Patent Document

CROSS REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit of U.S. Provisional Application No. 60/173,695, filed Dec. 30, 1999, which is hereby incorporated by reference in its entirety. 
    
    
     BACKGROUND OF THE INVENTION 
     This invention relates generally to valuation methods for financial instruments and more particularly to rapid valuation of large numbers of financial instruments. 
     A large number of assets such as loans, e.g., ten thousand loans or other financial instruments, sometimes become available for sale due to economic conditions, the planned or unplanned divestiture of assets or as the result of legal remedies. The sale of thousands of commercial loans or other financial instruments sometimes involving the equivalent of billions of dollars in assets must sometimes occur within a few months. Of course, the seller of assets wants to optimize the value of the portfolio, and will sometimes group the assets in “tranches.” The term “tranche” as used herein is not limited to foreign notes but also includes assets and financial instrument groupings regardless of country or jurisdiction. 
     Bidders may submit bids on all tranches, or on only some tranches. In order to win a tranche, a bidder typically must submit the highest bid for that tranche. In connection with determining a bid amount to submit on a particular tranche, a bidder often will engage underwriters to evaluate as many loans as possible within a tranche and within the available limited time. When the time for submitting a bid is about to expire, the bidder will evaluate the loans underwritten at that time, and then attempt to extrapolate a value to the loans that have not then been analyzed by the underwriters. 
     As a result of this process, a bidder may significantly undervalue a tranche and submit a bid that is not competitive or bid higher than the underwritten value and assume unquantified risk. Of course, since the objective is to win each tranche at a price that enables a bidder to earn a return, losing a tranche due to significant undervaluation of the tranche represents a lost opportunity. 
     Currently, business enterprises assess an acquisition or sale of assets and portfolios of assets on rapid schedules and often at great distances and varying time zones from the general management teams and functional heads which typically approve the offers for purchase or sale of these assets. Employees, partners and collaborators associated with the due diligence regarding the purchase of the assets are typically brought together for a relatively short duration of time to accomplish the due diligence. Typically due diligence activity is conducted in physical proximity to the sources of information associated with the assets. The collaborating personnel often do not have the benefit of training or knowledge of the complete set of analytical tools at their disposal nor do they have “best practices” from previous efforts of a similar nature. 
     Consolidation of employees and collaborators into a remote physical location for the duration of the due diligence effort is time consuming and expensive. In addition, persons on due diligence teams search for data and processes in an ad hock fashion, typically relying on a small subset of other personnel who have detailed information about information sources, underwriting, analytical tools, reports, and completed analysis. The subset of individuals who have the information become bottlenecks within a due diligence time line, driving up due diligence costs and adding time that could have otherwise been invested in more value added due diligence. Core information relevant to an asset portfolio bid is typically consolidated in a well controlled physical location, sometimes referred to as a war room. 
     It would be desirable to have a collaboration mechanism that brings the best of a company&#39;s previous experience and knowledge to bear on due diligence issues and that allows teams to become knowledgeable efficiently when considering assets purchases and to consolidate analytical building blocks in a repository that may be deployed quickly in future purchase deliberations, without the time and expense of the known war room approaches. 
     BRIEF SUMMARY OF THE INVENTION 
     In an exemplary embodiment, the invention is an integrated system which organizes a company&#39;s experiences, operating procedures, best practices, information sources, competitive information and analytical tools. In practice the goal when using the tool is to increase the profitability of an entity in a due diligence process while facilitating the ongoing operations for which the due diligence team members are responsible. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a flow diagram illustrating a known process for valuing a portfolio of loans; 
         FIG. 2  is a flow diagram illustrating valuing a portfolio of loans in accordance with one embodiment of the present invention; 
         FIG. 3  is a flow diagram illustrating, in more detail, one embodiment of a first portion of a rapid valuation process for large loan portfolios that breaks loans into categories of variance; 
         FIG. 4  is a flow diagram illustrating a second portion of a rapid valuation process for a large loan portfolios that aggregates from a basis to a tranche or portfolio basis; 
         FIG. 5  illustrates a probability distribution for exemplary assets whose recovery value is inferred; 
         FIG. 6  is a flow diagram of a supervised learning step of the process of  FIG. 3 ; 
         FIG. 7  is a flow diagram of an unsupervised learning step of the process of  FIG. 3 ; 
         FIG. 8  is an embodiment of the process for unsupervised learning; 
         FIG. 9  is an embodiment of the generation  1  (first pass) rapid loan valuation process; 
         FIG. 10  is a flow diagram of a fuzzy clustering method used in the unsupervised learning of  FIG. 8 ; 
         FIG. 11  is a pair of tables showing an example of model selection and model weighting for a rapid loan evaluation process; 
         FIG. 12  is a table showing exemplary attributes for a rapid loan valuation process; 
         FIG. 13  is a flow diagram of an exemplary clustering method for a rapid loan valuation process; 
         FIG. 14  is a system diagram; and 
         FIG. 15  is a diagram illustrating due diligence tools and processes. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       FIG. 1  is a diagram  10  illustrating a known process for valuing a large portfolio of assets  12  through an underwriting cycle and through to making a bid for purchasing asset portfolio  12 , for example, in an auction.  FIG. 1  is a high level overview of a typical underwriting and extrapolation process  10  which is not iterative and not automated. In diagram  10 , underwriters underwrite  14  a number of individual assets from portfolio  12  to generate an underwritten first portion  16  and an untouched remainder portion  18 . Before any of the assets are underwritten, first portion  16  is zero percent and remainder portion  18  is one hundred percent of portfolio  12 . As the underwriting process progresses, first portion  16  increases and remainder portion  18  decreases. The objective is to underwrite as many assets as possible before a bid is submitted for the purchase of asset portfolio. The team of underwriters continues individually underwriting  14  until just before a bid must be submitted. A gross extrapolation  20  is made to evaluate remainder portion  18 . The extrapolated value  20  becomes the non-underwritten inferred value  24 . The gross extrapolation generates a valuation  24  for remainder portion  18 . Valuation  22  is simply the total of the individual asset values in first portion  16 . However, valuation  24  is a group valuation generated by extrapolation and may be discounted accordingly. Valuations  22  and  24  are then totaled to produce the portfolio asset value  26 . Valuation processes are performed on each tranche of the portfolio. 
       FIG. 2  is a diagram illustrating one embodiment of a system  28  for rapid asset valuation. Included in  FIG. 2  are representations of process steps taken by system  28  in valuating asset portfolio  12 . System  28  individually evaluates (“touches”) every asset, except for a very small quantity  30  of untouched assets considered statistically insignificant or financially immaterial. Specifically, all assets in portfolio  12  other than quantity  30  undergo an iterative and adaptive valuation  32  in which the assets in portfolio  12  are individually valued, listed individually in tables and then selected from the tables and grouped into any desired or required groups or tranches for bidding purposes (as described below.) As in diagram  10 , underwriters begin a full underwrite  14  of individual assets in portfolio  12  to produce a fully underwritten first portion  16  of assets. Underwriters also underwrite  34  a sample of assets in a second portion  36  of portfolio  12 , and a computer  38  statistically infers  40  value for a third portion  42  of portfolio  12 . Computer  38  also repetitively generates 44 tables (described below) showing values assigned to the assets in portions  16 ,  36  and  42  as described below. In one embodiment, computer  38  is configured as a stand alone computer. In another embodiment, computer  38  is configured as a server connected to at least one client system through a network (shown and described in  FIG. 14 ), such as a wide-area network (WAN) or a local-area network (LAN). 
     For example, and still referring to  FIG. 2 , an unsampled and non-underwritten portion  46  of a third portion  42  of portfolio  12  is subjected to a statistical inference procedure  40  using fuzzy-C means clustering (“FCM”) and a composite High/Expected/Low/Timing/Risk (“HELTR”) score to generate two categories  48  and  50 . HELTR is defined as H—High cash flow, E—Expected cash flow, L—Low cash flow, T—Timing of cash flow (for example in months: 0–6, 7–18, 19–36, 37–60), and R—Risk assessment of borrower (9—boxer used by credit analysts). Category  48  is deemed to have sufficient commonality for evaluation as a whole. Category  50  is further divided into clusters  52  and  54  that are, in turn, further subdivided. Cluster  52  is divided into subclusters  56  and  58 , while cluster  54  is subdivided into subclusters  60 ,  62  and  64 . Cluster and subclusters are shown both in a “tree” chart  66  and as boxes in valuation block  68 . These individual asset values are then regrouped into tranches  70 ,  72  and  74  for bid purposes. Any number of tranches could be assembled in any arrangement set by the seller. 
     Individual asset data (not shown) for each asset in portfolio  12  is entered into a database  76  from which selected data  78  is retrieved based on a given criteria  80  for the iterative and adaptive process  32 . When criteria  80  is established for valuation of any asset, that established criteria  80  is stored in database  76  for use in valuating other asset data in database  76  which shares such an established criteria. Iterative and adaptive valuation process  32  thus develops  82  valuations (described below) and groups  84  them for use in bidding. 
       FIGS. 3 and 4  together form a flowchart  85  illustrating a functional overview of one embodiment of system  28  (shown in  FIG. 2 ) for evaluation of a large asset portfolio  12 . Valuation procedures  14 ,  34  and  40  (see also  FIG. 2 ) are simultaneously and sequentially used in system  28  in a manner described below. As described above, full underwriting  14  is a first type of valuation procedure. Grouping and sampling underwriting  34  with full underwriting of the samples is a second type of valuation procedure. Statistical inference  40  is a third type of valuation procedure, which is an automated grouping and automated valuation. Procedures  14 ,  34  and  40  are based on objective criteria established as described below. 
     “Underwriting” as used herein means a process in which a person (“underwriter”) reviews an asset in accordance with established principles and determines a current purchase price for buying the asset. During underwriting, the underwriter uses pre-existing or established criteria  80  for the valuations. “Criteria” means rules relevant to asset value and a rating based on such categories. For example, as a criteria, an underwriter might determine three years of cash flow history of the borrower to be a category of information relevant to asset valuation and might give a certain rating to various levels of cash flow. 
     Full underwriting  14  is done in two ways, a full cash basis manner  86  and a partial cash basis manner  88 . Both full cash basis manner  86  and partial cash basis manner  88  start with sets  90  and  92  of assets that are fully individually reviewed  14  (see  FIG. 2 ). Such full review  14  is usually due to the large dollar, or other appropriate currency, amounts of the assets being reviewed relative to other assets in the portfolio or due to the borrower being so well known or so reliable that the assets can be quickly and reliably fully underwritten or the assets are marked to market such that there is very little variance associated with the value of said assets. Asset set  90  is evaluated by underwriters  94  and each asset in set  90  receives a valuation with very little variation such as an asset backed with cash or a tradable commodity with full cash value and is placed in a full value table  96 . Selected individual values for assets in table  96  are stored as a fully underwritten group value  98 . 
     Set  92  is evaluated by a team of underwriters  100 , which could be the same as team  94 , but each asset receives a discounted or partial value and is placed in a partial value table  102 . Selected individual values for assets in a tranche in table  102  are stored as a partial value fully underwritten group value  104 . Criteria  80  (shown in  FIG. 2 ) for full cash basis manner  86  and partial cash basis manner  88  are stored in database  76  (shown in  FIG. 2 ) in a digital storage memory (not shown) of computer  38  (shown in  FIG. 2 ) for use in supervised learning  206  and unsupervised learning  208  of automated valuation  40 . 
     Sampling underwriting  34  is accomplished using two procedures, a full sampling  106  procedure and a partial sampling  108  procedure. Full sampling  106  is utilized for categories of large assets and includes a one hundred percent sampling  110  of the sample groups in the categories of assets being sampled. The assets in full sampling  106  are not individually underwritten but rather are underwritten in full sampling groups  112  based on a determined commonality. A resulting full sampling group valuation (not shown) is created and then desegregated based on a rule  114  to generate an individual full sample asset value table  116 . Individual full sample asset values in table  116  are then uploaded electronically into any full sampling group valuation  118  required for bidding as suggested by the grouping of assets in a tranche. The number of assets in an underwriting sample grouping can be as little as one to any number of assets. Partial sampling  108  is for medium categories of assets and includes forming a cluster sample group  120  by one hundred percent sampling of a representative group from within a cluster of the groups being sampled and random sampling of the other groups in the cluster. In partial sampling  108 , all groups are sampled, but some are partly valued by extrapolation from cluster sample group  120 . Partial sampling  108  includes an asset level re-underwrite  122  with manual data entry  125  to produce an alpha credit analyst table  126  which is given an asset class adjustment  128  to produce an adjusted credit analyst table  130 . As described above, individual assets are selected from adjusted credit analyst table  130  according to tranche grouping to produce a partial sampling credit value  132  for use in bidding on tranche  70  (shown in  FIG. 2 ). 
     Automatic valuation procedure  40  utilizes supervised learning process  206 , an unsupervised learning process  208  and an upload from a statistical inferencing algorithm  134  to generate an underwriting clusters table  136  which is stored in a digital storage device. In supervised learning process  206 , an experienced underwriter who knows what questions to ask to establish value, assists the computer in determining whether or not an asset is a good investment and how to value the asset. In unsupervised learning process  208 , the computer segments and classifies assets and objectively self-evaluates the assets based on feedback from the data. An underwriter periodically reviews the unsupervised learning process  208  to determine whether the computer is making sensible underwriting conclusions. The computer uses statistical algorithms  134  to make its inferences. For example, but not by way of limitation, one embodiment uses the Design For Six Sigma (“DFSS”) quality paradigm developed and used by General Electric Company and applied in a Due Diligence (“DD”) asset valuation process using a multi-generational product development (“MGPD”) mode to value the asset data with increasing accuracy. Learning processes  206  and  208  incorporate the accumulated knowledge as the valuation progresses into cash flow recovery and probability of recovery calculations on an ongoing, real time basis. Supervised learning process  206  uses business rules to identify clusters of assets having common aspects for valuation purposes. Unsupervised learning process  208  uses feedback from prior data valuations performed by procedure  40  to determine if progress is being made with respect to increasing valuation confidence. Identification of all available raw data and discovery of interrelationships of clusters of these available raw data is possible due to the use of high-speed computers, as is described below. 
     In one exemplary embodiment, a fuzzy clustering means (“FCM”) process of unsupervised organization of raw data using a HELTR scoring technique is employed to infer valuations of credit scores onto assets in portfolios, as described below. Such clustering techniques have been developed in response to more sophisticated classification segments to describe assets and high asset counts in portfolios that must be assessed in time periods that do not allow manual processing. 
     One exemplary method first organizes valuation scores (static and/or probabilistic recoveries) in a computerized system. Adjustments are then made to the valuation scores for special factors and business decisions. Then a reconciliation of multiple valuation scores describing the same asset and an overall adjustment to interview/override the inferred valuation is performed. 
     Organizing valuation scores is performed by collating, in electronic form, a cluster number, a cluster name, descriptive attributes of the cluster(s), probabilistic recovery values (an illustrative example is a HELTR score) and the underwriter&#39;s confidence in each cluster&#39;s valuation based upon the strengths of each cluster&#39;s descriptive attributes. The cluster number is a unique identifier of a specific set of descriptive attributes that are facts about an asset which a person skilled in evaluations uses to assess value of an asset. Examples of descriptive attributes include, but are not limited to, payment status, asset type, borrower&#39;s credit worthiness expressed as a score, location and seniority of a claim. The cluster name is, in one embodiment, an alpha-numeric name that describes the cluster&#39;s descriptive attributes or sources. One example of descriptive attributes is found in  FIG. 12 , described below. 
     Descriptive attributes are the facts or dimensions or vectors that were used to develop the asset&#39;s value. Computer logic is used to check for replicated clusters, if any, and alert the analysts or underwriters. 
     Because each asset can be described by many combinations of descriptive attributes, various levels of value for the same asset may occur. Probabilistic recovery values or credit score or any numerical indication of the asset&#39;s worth are indicators of worth designated at the discrete asset level. All of the information from the various descriptive attributes is synthesized such that a purchase or sale price can be ascertained as a fixed value or a probabilistic one. An illustrative embodiment used herein is the HELTR score. Each cluster has a unique set of descriptive attributes and designated HELTR score. 
     Every cluster&#39;s unique attributes contribute to a valuation of cluster value. Different combinations of attributes provide a higher confidence or confidence interval of a particular cluster&#39;s score. For example, if any asset was described as a green piece of paper with height equal to 2.5″ and width equal to 5″—one might ascribe a value of 0 to 1000 dollars and place very little confidence in this assessment. If this same asset was described with one more fact or attribute or vector as being a real $20 US bill, one would place a very high confidence factor on this cluster value of $20 US dollars. 
     A cluster&#39;s valuation and confidence is determined at a point in time and recorded. Sometimes new information becomes available and the analyst would like to alter the value(s). The value is altered manually or automatically with a data field and decision rules, in the automated fashion via computer code. The prior values are manipulated to reflect new information. As an illustrative example, assume the prior cluster confidence was recorded at 0.1 and it is learned that a different asset with exact descriptive attributes as in this cluster just sold for over the predicted “most probable” value. Rules were in effect such that if this event occurred, cluster confidence is multiplied by 10. 0.1×10=1 which is the revised cluster confidence. 
     The purpose of such a process is to reconcile multiple scores for the same asset, controlling for the confidence associated with each source of valuation of each dimension of valuation. Using the HELTR as an illustrative example with sample data points on a particular asset: 
     
