Patent Publication Number: US-2013241933-A1

Title: Methods and systems for providing interest rate simulation displays

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit of U.S. Provisional Application No. 60/682,605, filed May 18, 2005. The entire contents of that provisional application are incorporated herein by reference. 
    
    
     SUMMARY 
     In one embodiment, the present invention comprises simulation analyses and displays that enable visualization of potential future yield curve (“YC”) paths. After generating yield curve data, relevant interest rates are applied to assets or liabilities in an issuer&#39;s portfolio. This enables generation of a probabilistic map of future interest income and future interest expense based on simulated interest rates and particular characteristics of the issuer&#39;s asset and liability portfolios. In another embodiment, present value is used instead of interest expense. 
     In one embodiment, after a probabilistic map is developed, potential strategies are layered in using derivative securities or changes to the level of assets or liabilities in order to estimate the impact that the strategies will have on the various probabilities of future interest expense and interest income possibilities. 
     This data preferably is presented in a graphical form that distills the main components of risk and return of various strategies, which in turn allows clients to make more informed decisions on the merits and risks of various strategies. These presentations provide clients with better understanding and insight, and have been used to help corporate boards build actionable plans to augment their risk management strategies. 
     A preferred embodiment uses two or more different assumptions for future interest rates and applies historical volatilities and correlations to address the stochastic elements. 
     For a particular company, an estimate of assets and liabilities that earn or pay interest may be used. At least one embodiment can work with summary data, such as maturity buckets, average coupon, duration, and floating rate sensitivity, or an extensive analysis using every asset or liability in the client&#39;s portfolio may be run. The manner in which data is presented to clients helps those clients make better decisions. 
     In one aspect, the invention comprises a computer system comprising means for displaying on a computer screen a chart illustrating level and volatility of a projected accounting performance based on a plurality of possible future interest rates, wherein the chart comprises a 50th percentile line, a 95th percentile line, and a 5th percentile line, and wherein the 50th percentile line, 95th percentile line, and 5th percentile line represent probability distribution over time of the projected accounting performance. 
     In various embodiments: (1) wherein the 95th percentile line and the 5th percentile line form a cone that models potential volatility of the projected accounting performance; (2) the projected accounting performance is projected accounting performance per quarter; (3) the projected accounting performance is based on at least one interest rate scenario; (4) the at least one interest rate scenario comprises one or more of: a forwards scenario; an X/Y mean reversion scenario; a Z year pattern assumption scenario; and an inverted yield curve scenario; (5) the accounting performance comprises at least one of: net interest margin, interest expense, interest income, and present value; and (6) the accounting performance comprises a combination of two or more of: net interest margin, interest expense, interest income, and present value. 
     In another aspect, the invention comprises a computer system comprising: means for calculating output of an interest rate simulation model; and means for receiving the output and based thereon displaying on a computer screen a median high-low chart comprising one or more vertical bars, wherein each of the one or more vertical bars represents a probability distribution, wherein each of the one or more vertical bars comprises a center dot, an uppermost dot, and a lowermost dot, and wherein the center dot represents an expected level of interest cost. 
     In various embodiments: (1) for each of the one or more vertical bars, the uppermost dot represents a 95% best case for projected accounting performance and the lowermost dot represents a 95% worst case for projected accounting performance; (2) the projected accounting performance comprises one or more of: net interest margin, interest expense, interest income, and present value; (3) at least one of the one or more vertical bars corresponds to an interest rate scenario; (4) the interest rate scenario comprises at least one of: a forwards scenario; an X/Y mean reversion scenario; a Z year pattern assumption scenario; and an inverted yield curve scenario; (5) the chart comprises, for at least one of the one or more vertical bars that corresponds to an interest rate scenario, one or more vertical bars corresponding to a risk management product scenario; and (6) the risk management product scenario comprises a scenario for one or more of: swaps, collars, caps, floors, swaptions, and forward starting swaps. 
     In another aspect, the invention comprises a method comprising: displaying on a computer screen a chart illustrating level and volatility of a projected accounting performance based on a plurality of possible future interest rates, wherein the chart comprises a 50th percentile line, a 95th percentile line, and a 5th percentile line, and wherein the 50th percentile line, 95th percentile line, and 5th percentile line represent probability distribution over time of the projected accounting performance. 
     In various embodiments: (1) the 95th percentile line and the 5th percentile line form a cone that models potential volatility of the projected accounting performance; (2) the projected accounting performance is projected accounting performance per quarter; (3) the projected accounting performance is based on at least one interest rate scenario; (4) the at least one interest rate scenario comprises one or more of: a forwards scenario; an X/Y mean reversion scenario; a Z year pattern assumption scenario; and an inverted yield curve scenario; (5) the accounting performance comprises at least one of: net interest margin, interest expense, interest income, and present value; and (6) the accounting performance comprises a combination of two or more of: net interest margin, interest expense, interest income, and present value. 
     In another aspect, the invention comprises a method comprising: calculating output of an interest rate simulation model; receiving the output; and based on the output, displaying on a computer screen a median high-low chart comprising one or more vertical bars, wherein each of the one or more vertical bars represents a probability distribution, wherein each of the one or more vertical bars comprises a center dot, an uppermost dot, and a lowermost dot, and wherein the center dot represents an expected level of interest cost. 
