Abstract:
A data driven and forward looking risk and reward appetite methodology for consumer and small business is described. The methodology includes customer segmentation to create pools of homogeneous assets in terms of revenue and loss characteristics, forward looking simulation to forecast expected values and volatilities of revenue and loss, and risk and reward optimization of the portfolio. One methodology used for modeling revenue and loss is a generalized additive effect decomposition model to fit historical data. Based on the model, a segmentation procedure is performed, which allows for creation of groups of customers with similar revenue and loss characteristics. An estimation procedure for the model is developed and a simulation strategy to forecast and simulate revenue and loss volatility is developed. Efficient frontier curves of risk (e.g., return volatility) and reward (e.g., expected return) are created for the current portfolio under various economic scenarios.

Description:
BACKGROUND 
   A business seeks to improve on the assets of its portfolio. Risk and reward associated with one or more portfolios changes over time depending on a number of different economic conditions. Businesses assess the returns of particular assets versus the volatility in order to try to better manage their portfolio and reach a desired state. A balance is needed between business growth opportunities and a business&#39;s portfolio in order to take into account various macroeconomic scenarios and their impact on the business&#39;s portfolio. 
   SUMMARY 
   In light of the foregoing background, the following presents a simplified summary of the present disclosure in order to provide a basic understanding of some aspects of the invention. This summary is not an extensive overview of the invention. It is not intended to identify key or critical elements of the invention or to delineate the scope of the invention. The following summary merely presents some concepts of the invention in a simplified form as a prelude to the more detailed description provided below. 
   Understanding the dynamics of credit risk with respect to time is useful. Aspects of the present invention provide a method that identifies the historical performance and current state of any given portfolio of an entity. Aspects of the present invention aid a managing entity to pro-actively steer an entity by making informed policy decisions, inherently making a positive impact on shareholder value, considering internal policy and external macro-economic effects on any given portfolio. 
   Aspects of the present invention are directed to an end to end process of applying statistical methods to produce unique analysis to a portfolio. The method may include collecting and organizing segmented data and decomposing performance data into seasoning, vintage, and cycle effects. The method may further form statistical clusters for the basis of predicting performance. Cycle and macroeconomic forecasts may be applied to the clustered segments, and a product or portfolio of an entity may be optimized using the prediction data. 
   Still other aspects of the present invention are directed to a strategic portfolio and segment level tool derived from account level data that may identify the historical and predicted efficient frontier of a portfolio. The tool may include attrition, delinquency, revenue, loss, balance, and recovery information. The tool may include historical, forecast, optimization, and auto-validation capabilities. The tool also may be configured to run multiple simulation and optimization scenarios, such as the effect of a bull market, a bear market, a base market, through a particular cycle, and even customized, such as the 1991 recession. Aspects of the present invention allow for analysis of a plurality of metrics, including volatility. Still further aspects allow a user to drill down in the outputted data to obtain useful graphical results and spreadsheet data. In accordance with yet another aspect, the method decomposes and isolates the maturation effects from vintage effects from macroeconomic/cycle/other effects at a segment, vintage, and total portfolio level. 