       
         
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                   
               
               
                 Cluster 
                 Cluster 
                   
                   
                   
                   
                 Valuative 
                   
                   
                   
                   
               
               
                 Number 
                 Name 
                 High 
                 Exp 
                 Low 
                 Time 
                 Confidence 
                 High 
                 Exp 
                 Low 
                 Time 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1 
                 Lien 
                 .85 
                 62 
                 .15 
                 3 
                 3 
                 (.3/1 65)( 85) 
                 (3/1 65)( 62) 
                 (3/1 65)( 15) 
                 (3/1.65)(3) 
               
               
                   
                 positions - 
               
               
                   
                 recourse 
               
               
                 2 
                 Asset 
                 45 
                 4 
                 .31 
                 3 
                 7 
                 (7/1 65)(.45) 
                 (7/1. 65)(.4) 
                 (7/1.65)(.31) 
                 (7/1.65)(3) 
               
               
                   
                 classification 
               
               
                   
                 - industry - 
               
               
                   
                 age 
               
               
                 3 
                 Coordinates - 
                 .9 
                 .5 
                 2 
                 2 
                 .65 
                 (.65/1.65)( 9) 
                 (65/1 65)( 5) 
                 (.65/1.54)( 2) 
                 (65/1 65)(2) 
               
               
                   
                 use - 
               
               
                   
                 borrower 
               
               
                 n 
                 x 
               
               
                   
                   
                   
                   
                   
                   
                 1.65 
                 6999 
                 4792 
                 2374 
                 2 6059 
               
               
                   
               
             
          
         
       
     
     The cluster consensus valuation is a high value of 0.6999, most likely 0.4792, low 0.2374 with a timing of 2.6059. Different logic can be applied to manipulate any of the weights. 
     The consensus scores are developed in the context of global assumptions. Should a global assumption change occur, process steps  128 ,  138  are included in the methodology to weight the consensus score. Illustrative examples are fraud discovery in certain valuation factors, macroeconomic changes, fungible market value established for an asset class, and loss of or increase of inferenced asset valuation methodologies relative to other methodologies being employed. 
     In another embodiment, a cross correlation tool is used to quickly understand and describe the composition of a portfolio. Typically, the tool is used to correlate a response of a user selected variable versus other variables in an asset portfolio. The tool quickly identifies unexpectedly high or low correlation between two attribute variables and the response variable. Attribute variables are of two types, continuous and categorical. The cross correlations are computed by the correlation tool between all variables of interest and their bin or level and presented, in one embodiment, in a two dimensional matrix for easy identification of trends amongst the assets in the portfolios. 
     First, the cross-correlation tool identifies attribute variables in the portfolio of assets as one of continuous or categorical. For each variable aggregation levels are computed by bins for continuous variables and by value for categorical variables. 
     A user looking to identify correlations with the tool will select a response variable, Y r , for example, an expected recovery or count. For all combinations of pairs of attribute variables (x 1  and x 2 ) and their levels (a and b), compute the average value of the response variable, Y r , according to:
 
 Y   r =sum( Y ( x 1 =a  and  x 2 =b )/count( x 1 =a  and  x 2 =b ).
 