     In various embodiments: (1) for each of the one or more vertical bars, the uppermost dot represents a 95% best case for projected accounting performance and the lowermost dot represents a 95% worst case for projected accounting performance; (2) the projected accounting performance comprises one or more of: net interest margin, interest expense, interest income, and present value; (3) at least one of the one or more vertical bars corresponds to an interest rate scenario; (4) the interest rate scenario comprises at least one of: a forwards scenario; an X/Y mean reversion scenario; a Z year pattern assumption scenario; and an inverted yield curve scenario; (5) the chart comprises, for at least one of the one or more vertical bars that corresponds to an interest rate scenario, one or more vertical bars corresponding to a risk management product scenario; and (6) the risk management product scenario comprises a scenario for one or more of: swaps, collars, caps, floors, swaptions, and forward starting swaps. 
     In another aspect, the invention comprises a computer system comprising: a computer operable to display on a computer screen a chart illustrating level and volatility of a projected accounting performance based on a plurality of possible future interest rates, wherein the chart comprises a 50th percentile line, a 95th percentile line, and a 5th percentile line, and wherein the 50th percentile line, 95th percentile line, and 5th percentile line represent probability distribution over time of the projected accounting performance. 
     In various embodiments: (1) the 95th percentile line and the 5th percentile line form a cone that models potential volatility of the projected accounting performance; (2) the projected accounting performance is projected accounting performance per quarter; (3) the projected accounting performance is based on at least one interest rate scenario; (4) the at least one interest rate scenario comprises one or more of: a forwards scenario; an X/Y mean reversion scenario; a Z year pattern assumption scenario; and an inverted yield curve scenario; (5) the accounting performance comprises at least one of: net interest margin, interest expense, interest income, and present value; and (6) the accounting performance comprises a combination of two or more of: net interest margin, interest expense, interest income, and present value. 
     In another aspect, the invention comprises a computer system comprising a processor operable to software operable to: calculate output of an interest rate simulation model; receive the output; and based on the output, display on a computer screen a median high-low chart comprising one or more vertical bars, wherein each of the one or more vertical bars represents a probability distribution, wherein each of the one or more vertical bars comprises a center dot, an uppermost dot, and a lowermost dot, and wherein the center dot represents an expected level of interest cost. 
     In various embodiments: (1) for each of the one or more vertical bars, the uppermost dot represents a 95% best case for projected accounting performance and the lowermost dot represents a 95% worst case for projected accounting performance; (2) the projected accounting performance comprises one or more of: net interest margin, interest expense, interest income, and present value; (3) at least one of the one or more vertical bars corresponds to an interest rate scenario; (4) the interest rate scenario comprises at least one of: a forwards scenario; an X/Y mean reversion scenario; a Z year pattern assumption scenario; and an inverted yield curve scenario; (5) the chart comprises, for at least one of the one or more vertical bars that corresponds to an interest rate scenario, one or more vertical bars corresponding to a risk management product scenario; and (6) the risk management product scenario comprises a scenario for one or more of: swaps, collars, caps, floors, swaptions, and forward starting swaps. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  illustrates assumptions used in a preferred embodiment. 
         FIGS. 2-5  depict swap rates over time for various interest rate scenarios. 
         FIG. 6  depicts annualized interest rate volatility. 
         FIGS. 7-10  depict preferred displays of results of interest rate simulations performed on a portfolio of assets and liabilities at different probability levels. 
         FIG. 11  illustrates distribution of Net Interest Margin (NIM) over time for various scenarios. 
         FIG. 12  depicts a median high-low chart for different interest rate environments at 95% confidence levels. 
         FIGS. 13-14  illustrate distribution of 2006 NIM over time for various scenarios. 
         FIGS. 15-16  illustrate distribution of 2007 NIM over time for various scenarios. 
         FIGS. 17-18  illustrate distribution of 2008 NIM over time for various scenarios. 
         FIGS. 19-20  illustrate distribution of 2009 NIM over time for various scenarios. 
         FIGS. 21-26  illustrate results of a blended scenario. 
         FIGS. 27-30  illustrate NIM impact per quarter for various scenarios. 
         FIGS. 31-34  provide a comparison of results for doing nothing (“current”) versus “swapped” for 2005. 
         FIGS. 35-38  provide a comparison of results for doing nothing (“current”) versus “swapped” for 2006. 
         FIGS. 39-42  provide a comparison of results for doing nothing (“current”) versus “swapped” for 2007. 
         FIGS. 43-46  provide a comparison of results for doing nothing (“current”) versus “swapped” for 2008. 
         FIGS. 47-50  provide a comparison of results for doing nothing (“current”) versus “swapped” for 2009. 
         FIG. 51  illustrates assumptions used in a preferred embodiment. 
         FIGS. 52-55  depict swap rates over time for various interest rate scenarios. 
         FIG. 56  depicts annualized interest rate volatility. 
         FIG. 57  depicts results of a Monte Carlo simulation of 1000 potential paths for 3-month LIBOR for the next five years based on the forward curve and historical volatility. 
         FIGS. 58-61  depict displays of interest expense per quarter for various scenarios. 
         FIG. 62  depicts a display of various probability distributions for various swap scenarios. 
         FIGS. 63-66  depict IE based on 43% floating interest rate projections. 
         FIGS. 67-70  depict 43% relative to current. 
         FIGS. 71-74  depict IE based on 60% floating interest projections. 
         FIGS. 75-78  depict 60% relative to current. 
         FIG. 79  depicts historical implied LIBOR Forward Curves at various points dating back to 1990. 
         FIGS. 80-81  depict annual NPV savings from a 5- and 7-year swap to floating. 
         FIGS. 82-83  depict ABC&#39;s “efficient frontier.” 
         FIGS. 84A-84B ,  85 A- 85 B and  86 A- 86 B depict examples of risk management strategies. 
     