   This Summary is provided to introduce a selection of concepts in a simplified form that are further described below in the Detailed Description. The Summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used to limit the scope of the claimed subject matter. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     A more complete understanding of aspects of the present invention and the advantages thereof may be acquired by referring to the following description in consideration of the accompanying drawings, in which like reference numbers indicate like features, and wherein: 
       FIG. 1  illustrates a schematic diagram of a general-purpose digital computing environment in which certain aspects of the present invention may be implemented; 
       FIG. 2  is an illustrative block diagram of workstations and servers that may be used to implement the processes and functions of certain embodiments of the present invention; 
       FIG. 3  is a flow chart of an illustrative method for forecasting expected values and volatilities of revenue and loss and optimizing a business&#39;s portfolio in accordance with at least one aspect of the present invention; 
       FIG. 4  is a block diagram of an illustrative risk reward appetite process in accordance with at least one aspect of the present invention; 
       FIG. 5  is a block diagram of an illustrative hierarchical view of segmented effects in accordance with at least one aspect of the present invention; 
       FIG. 6  is an illustrative diagram of an example maturation effect decomposition of net credit loss in accordance with at least one aspect of the present invention; 
       FIG. 7  is an illustrative diagram of an example vintage effect decomposition of net credit loss in accordance with at least one aspect of the present invention; 
       FIG. 8  is an illustrative diagram of an example cycle effect decomposition of net credit loss in accordance with at least one aspect of the present invention; 
       FIG. 9  is an illustrative diagram of an example total effect decomposition of net credit loss in accordance with at least one aspect of the present invention; 
       FIG. 10  is an illustrative seasoning effect factor analysis chart in accordance with at least one aspect of the present invention; 
       FIG. 11  is an illustrative vintage effect factor analysis chart in accordance with at least one aspect of the present invention; 
       FIG. 12  is an illustrative cycle effect factor analysis chart in accordance with at least one aspect of the present invention; 
       FIG. 13  is an illustrative chart isolating special causes in a cycle effect in accordance with at least one aspect of the present invention; 
       FIG. 14  is an illustrative chart for creating a cycle effect library for segment clusters in accordance with at least one aspect of the present invention; 
       FIGS. 15A-15D  are illustrative charts for characterizing segment clusters of cycle volatility in accordance with at least one aspect of the present invention; 
       FIG. 16  is an illustrative clustering chart using seasoning effects of multiple risk/reward metrics in accordance with at least one aspect of the present invention; 
       FIG. 17  is an illustrative clustering chart using cycle effects of multiple risk/reward metrics in accordance with at least one aspect of the present invention; 
       FIG. 18  are illustrative life cycle vintage prediction and simulation charts in accordance with at least one aspect of the present invention; 
       FIG. 19  is an illustrative sensitivity analysis of portfolio risk and return for various economic scenarios in accordance with at least one aspect of the present invention; 
       FIG. 20  is a graphical user interface depicting a segment risk/reward ratio in accordance with at least one aspect of the present invention; and 
       FIG. 21  is an illustrative chart for characterizing risk and reward for portfolios in accordance with at least one aspect of the present invention. 
   

   DETAILED DESCRIPTION 
   In the following description of the various embodiments, reference is made to the accompanying drawings, which form a part hereof, and in which is shown by way of illustration various embodiments in which the invention may be practiced. It is to be understood that other embodiments may be utilized and structural and functional modifications may be made. 
     FIG. 1  illustrates a block diagram of a generic computing device  101  (e.g., a computer server) that may be used according to an illustrative embodiment of the invention. The computer server  101  may have a processor  103  for controlling overall operation of the server and its associated components, including RAM  105 , ROM  107 , input/output module  109 , and memory  115 . 
   I/O  109  may include a microphone, keypad, touch screen, and/or stylus through which a user of device  101  may provide input, and may also include one or more of a speaker for providing audio output and a video display device for providing textual, audiovisual and/or graphical output. Software may be stored within memory  115  and/or storage to provide instructions to processor  103  for enabling server  101  to perform various functions. For example, memory  115  may store software used by the server  101 , such as an operating system  117 , application programs  119 , and an associated database  121 . Alternatively, some or all of server  101  computer executable instructions may be embodied in hardware or firmware (not shown). As described in detail below, the database  121  may provide centralized storage of account information and account holder information for the entire business, allowing interoperability between different elements of the business residing at different physical locations. 
   The server  110  may operate in a networked environment supporting connections to one or more remote computers, such as terminals  141  and  151 . The terminals  141  and  151  may be personal computers or servers that include many or all of the elements described above relative to the server  101 . The network connections depicted in  FIG. 1  include a local area network (LAN)  125  and a wide area network (WAN)  129 , but may also include other networks. When used in a LAN networking environment, the computer  101  is connected to the LAN  125  through a network interface or adapter  123 . When used in a WAN networking environment, the server  101  may include a modem  127  or other means for establishing communications over the WAN  129 , such as the Internet  131 . It will be appreciated that the network connections shown are illustrative and other means of establishing a communications link between the computers may be used. The existence of any of various well-known protocols such as TCP/IP, Ethernet, FTP, HTTP and the like is presumed, and the system can be operated in a client-server configuration to permit a user to retrieve web pages from a web-based server. Any of various conventional web browsers can be used to display and manipulate data on web pages. 
   Additionally, an application program  119  used by the server  101  according to an illustrative embodiment of the invention may include computer executable instructions for invoking user functionality related to communication, such as email, short message service (SMS), and voice input and speech recognition applications. 
