional offers, average cross-selling rate for one or more products, average annual dollars of revenue generated, average annual dollars of finance charges paid, annual profit per account, etc. are examples of measures that can be captured and utilized in the action table framework. Optimization of policies embodied in an action table to achieve a stated objective, or possibly multiple objectives, can be accomplished by simulation and experimentation with different policy modification schemes under varying assumptions, or by deploying optimization methods directly. Direct application of optimization via a linear programming approach includes the formulation of the pertinent action table cell components as an activity n-tuple (subscripted variable), formulation of the policy objective as a function of the activity variables, with associated objective function coefficients, the specification of risk constraints based upon the cell risk index functions, and specification of bounds on marginal totals and values in the rows of the single, or multi-stage, action table that constitute the right-hand side values of the set of linear constraints. For more complex policy optimization problems, simultaneous objective functions (including hierarchical subordinate objectives) may be specified and the optimization problem may be solved using goal programming and other techniques that are commonplace in the field of operations research.
It is further noted that the systems and methods disclosed herein may be implemented on various types of computer architectures, such as for example on a single general purpose computer or workstation, or on a networked system, or in a client-server configuration, or in an application service provider configuration.
It is further noted that the systems and methods may include data signals conveyed via networks (e.g., local area network, wide area network, internet, etc.), fiber optic medium, carrier waves, wireless networks, etc. for communication with one or more data processing devices. The data signals can carry any or all of the data disclosed herein that is provided to or from a device.
Additionally, the methods and systems described herein may be implemented on many different types of processing devices by program code comprising program instructions that are executable by the device processing subsystem. The software program instructions may include source code, object code, machine code, or any other stored data that is operable to cause a processing system to perform methods described herein. Other implementations may also be used, however, such as firmware or even appropriately designed hardware configured to carry out the methods and systems described herein.
The systems' and methods' data (e.g., associations, mappings, etc.) may be stored and implemented in one or more different types of computer-implemented ways, such as different types of storage devices and programming constructs (e.g., data stores, RAM, ROM, Flash memory, flat files, databases, programming data structures, programming variables, IF-THEN (or similar type) statement constructs, etc.). It is noted that data structures describe formats for use in organizing and storing data in databases, programs, memory, or other computer-readable media for use by a computer program.
The systems and methods may be provided on many different types of computer-readable media including computer storage mechanisms (e.g., CD-ROM, diskette, RAM, flash memory, computer's hard drive, etc.) that contain instructions for use in execution by a processor to perform the methods' operations and implement the systems described herein.
The computer components, software modules, functions, data stores and data structures described herein may be connected directly or indirectly to each other in order to allow the flow of data needed for their operations. It is also noted that a module or processor includes but is not limited to a unit of code that performs a software operation, and can be implemented for example as a subroutine unit of code, or as a software function unit of code, or as an object (as in an object-oriented paradigm), or as an applet, or in a computer script language, or as another type of computer code. The software components and/or functionality may be located on a single computer or distributed across multiple computers depending upon the situation at hand.
As another example of the wide scope of the systems and method described herein, FIG. 12 depicts a system that has been configured to modify the criteria 920 for factors of stage 1 900 as described above to add categories of factors that have the greatest causality on the final outcome based on established expert judgment. As shown at 1000 in FIG. 13 for example, there can be five categories (known as the 5 C's of credit in the industry), namely character, capacity, capital, collateral, and conditions. Character usually is assessed based on current and past credit usage and willingness to pay as measured by past payment history (spanning possibly both credit and non-credit obligations). Capacity would deal with income, monthly obligations, debt-to-income ratio, and payment shock. Capital would address net worth, liquid assets, months of reserves, and down payment/loan-to-value ratio. Collateral would cover properties (location, age, physical attributes) of the item being financed any pledged assets, the valuation of those assets, and price volatility/liquidity over time. Conditions refers to the product terms (loan amount, maturity, pricing, payment options, etc.), and market/competitive forces. In addition, there are channel and geographic factors that can be utilized.
The system can be configured to overcome other issues in the credit scoring field. As background, the use of credit scoring has caused focus in lending to be credit bureau-specific, and frequently consumer and small business scorecards are built solely based on this data. There are six main areas of credit bureau data that scorecards typically focus on as described below:

    
    
