Source: https://patents.google.com/patent/US20020116309A1/en
Timestamp: 2018-06-18 06:49:58
Document Index: 694392947

Matched Legal Cases: ['Application No. 60', 'art 85', 'ART) 252', 'ART) 6', 'ART) 329', 'art 66']

US20020116309A1 - Methods and systems for efficiently sampling portfolios for optimal underwriting - Google Patents
Methods and systems for efficiently sampling portfolios for optimal underwriting Download PDF
US20020116309A1
US20020116309A1 US09737628 US73762800A US2002116309A1 US 20020116309 A1 US20020116309 A1 US 20020116309A1 US 09737628 US09737628 US 09737628 US 73762800 A US73762800 A US 73762800A US 2002116309 A1 US2002116309 A1 US 2002116309A1
US09737628
US7003484B2 (en )
A method of valuation of large groups of assets by partial full underwriting, partial sample underwriting and inferred values of the remainder using an iterative and adaptive supervised and unsupervised statistical evaluation of all assets and statistical inferences drawn from the evaluation and applied to generate the inferred asset values. Individual asset values are developed and listed in relational tables so that individual asset values can be rapidly taken from the tables and quickly grouped in any desired or prescribed manner for bidding purposes. The assets are collected into a database, divided into categories by credit variable, subdivided by ratings as to those variables and then rated individually. The assets are then regrouped according to a bidding grouping and a collective valuations established by cumulating the individual valuations.
This application claims the benefit of U.S. Provisional Application No. 60/173,957, filed Dec. 30, 1999, which is hereby incorporated by reference in its entirety.
[0008]FIG. 1 is a flow diagram illustrating a known process for valuing a portfolio of assets;
[0009]FIG. 2 is a flow diagram illustrating valuing a portfolio of assets in accordance with one embodiment of the present invention;
[0010]FIG. 3 is a flow diagram illustrating, in more detail, one embodiment of a first portion of a rapid valuation process for large asset portfolios that breaks assets into categories of variance;
[0011]FIG. 4 is a flow diagram illustrating a second portion of a rapid valuation process for a large asset portfolios that aggregates from a basis to a tranche or portfolio basis;
[0012]FIG. 5 illustrates a probability distribution for exemplary assets whose recovery value is inferred;
[0013]FIG. 6 is a flow diagram of a supervised learning step of the process of FIG. 3;
[0014]FIG. 7 is a flow diagram of an unsupervised learning step of the process of FIG. 3;
[0015]FIG. 8 is an embodiment of the process for unsupervised learning;
[0016]FIG. 9 is an embodiment of the generation 1 (first pass) rapid asset valuation process;
[0017]FIG. 10 is a flow diagram of a fuzzy clustering method used in the unsupervised learning of FIG. 8;
[0018]FIG. 11 is a pair of tables showing an example of model selection and model weighting for a rapid asset evaluation process;
[0019]FIG. 12 is a table showing exemplary attributes for a rapid asset valuation process; and
[0020]FIG. 13 is a cluster diagram of an exemplary clustering method for a rapid asset valuation process; and
[0021]FIG. 14 is a computer network schematic.
[0022]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.
[0023]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).
[0026]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.
1 Lien 85 62 .15 3 3 (3/1 65)(85) (3/1 65)(62) (3/1 65)(15) (3/1 65)(3)
2 Asset 45 4 31 3 7 (7/1 65)(45) (7/1 65)(4) (7/1 65)(31) (7/1 65)(3)
3 Coordinates - 9 5 2 2 65 (65/1 65)(9) (65/1 65)(5) (65/1 54)(2) (65/1 65)(2)
1 65 6999 4792 2374 2 6059
A deviation, Yerror, of the chosen response variable, Y1, from the expected value, Yexpect, using weighted values of occurrence of x1=a and x2=b separately, is calculated by:
[0050]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”).
[0072]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.
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 ] × [ ∑ 1 N   x i ] 2 [ ∑ 1 n   x i ] 2 × ∑ 1 N   ( y i - Rx i ) 2 N - 1
yi=recovery for sample i R = ∑ 1 N   y i ∑ 1 N   x i = cluster   expected   recovery   %
h 2 = k 2 × n  [ 1 - n N ] × [ ∑ 1 N   x i ] 2 [ ∑ 1 n   x i ] 2 × ∑ 1 N   ( y i - Rx i ) 2 N - 1 ( Equation   C )
h = error   tolerance   for   estimating   Y = ∑ 1 N   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 )
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.
ple Cume
Size Exp Rec Exp Rec Cume UPS Exp Rec % Residual
2 716,951 1,496,082 5,477,631 27 5% 27,259
4 481,798 2,337,206 8,538,875 27 4% (20,958)
2,000,000 5.0% 44 160,329
1,000,000 25.0% 12 123,821
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's net present value (“NPV”) to be above 0 is assessed using the project'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 HRR 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.
[0097]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.
[0098]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).
[0101]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.
[0102]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.
Sum of SSE(CART) 252,008,256,587,362 26,877,527,094,865 278,965,783,682,227
Sum of SSE(CART) 6,139,933,273,655 83,849,226,818,428 89,989,160,092,064
Sum of SSE(CART) 329,869,566,635,764 92,347,778,018,417 422,217,344,655,182
Lastly all the segments are ranked based on the error ratio computed in the second step and the R 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 R2 and superior models are assembled using these metrics.
[0112]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.
[0113]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.
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 )
The degree of membership μik is defined by μ ik = 1 ∑ j = 1 c   (  X k - V i  2  X k - V j  2 ) 1 m - 1 ( Equation   G )
Intuitively, μik , the degree of membership of the data point Xk in the cluster centroid Vi, increases as Xk is getting closer to Vi. At the same time, μik would get smaller as Xk is getting farther away Vj (other clusters).