   Computing device  101  and/or terminals  141  or  151  may also be mobile terminals including various other components, such as a battery, speaker, and antennas (not shown). 
   The invention is operational with numerous other general purpose or special purpose computing system environments or configurations. Examples of well known computing systems, environments, and/or configurations that may be suitable for use with the invention include, but are not limited to, personal computers, server computers, hand-held or laptop devices, multiprocessor systems, microprocessor-based systems, set top boxes, programmable consumer electronics, network PCs, minicomputers, mainframe computers, distributed computing environments that include any of the above systems or devices, and the like. 
   The invention may be described in the general context of computer-executable instructions, such as program modules, being executed by a computer. Generally, program modules include routines, programs, objects, components, data structures, etc. that perform particular tasks or implement particular abstract data types. The invention may also be practiced in distributed computing environments where tasks are performed by remote processing devices that are linked through a communications network. In a distributed computing environment, program modules may be located in both local and remote computer storage media including memory storage devices. 
   Referring to  FIG. 2 , an illustrative system  200  for implementing methods according to the present invention is shown. As illustrated, system  200  may include one or more workstations  201 . Workstations  201  may be local or remote, and are connected by one or communications links  202  to computer network  203  that is linked via communications links  205  to server  204 . In system  200 , server  204  may be any suitable server, processor, computer, or data processing device, or combination of the same. Server  204  may be used to process the instructions received from, and the transactions entered into by, one or more participants. 
   Computer network  203  may be any suitable computer network including the Internet, an intranet, a wide-area network (WAN), a local-area network (LAN), a wireless network, a digital subscriber line (DSL) network, a frame relay network, an asynchronous transfer mode (ATM) network, a virtual private network (VPN), or any combination of any of the same. Communications links  202  and  205  may be any communications links suitable for communicating between workstations  201  and server  204 , such as network links, dial-up links, wireless links, hard-wired links, etc. 
   An efficient frontier curve is commonly known in the art to depict trade-offs between potential risk and reward. Whenever possible, it is preferable to direct strategy and action (e.g., new account origination, account management such as pricing and line of credit assignment, and securitization for the purpose of risk transfer) to move the portfolio performance at the frontier line where maximum reward (e.g., expected return) with minimum risk performance lie. The frontier line can guide decision makers to set risk appetite (e.g., set reasonable expected value of return and its associated volatility implication). The curve can also be used to evaluate the performance of on-going actions whether they are moving managed portfolio closer to its “ideal” benchmark performance. To apply the risk/reward appetite concept to consumer products, the following steps may be implemented:
     1. Perform customer segmentation to divide the portfolio into “investment units” with distinct return (revenue and loss) characteristics among segments and similar characteristics within segment;   2. Create performance models to predict revenue and loss including the impact of economic cycles to the performance;   3. Characterize correlations among segments;   4. Simulate return of each segments including their variation; and   5. Optimize portfolio by
       a. Adjusting the “investment size” of each segments to setup direction for new account origination and risk distribution through securitization, and   b. Adjusting possible pricing alternatives as suggested by “reduced gradient” and “shadow price” information from optimization.   
       

   To perform customer segmentation, factors driving distinct performance characteristics such as the following are included: credit risk factors (e.g., FICO, LTV), product types, acquisition channels, geography, and customer relationships (customer with multiple product relationships). Considering “vintage” information (e.g., “age” or “length” of relationship is a characteristic of credit performance, the data uses include two trajectories: month on book (m) to characterize the vintage effects and calendar time (t) to characterize the exogenous effects. A portfolio may be divided into 23 FICO bands of 10 point increment, 10 geographical regions, 2 types of customer relationship (Yes/No), 15 types of products/subproducts, and 4 possible channels. Thus, there are at least 23×10×2×15×4=27,600 possible segments. In practice, it is impractical and not necessary to have such large number of segments. To reduce the number of segments into a manageable size, statistical segmentation is performed to merge segments with similar performance together, as described in below. 