        1) Depth of experience with credit (number and age of trade lines, average months in file over all trades)
        2) Search for Credit (number of inquiries by lenders over a set period of time)
        3) Credit products used and prevalence of certain categories of them (e.g. the ratio of installment to revolving trade lines)
        4) Credit utilization (There is a tipping point between insufficient and too much usage typically, e.g. if 66% utilization is exceed, subtract points, whereas if below the threshold down to a floor amount, points would be added.)
        5) Payment performance over time, including frequency and severity of delinquency or derogatory credit (there may or may not be a minimum dollar threshold, such as $100, for an item to count. Frequency and age of delinquent payments are key aspects in rating performance)
        6) Public records (bankruptcy, court judgments, liens, charge-offs) Again, there may or may not be a minimum dollar threshold, such as $100, for an item to count.

Credit scoring seeks to discriminate between good and bad credits using statistical modeling (discriminant analysis, correlation and regression analysis, etc.) Variables are included in the model if, at the margin, they provide the maximum predictive lift among the remaining candidate variables. The process halts when the addition of any factor fails to significantly improve the model's ability to correctly identify good and bad credits. Because of this fact, even causal factors, such as income level, debt ratio, net worth, and months of reserves, may not be included in the model. In a sense, the models determine what the evaluation criteria will be, and this is based largely on the data that are made available. Many lenders create judgmental overlays that are applied “after the fact” for credit scoring models in order to enforce rules based on credit policy guidelines and the prevailing market conditions, i.e. model first, and then apply judgment. Finally, the credit bureau scores that are calculated for consumers are actually based upon ten different scorecards. A particular scorecard is selected for a consumer based on how thick/thin their credit bureau file is and also on their payment performance category (e.g. good, mild delinquency, moderate delinquency, severe delinquency/public records). This amounts to a behavioral segmentation scheme.

    
    


In contrast, FIG. 14 depicts a system that can be configured to provide a software module 1100 to allow for judgmental factors to be “instilled” into the model. The judgmental factors supplied by a user to the module 1100 can be included in the primary (stage 1) action table as shown in FIG. 14. In this way, there is less risk of relying too much on the models to the point where common sense would dictate otherwise. Also, there is far less model risk when a significant foundation of the model rests on. The approach can be “judgment first, then apply models for fine tuning” to avoid the tail wagging the dog syndrome.
Relative to segmentation, the system of FIG. 14 can leverage the credit contour (CC) of the credit applicant, where credit contour is a distinctive pattern of values relating to capacity, capital, and payment history for a consumer or business. Once the CC is known, the borrower can be mapped to the proper segment for decisioning. Consider the following 12 segment “generic credit market” model:
















Payment History (Credit + Non-Credit)
3 values (G/F/P)



Capacity (Income + DTI)
2 values (H/L)



Capital (Liquid Reserves + Down payment/LTV)
2 values (H/L)










Further, only certain products/programs would be available within the segments. In this situation, the stage 1 action table might contain secondary factors based upon the segment assignment 1200.

The system can also be configured to limit the action table loan decisioning/pricing to at most 2 stages and to handle calculating the overall risk of default based upon the joint probabilities of stage 1 plus stage 2 factors. As discussed above, with the one stage system, the cell odds estimate is ωθ, so that ωψ=ωθ*ωξ amounts to a refinement of the stage one estimate. Note the assumption of independence here. This can be viewed as:

    
    
        A) Independence need not hold for the group of applicants approved at the first stage since their odds estimate is never refined further;
        B) Any approximations derived without the assumption would be less accurate since abandonment at the assumption would entail the calculation of a matrix of conditional probabilities at the form P(ωξ|θ) which represents n×m terms (where n, m are the number of cells in action tables one and two respectively) and, in many instances, the data are too sparse for these calculations to be meaningful.”

First, if the previously defined credit contour is used as a segmentation scheme, then the population odds for individual segments may be estimated and applied to the action table cell risk estimates to arrive at a probability of default in the case of a single stage system. Alternatively, if the Five C's of credit (or some subset) is used as a source for stage one factors, then the total number of stages can be limited to just two. Recall that in stage one we specify, for every handle cell, whether secondary factors are required to render a decision to approve the loan. If secondary factors are not required, then the approve or decline decision appears in the handle cell. If secondary factors are required, then the business rules for qualifying the loans falling into the handle cell are specified fully and the handle cell action is designated as “Stage 2.” The stage 2 action table has handle cell numbers beginning with the number equal to the number of cells in the handle plus one. If the stage 1 action table has “n” cells, then the total number of cells for all stages is at most “2n.”