     An expected value, Y expect , of the response variable is calculated according to:
 
 Y   expect =(sum( Y ( x 1 =a ))*count( x 1 =a )+sum( Y ( x 2 =b ))*count( x 2= b ) ))/(count( x 1 =a )*count( x 2 =b )).
 
     A deviation, Y error , of the chosen response variable, Y r , from the expected value, Y expect , using weighted values of occurrence of x1=a and x2=b separately, is calculated by:
 
 Y   error   =Y   r   −Y   expect .
 
     In one embodiment, expected values and deviations are displayed in multi-dimensional displays to make variations from expected values easy to identify. 
     In another exemplary embodiment, a transfer function process that converts raw data into the ultimate bid price is used, as described below. Table  136  is electronically adjusted using modified coefficients developed in procedures  14 ,  34  and  40  to give a coefficient adjustment to a credit score  138  for the asset and to generate an adjusted credit analyst table  140  of inferred individual asset credit values. Individual asset values are taken from table  140  as required by tranche grouping to generate an inferred credit valuation  142 . Finally an extrapolation is made on the negligible remainder  30  of “untouched” assets to generate a table of untouched assets  144 . Values from table  144  are selected to generate an untouched asset valuation. 
     Full cash valuation  98 , partial cash valuation  104 , full sampling credit valuation  118 , partial credit values  132 , inferred credit value  142  and any value assigned from untouched asset table  144  are cumulated and are mutually exclusive with the priority being full cash valuation  98  to inferred credit value  142  consecutively. A sum of the valuations represents value of the portfolio. 
       FIG. 4  is a flow diagram of a bid preparation stage  168  performed by system  28  (shown in  FIG. 2 ). The cumulated valuations  98 ,  104 ,  118 ,  132 ,  142  and  144  are combined in a risk preference loan level valuation step  146 . A deterministic cash flow bridge  148  is produced using a cash flow timing table  150  to develop a stochastic cash flow bridge  152 . A stochastic or probabilistic cash flow bridge  152  is created and used to determine a proposed tranche bid price  154  to which is applied a tranche model  156  iteratively until a certain threshold  158  is reached. Threshold  158  is, for example, an internal rate of return (“IRR”) greater than some value, a certain time to profit (“TTP”), and a positive net present value (“NPV”). 
     In general, NPV is defined as: 
     
       
         
           
             
               
                 
                   NPV 
                   = 
                   
                     
                       c 
                       0 
                     
                     + 
                     
                       
                         c 
                         1 
                       
                       
                         1 
                         + 
                         r 
                       
                     
                   
                 
               
               
                 
                   (Equation  A) 
                 
               
             
           
         
       
     
     where C 0  is the investment at time 0, C 1  is the expected payoff at time  1 , and r is the discount factor. The basic idea is that a dollar today is worth more than a dollar tomorrow. 
     In the case of insurance policies, NPV is defined as: 
                   NPV   =       ∑   P     -     ∑   E     -       (     ∑   C     )     ×     A     E   w                   (Equation  B)               
where P is the premium, E is the expected nominal cost, and C is the claim cost. In essence, Equation B is how net income as the difference of profit and weighted expected risk is generated. Note that the summation is summing across all the policies in a specific segment. Also note that all the premium, nominal cost, and claim cost have been discounted before entering the equation. As a result, a profitability score is generated.
 