   Once segmentation is completed, a model is developed by fitting historical data. The model implies that performance characteristics are decomposed into two additive components: maturation curve to characterize vintage (e.g., months on book) effect under “economic-neutral” condition and exogenous curve to characterize the effect of exogenous factors (e.g., economic cycle, management policy changes). The decomposition clearly evaluates the maturation and exogenous effects. The exogenous curve facilitates “scenario” forecasting to evaluate segment performance under different economic scenarios. Modeling the maturation curve is purposed by using a “quasi-parametric” approach of superposition of multiple logistic functions and decompose further the exogenous effect into irregular patterns due to special economic events, short term seasonal effects, and long term overall trend. The long term overall trend is linked to macroeconomic factor using factor models described below. 
   Forecast and simulation of each vintage performance predict future performance. Model validation and simulation approach is described below. Based on the simulation output, portfolio optimization and efficient frontier curves are created under different macroeconomic scenarios. The optimization approach is described below. 
   In the following, the data structure used in the analysis is described in addition to the general model proposal. The use of individual account level information monthly performance summarized aggregated at segment level is proposed. Therefore, the first step of data preparation is to summarize monthly performance variables at segment level characterized by vintage (e.g., month and year of origination) and monthly calendar time. 
     FIG. 4  is a block diagram of an illustrative risk reward appetite process/system in accordance with at least one aspect of the present invention.  FIG. 4  represents a general overall of various aspects of the entire process/system. Components  411 - 417  may constitute the components that operate with respect to the data collection process step  401  of the present invention. Within component  411 , input data may be enriched/processed. Performance segmentation on data occurs within component  413 . Historical performance data mart component  315  maintains historical customer account data. Historical performance input series component  317  performs decomposition on segmented historical customer account level data. 
   Components  421 - 427  may constitute the components that operate with respect to the segmentation process step  403  of the present invention. A business segment assessment component  421  is included. Segmentation model processing occurs with respect to component  423 . Segmentation modeling validation may occur with respect to component  325 . Component  327  may perform segmentation scheme normalization. Components  431 - 437  may constitute the components that operate with respect to the simulation process step  405  of the present invention. A simulation metric assessment component  431  is included. Financial assumptions may be accounted for by component  433 . Simulation modeling processing occurs with respect to component  435 . Simulation modeling validation may occur with respect to component  337 . 
   Components  441 - 447  may constitute the components that operate with respect to the optimization process step  407  of the present invention. A sensitivity screening component  441  is included. Business constraint formulation processing occurs with respect to component  443 . Optimization modeling may occur with respect to component  345 . Component  327  may perform business option evaluation. Components  451 - 457  may constitute the components that operate with respect to the strategy development process step  409  of the present invention. Decisions on a risk appetite for a portfolio may occur with respect to component  451 . The risk appetite may be integrated into one or more business plans by component  453 . Execution, control, testing, and piloting of the strategy processing occurs with respect to component  455 . Pilot results may be continuously monitored with respect to component  357 . 
     FIG. 3  is a flow chart of an illustrative method for forecasting expected values and volatilities of revenue and loss and optimizing a business&#39;s portfolio in accordance with at least one aspect of the present invention. Steps  301 - 313  may constitute data gathering steps of a risk and reward appetite model. In step  301 , customer account level historical data is inputted into the system. Any of a multitude of historical data with respect to revenue and loss for various aspects of various customers&#39; portfolio may be included. Proceeding to step  303 , a data extraction and summarization process and model are implemented on the customer account level historical data. In this step, the historical data with respect to various revenues and losses is processed with respect to any of a number of various scenarios for data utilization. 
   Proceeding to step  305 , segmented customer data may be stored for processing by other steps of the present invention. The segmented customer data from step  305  then is utilized as an input to step  307  where performance decomposition is performed on the data. In step  307 , the segmented customer data is decomposed into various effects for output. Specifically, the segmented customer data is decomposed into seasoning effect output data  309 , cycle effect output data  311 , and vintage effect output data  313 . The seasoning effect data  309 , cycle effect data  311 , and vintage effect data  313  may be derived from a number of different processes including a performance measure that utilizes a deterministic functional effect of seasoning as a function of months on the book, a mean-reverting stochastic process as a function of calendar time conditional on multivariate macroeconomic stochastic variables, such as unemployment and interest rate, a stochastic process of vintage effect as a function of origination condition, such as an underwriting policy and strategy at a particular time, in addition to other independent variables. 
     FIG. 6  is an illustrative diagram of an example maturation/seasoning effect decomposition of net credit loss in accordance with at least one aspect of the present invention.  FIG. 10  is an illustrative seasoning effect factor analysis chart in accordance with at least one aspect of the present invention. Such outputs may be generated as part of the seasoning effect data  309 . 