    
    
     DETAILED DESCRIPTION 
     In one embodiment, the present invention generates a plurality of future interest rate paths to calculate a range of interest revenue and interest expense levels produced by a company&#39;s current interest rate sensitive asset and liability portfolios, respectively. 
     A first example herein describes preferred treatment of company “XYZ,” and illustrates exemplary data displays of preferred embodiments. 
     By analyzing a combined interest revenue/expense projection and evaluating impact on XYZ&#39;s future earnings, the frequency of achieving undesirable future earnings levels can be calculated. 
     A preferred analysis is driven by the following assumptions (see  FIG. 1 ): 
     Assumptions regarding asset/liability portfolios: duration; coupons; maturities; for liabilities, payment schedule and refinancing assumptions; and for assets, reinvestment assumptions. 
     Assumptions regarding interest rate expectations: expected future levels; speed of adjustment to future levels; and interest rate volatility and correlations. 
     Assumptions regarding time period of analysis: 10 years. 
     Assumptions regarding XYZ&#39;s objective functions: maximize expected Net Interest Margin (“NIM”); minimize volatility of expected NIM; and minimize volatility of NIM without compromising NIM. NIM is the dollar difference between interest income and interest expenses, expressed as a percentage of average earning assets. 
     Assumptions regarding determination of extent of risk: how much floating-rate exposure XYZ can take before compromising its objective functions; and how much risk XYZ is willing to take. 
       FIGS. 2-5  depict swap rates over time for various interest rate scenario assumptions. XYZ&#39;s NIM is analyzed assuming a broad range of interest rate scenarios. 
       FIG. 2  depicts a base case (“forwards”), which assumes that forward rates follow the current forward curve. 
       FIG. 3  illustrates a 10-year mean reversion case, in which interest rates are expected to rise gradually over 5 years, to 10 year historical averages. More generally, this scenario can be characterized as an X/Y mean reversion, where X is the number of years over which interest rates are assumed to rise (or fall), and Y is the number of years over which historical averages are taken. 
       FIG. 4  illustrates a 1994-1999 pattern case, in which expected rates mimic changes in interest rates from 1994 to 1999. Generally, this is a “5 year pattern” assumption, and even more generally is a Z year pattern assumption, where Z is a specified number of years. 
       FIG. 5  illustrates an inverted yield curve case, in which the “short end” of the curve increases by 25 bps and the “long end” of the curve increases by 10 bps per quarter. 
     Based on interest rate movements over the past 10 years, future interest rates are estimated to move to their expected values using the interest rate volatilities and correlations shown in  FIG. 6  and TABLE 1. 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Correlations (1995-2005) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
            