     If threshold conditions  160  are met, bid  154  is subjected to a simulated bid opening analysis  161  to predict whether the bid can be expected to be a winning bid. An outcome of a sealed bid auction depends on sizes of the bids received from each bidder. Execution of the auction involves opening all of the bids and selling the items up for auction to the highest bidder. In traditional sealed bid auctions, bidders are not allowed to change their bids once their bid is submitted and bidders do not know the bids placed by other bidders until the bids are opened, making the outcome of the auction uncertain. By placing higher bids, a probability that the auction will be won is higher, but value gain is lower if it was possible to have won the auction at a lower price. 
     Simulating competitive bidding increases the probability of capturing the highest upside of profitability by setting a range of bid/sale prices that have a propensity to exhaust any competing bidder&#39;s purses before ones own purse such that the most desirable assets transact with the highest preservation of capital. Pricing decisions are brought into focus by an analytically robust process because pure anecdotal business judgment can be augmented by a data driven approach not subject to a hidden agenda, personality or unilateral knowledge. 
     Each potential bidder has a range of possible bids that might be submitted to a sealed bid auction. The range of bids can be expressed as a statistical distribution. By stochastically sampling from a distribution of bid values, one possible auction scenario may be simulated. Further by using an iterative sampling technique, for example a Monte Carlo analysis, many scenarios are simulated to produce a distribution of outcomes. The distribution of outcomes include a probability of winning the auction item(s) and the value gain. By varying the value of ones own bid, a probability of winning the auction against ones own bid price can be determined. 
     The following core elements are used to simulate a competitive bidding yield, codification of market rules and contracts into computerized business rules, codification of potential competition/market forces, forecasted budgets and priorities into a preference matrix, one&#39;s own bidding capacity, preferences, risk/return tradeoffs agreed to codified into a preference matrix, and a computerized stochastic optimization. 
     Analysis  160  simulates a competitive environment with other companies having various financial capabilities bidding against the bids calculated by system  28 . In one embodiment, analysis  160 , for example and without limitation, includes a total bid limit such as would be the case where the total value of the assets exceed the financial capabilities of the entity using system  28 . In one embodiment, analysis  160  might assess the profitability, in such case of limited resources to bid, of bidding on various combinations of tranches. Analysis  160  also takes into account past history in bidding against known competitors and information on the various types of assets preferred by competing bidders. In analysis  160 , the tranche bid is then evaluated and set by management  162  and a final tranche bid  164  made. All valuations prior to the making of the bid  164  can be repeated as desired. Further, since the process is self-adjusting and iterative, the tranche bid price  164  tends to climb upward with each iteration as more and more value is found by the iterations performed by system  28 . 
     The process described by flowchart  85  includes an evaluation stage  166  (shown in  FIG. 3 ) and a bid preparation stage  168  (shown in  FIG. 4 ). Evaluation stage  166  includes procedures  14 ,  34  and  40 . Evaluation stage  166  runs constantly until stopped, with the automatic valuation procedure  40  and sampling procedures  34  attempting to find extra value in various assets or categories of assets. 
     Referring once again to  FIG. 2 , and in accordance with rapid asset valuation, data categories  170 ,  172  and  174  within the assets of portfolio  12  are identified on each asset and stored in database  76 . Iterative and adaptive valuation process  32  takes portions of selected data  78  and applies criteria  80  to the portions of selected data  78  in a statistical manner to increase the known asset value rather than the asset value being a gross extrapolation  20 . In accordance with method  28  the assets are divided into at least first portion  16 , second portion  36  and third portion or remainder  42 . Using procedure  14 , the assets in portion  16  are fully underwritten to determine valuation  98  and partial value fully underwritten valuation  104  and to establish criteria  80  for such valuation. Using procedure  34 , process  28  samples a quantity of assets from second portion  36  representative of groups in second portion  36  to determine full sampling group valuation  118  and partial sampling credit values  132  for second portion  36  and to establish additional criteria  80  for such valuation. Using procedure  40 , partially supervised learning process  206  and partially unsupervised learning process  208  are performed by an automated analyzer such as computer  38  of  FIG. 2 . In order to learn, the automated analyzer extracts established criteria  80  and selected data  78  as to third portion or remainder  42  and divides third portion  42  into portions  46 , and then further divides each portion  46  into categories  48  and  50  and category  50  into clusters  52 ,  54  and clusters  52 ,  54  into subclusters  56 ,  58 ,  60 ,  62  and  64  using criteria  80  imported from database  76  and each of processes  206  and  208 . Individual asset valuations are established for the assets in subclusters  56 ,  58 ,  60 ,  62  and  64  by statistical inference. 
     The individual asset valuations are listed in cluster tables  136  (see  FIG. 3 ) and after adjustment  138 , listed in a credit analyst table  140 . The established criteria  80  are objective since criteria  80  come from database  76  where they have been placed during full underwriting procedure  14  and sample underwriting procedure  34 . In other words, information obtained in full value table  96 , partial value table  102 , table  116 , alpha credit analyst table  126 , adjusted credit analyst table  130 , adjusted credit analyst table  140  and untouched asset table  144  for all assets is placed into database  76  in a digital storage device, such as the hard disk storage  178  of computer  38 , and correlations are made by procedure  40  with criteria  80  from procedures  14  and  34 . During procedure  40 , criteria  80  which are of statistical significance with an acceptable degree of reliability, are entered. That is, procedure  40  iteratively learns as it values and establishes criteria  80 . Supervised learning process  206  and unsupervised learning process  208  increase the accuracy of statistically inferred valuation  142  by correlating to established criteria  80  in database  76  on assets in fully underwritten first portion  16  and assets in sample underwritten second portion  36 . Selected data  78  related to one or more assets in third portion  42  similar to selected data  78  on assets in portions  16  and/or  36  are located in database  76  and then by statistical inference, a value for each asset in third portion  42  is determined from the located information. 
     During the process described by flowchart  85 , assets are valued at an individual asset level, and the individual asset values are tabulated or grouped in one or more combinations. To have maximum flexibility for various bidding scenarios, any subset of portfolio  12  is valued and priced separately in a particular time frame. In known process  10 , if a seller of assets regroups the assets, for example from groupings by asset company to groupings by geographical location of borrowers, revaluation of bids may be inadequate because gross extrapolation  20  will need to be performed. In using system  28 , because individual asset values are developed and listed in tables  96 ,  102 ,  116 ,  130 ,  140  and  144 , these values can be electronically regrouped into different valuations  98 ,  104 ,  118 ,  132 ,  142  whose “food chain” selection criteria is mutually exclusive and selectable by the analysts conducting the evaluation and is further described below. If the seller groups the assets, then grouping according to seller groups or tranches is easily made and an appropriate valuation  146  developed for that tranche. The individual asset values are thus easily regrouped for third portion  42  to objectively obtain an inferred valuation  142  for that group or tranche. 
     Many methods may be employed to establish asset value. Depending upon the objectives of the valuation, the relative merits of different valuation methodologies establish the desirability of the valuation techniques for a particular asset. One methodology is similar to a “food chain” which preserves assumption development methods yet selects the intervals with the highest confidence intervals. 
     In one introductory illustrative example of a food chain, one may prefer to value a financial asset more by what similar assets trade in the open market for versus an individual&#39;s opinion. In rank order, the market-to-market value is selected over an individual&#39;s opinion. 
     In the same way assets in a portfolio with a forecasted cash flow recovery may be evaluated by a number of valuation techniques. The typical objective is to establish, with as high a probability available, what the future cash flow will be. The valuation methodologies are ranked in order of their capability to accurately quantify cash flow, or cash equivalent, forecasts with the least downside variances and/or maximum upside variances. The asset is valued by all available methods that have merit, or may have business logic rules to eliminate duplicate work when it is known that more accurate methods will preclude the need to assess an asset&#39;s valuation once the best method has been employed. 
     In order to provide the best forecast of asset value, assets are evaluated by each method within a food chain until such time as they are valued by the best available method for each particular asset. Once this best value is found, the asset is said to have its value, irrespective to other values lower (with more variance) in the food chain and is sent to the completed state. 
     As an example, a portfolio of assets is evaluated using a food chain. The first valuation method in the food chain is the one which most closely matches the valuation objectives—namely to find the value with the highest degree of accuracy (tightest confidence interval). As soon as the asset is valued by a methodology for which a value was established for that unique asset, it is sent to the valuation table and removed from any further steps in the food chain. A list of assets from the original portfolio that did not match any valuation methods is kept in the untouched asset table. The objective is to drive this untouched table to zero assets. 
     One example of a food chain is as follows, in order of preference. (a) 100% cash in hand for the asset, (b) partial cash in hand for the asset, (c) liquid market value for like asset, (d)direct underwrite, and (e) inferred underwrite. 
     The food chain approach provides an ability to find the best probability distribution shape, reduces probability distribution variance (especially on the downside tails), provides capability to establish probability distributions quickly while preserving all available knowledge in the constituencies and provides the ability to provide the best estimate of value at any point in the discovery process. 
     As shown in  FIG. 4 , the general framework of bid preparation stage  168  is to price bid  164  similar to option valuation paradigms where the winning investor will have the right, but not the obligation, to recover the investment. The values are desegregated into three parts for each tranche, a time value of money component, an inherent value component and a probable cash flow component. The time value of money and the inherent value are deterministically calculated and have little variation once established. The time value of money is computed by taking a firm&#39;s cost of capital for a low risk investment multiplied by the investment for the applicable period which represents an opportunity for alternate investment that is foregone in order to make the present investment. Inherent value is a known liquid asset value, which is in excess of the purchase price and is available immediately after taking control of the assets. One embodiment is a well traded security purchased below market value as part of a portfolio. Probable cash flow variance is a function of the assumptions a due diligence team makes and the process it selects to convert raw data into a cash flow recovery stream. The systems described herein are configured to reduce negative variances and find value. 
       FIG. 5  is a triangular probability distribution graph for a typical minimum three-point asset evaluation  180 . In accordance with process  40  a minimum of three cases per financial instrument are evaluated. A vertical axis  182  denotes increasing probability and a horizontal axis  184  denotes increasing portion of recovery. A liquidation or worst case percentage  186  of a face value line  188 , a best case percentage  190  of face value  188 , and a most probable case percentage and recovery value  192  of face value  188  are shown. The probability of worse case percentage  186  is zero, the probability of best case scenario  190  is zero and a probability  194  of the most probable percentage  192  of recovery is a value represented by point  196 . The size of an area  198  under a curve  200  defined by a line connecting points  186 ,  196  and  190  is representative of value in the asset. The notational asset value holds to an area  202  of a rectangle bounded by a 100% probability line  204  of a 100% recovery of face value  188  is a measure of the portion of face value  188  that can be attributed to the asset represented by curve  200 . Points  186 ,  196  and  190  and lines  188  and  204 , and thus areas  198  and  202 , will vary depending on selected data  78  chosen for the asset in question and criteria  80  applied to the asset and ascribed probabilities of asset value recovery. Horizontal axis  184  can be expressed in currency units (e.g. dollars) rather than percentage of face value. When currency units are used, areas  198  under curves  200  for different assets will be in currency units and thus areas  198  relate to each other in magnitude and hence in significance to overall bids  70 ,  72  and  74 . The more that is known about the asset, the more curve  200  can be refined. Statistics are applied to curve  200  as criteria  80  are established to help establish the location of points  186 ,  196  and  190  and hence area  198  and thus the expected value of the asset. The timing of cash flows, which affects value, can be based upon histogram results of the timing attributes. 
     For example, the cash flow recovery timing can be broken down into three bins of 0–6 months, 7–12 months, 13–18 months, and so on. The automated analyzer  38  using algorithm  134  can select the bin width based upon a sensitivity study trade off of timing to valuation against the gauge recovery and rate determined possible by an underwriter. In an exemplary embodiment, a minimum of 4 bins should be utilized when the discount factor is more than 25%. For a discount factor between 10 and 25, a minimum of 6 bins should be used to cover the likely recovery periods. 
     In accordance with procedure  40  other sources of data are chosen that an underwriter would be able to utilize to assess value in a financial instrument. Criteria  80 , established by underwriting teams  94 ,  100   114 ,  122  and  140  in procedures  14  and  34 , are useful in that regard. In accordance with the process described by flowchart  85 , raw data is turned into a recovery and a rule set is selected to apply a valuation to the raw data and this rule set is coded into the valuation database in the form of criteria  80 . Each time a cluster is touched by multiple hits during a valuation in procedures  14 ,  34  or  40 , a consensus forecast is developed and applied to the cluster. In accordance with system  28 , the probability distributions of cash flows and timing at the tranche level is determined by developing valuation transfer function  146  at the asset level which will take raw data, rationalize the assumptions that data will generate and aggregate the valuations of the individual assets in the tranche. 
     Since all recoveries are not homogeneous, a method to establish the variability of cash flow recoveries is provided. Individual assets are clustered by group exposure. As much face value as possible is traditionally underwritten in the time permitted, recognizing that a sizable sample remains for clustering. Clustering reserves are estimated using a sample size equal to one hundred forty five plus 2.65% of the face count and a regression analysis of variance. This produces sample sizes of thirty for a face count of 100 assets, 150 for a face count of 1,000 assets, 400 for a face count of 5,000 assets, 500 for a face count of 10,000 assets, and 600 for a face count of 20,000 assets. 
     During statistical inference procedure  40 , assets remaining in third portion  42  of portfolio  12  are clustered by descriptive underwriting attributes or criteria  80  and random samples are taken from each cluster and the sample underwritten. In one embodiment, sampling from a cluster in procedure  40  is stopped when asset level mean variance falls below 10%. In another embodiment, sampling is stopped when tranche level mean variance falls below 15%. Portfolio mean variance is not used as a stop point if the potential unit of sale is less than the entire portfolio. In accordance with procedure  40 , recovery valuation of the cluster sampling is inferred onto the corresponding cluster population. In using system  28 , the goal is to touch each inferred asset valuation via three or more unique clusters. During procedure  40  a cluster&#39;s underwriting confidence and descriptive attribute&#39;s relevance is weighed. 
     By way of example, without limitation, 0=no confidence that this cluster&#39;s descriptive attributes will provide a meaningful valuation; 1=complete confidence that this cluster&#39;s descriptive attributes will provide as accurate of a valuation as individually underwriting each instrument, and numbers between 1 and 0 indicate partial confidence in the valuation. Reconciliation of these values occurs within adjusted credit analyst table  130 . In procedure  40  cash flow at asset level is then adjusted by macroeconomic coefficients within adjusted credit analyst table  140 . Macroeconomic coefficients are, in one embodiment, associated with major asset classes such as for example, without limitation, real-estate residential loan or commercial equipment loan. The coefficients can be globally applicable, such as by way of example without limitation, legal climate, gross domestic product (“GDP”) forecast, guarantor climate, collections efficiency, borrower group codes, and the like. 
     One method for sampling a portfolio includes searching among key asset, borrower, and collateral characteristics for attributes which heavily influence/generate risk. Table A below provides one example list of portfolio attributes in an asset valuation scenario. 
     
       
         
               
             
               
               
             
           
               
                 TABLE A 
               
               
                   
               
               
                 Portfolio attributes 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Borrower Size (by Borrower Group UPB) 
               
               
                   
                 Secured 
               
               
                   
                 Syndicated (yes/no) 
               
               
                   
                 Guaranteed 
               
               
                   
                 Loan Type (Term, Revolving, etc.) 
               