The ith cluster centroid Vi is defined by V i = ∑ k = 1 n   ( μ ik ) m  X k ∑ k = 1 n   ( μ ik ) m ( Equation   H )
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 )
[0135]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.
[0136]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”.
[0137]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.
1. A method for sampling assets in an asset portfolio for optimal underwriting coverage when only a portion of the assets are to be underwritten, said method comprising the steps of:
determining descriptive attributes of assets in the portfolio;
encoding individual attributes; and
clustering the assets for underwriting based upon occurrences of the descriptive attributes.
2. A method according to claim 1 further comprising the steps of determining a number of samples to be submitted for further underwriting review.
3. A method according to claim 2 wherein said step of determining a number of samples to be submitted for further underwriting review further comprises the steps of:
establishing a confidence level regarding the total recoveries probable in each segment of the portfolio;
establishing a precision to which total recoveries in each segment are estimated; and
providing an estimate of a level and a range of recoveries as a percentage of total Unpaid Principal Balance (UPB).
4. A method according to claim 3 wherein said step of establishing a confidence level regarding the total recoveries probable further comprises the step of determining a sample size, n, for the cluster of assets according to:
h 2 = k 2 × n  [ 1 - n N ] × [ ∑ 1 N   x i ] 2 [ ∑ 1 n   x i ] 2 × ∑ 1 N   ( y i - Rx i ) 2 N - 1
h=desired precision
R = ∑ 1 N   y i ∑ 1 N   x i = cluster   expected   recovery   %
5. A method according to claim 4 wherein said step of providing an estimate of a level and a range of recoveries further comprises the step of estimating a level and range of recoveries according to:
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
6. A method according to claim 1 wherein said step of clustering the assets for underwriting further comprises the step of using a supervised clustering process to cluster the assets.
7. A method according to claim 1 wherein said step of clustering the assets for underwriting further comprises the step of using an unsupervised clustering process to cluster the assets.
8. A method according to claim 1 wherein said step of clustering the assets for underwriting further comprises the step of using a Monte Carlo process to cluster the assets.
9. A system configured to sample assets in an asset portfolio for optimal underwriting coverage, said system comprising:
at least one client system connected to said server through a network, said server further configured to:
determine descriptive attributes of assets in the portfolio;
encode individual attributes; and
cluster the assets for underwriting based upon occurrences of the descriptive attributes.
10. A system according to claim 9 further configured to determine a number of samples to be submitted for further underwriting review.
11. A system according to claim 10 wherein said server configured to:
establish a confidence level regarding the total recoveries probable in each segment of the portfolio;
establish a precision to which total recoveries in each segment are estimated; and
provide an estimate of a level and a range of recoveries as a percentage of total Unpaid Principal Balance (UPB).
12. A system according to claim 11 wherein said server configured to determine a sample size, n, for the cluster of assets according to:
cluster expected recovery %
by solving for n.
13. A system according to claim 12 wherein said server configured to estimate a level and range of recoveries according to:
 Y ^ R - μ Y ^ R  ≤ k  Var  ( Y ^ R )   with   probability ≥ 1 - 1 k 2 .
14. A system according to claim 9 wherein said server configured to use a supervised clustering process to cluster the assets.
15. A system according to claim 9 wherein said server configured to use an unsupervised clustering process to cluster the assets.
16. A system according to claim 9 wherein said server configured to use a Monte Carlo process to cluster the assets.
17. A computer for sampling assets in an asset portfolio for optimal underwriting coverage, said computer including a database of asset portfolios and valuation process analytics, said computer programmed to:
18. A computer according to claim 17 programmed to determine a number of samples to be submitted for further underwriting review.
19. A computer according to claim 18 programmed to:
establish a confidence level regarding total recoveries probable in each segment of the portfolio;
20. A computer according to claim 19 programmed to determine a sample size, n, for the cluster of assets according to:
21. A computer according to claim 20 programmed to estimate a level and range of recoveries according to:
22. A computer according to claim 17 programmed to use a supervised clustering process to cluster the assets.
23. A computer according to claim 17 programmed to use an unsupervised clustering process to cluster the assets.
24. A computer according to claim 17 programmed to use a Monte Carlo process to cluster the assets.
US09737628 1999-12-30 2000-12-14 Methods and systems for efficiently sampling portfolios for optimal underwriting Active 2023-11-12 US7003484B2 (en)
US17395799 true 1999-12-30 1999-12-30
US09737628 US7003484B2 (en) 1999-12-30 2000-12-14 Methods and systems for efficiently sampling portfolios for optimal underwriting
EP20000986690 EP1212694A2 (en) 1999-12-30 2000-12-21 Methods and systems for efficiently sampling portfolios for optimal underwriting
JP2001550609A JP2003529139A (en) 1999-12-30 2000-12-21 Portfolio efficient sampling method and system for optimum under light
PCT/US2000/034917 WO2001050318A9 (en) 1999-12-30 2000-12-21 Methods and systems for efficiently sampling portfolios for optimal underwriting
CN 00806994 CN1378673A (en) 1999-12-30 2000-12-21 Methods and systems for efficiently sampling portfolios for optimal underwriting
CA 2362446 CA2362446A1 (en) 1999-12-30 2000-12-21 Methods and systems for efficiently sampling portfolios for optimal underwriting
US20020116309A1 true true US20020116309A1 (en) 2002-08-22
US7003484B2 US7003484B2 (en) 2006-02-21
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