               
                   
                 3 m 
                 6 m 
                 1 yr 
                 2 yr 
                 3 yr 
                 4 yr 
                 5 yr 
                 7 yr 
                 10 yr 
                 30 yr 
               
               
                   
               
               
                  3 m  
                 100% 
                  89% 
                  69% 
                  39% 
                  35% 
                  33% 
                  32% 
                  31% 
                  29% 
                  23% 
               
               
                  6 m 
                  89% 
                 100% 
                  90% 
                  56% 
                  52% 
                  49% 
                  48% 
                  46% 
                  43% 
                  35% 
               
               
                  1 yr  
                  69% 
                  90% 
                 100% 
                  69% 
                  67% 
                  63% 
                  61% 
                  59% 
                  55% 
                  46% 
               
               
                  2 yr  
                  39% 
                  56% 
                  69% 
                 100% 
                  98% 
                  95% 
                  93% 
                  90% 
                  84% 
                  72% 
               
               
                  3 yr  
                  35% 
                  52% 
                  67% 
                  98% 
                 100% 
                  99% 
                  97% 
                  95% 
                  90% 
                  79% 
               
               
                  4 yr  
                  33% 
                  49% 
                  63% 
                  95% 
                  99% 
                 100% 
                  99% 
                  97% 
                  93% 
                  83% 
               
               
                  5 yr  
                  32% 
                  48% 
                  61% 
                  93% 
                  97% 
                  99% 
                 100% 
                  99% 
                  95% 
                  86% 
               
               
                  7 yr  
                  31% 
                  46% 
                  59% 
                  90% 
                  95% 
                  97% 
                  99% 
                 100% 
                  98% 
                  90% 
               
               
                 10 yr 
                  29% 
                  43% 
                  55% 
                  84% 
                  90% 
                  93% 
                  95% 
                  98% 
                 100% 
                  93% 
               
               
                 30 yr 
                  23% 
                  35% 
                  46% 
                  72% 
                  79% 
                  83% 
                  86% 
                  90% 
                  93% 
                 100% 
               
               
                   
               
            
           
         
       
     
     NIM Projections 
       FIGS. 7-10  display outputs of interest rate simulations performed on a portfolio of assets and liabilities.  FIG. 7  depicts level and “volatility” of projected NIM, under various scenarios. 
     The “expected” line is the 50th percentile line (the line in the middle of the five lines). The other lines further illustrate the probability distribution over time. For example, the top line is the 95th percentile line, and the bottom line is the 5th percentile line—indicating a 90% chance that the NIM will fall between those two lines. The “cone” formed by these lines models the “potential volatility” of the projected NIM. 
     In this example, the displays show that, while NIM is likely to increase in most scenarios, a repeat of the 1994-1999 scenario (falling rates) over the next five years would cause a deterioration in margins over time. 
     NIM—2005 YE Statistics 
       FIGS. 11-12  illustrate distribution of 2005 NIM over time for various scenarios. TABLE 2 lists summary 2005 statistics. 
     
       
         
           
               
             
               
                 TABLE 2 
               
             
            
               
                   
               
               
                 Summary Statistics 
               
            
           
           
               
               
            
               
                   
                 Scenario 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                   
                 5 yr Mean 
                 1994-2004 
                 Inverted 
               
               
                   
                 ($ mm) 
                 Forwards 
                 Rev 
                 Pattern 
                 Curve 
               
               
                   
               
               
                 Expected 2005 
                   
                 $300 
                 $285 
                 $318 
                 $298 
               
               
                 NIM 
                   
                   
                   
                   
                   
               
               
                 95% Best Case 
                   
                 $323 
                 $304 
                 $343 
                 $320 
               
               
                 95% Worst Case 
                   
                 $280 
                 $267 
                 $296 
                 $278 
               
               
                 Std. Dev. 
                   
                  $13 
                  $11 
                  $14 
                  $13 
               
               
                 95% Value-at-Risk 
                   
                  $20 
                  $18 
                  $22 
                  $20 
               
               
                 (VaR) 
               
               
                   
               
            
           
         
       
     
       FIG. 12  depicts a median high-low chart. Prior use of such a chart to illustrate a risk management concept is not known. An expected level of interest cost is the center dot in each vertical bar, each of which represents a probability distribution. The uppermost and lowermost dots in each bar represent the 95% best and 95% worst cases, respectively. This clearly illustrates the corresponding risk exposures and associated expected costs for the various interest rate scenarios. This quantifies, in a manner easily perceived by even a casual viewer, the expected benefits, costs, and risks of each scenario. 
     Thus,  FIG. 12  depicts a median high-low chart for different interest rate environments, preferably used in conjunction with one or more interest rate simulation models. 
     NIM—2006 YE Statistics 
       FIGS. 13-14  illustrate distribution of 2006 NIM over time for various scenarios. TABLE 3 lists summary 2006 statistics. 
     