               
                   
                 % UPB from Liens in First Position 
               
               
                   
                 Collection Score (0 = Bad, 1 = Good) 
               
               
                   
                 12-month collections % of UPB 
               
               
                   
                 % of Last Payment for Principal 
               
               
                   
                 # Borrower Loans 
               
               
                   
                 Loan&#39;s portion of borrower UPB 
               
               
                   
                 Single Family Residence 
               
               
                   
                 Residential 
               
               
                   
                 Retail 
               
               
                   
                 Industrial 
               
               
                   
                 Hospital 
               
               
                   
                 Hospitality 
               
               
                   
                 Multifamily 
               
               
                   
                 Land Developed/Undeveloped/Other 
               
               
                   
                 Office 
               
               
                   
                 Stock/Margin Loans 
               
               
                   
                   
               
             
          
         
       
     
     Segmentation of the asset attributes is accomplished by encoding of attributes into “dummy variables”. For example, a common asset attribute is “Has borrower made a payment in the last 12 months?”, which would be encoded in a variable as a “1” if the answer is yes, and “0” otherwise. Similar “dummy variables” are used for other asset attributes. 
     The segmentation procedure is completed by using any statistical procedure which process the encoded asset attributes in such a way so as to segment the portfolio into groups of similar assets. One such algorithm is K-means clustering. In an example, where three asset attributes, Unpaid Principal Balance (UPB), Probability of Payment, a scale from 0 to 1; and Secured Score, a probability of being secured by real estate collateral are used, the assets might be classified into five groups with similar attributes. 
     Once the groupings of assets is made, the number of samples to be taken and submitted for further underwriting review is calculated by establishing the confidence level with which statements can be made about the total recoveries in each segment (k), establishing the precision with which one wishes to estimate the total recoveries in each segment (h) and providing an a priori estimate of the level and range of recoveries as a percentage of total Unpaid Principal Balance (UPB) (R), according to: 
     
       
         
           
             
               Var 
               ⁡ 
               
                 ( 
                 
                   
                     Y 
                     ^ 
                   
                   R 
                 
                 ) 
               
             
             = 
             
               
                 n 
                 ⁡ 
                 
                   [ 
                   
                     1 
                     - 
                     
                       n 
                       N 
                     
                   
                   ] 
                 
               
               × 
               
                 
                   
                     [ 
                     
                       
                         
                           ∑ 
                           N 
                         
                         1 
                       
                       ⁢ 
                       
                         x 
                         i 
                       
                     
                     ] 
                   
                   2 
                 
                 
                   
                     [ 
                     
                       
                         
                           ∑ 
                           n 
                         
                         1 
                       
                       ⁢ 
                       
                         x 
                         i 
                       
                     
                     ] 
                   
                   2 
                 
               
               × 
               
                 
                   
                     
                       ∑ 
                       N 
                     
                     1 
                   
                   ⁢ 
                   
                     
                       ( 
                       
                         
                           y 
                           i 
                         
                         - 
                         
                           Rx 
                           i 
                         
                       
                       ) 
                     
                     2 
                   
                 
                 
                   N 
                   - 
                   1 
                 
               
             
           
         
       
         
         
           
             n=sample size 
             N=cluster size 
             x 1 =UPB for sample i 
             y 1 =recovery for sample i 
           
         
       
    
     
       
         
           
             R 
             = 
             
               
                 
                   
                     
                       ∑ 
                       N 
                     
                     1 
                   
                   ⁢ 
                   
                     y 
                     i 
                   
                 
                 
                   
                     
                       ∑ 
                       N 
                     
                     1 
                   
                   ⁢ 
                   
                     x 
                     i 
                   
                 
               
               = 
               
                 cluster 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 expected 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 recovery 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 % 
               
             
           
         
       
     
     
       
         
           
             
               
                 
                   
                     h 
                     2 
                   
                   = 
                   
                     
                       k 
                       2 
                     
                     × 
                     
                       n 
                       ⁡ 
                       
                         [ 
                         
                           1 
                           - 
                           
                             n 
                             N 
                           
                         
                         ] 
                       
                     
                     × 
                     
                       
                         
                           [ 
                           
                             
                               
                                 ∑ 
                                 N 
                               
                               1 
                             
                             ⁢ 
                             
                               x 
                               i 
                             
                           
                           ] 
                         
                         2 
                       
                       
                         
                           [ 
                           
                             
                               
                                 ∑ 
                                 n 
                               
                               1 
                             
                             ⁢ 
                             
                               x 
                               i 
                             
                           
                           ] 
                         
                         2 
                       
                     
                     × 
                     
                       
                         
                           
                             ∑ 
                             N 
                           
                           1 
                         
                         ⁢ 
                         
                           
                             ( 
                             
                               
                                 y 
                                 i 
                               
                               - 
                               
                                 Rx 
                                 i 
                               
                             
                             ) 
                           
                           2 
                         
                       
                       
                         N 
                         - 
                         1 
                       
                     
                   
                 
               
               
                 
                   (Equation  C) 
                 
               
             
           
         
       
         
         
           
             h=error tolerance for estimating 
           
         
       
    
     
       
         
           
             Y 
             = 
             
               
                 
                   ∑ 
                   N 
                 
                 1 
               
               ⁢ 
               
                 
                   y 
                   i 
                 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 with 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   
                     Y 
                     ^ 
                   
                   R 
                 
               
             
           
         
       
     
     
       
         
           
             
               
                 
                   
                     
                       Y 
                       ^ 
                     
                     R 
                   
                   = 
                   
                     
                       
                         R 
                         ^ 
                       
                       × 
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           N 
                         
                         ⁢ 
                         
                           x 
                           i 
                         
                       
                     
                     = 
                     
                       
                         
                           
                             
                               ∑ 
                               
                                 i 
                                 = 
                                 1 
                               
                               n 
                             
                             ⁢ 
                             
                               y 
                               i 
                             
                           
                           
                             
                               ∑ 
                               
                                 i 
                                 = 
                                 1 
                               
                               n 
                             
                             ⁢ 
                             
                               x 
                               i 
                             
                           
                         
                         × 
                         
                           
                             ∑ 
                             
                               i 
                               = 
                               1 
                             
                             N 
                           
                           ⁢ 
                           
                             x 
                             i 
                           
                         
                       
                       = 
                       
                         
                           
                             
                               ∑ 
                               
                                 i 
                                 = 
                                 1 
                               
                               n 
                             
                             ⁢ 
                             
                               
                                 ρ 
                                 i 
                               
                               ⁢ 
                               
                                 x 
                                 i 
                               
                             
                           
                           
                             
                               ∑ 
                               
                                 i 
                                 = 
                                 1 
                               
                               n 
                             
                             ⁢ 
                             
                               x 
                               i 
                             
                           
                         
                         × 
                         
                           
                             ∑ 
                             
                               i 
                               = 
                               1 
                             
                             N 
                           
                           ⁢ 
                           
                             x 
                             i 
                           
                         
                       
                     
                   
                 
               
               
                 
                   (Equation D) 
                 
               
             
           
         
       
         
         
           
             k=constant in Tchebyshev&#39;s Formula: 
           
         
       
    
     
       
         
           
             
                
               
                 
                   
                     Y 
                     ^ 
                   
                   R 
                 
                 - 
                 
                   μ 
                   
                     
                       Y 
                       ^ 
                     
                     R 
                   
                 
               
                
             
             ≤ 
             
               k 
               ⁢ 
               
                 
                   Var 
                   ⁡ 
                   
                     ( 
                     
                       
                         Y 
                         ^ 
                       
                       R 
                     
                     ) 
                   
                 
               
               ⁢ 
               with 
               ⁢ 
               
                   
               
               ⁢ 
               probability 
             
             ⁢ 
             
                 
             
             ≥ 
             
               1 
               - 
               
                 1 
                 
                   k 
                   2 
                 
               
             
           
         
       
     
     By solving Equation C for n, required sample size for the given cluster is obtained. Solving Equation C further allows the user to state, with probability 
             1   -     1     k   2             
the calculated sample size, n, and associated underwritten values will estimate the total cluster recoveries to within an error of h, assuming that estimates of total segment recoveries are determined using Equation D.
 
     In practice, it is difficult to estimate variability in total recoveries without available data. A spreadsheet tool implements the above by generating data in a Monte Carlo simulation, and guiding the user through an analysis of the results until a favorable sample size is derived. 
     Table B provides an example output from a study of a group of 20 loans, with estimated (expected) recoveries between 20% and 30% of UPB, and a range of UPB between 1 MM and 2 MM. Eight samples are needed to estimate the total recoveries for the 20 loans to within 10% of actual, with 75% confidence. 
     
       
         
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
             
               
               
               
               
             
           
               
                 TABLE B 
               
               
                   
               
             
             
               
                 Sample Size Spreadsheet Wizard 
               
             
          
           
               
                 Sample 
                   
                 Cume 
                   
                 Exp  
                   
               
               
                 Size 
                 Exp Rec 
                 Exp Rec 
                 Cume UPB 
                 Rec % 
                 Residual 
               
               
                   
               
             
          
           
               
                 1 
                 779,131 
                 779,131 
                 2,936,279 
                 26 5% 
                 − 
               
               
                 2 
                 716,951 
                 1,496,082 
                 5,447,631 
                 27 5% 
                 27,259 
               
               
                 3 
                 359,327 
                 1,855,409 
                 6,702,090 
                 27 7% 
                 12,042 
               
               
                 4 
                 481,798 
                 2,337,206 
                 8,538,875 
                 27 4% 
                 (20,956) 
               
               
                 5 
                 606,774 
                 2,943,980 
                 10,706,452 
                 27 5% 
                 10,750 
               
               
                 6 
                 418,899 
                 3,362,880 
                 12,207,495 
                 27 5% 
                 5,397 
               
               
                 7 
                 622,516 
                 3,985,396 
                 14,609,180 
                 27 3% 
                 (32,665) 
               
               
                 8 
                 594,799 
                 4,580,195 
                 16,911,278 
                 27 1% 
                 (28,694) 
               
               
                 9 
                 713,922 
                 5,294,117 
                 19,440,132 
                 27 2% 
                 25,241 
               
               
                 10 
                 494,230 
                 5,788,346 
                 21,153,615 
                 27 4% 
                 25,363 
               
               
                 11 
                 735,334 
                 6,523,680 
                 24,031,814 
                 27 1% 
                 (45,983) 
               
               
                 12 
                 683,155 
                 7,206,835 
                 26,387,193 
                 27 3% 
                 39,857 
               
               
                 13 
                 748,413 
                 7,955,248 
                 29,256,251 
                 27 2% 
                 (31,730) 
               
               
                 14 
                 419,885 
                 8,375,133 
                 30,726,773 
                 27 3% 
                 19,068 
               
               
                 15 
                 757,050 
                 9,132,183 
                 33,682,971 
                 27 1% 
                 (44,439) 
               
               
                 16 
                 553,674 
                 9,685,857 
                 35,690,262 
                 27 1% 
                 8,922 
               
               
                 17 
                 761,579 
                 10,447,435 
                 38,234,459 
                 27 3% 
                 66,386 
               
               
                 18 
                 677,811 
                 11,125,246 
                 40,756,944 
                 27 3% 
                 (10,741) 
               
               
                 19 
                 563,811 
                 11,689,057 
                 42,688,952 
                 27 4% 
                 34,790 
               
               
                 20 
                 434,763 
                 12,123,821 
                 44,160,329 
                 27 5% 
                 30,810 
               
               
                   
               
             
          
           
               
                   
                   
                 Expected 
                   
               
               