    
    


As an example, FIG. 15 illustrates at 1300 a two-stage action table to handle small business loans. In this example, the stage 2 action table begins with action cell number 25. Suppose in the example that handle cells with risk category 0 were approved and those with risk category 4 were declined, and that handle cells with risk categories 1, 2, and 3 are referred on to stage 2. Then there are 20 stage 2 action table cells, numbered 25 through 44. Loans approved in stage 2 maintain the stage 2 action cell number. Those that are declined revert back to their primary handle cell number. For example, suppose that a loan falling onto handle number 22 is approved in stage 2. Then we can derive the associated action table reference number by adding the primary handle action table number (22) to the number of entries in the stage 2 table (20) and add the number of non-stage 2 handle cells that possess a higher handle cell number (2)=44. For a loan falling onto handle number 2 is approved in stage 2, the associated action table reference is calculated to be the primary handle action table number (2) plus the number of entries in the stage 2 table (20), plus the number of non-stage 2 handle cells that possess a higher handle cell number (3)=25.
As shown in FIG. 16, a system can also be configure to accommodate changes in policy that result in a loosening or tightening of credit. In credit scoring, there are typically two ways to tighten/loosen credit. The first is to simply change the score cutoff, raising it to tighten credit, and lowering it to loosen credit. The second way is to apply low or high-side overrides. The second alternative is not under control of the scorecard and it tends to invalidate the use of scoring by second-guessing the result.
A system can be configured to include a credit adjustment process as shown at 1400. The credit adjustment process can operate in different ways. A first way (as shown at 1430 in FIG. 17) is to include/exclude specific action cells in the various stages of decisioning. A second way (as shown at 1440 in FIG. 18) would be to add or remove secondary factor rules within one or more action table cells (e.g., usually in stage 2). An advantage of such a system is that there are no system overrides. In the case of the second type of adjustment, however, the composition of any particular cell, based upon the rules applied, may change. This means that over time, the population of credit applicants falling into a particular action cell may vary somewhat in their secondary qualifications, but they will still possess the same basic credit factors as others in the same cell—i.e. they will have the same credit contour. The multi-dimensional acceptance rate forecasts and acceptee population mix percentage distributions that are based upon the development sample will vary to a greater extent for the cells where secondary factors have been modified.
Credit adjustment may depend upon whether the primary factors are used in the stage 1 action table or if they are used for segmentation and the secondary factors are present in the stage 1 action table. In the former case, the secondary factor adjustment method would likely be the predominate one. That said, the two approaches are not mutually exclusive. A change in credit policy might involve adjustment of the action associated with one or more cells, coupled with the modification of secondary factors and thresholds associated with primary cells where the actions are neither to approve or decline, but to go to stage 2.
With respect to model validation and maintenance, a system can be configured as shown in FIG. 19 to perform analyses to assess model reasonableness and gauge performance. For example, software module 1500 can analyze natural orderings of cells 1510, such as based on broad categorizations of action table reference numbers, which can be used to raise flags if risk rankings are in non-intuitive order. For example, if two cells are identical except that one has a weaker rating than the other in one category, and yet it is ranked as less risky, then this would not make sense and further investigation to determine the root cause would be required. This provides an added safety net against a faulty model or bad data, etc.
Furthermore as discussed above, system maintenance can be concerned with the degree of risk associated with an action cell, or the percentage of applicants falling into an action cell. For this approach and as shown in FIG. 20, software module 1600 can help examine certain statistical characteristics of the cells. For example, a software module as shown in FIG. 21 at 1610 can examine the residual values in each cell, when compared with the development sample, or cumulative experience through the prior reporting period. Cell estimates can be adjusted accordingly as described above with respect to system updating. The system can also include a software module 1620 for adding, to the cell counts, tallies of loan applications and good/bad performing loans, at regular intervals.
Another embodiment is to examine the relationship between action cells with respect to both of these measures. More specifically, the ordering of the action cells by applicant percentage and by risk index, can be captured at different points in time and any changes can be compared and the implications assessed. Yet another approach would be to analyze deciles, or quintiles, and observe where action cells fall and if some are migration towards the riskier (rightmost) tail of the distribution.