       
         
           
               
             
               
                 TABLE 3 
               
             
            
               
                   
               
               
                 Summary Statistics - 2006 
               
            
           
           
               
               
            
               
                   
                 Scenario 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                   
                 5yr Mean 
                 1994-2004 
                 Inverted 
               
               
                   
                 ($ mm) 
                 Forwards 
                 Rev 
                 Pattern 
                 Curve 
               
               
                   
               
               
                 Expected 2006 
                   
                 $439 
                 $418 
                 $407 
                 $460 
               
               
                 NIM 
                   
                   
                   
                   
                   
               
               
                 95% Best Case 
                   
                 $510 
                 $483 
                 $465 
                 $536 
               
               
                 95% Worst Case 
                   
                 $379 
                 $363 
                 $357 
                 $395 
               
               
                 Std. Dev. 
                   
                  $39 
                  $36 
                  $33 
                  $43 
               
               
                 95% Value-at- 
                   
                  $60 
                  $55 
                  $50 
                  $65 
               
               
                 Risk (VaR) 
               
               
                   
               
            
           
         
       
     
     NIM—2007 YE Statistics 
       FIGS. 15-16  illustrate distribution of 2007 NIM over time for various scenarios. TABLE 4 lists summary 2007 statistics. 
     
       
         
           
               
             
               
                 TABLE 4 
               
             
            
               
                   
               
               
                 Summary Statistics 
               
            
           
           
               
               
            
               
                   
                 Scenario 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                   
                 5 yr Mean 
                 1994-2004 
                 Inverted 
               
               
                   
                 ($ mm) 
                 Forwards 
                 Rev 
                 Pattern 
                 Curve 
               
               
                   
               
               
                 Expected 2007 
                   
                 $605 
                 $590 
                 $526 
                 $681 
               
               
                 NIM 
                   
                   
                   
                   
                   
               
               
                 95% Best Case 
                   
                 $770 
                 $749 
                 $656 
                 $880 
               
               
                 95% Worst Case 
                   
                 $480 
                 $468 
                 $427 
                 $532 
               
               
                 Std. Dev. 
                   
                  $89 
                  $86 
                  $70 
                 $105 
               
               
                 95% Value-at- 
                   
                 $125 
                 $122 
                  $99 
                 $149 
               
               
                 Risk (VaR) 
               
               
                   
               
            
           
         
       
     
     NIM—2008 YE Statistics 
       FIGS. 17-18  illustrate distribution of 2008 NIM over time for various scenarios. TABLE 5 lists summary 2008 statistics. 
     
       
         
           
               
             
               
                 TABLE 5 
               
             
            
               
                   
               
               
                 Summary Statistics 
               
            
           
           
               
               
            
               
                   
                 Scenario 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                   
                 5 yr Mean 
                 1994-2004 
                 Inverted 
               
               
                   
                 ($ mm) 
                 Forwards 
                 Rev 
                 Pattern 
                 Curve 
               
               
                   
               
               
                 Expected 2008 
                   
                 $785 
                 $784 
                 $616 
                 $974 
               
               
                 NIM 
                   
                   
                   
                   
                   
               
               
                 95% Best Case 
                   
                 $1,134  
                 $1,132  
                 $864 
                 $1,419  
               
               
                 95% Worst Case 
                   
                 $534 
                 $531 
                 $434 
                 $657 
               
               
                 Std. Dev. 
                   
                 $189 
                 $191 
                 $137 
                 $242 
               
               
                 95% Value-at- 
                   
                 $251 
                 $253 
                 $182 
                 $318 
               
               
                 Risk (VaR) 
               
               
                   
               
            
           
         
       
     
     NIM—2009 YE Statistics 
       FIGS. 19-20  illustrate distribution of 2009 NIM over time for various scenarios. TABLE 6 lists summary 2009 statistics. 
     