     FIG. 7  is an illustrative diagram of an example vintage effect decomposition of net credit loss in accordance with at least one aspect of the present invention.  FIG. 11  is an illustrative vintage effect factor analysis chart in accordance with at least one aspect of the present invention. Such an output may be generated as part of the vintage effect data  313 . 
     FIG. 8  is an illustrative diagram of an example cycle effect decomposition of net credit loss in accordance with at least one aspect of the present invention.  FIG. 12  is an illustrative cycle effect factor analysis chart in accordance with at least one aspect of the present invention.  FIG. 13  is an illustrative chart isolating special causes in a cycle effect in accordance with at least one aspect of the present invention. Such outputs may be generated as part of the cycle effect data  311 . With respect to  FIG. 13 , the outputted data may be useful in identifying temporal changes that may be correlated to known events, such as a low interest rate or a new bankruptcy policy. 
   Moving to step  315  in  FIG. 3 , segment clustering may occur where certain segments of seasoning effect data, cycle effect data, and/or vintage effect data are accounted for together.  FIG. 5  is a block diagram of an illustrative hierarchical view of segmented effects in accordance with at least one aspect of the present invention. As shown, an entire portfolio view  501  may be broken down by individual effects, such as seasoning effect  503 , cycle effect  523 , and vintage effect  543 . In addition, the individual effects,  503 ,  523 , and  543 , may be further super segmented. Seasoning effect  503  is shown to include three super segments A  505 , B  507 , and C,  509 . Super segment C  509  is shown to be further segmented to Segment C. 1   511  and Segment C. 2   513 . Cycle effect  523  is shown to include three super segments A  525 , B  527 , and C,  529 . Super segment C  529  is shown to be further segmented to Segment C. 1   531  and Segment C. 2   533 . Vintage effect  543  is shown to include three super segments A  545 , B  547 , and C,  549 . Super segment C  549  is shown to be further segmented to Segment C. 1   551  and Segment C. 2   553 . As should be understood, these Segments and Super Segments in  FIG. 5  are merely illustrative and that other and additional segment levels may be utilized and/or incorporated within the present invention. 
   The common cluster of cycle volatility represent how the segments within a cluster react similarly to common environmental factors. In accordance with one illustrative example, a mixture of Gaussian stochastic processes may be applied to identify optimal clusters. Each segment may have a different sensitivity to the common factor represented by the multitude of strength regression coefficients. The difference among clusters may indicate that each cluster volatility is driven by a different set of environmental factors. Each cluster may be linked to a distinct set of macroeconomic factors.  FIG. 14  is an illustrative chart for creating a cycle effect library in accordance with at least one aspect of the present invention. In this example, four clusters are represented with respect to its scaled cycle effect over time. 
     FIGS. 15A-15D  are illustrative charts for characterizing clusters of cycle volatility in accordance with at least one aspect of the present invention. In the example of  FIG. 15A , a cluster  1  including 24 segments is shown with a representation of the cycle volatility with respect to three different macroeconomic variables. In the example of  FIG. 15B , a cluster  2  including 22 segments is shown with a representation of the cycle volatility with respect to two of the three different macroeconomic variables from  FIG. 15A . In the example of  FIG. 15C , a cluster  3  including 15 segments is shown with a representation of the cycle volatility with respect to two of the three different macroeconomic variables from  FIG. 15A . 
     FIG. 16  is an illustrative clustering chart using seasoning effects of multiple risk/reward metrics in accordance with at least one aspect of the present invention. As shown, various segments  1 - 5  are illustrated with respect to various macroeconomic variables.  FIG. 17  is an illustrative clustering chart using cycle effects of multiple risk/reward metrics in accordance with at least one aspect of the present invention. As shown, various segments  1 - 5  are illustrated with respect to various macroeconomic variables. 
   Returning to  FIG. 3 , from step  315 , the clustered segments may be stored within a generated cluster decoder/encoder table in step  317 . The table generated from step  317  may be an input for a model library decomposition process in step  319 . The model library decomposition process in step  319  may also utilize the segmented customer data from step  305 . The data from step  319  may then be stored in various libraries, including a vintage effect library  321 , a seasoning effect library  323 , and a cycle effect library  325 . The data stored in libraries  321 ,  323 , and  325  may also be outputted to a user as needed. 