                 N (cluster size) 
                 n (sample size) 
                 Recovery % 
                   
               
               
                 20 
                    6 
                 27 5% 
                   
               
               
                 Face Range 
                 ER % Range 
                 Face Value 
                   
               
               
                 2,000,000 
                 5.0%  
                 44,160,329 
                   
               
               
                 Min Face 
                 Min ER % 
                 Expected Recovery 
                   
               
               
                 1,000,000 
                 25.0% 
                 12,123,821 
                   
               
               
                 Confidence 
                 K 
                 Precision 
                 Precision % 
               
               
                 75.0% 
                    2.00 
                 1,212,382  
                 10.0% 
               
               
                   
               
             
          
         
       
     
     The appropriate variance adjusted forecast is made for each asset and the valuation tables are constructed to include every asset in the portfolio. The recovery is valued with continuous probabilities at the unit of sale, which in one embodiment is a tranche. In the use of system  28 , internal rate of return (“IRR”) and variance would then be assessed. Preferred tranches have lower variances for a given IRR. The probability of each tranche&#39;s net present value (“NPV”) to be above 0 is assessed using the project&#39;s discount rate. A discount rate is determined from the opportunity cost of capital, plus FX swap cost, plus risks in general uncertainties inherent in the variances of forecasted cash flow recovery. If it appears that there is more than a five-percent certainty that the project will have a negative NPV, no bid is made. Deal evaluation is by tranche with decision criteria being IRR, risk variance of the IRR in a tranche, estimated willingness and ability of the tranche to pay, time to profit (“TPP”) and the risk variance in the payback by tranche, and NPV of the expected cash flow by tranche discounted to risk free rate. 
     In competitive bid circumstances when the content of asset portfolios is not negotiable, the investor or seller has a strong financial incentive to select only the portions of total assets available for transaction that will give their aggregated financial structure the best risk/return. Meeting minimum risk/return expected values with assets that will have a higher probability of maximum upside probabilities is even more attractive to investors. 
     The aggregated portfolio is divided into separately marketable sub portfolios or tranches. Each tranch has a forecasted cash flow probability distribution and time duration from prior analytics. These tranches are then given a trial price. The new assets are combined with the existing asset performance of the selling or buying party and subjected to Monte Carlo case generation (with associated cross correlations accounted for). 
     The tranch selection process includes a random selection of trances not to buy. Once the portfolio effects take on a pattern, the best selection of tranches to purchase, at what price, subject to constraints is found by stochastic optimization. 
     Using NPV can be misleading due to the effects associated with double discounting which will occur when pessimistic case scenarios are discounted to obtain PV. Using time to profit is used to overcome this limitation and the marginal capital cost or risk free rate is used in the discounting as determined by analysts conducting the evaluation. 
     Supervised learning process  206  of inferred valuation procedure  40  and steps  120 ,  122  and  126  of partial sampling procedure  108  have substantial similarity in that the underwriter is actively involved in the process, but the process is automated.  FIG. 6  is a flow diagram illustrating a process  210  for automated underwriting of segmentable financial instrument assets. First clusters of financial instruments are defined  212  by common attributes. An expert opinion  214  of value is given for selected samples from the defined clusters based upon the attributes. This opinion is used in a sample underwriting process  216  and values are checked for combinations of attributes and reconciled  218 . Process  210  then selects and sets  220  the individual attributes to be used and then classifies  222  individual assets into clusters. Cluster valuation is applied  224  to each cluster asset. Using the cluster valuation, the values are desegregated by a rule  226  to create a credit analyst table  228 . 
       FIG. 7  is a flow diagram of one exemplary embodiment of unsupervised learning  208  that includes several modules. A data acquisition module  230  collects relevant data  78  wherever available. A variable selection module  232  identifies the asset relevant variables deemed critical by credit review or with the most discriminate power in separating various asset groups. A hierarchical segmentation module  234  segments the entire portfolio of assets into bins based on critical variables selected by analysts. A FCM module  236  further classifies each bin into clusters based on natural structure of the asset data. An underwriting review module  238  assigns projected cash flow and risk scores  138  (shown in  FIG. 3 ) to each cluster. This score is then supplied to the individual asset values in credit analyst table  136  for the assets from the clusters being adjusted in procedure  40  to produce adjusted credit analyst table  140 . The process is iterative and continuous and can be performed by computer so that it continues while standard underwriting is being performed elsewhere. 
       FIG. 8  illustrates an alternate exemplary inferred valuation process  240  used in place of the process described in  FIGS. 3 and 4 . In alternate process  240 , a seven-step process is used to rapidly value a real estate loan portfolio using a combination of full underwriting, partial underwriting and inferred valuation. First, assets are sampled  242  according to risk. Second, assets are underwritten  244 , and valuations recorded. Third, market value clusters are formed  246 , such as by FCM, as described below. Fourth, regression models are built  248 , for the underwritten assets. A best model is selected  250 , for the underwritten assets from among those built  248  earlier. Sixth, the counts for the selected models are calculated  252 . Seventh, models are applied  254 , as selected  250  to non-underwritten or inferentially valued portion  42  of portfolio  12  in a manner weighted by the counts to predict individual values for each of the non-underwritten assets. The individual asset values produced according to process  240  are then placed in adjusted credit analyst table  140  (see  FIG. 3 ). 
     In sampling assets  242 , underwriters use stratified random sampling to select assets for detailed review. Strata are constructed from collateral attributes. Examples of collateral attributes for real estate portfolios include, collateral usage (commercial or residential), previous appraisal amount, market value cluster (predicted from previous appraisal amount, land area, building area, current appraisal amount, court auction realized price, property type and property location. Typically, assets are sampled in an adverse manner, i.e., purposely selected from a list ordered by decreasing Unpaid Principal Balance (“UPB”) or Previous Appraisal Amount (“PAA”). 
     Underwriting  244  is a largely manual process in which expert underwriters ascribe a notion of worth to collateral assets. The underwritten valuations are stored in a master database table, such as database  76  (shown in  FIG. 2 ). Valuations are typically summarized in terms of monetary units (e.g., 100,000 KRW), at then current market prices. 
       FIG. 9  is a high level overview  290  of the automated portion of the process employed by system  28 . Automated procedures are used by underwriters to assist in full underwriting based on procedure  34  (see also  FIG. 3 ). Knowledge captured in procedure  34  is applied in inferred valuation procedure  40  to reduce cost and uncertainty in due diligence valuations of financial instruments and to reduce cost and variability between due diligence valuations. The valuations are subjected to a cash flow model which includes asset level valuation  146 , deterministic cash flow bridge  148 , stochastic cash flow bridge  152  and cash flow table  150 . The resultant bid valuation  154  is subjected to gaming strategies  160  and management adjustments  162  to produce the final bid  164 . 
       FIG. 10  is a flow diagram of an exemplary embodiment of forming clusters  246 . In forming clusters  246 , underwriters, with the aid of algorithms, such as for example algorithms  134  (shown in  FIG. 3 ) perform an analysis using a Classification And Regression Tree (“CART”) based model, which results in a grouping of UW assets by Collateral Usage and Market Value (“CUMV”) groups, using Previous Appraisal Amount (“PAA”) as the driving variable. 
     Two approaches to assess the performance of a CART based model are outlined below. One approach utilizes a ratio of the sum of squared error (SSE) of a CART based approach to that of a simple model, called an error ratio. A simple model is a model which assigns an average asset price to all assets. The second approach computes a coefficient of determination, denoted as R 2 , and defined as
 
 R   2 =1−( SSE/SST ),
 
where SST is a sum of squares total.
 
     R 2  is the contribution of a single asset within each segment relative to the entire population, a higher R 2  value for an asset within a particular segment, the higher is the contribution. The different portfolio segments are ranked based on the two approaches giving an indication of how good the predictive capabilities of the model are within each portfolio segment, giving a comfort level to the bidder in terms of pricing, for example, each tranche. 
     
       
         
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE C 
               
             
             
               
                   
               
               
                 Rank Error Ratios and R 2  value per asset 
               
             
          
           
               
                   
                   
                   
                   
                   
                 Rank 
                   
               
               
                   
                   
                   
                   
                   
                 Error 
                 R-Squared pe 
               
               
                   
                   
                   
                   
                   
                 Ratio for 
                 Loan for C 
               
               
                 Tranche CO 
                 Data 
                 B 
                 C 
                 Grand Total 
                 C loans 
                 loans 
               
               
                   
               
             
          
           
               
                 CO 01 
                 Sum of a Curr UPB THB 
                 645,959,109 
                 82,692,009 
                 728,651,119 
                   
                   
               
               
                   
                 Count of Loan No 
                 66 
                 10 
                 76 
                   
                   
               
               
                   
                 Sum of SST 
                 599,969,990,091,044 
                 72 331 126 127,460 
                 672 301,116,218,504 
                   
                   
               
               
                   
                 Sum of SSE(CART) 
                 252,088,256 587 362 
                 26 877 527,094,865 
                 278,965,783,682,227 
                   
                   
               
               
                   
                 Sum of SSE(Simple) 
                 440,700,263,795,025 
                 36,637,006,656,009 
                 477 337,270,451,034 
                 0.733617 
                 0.18% 
               
               
                 CO 02 
                 Sum of a Curr UPB THB 
                 58,779 400 
                 379 765,147 
                 438 544,547 
                   
                   
               
               
                   
                 Count of Loan No 
                 9 
                 118 
                 127 
                   
                   
               
               
                   
                 Sum of SST 
                 32,332 549,696,133 
                 1 039,401,135,208 180 
                 1,071,733 684,904,320 
                   
                   
               
               
                   
                 Sum of SSE(CART) 
                 6,139,933,273,655 
                 83 849 226,818 428 
                 89,989,160,092,084 
                   
                   
               
               
                   
                 Sum of SSE(Simple) 
                 7,037,799 486,368 
                 136,366,441,963,041 
                 143,404,241,449,409 
                 0.614882 
                 0.06% 
               
               
                 CO 03 
                 Sum of a Curr UPB THB 
                 798,969,257 
                 276,915,573 
                 1,075,884,830 
                   
                   
               
               
                   
                 Count of Loan No 
                 98 
                 99 
                 197 
                   
                   
               