       
         
           
               
             
               
                 TABLE 6 
               
             
            
               
                   
               
               
                 Summary Statistics 
               
            
           
           
               
               
            
               
                   
                 Scenario 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                   
                 5 yr Mean 
                 1994-2004 
                 Inverted 
               
               
                   
                 ($ mm) 
                 Forwards 
                 Rev 
                 Pattern 
                 Curve 
               
               
                   
               
               
                 Expected 2009 
                   
                 $924 
                 $946 
                 $620 
                 $1,234  
               
               
                 NIM 
                   
                   
                   
                   
                   
               
               
                 95% Best Case 
                   
                 $1,465  
                 $1,511  
                 $961 
                 $1,973  
               
               
                 95% Worst Case 
                   
                 $542 
                 $551 
                 $373 
                 $716 
               
               
                 Std. Dev. 
                   
                 $293 
                 $304 
                 $188 
                 $395 
               
               
                 95% Value-at-Risk 
                   
                 $381 
                 $395 
                 $247 
                 $518 
               
               
                 (VaR) 
               
               
                   
               
            
           
         
       
     
     Blended Scenario 
       FIGS. 21-26  illustrate results of a blended scenario (33% scenario 1+33% scenario 2+17 scenario 3+17% scenario 4). TABLE 7 lists summary statistics. 
     
       
         
           
               
               
               
               
               
               
               
             
               
                 TABLE 7 
               
               
                   
               
               
                 Summary 
                   
                   
                   
                   
                   
                   
               
               
                 Statistics 
                 ($mm)  
                 2005 
                 2006 
                 2007 
                 2008 
                 2009 
               
               
                   
               
             
            
               
                 Expected NIM 
                   
                 $298 
                 $430 
                 $600 
                 $788 
                 $932 
               
               
                 95% Best Case 
                   
                 $319 
                 $498 
                 $762 
                 $1,140 
                 $1,480 
               
               
                 95% Worst Case 
                   
                 $278 
                 $373 
                 $476 
                 $535  
                 $546 
               
               
                 Std. Dev. 
                   
                 $12 
                 $38 
                 $87 
                 $190 
                 $296 
               
               
                 95% Value-at-Risk 
                   
                 $19 
                 $57 
                 $123 
                 $253 
                 $386 
               
               
                 (VaR) 
               
               
                   
               
            
           
         
       
     
     Dual Swap Strategy Impact on NIM 
     In a majority of the outcomes for the scenarios analyzed, XYZ&#39;s portfolio is better positioned for NIM gains after execution of a dual swap strategy. See  FIGS. 27-30 . 
     Dual Swap Strategy vs. Doing Nothing—YE 2005 
       FIGS. 31-34  provide a comparison of results for doing nothing (“current”) versus “swapped” for 2005. 
     Dual Swap Strategy vs. Doing Nothing—YE 2006 
       FIGS. 35-38  provide a comparison of results for doing nothing (“current”) versus “swapped” for 2006. 
     Dual Swap Strategy vs. Doing Nothing—YE 2007 
       FIGS. 39-42  provide a comparison of results for doing nothing (“current”) versus “swapped” for 2007. 
     Dual Swap Strategy vs. Doing Nothing—YE 2008 
       FIGS. 43-46  provide a comparison of results for doing nothing (“current”) versus “swapped” for 2008. 
     Dual Swap Strategy vs. Doing Nothing—YE 2009 
       FIGS. 47-50  provide a comparison of results for doing nothing (“current”) versus “swapped” for 2009. 
     A second example describes preferred treatment of company “ABC,” and illustrates preferred operation of a “fixed/floating decision framework.” 
     In this example, IRSF generates a plurality of future interest rate paths to calculate a range of interest expense levels produced by ABC&#39;s current interest rate sensitive liability portfolio. 
     Our analysis is driven by the following assumptions (see  FIG. 51 ): 
     Assumptions regarding asset/liability portfolios: duration; coupons; maturities; for liabilities, payment schedule and refinancing assumptions; and for assets, reinvestment assumptions. 
     Assumptions regarding interest rate expectations: expected future levels; speed of adjustment to future levels; and interest rate volatility and correlations. 
     Assumptions regarding time period of analysis: 6 years, 7 months. 
     Assumptions regarding ABC&#39;s objective functions: maximize expected Interest Expense (“IE”); minimize volatility of IE; and minimize volatility of IE without compromising lower IE. 
     Assumptions regarding determination of extent of risk: how much floating-rate exposure ABC can take before compromising its objective functions; and how much risk ABC is willing to take. 
       FIGS. 52-55  depict swap rates over time for various interest rate scenario assumptions. ABC″S IE is analyzed assuming different interest rate scenarios. 
       FIG. 52  depicts a base case (“forwards”);  FIG. 53  illustrates a 10-year mean reversion case;  FIG. 54  illustrates a 1994-1999 pattern case; and  FIG. 55  illustrates an inverted yield curve case. 
     Based on interest rate movements over the past 10 years, we estimate that future interest rates move to their expected values using the interest rate volatilities and correlations shown in  FIG. 56  and TABLE 8. 
     