## Claims

1. A computer-implemented system for evaluating risks associated with alternative strategies for assessing an entity with respect to a predetermined objective, wherein software instructions operate within a processor-based environment, said system comprising:
a computer-readable action table;
wherein the action table contains a plurality of possible actions that can be taken with respect to the predetermined objective for various entity profiles;
wherein the action table contains an action for each entity profile;
wherein the possible actions of the action table relate to a credit approval process, credit collection process, or promotion process;
wherein criteria for factors of the action table are based upon a plurality of credit-risk assessment categories;
wherein the plurality of credit-risk assessment categories include character criteria, capacity criteria, capital criteria, collateral criteria, or conditions criteria;
one or more computer-readable statistical data stores that are configured to contain risk amounts associated with each entity profile;
wherein the one or more statistical data stores are configured to contain inferred percentage distribution of applicants associated with each entity profile;
one or more profile identification data stores;
wherein a computer-readable profile identification data store contains entity identification information for use in determining an action for the entity;
software instructions to determine an action for the entity by comparing characteristics associated with the entity with characteristics associated with the entity profiles contained in the action table;
one or more computer-readable improvement data stores;
wherein an improvement data store provides an indication in an improvement in risk based upon a change in one or more characteristics for an entity profile;
one or more computer-readable protected class data stores;
wherein a protected class data store provides an indication of an impact of a policy change on a particular protected class, both with respect to an approval, collection, or promotion decision and relative to one or more characteristics, or combinations of characteristics, for an entity profile;
software instructions for analyzing cell orderings and cell distributions in the action table;
said analyzing cell orderings and cell distributions includes determining degree of risk associated with an action cell or percentage of credit applicants associated with an action cell;
one or more data processors configured to execute the software instructions for determining the action for the entity and the software instructions for analyzing the cell orderings and the cell distributions.

2. The system of claim 1, wherein the action table is used within a multi-stage system to determine whether an entity is to be approved in the credit approval process;
wherein criteria for factors of a first stage comprise the plurality of credit-risk assessment categories;
wherein the first stage includes accept or decline or investigate actions;
wherein a second stage is used if the decision from the first stage is an investigate action.

3. The system of claim 1, wherein the possible actions indicate accept or decline decisions with respect to the credit approval process or indicate what products are to be offered or indicate what pricing is to be used.

4. The system of claim 1, wherein the possible actions indicate decisions with respect to a sub-approval process.

5. The system of claim 1, wherein the character criteria include criteria related to current and past credit usage and willingness to pay as measured by past payment history.

6. The system of claim 1, wherein the capacity criteria include criteria related to income, monthly obligations, debt-to-income ratio, and payment shock.

7. The system of claim 1, wherein the capital criteria include criteria related to net worth, liquid assets, months of reserves, and down payment/loan-to-value ratio.

8. The system of claim 1, wherein the collateral criteria include criteria related to properties of the item being financed, any pledged assets, the valuation of those assets, and price volatility or liquidity over time.

9. The system of claim 8, wherein the properties of the item being financed include location and age of the item being financed.

10. The system of claim 1, wherein the conditions criteria include criteria related to product terms and market forces.

11. The system of claim 10, wherein the product terms include loan amount, maturity, pricing, and payment options.

12. The system of claim 1, wherein the action table is used within a single-stage system to determine whether an entity is to be approved in the credit approval process;
wherein criteria for factors of the single-stage system comprise the plurality of credit-risk assessment categories;
wherein, with a credit contour being used as a segmentation scheme, the population odds for individual segments are estimated and applied to action table cell risk estimates to determine a probability of default.

13. The system of claim 12, wherein the action table is used within a multi-stage system to determine whether an entity is to be approved in the credit approval process;
wherein the multi-stage system contains a first stage and a second stage;
wherein criteria for factors of the first stage comprise the plurality credit-risk assessment categories;
wherein the first stage includes for every handle cell, a decision of whether secondary factors are required to render a decision to approve a loan;
wherein if secondary factors are not required, then the approve or decline decision appears in the handle cells of the first stage;
wherein if secondary factors are required, then business rules for qualifying the loans are associated with the handle cells, and actions of the handle cells are associated with the second stage cells.

14. The system of claim 13, wherein an action table of the second stage has handle cell identifiers that are based upon a number equal to number of cells in the handle.

15. The system of claim 1 further comprising:
action table cell processing software instructions for including or excluding one or more action cells in order to generate a decision.