               
                   
                 Sum of SST 
                 2,869,807,879,172,670 
                 1,017,087,163,438,760 
                 3,886 895,042,611,430 
                   
                   
               
               
                   
                 Sum of SSE(CART) 
                 729,304,505,050 836 
                 65,902,258,632,574 
                 795,206 763,683,411 
                   
                   
               
               
                   
                 Sum of SSE(Simple) 
                 929,822,648,064 552 
                 41,730,444,375,417 
                 971,553 092,439,969 
                 1.579237 
                 0.46% 
               
               
                 CO 04 
                 Sum of a Curr UPB THB 
                 916,281,888 
                 184,828,399 
                 1,101,110,287 
                   
                   
               
               
                   
                 Count of Loan No 
                 116 
                 28 
                 144 
                   
                   
               
               
                   
                 Sum of SST 
                 927 232,177,539,735 
                 223 991,862,418,471 
                 1 151,224,039,958,210 
                   
                   
               
               
                   
                 Sum of SSE(CART) 
                 329,869,566,636,764 
                 92,347,778,018,417 
                 422 217,344,665,182 
                   
                   
               
               
                   
                 Sum of SSE(Simple) 
                 688,543,329,448,792 
                 62,722,788,782,158 
                 751,266,118,230,950 
                 1.472316 
                 0.11% 
               
               
                 CO 05 
                 Sum of a Curr UPB THB 
                 221,769,281 
                 41,505 412 
                 263,274,692 
                   
                   
               
               
                   
                 Count of Loan No 
                 36 
                 19 
                 55 
                   
                   
               
               
                   
                 Sum of SST 
                 270,033,444,922,605 
                 164,601,058,694,453 
                 434,634,503,617,058 
                   
                   
               
               
                   
                 Sum of SSE(CART) 
                 28,547,982,198 098 
                 10,191 006,095 769 
                 38,738,988,293,867 
                   
                   
               
               
                   
                 Sum of SSE(Simple) 
                 28,897,015,065 918 
                 8,519,509,247,449 
                 37,416 524,313,367 
                 1.196196 
                 0.14% 
               
               
                 Total Sum of a Curr 
                   
                 2,641,758,934 
                 965,706,540 
                 3,607,465,475 
                   
                   
               
               
                 UPB THB 
                   
                   
                   
                   
                   
                   
               
               
                 Total Count of Loan 
                   
                 325 
                 274 
                 599 
                   
                   
               
               
                 No 
                   
                   
                   
                   
                   
                   
               
               
                 Total Sum of SST 
                   
                 4,699,378,041,422,190 
                 2,517,412,345,887,330 
                 7,216,788,387,309,520 
                   
                   
               
               
                 Total Sum of SSE 
                   
                 1,345,950,243 746,720 
                 279,167 796,660 054 
                 1,625,118,040,406,770 
                   
                   
               
               
                 (CART) 
                   
                   
                   
                   
                   
                   
               
               
                 Total Sum of SSE 
                   
                 2,095,001,055,860,660 
                 285,976,191,024,073 
                 2,380,977,246,884,730 
                 0.976192 
                 0.22% 
               
               
                 (Simple) 
               
               
                   
               
               
                   
                 R-Squared (CART) 
                 71 4% 
                 88 9% 
                 77 5% 
                   
                   
               
               
                   
                 R-Squared (Simple) 
                 55 4% 
                 88 6% 
                 67.0% 
               
               
                   
               
             
          
         
       
     
     A first step is to define relevant portfolio segmentations. The segmentations could be pre-defined tranches, for example, based on industry, Unpaid Balance (UPB) amounts, region or customer risk. Table C above is an example of defined segments based on tranches and asset rankings (B or C). 
     Table C provides an example output from a study of a portfolio with five tranches and two different asset types (B and C). The table shows how the error ratio is ranked for the different segments. Also, the R 2  values for each asset are also computed for assets of type C within each segment. 
     A second step is to compute SSE values for each portfolio segment of interest for the CART model and for the simple model (extrapolation of an average price). An error ratio is computed from the SSE based on the CART model divided by an SSE based on the simple model. If the error ratio is less than one, then the CART based model is a better predictor than the simple model. As an added benefit, a superior model can be assembled as a “hybrid” combination of the CART and simple models, by choosing the model which performs best in each segment, according to the error ratio metric. 
     A third step is to compute R 2  values for each asset within each portfolio segment. R 2  per asset is computed as (SST per segment−SSE per segment)/(overall SST for all assets×number of assets within each segment). 
     Lastly all the segments are ranked based on the error ratio computed in the second step and the R 2  values computed in the third step. The model is accurate in predicting price values for segments that rank high on both of the two metrics, the error ratio and R 2  and superior models are assembled using these metrics. 
     Table D shows the relative ranking of the five tranches for the assets of type C (from Table C) on the basis of the two performance metrics. 
     
       
         
               
             
               
               
               
               
               
             
           
               
                 TABLE D 
               
             
             
               
                   
               
               
                 Portfolio Segment Ranking 
               
             
          
           
               
                 Tranche CO 
                 C 
                 R-Squared 
                 Rank Error Ratio 
                 Rank R-squared 
               
               
                   
               
               
                 CO 01 
                 0.73 
                 0.18% 
                 2 
                 2 
               
               
                 CO 02 
                 0.61 
                 0.06% 
                 1 
                 5 
               
               
                 CO 03 
                 1.58 
                 0.46% 
                 5 
                 1 
               
               
                 CO 04 
                 1.47 
                 0.11% 
                 4 
                 4 
               
               
                 CO 05 
                 1.20 
                 0.14% 
                 3 
                 3 
               
               
                   
               
             
          
         
       
     
       FIG. 10  is a flow diagram illustrating an exemplary embodiment of forming clusters  246  using FCM to choose clusters for modeling. Computer  38  (shown in  FIG. 2 ) forms clusters  246  by taking selected data  78  and performing FCM analysis to produce the clusters. 
       FIG. 11  illustrates building models  248 , selecting best models  250  and calculating counts  252  in which six models are built using database  76 . Computer  38  (shown in  FIG. 3 ) performs this process. Model building  248  is used to assist the underwriter in prioritizing assets for full underwriting  14  and sample-based underwriting  34 , as well as for inferential valuation. 
     The lower portion of  FIG. 11  is a table illustrating an exemplary embodiment of selecting best models  250  from six models built in accordance with building models  248   d . The models differ according to which variables are used as X&#39;s. All models use CUMV Cluster (these are present for all assets). The models from building models  248  are used to predict Court Auction Value (“CAV”)  256  in addition to Market Value (“MAV”)  258 . Other embodiments (not shown) use other models to predict other values 
     In selecting best models  250 , the best models of K regression models under consideration (here, K=6), are selected. The best model is chosen for each UW asset, according to the following metric: 
                 min   k     ⁢     {       abs   ⁡     (     y   -       y   ^     k       )       ,     1   ⁢     E   99         }       ,         
where y is the UW value to be predicted, and ŷ k  is a prediction from the k th  regression model, for k=1, 2, . . . , K.
 
     In calculating counts  252 , the number of times each of the K models is selected within each CUMV cluster is counted.  FIG. 11  contains these counts for CAV and MAV modeling scenarios. Other modeling scenarios are used in other embodiments. 
     When applying models  254 , the weighted average prediction from all models that yielded a prediction for each non-UW asset is used. The weights are constructed from the frequencies of the counts calculated  252 , and the predictions come from the modeling process. In one embodiment, a commercial statistical analysis software (SAS) system is used to produce the models. An artifact of using the SAS system is that each non-UW asset will get a predicted UW value from each model for which the non-UW asset has each input variable, i.e., “X variable” present. Other modeling packages share this trait.) Equation E below details the procedure. 
     
       
         
           
             
               
                 
                   
                     
                       y 
                       
                         _ 
                         ^ 
                       
                     
                     l 
                   
                   = 
                   
                     
                       
                         ∑ 
                         
                           i 
                           , 
                           j 
                           , 
                           k 
                         
                       
                       ⁢ 
                       
                         
                           I 
                           lk 
                         
                         ⁢ 
                         
                           f 
                           ijk 
                         
                         ⁢ 
                         
                           
                             y 
                             ^ 
                           
                           lk 
                         
                       
                     
                     
                       
                         ∑ 
                         
                           i 
                           , 
                           j 
                           , 
                           k 
                         
                       
                       ⁢ 
                       
                         
                           I 
                           lk 
                         
                         ⁢ 
                         
                           f 
                           ijk 
                         
                       
                     
                   
                 
               
               
                 
                   (Equation  E) 
                 
               
             
           
         
       
     
     In Equation C, I lk =1 if model k produced a prediction for asset l, and is zero otherwise; f ijk =count of times model k was selected for UW assets among the i th  CUMV type (i=1,2), and the j th  CUMV cluster (j=1,2,3); and ŷ lk =prediction for y l  from model k. Note there is only a contribution from each modeling approach for which an asset has a prediction, with each being weighted by the number of times the modeling approach was selected for all UW assets of the same CUMV cluster. 
     Process  240  is also used to estimate a Lower Confidence Limit (“LCL”) and Upper Confidence Limit (“UCL”) for the mean prediction, with a substitution of the corresponding statistic for ŷ lk  in Equation E. 
     Referring back again to  FIG. 3 , supervised learning process  206  and unsupervised learning process  208  use clustering. “Clustering” is a tool that attempts to assess the relationships among patterns of the data set by organizing the patterns into groups or clusters such that patterns within a cluster are more similar to each other than are patterns belonging to different clusters. That is, the purpose of clustering is to distill natural groupings of data from a large data set, producing a concise representation of a system&#39;s behavior. Unsupervised learning step  208 , employs a fuzzy clustering method (“FCM”) and knowledge engineering to group assets automatically for valuation. FCM is a known method that has been widely used and applied in statistical modeling. The method aims at minimizing intra-cluster distance and maximizing inter-cluster distance. Typically the Euclidean distance is used. 
     FCM  248  (see  FIG. 10 ) at the same time minimizes the intra-cluster distance and maximizes the inter-cluster distance. Typically the Euclidean distance is used. FCM is an iterative optimization algorithm that minimizes the cost function 
                   J   =       ∑     k   =   1     n     ⁢       ∑     i   =   1     c     ⁢       μ   ik   m     ⁢              X   k     -     V   i            2                   (     Equation   ⁢           ⁢   F     )               
where n is the number of data points; c is the number of clusters, X k  is the k th  data point; V i  is the i th  cluster centroid; μ ik  is the degree of membership of the k th  data in the i th  cluster; m is a constant greater than 1 (typically m=2). Note that μ lk  is a real number and bounded in [0,1]. μ ik =1 means that i th  data is definitely in k th  cluster, while μ ik =0 means that i th  data is definitely not in k th  cluster. If μ ik =0.5, then it means that i th  data is partially in k th  cluster to the degree 0.5. Intuitively, the cost function would be minimized if each data point belongs exactly to a specific cluster and there is no partial degree of membership to any other clusters. That is, there is no ambiguity in assigning each data point to the cluster to which it belongs.
 