       
         
           
               
             
               
                 TABLE 8 
               
             
            
               
                   
               
               
                 Correlations (1999-2004) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
            
               
                   
                 3 m 
                 6 m 
                 1yr  
                 2 yr 
                 3 yr 
                 4 yr 
                 5 yr  
                 7 yr 
                 10 yr 
                 30 yr 
               
               
                   
               
               
                  3 m  
                 100% 
                  89% 
                  69% 
                  39% 
                  35% 
                  33% 
                  32% 
                  31% 
                  29% 
                  23% 
               
               
                  6 m 
                  89% 
                 100% 
                  90% 
                  56% 
                  52% 
                  49% 
                  48% 
                  46% 
                  43% 
                  35% 
               
               
                  1 yr 
                  69% 
                  90% 
                 100% 
                  69% 
                  67% 
                  63% 
                  61% 
                  59% 
                  55% 
                  46% 
               
               
                  2 yr  
                  39% 
                  56% 
                  69% 
                 100% 
                  98% 
                  95% 
                  93% 
                  90% 
                  84% 
                  72% 
               
               
                  3 yr 
                  35% 
                  52% 
                  67% 
                  98% 
                 100% 
                  99% 
                  97% 
                  95% 
                  90% 
                  79% 
               
               
                  4 yr 
                  33% 
                  49% 
                  63% 
                  95% 
                  99% 
                 100% 
                  99% 
                  97% 
                  93% 
                  83% 
               
               
                  5 yr  
                  32% 
                  48% 
                  61% 
                  93% 
                  97% 
                  99% 
                 100% 
                  99% 
                  95% 
                  86% 
               
               
                  7 yr 
                  31% 
                  46% 
                  59% 
                  90% 
                  95% 
                  97% 
                  99% 
                 100% 
                  98% 
                  90% 
               
               
                 10 yr 
                  29% 
                  43% 
                  55% 
                  84% 
                  90% 
                  93% 
                  95% 
                  98% 
                 100% 
                  93% 
               
               
                 30 yr 
                  23% 
                  35% 
                  46% 
                  72% 
                  79% 
                  83% 
                  86% 
                  90% 
                  93% 
                 100% 
               
               
                   
               
            
           
         
       
     
     Monte Carlo Simulation 
     The Monte Carlo simulation shown in  FIG. 57  represents 1000 potential paths for 3 m LIBOR for the next five years based on the forward curve and historical volatility. The average of these distributions represents the expected outcome, which in this case would be the forward curve scenario. 
     Current IE Projections—5% Floating 
     On average ABC is expected to realize $486-501 million in IE per year across all four scenarios (see  FIGS. 58-61 ). 
     Observations 
     Interest expense growth is primarily explained by higher leverage on a pro-form a basis due to $500 million of new fixed rate debt issued annually and 15% annual increase in current portfolio (“CP”) balance. The similarity of median interest expense and VaR results across all four scenarios is explained by: (a) relatively small percentage of fixed rate re-pricings over analysis horizon (29% of ABC&#39;s fixed rate debt re-prices by the end of 2011), and (b) minimal amount of floating rate debt in the capital structure over the analysis horizon (floating rate percentages decline over time, since pro form a assumptions reflect more fixed rate debt being added to the capital structure relative to CP). 
     While there are differences in the risk distribution of interest expense across rate scenarios, the amounts are insignificant in the context of ABC&#39;s overall interest expense. 
     Interest Rate Simulation Results: Swap Scenarios 
       FIG. 62  depicts essentially the same data as listed in TABLE 9. But the display in  FIG. 62  presents the data much more advantageously, allowing a viewer to see, all one page, various probability distributions for a plurality of swap scenarios (current, 23% floating, etc.) and interest rate scenarios (forwards, mean reversion, etc.). The same display also can be used for other products (e.g., caps or collars) to show how the products impact a risk profile. 
     For example, a viewer can easily see that an inverted yield curve scenario presents the greatest financial risk to ABC, and that, at 27% floating, ABC does not materially increase its Value at Risk (“VaR”) in 3 out of 4 scenarios. Furthermore, a viewer can easily see the expected reduction in annual interest expense and visually compare this expected reduction to the expected increase in VaR risk. 
     Generally, the chart depicted in  FIG. 62  may comprise, for each interest rate scenario, one or more vertical bars corresponding to a risk management product scenario, and the risk management product scenario may be for one or more of: swaps, collars, caps, floors, swaptions, and forward starting swaps, and other risk management products. 
     