   Proceeding from the libraries  321 ,  323 , and  325 , a prediction process may be utilized in addition to mixed effect decomposition. In step  329 , a historical super segment and portfolio aggregation process may be implemented utilizing the data stored in vintage effect library  321 , seasoning effect library  323 , and/or cycle effect library  325 . The output of step  329  may then be stored in step  331 .  FIG. 9  is an illustrative diagram of an example total effect decomposition of net credit loss in accordance with at least one aspect of the present invention. The chart illustrated in  FIG. 9  may be generated form the data decomposed in step  329 . 
   The prediction components of the aspects of the process of the present invention may include components  321 - 327 ,  333 - 345 , and  349 - 353 . Data from cycle effect library  325  may be inputted to an econometric variable and lag selection process in step  335 . In addition, macroeconomic data and scenarios may be inputted to the process in step  335  from step  327 . Macroeconomic data and scenarios may include baseline, bull, and bear economic scenarios. From step  335 , an econometric model may be generated and stored in step  339 . Concurrently, output from the macroeconomic data and scenarios in step  327  is inputted into a stochastic process model and simulation in step  337 . Output from step  337  may be stored as macroeconomic volatility simulation and scenarios in step  349 . 
   The output of step  349  may be inputted to a credit cycle simulation and prediction process in step  351 . In addition, data from the econometric model stored in step  339  also may be inputted into the process in step  351 . Output of the credit cycle simulation and prediction process in step  351  may be stored in step  353 . The cycle effect prediction data in step  353  may be outputted to a user as needed. 
   The cycle effect prediction data form step  353  may be inputted to a segment and portfolio prediction process in step  343 . In addition, historical trend data from step  333 , that includes various data from vintage effect library  321 , seasoning effect library  323 , and cycle effect library  325 , may be inputted to the segment and portfolio prediction process in step  343 . Still further, data with respect to new acquisition and portfolio management plans stored in step  341  may be inputted in the segment and portfolio prediction process in step  343 . Output of the segment and portfolio prediction process in step  343  may be stored in step  345 . The performance forecast data in step  345  may be outputted to a user as needed.  FIG. 18  are illustrative life cycle vintage prediction and simulation charts in accordance with at least one aspect of the present invention. In the example, a principle seasoning curve for various vintages is shown.  FIG. 19  is an illustrative sensitivity analysis of portfolio risk and return for various economic scenarios, such as a baseline and a bear, in accordance with at least one aspect of the present invention. 
   The optimization components of the aspects of the process of the present invention may include components  341 - 347  and  351 - 359 . Output data from performance forecast process in step  345  may be inputted into a portfolio optimization process in step  357 . In addition, the cycle effect prediction data stored in step  353  may be inputted into the portfolio optimization process in step  357 . Still further, other data, such as business constraints and growth target data stored in step  355  may be accounted for and inputted into the portfolio optimization process in step  357 . Output of the portfolio optimization process in step  357  may be stored in step  359 . The efficient frontier data stored in step  359  may be outputted to a user as needed. The efficient frontier data in step  359  may include alternative balance allocations for the portfolio, an optimal acquisition plan, and performance benchmarks. 
     FIG. 20  is a graphical user interface depicting a segment risk/reward ratio in accordance with at least one aspect of the present invention. Comparing segment risk/reward performance relative to each other may be utilized to set a direction for origination and account management. The effects of management may be seen with respect to a medium performance line and variables and effects may be taken into account to predict the effect of changing one or more variables.  FIG. 21  is an illustrative chart for characterizing risk and reward for portfolios in accordance with at least one aspect of the present invention. The line illustrates an optimal percent expected risk adjusted return with respect to percent volatility of a portfolio. This illustrative chart identifies the current status and can show the effect of change and/or prediction. 
   While illustrative systems and methods as described herein embodying various aspects of the present invention are shown, it will be understood by those skilled in the art, that the invention is not limited to these embodiments. Modifications may be made by those skilled in the art, particularly in light of the foregoing teachings. For example, each of the elements of the aforementioned embodiments may be utilized alone or in combination or subcombination with elements of the other embodiments. It will also be appreciated and understood that modifications may be made without departing from the true spirit and scope of the present invention. The description is thus to be regarded as illustrative instead of restrictive on the present invention.