     The degree of membership μ lk  is defined by 
     
       
         
           
             
               
                 
                   
                     μ 
                     ik 
                   
                   = 
                   
                     1 
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           1 
                         
                         c 
                       
                       ⁢ 
                       
                         
                           ( 
                           
                             
                                
                               
                                 
                                   X 
                                   k 
                                 
                                 - 
                                 
                                   V 
                                   i 
                                 
                               
                                
                             
                             
                               
                                  
                                 
                                   
                                     X 
                                     k 
                                   
                                   - 
                                   
                                     V 
                                     j 
                                   
                                 
                                  
                               
                               2 
                             
                           
                           ) 
                         
                         
                           1 
                           
                             m 
                             - 
                             1 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     G 
                   
                   ) 
                 
               
             
           
         
       
     
     Intuitively, μ lk , the degree of membership of the data point X k  in the cluster centroid V i , increases as X k  is getting closer to V i . At the same time, μ ik  would get smaller as X k  is getting farther away V j  (other clusters). 
     The i th  cluster centroid V i  is defined by 
     
       
         
           
             
               
                 
                   
                     V 
                     i 
                   
                   = 
                   
                     
                       
                         ∑ 
                         
                           k 
                           = 
                           1 
                         
                         n 
                       
                       ⁢ 
                       
                         
                           
                             ( 
                             
                               μ 
                               ik 
                             
                             ) 
                           
                           m 
                         
                         ⁢ 
                         
                           X 
                           k 
                         
                       
                     
                     
                       
                         ∑ 
                         
                           k 
                           = 
                           1 
                         
                         n 
                       
                       ⁢ 
                       
                         
                           ( 
                           
                             μ 
                             ik 
                           
                           ) 
                         
                         m 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     H 
                   
                   ) 
                 
               
             
           
         
       
     
     Intuitively, V i , the i th  cluster centroid, is the weighted sum of the coordinates of X k , where k is the number of data points. 
     Starting with a desired number of clusters c and an initial estimate for each cluster center V i , i=1, 2, . . . , c, FCM will converge to a solution for V l  that represents either a local minimum or a saddle point of the cost function. The quality of the FCM solution, like that of most nonlinear optimization problems, depends strongly on the choice of initial values—the number c and the initial cluster centroids V i ). 
     In one exemplary embodiment, the entire portfolio  12  is segmented by unsupervised fuzzy clustering and each cluster is reviewed by under-writing experts. thereby assisting the underwriters in choosing the financial instruments for full underwriting  14  and sample underwriting  34 . Alternatively, this FCM can be applied just to portion  42 . As a result, each cluster gets assigned a HELTR composite score for purposes of adjustment  138  (see  FIG. 3 ) In essence, the HELTR composite score captures both expected and range of cash flow, its timing and the risk associated with each cluster. 
     Referring now to  FIG. 2 , the ratio of full underwrite portion  16  to the total portfolio  12  is in one exemplary embodiment 25% of the assets and 60% of the face value of all assets. Full underwriting of these assets is warranted due to their size and value. However, this underwriting is fairly uniform for all underwriters, so the underwriting is not likely to produce significant bidding variances. The remaining 40%, however, comprising portions  36  and  42 , which in the exemplary embodiment constitute 75% of the assets but only 40% of the face value are highly speculative until underwritten. To the extent value can be found in portions  36  and  42   f , for example without limitation, an additional five percent over gross extrapolation, the difference meaning the difference between winning and losing the entire portfolio bid or the entire tranche bid meaning hundreds of millions of dollars difference in profit. 
     In the case of insurance policies, in accordance with procedure  40 , statistics are used in an attempt to answer three basic questions: (a) How should we collect our data? (b) How should we summarize the data we collected? And (c) How accurate are our data summaries? Algorithm  134  answers question (c), and is a computer-based method without complicated theoretical proofs. Algorithm  134  for insurance policy inferential valuations is suitable for answering statistical inferences that are too complicated for traditional statistical analysis. Algorithm  134  for insurance policy valuation simulates the distribution of statistical estimates by repeatedly sampling with replacement. The algorithm generally is composed of three main steps: (I) Sampling with replacement, (II) Evaluating statistics of interest, and (III) Estimating standard deviation. 
     In accordance with insurance algorithm  134 , estimates of NPV standard error are performed as follows. For each of the risk models and for each segment in the models, assuming there are N policies in the segment, n samples are selected using sampling with replacement (for example, n=100). Each sample contains N policies, too, in this example. For each sample, and for all historical policies: 
                     A     E   w       =       ∑     (   Act   )           ∑     (   Wtdexp   )       0.72858               (     Equation   ⁢           ⁢   I     )               
Next, net present value is generated by
 
                   NPV   =       ∑   P     -     ∑   E     -       (     ∑   C     )     ×     A     E   w                   (     Equation   ⁢           ⁢   J     )               
for recent policies. Compute the sample standard deviation for the n NPV values. In Equation I, Act is the actual claim and Wtdexp is the weighted expected claim for each individual policy.
 
       FIG. 12  is a table of exemplary criteria  80  and exemplary rule sets for credit scoring  138 . Other criteria could be selected depending on the type of financial instrument and particular bidding conditions or any other desires or preferences of the bidder. 
       FIG. 13  is a more detailed tree chart diagram  260  similar to tree chart  66  (see lower portion of  FIG. 2 ). In  FIG. 13 , the segregation is by (a) whether secured, (b) whether revolving, (c) whether the last payment was zero. The result is six clusters  262 ,  264 ,  266 ,  268   270 ,  272 , casually known as a “shaker tree”. 
       FIG. 14  illustrates an exemplary system  300  in accordance with one embodiment of the present invention. System  300  includes at least one computer configured as a server  302  and a plurality of other computers  304  coupled to server  302  to form a network. In one embodiment, computers  304  are client systems including a web browser, and server  302  is accessible to computers  304  via the Internet. In addition, server  302  is a computer. Computers  304  are interconnected to the Internet through many interfaces including a network, such as a local area network (LAN) or a wide area network (WAN), dial-in-connections, cable modems and special high-speed ISDN lines. Computers  304  could be any device capable of interconnecting to the Internet including a web-based phone or other web-based connectable equipment, including wireless web and satellite. Server  302  includes a database server  306  connected to a centralized database  76  (also shown in  FIG. 2 ) which contains data describing sets of asset portfolios. In one embodiment, centralized database  76  is stored on database server  306  and is accessed by users at one of computers  304  by logging onto server sub-system  302  through one of computers  304 . In an alternative embodiment centralized database  76  is stored remotely from server  302 . Server  302  is further configured to receive and store information for the asset valuation methods described above. 
     While system  300  is described as a networked system, it is contemplated that the methods and algorithms described herein for examination and manipulation of asset portfolios are capable of being implemented in a stand-alone computer system that is not networked to other computers. 
       FIG. 15  is a diagram  320  illustrating due diligence tools and processes implemented within system  300 . Diagram  320  includes repositories of due diligence information including a dictionary  322 , a tool library  324 , a deal pitch repository  326 , links  328  and dashboards  330  where overviews regarding due diligence information can be accessed. A workspace  332  allows storage of due diligence information being compiled by a due diligence team. A results area  334  includes previously stored results of prior exercises including bid results. A deal valuation area  336  includes stored valuations of former and current deals for comparison. 
     The system informally referred to as a Virtual War Room diagrammed in diagram  320  includes a high level map and associated descriptions of the due diligence roles and responsibilities such that collaborators can see who has functional responsibilities, how the team members as individuals fit into the due diligence exercise and who to contact for assorted information. Also included is a project timeline with milestones and tasks arranged as both Gantt charts, PERT charts and text such that key deliverable timing is developed with inputs from the team, and then is made available to a global due diligence team. The project timeline serves as a control mechanism to keep the due diligence on schedule and to account for “what if” changes to schedule. 
     A project feedback mechanism within dashboard  330  includes an easily readable set of graphical indicators which tracks key due diligence deliverables, for example, types and quantities of underwriting completed, total project budget, and status of deliverables. A project calendar with notable local and global dates, holidays, vacations, and deliverables identified is within the feedback mechanism as is contact information for team members and collaborator&#39;s including telephone, email and address information. A project “to do” list and status such that the global team captures vital tasks to be completed and keeps visibility on the status thereof is further contemplated. 
     System  300  (shown in  FIG. 14 ) includes a shared storage place for the various functions to keep the project files and information in such a fashion that the collaborators can easily have access to the information with ease of retrieval. A centralized information flow map that identifies the sources and uses of information utilized to make the decisions needed on the due diligence team objectives. An example is the conversion of raw data, through associated calculations and data manipulations in order to set the bid price. 
     A centralized repository for the financial models and data manipulation and business process tools that are available for use on the due diligence is within system  300  as is a centralized repository for the historical “best practices” that the business collates and codifies from past due diligence exercises, or elsewhere such that the team can easily deploy and recall the firm&#39;s knowledge and lessons learned from past experiences. A centralized “gold standard” database of all relevant valuation information and facts associated with the due diligence. This database is checked for data integrity and has limited access with controlled backups. Underwriting data is centrally stored as is the valuation process so that all underwriting is not predicated by an onsite presence, but can be effected remotely. 
     While the invention has been described in terms of various specific embodiments, those skilled in the art will recognize that the invention can be practiced with modification within the spirit and scope of the claims.

Technology Category: 3