16. The system of claim 15, wherein said including or excluding one or more action cells obviates a requirement of system overrides for relaxing or tightening credit policy accommodations.

17. The system of claim 1 further comprising:
action table cell modification software instructions for modifying secondary factor rules within one or more cells of the action table.

18. The system of claim 17, wherein said modifying of the secondary factor rules includes adding or removing the secondary factor rules within the one or more cells of the action table.

19. The system of claim 1, wherein said analyzing cell orderings and cell distributions includes determining residual values in each action cell with respect to a development sample data or historical data;
wherein the estimates for action cells are adjusted based upon the determined residual values.

20. The system of claim 19, wherein counts of the action cells are based upon number of loan applications and good-bad performing loans.

21. The system of claim 19, wherein the historical data includes data acquired from a prior credit reporting period.

22. The system of claim 1, wherein said analyzing cell orderings and cell distributions includes ordering of the action cells by applicant percentage, or by risk index, or by applicant percentage and risk index.

23. The system of claim 1 further comprising:
software instructions for determining degree of risk associated with an action cell,
said determining degree of risk includes analyzing probability distribution segments to determine if the action cell is associated with a riskier tail of the probability distribution.

24. A computer-implemented method for evaluating risks associated with alternative strategies for assessing an entity with respect to a predetermined objective, said method comprising:
determining, using one or more data processors, an action for the entity by comparing characteristics associated with the entity with characteristics associated with entity profiles contained in an action table;
wherein an improvement data store provides an indication in an improvement in risk based upon a change in one or more characteristics for an entity profile;
wherein a protected class data store provides an indication of an impact of a policy change on a particular protected class, both with respect to an approval, collection, or promotion decision and relative to one or more characteristics, or combinations of characteristics, for an entity profile;
analyzing, cell orderings and cell distributions in the action table;
said analyzing cell orderings and cell distributions includes determining degree of risk associated with an action cell or percentage of credit applicants associated with an action cell;
wherein the action table contains a plurality of possible actions that can be taken with respect to the predetermined objective for various entity profiles;
wherein the action table contains an action for each entity profile;
wherein the possible actions of the action table relate to a credit approval process, credit collection process, or promotion process;
wherein criteria for factors of the action table are based upon a plurality of credit-risk assessment categories;
wherein the plurality of credit-risk assessment categories include character criteria, capacity criteria, capital criteria, collateral criteria, or conditions criteria;
wherein one or more computer-readable statistical data stores are configured to contain risk amounts associated with each entity profile;
wherein the one or more statistical data stores are configured to contain inferred percentage distribution of applicants associated with each entity profile;
wherein a computer-readable profile identification data store contains entity identification information for use in determining an action for the entity.

25. A computer-implemented system for evaluating risks associated with alternative strategies for assessing an entity with respect to a predetermined objective, wherein software instructions operate within a processor-based environment, said system comprising:
a computer-readable action table;
wherein the action table contains a plurality of possible actions that can be taken with respect to the predetermined objective for various entity profiles;
wherein the action table contains an action for each entity profile;
wherein the possible actions of the action table relate to a credit approval process, credit collection process, or promotion process;
wherein criteria for factors of the action table are based upon a plurality of credit-risk assessment categories;
wherein the plurality of credit-risk assessment categories include character criteria, capacity criteria, capital criteria, collateral criteria, or conditions criteria;
one or more computer-readable statistical data stores that are configured to contain risk amounts associated with each entity profile;
wherein the one or more statistical data stores are configured to contain inferred percentage distribution of applicants associated with each entity profile;
one or more profile identification data stores;
wherein a computer-readable profile identification data store contains entity identification information for use in determining an action for the entity;
software instructions to determine an action for the entity by comparing characteristics associated with the entity with characteristics associated with the entity profiles contained in the action table;
one or more computer-readable improvement data stores;
wherein an improvement data store provides an indication in an improvement in risk based upon a change in one or more characteristics for an entity profile;
one or more computer-readable protected class data stores;
wherein a protected class data store provides an indication of an impact of a policy change on a particular protected class, both with respect to an approval, collection, or promotion decision and relative to one or more characteristics, or combinations of characteristics, for an entity profile;
software instructions for incorporating judgmental factors from a user into a stage of the action table for determining an action for the entity;
one or more data processors configured to execute the software instructions for determining the action for the entity and the software instructions for incorporating judgmental factors.