       
         
           
               
               
               
               
               
             
               
                 TABLE 9 
               
             
            
               
                   
               
               
                   
                 Forwards 
                 Mean Reversion 
                 1994-2000 Pattern 
                 Inverted YC 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Summary 
                   
                 27% 
                 43% 
                 60% 
                   
                 27% 
                 43% 
                 60% 
                   
                 27% 
                 43% 
                 60% 
                   
                 27% 
                 43% 
                 60% 
               
               
                 Statistics 
                   
                 Float- 
                 Float- 
                 Float- 
                   
                 Float- 
                 Float- 
                 Float- 
                   
                 Float- 
                 Float- 
                 Float- 
                   
                 Float- 
                 Float- 
                 Float- 
               
               
                 (mm) 
                 current 
                 ing 
                 ing 
                 ing 
                 current 
                 ing 
                 ing 
                 ing 
                 current 
                 ing 
                 ing 
                 ing 
                 current 
                 ing 
                 ing 
                 ing 
               
               
                   
               
               
                  5th Percentile 
                 $456 
                 $440 
                 $419 
                 $395 
                 $456 
                 $434 
                 $410 
                 $382 
                 $450 
                 $439 
                 $407 
                 $381 
                 $460 
                 $447 
                 $428 
                 $405 
               
               
                 50th Percentile 
                 $494 
                 $490 
                 $486 
                 $481 
                 $495 
                 $482 
                 $470 
                 $459 
                 $486 
                 $487 
                 $465 
                 $455 
                 $501 
                 $502 
                 $501 
                 $501 
               
               
                 95th Percentile 
                 $562 
                 $587 
                 $610 
                 $638 
                 $565 
                 $575 
                 $587 
                 $602 
                 $548 
                 $575 
                 $576 
                 $595 
                 $576 
                 $611 
                 $642 
                 $681 
               
               
                 Std. Deviation 
                 $32 
                 $48 
                 $64 
                 $83 
                 $33 
                 $45 
                 $59 
                 $76 
                 $30 
                 $45 
                 $57 
                 $73 
                 $35 
                 $53 
                 $73 
                 $94 
               
               
                 95% VaR 
                 $63 
                 $87 
                 $112 
                 $141 
                 $65 
                 $84 
                 $104 
                 $128 
                 $58 
                 $80 
                 $100 
                 $126 
                 $69 
                 $97 
                 $126 
                 $162 
               
               
                   
               
            
           
         
       
     
     TABLE 10 summarizes the rate scenarios and key takeaways for ABC. 
     
       
         
           
               
               
               
               
               
             
               
                 TABLE 10 
               
               
                   
               
               
                   
                 Scenario 1: 
                 Scenario 2: 
                 Scenario 3: 
                 Scenario 4: 
               
               
                   
                 Forwards 
                 Mean Reversion 
                 1994-2000 
                 Curve Inversion 
               
               
                   
               
             
            
               
                 Scenario 
                 Short Rates ↑ 175 
                 Parallel curve 
                 Rapid ↑ in 
                 Short end of 
               
               
                 Recap 
                 bps 
                 shift 150 bps 
                 short rates, then 
                 the curve increases 
               
               
                   
                 Term Rates ↑ 75 
                 higher over time 
                 level off 
                 by 50 bps per 
               
               
                   
                 bps 
                   
                 Rapid ↓ in term 
                 annum and long 
               
               
                   
                 Curve Flatter 
                   
                 rates, then level off 
                 end of the curve 
               
               
                   
                   
                   
                 Curve flatter 
                 increases by 20 bps 
               
               
                   
                   
                   
                   
                 per annum 
               
               
                 Key 
                 Median interest 
                 Median 
                 Almost 
                 Highest 
               
               
                 Take- 
                 expense across different 
                 interest expense 
                 identical to mean 
                 amount of median 
               
               
                 aways 
                 levels of floating rate 
                 savings are 
                 reversion 
                 interest expense 
               
               
                   
                 exposure is relatively 
                 material and 
                   
                 and Value at Risk 
               
               
                   
                 unchanged, however 
                 standard 
                   
                   
               
               
                   
                 standard deviation 
                 deviation is 
                   
                   
               
               
                   
                 increases nearly 3 times 
                 smaller compared 
                   
                   
               
               
                   
                 compared to current profile. 
                 to scenarios 1 and 4 
               
               
                   
               
            
           
         
       
     
       FIGS. 63-66  depict IE based on 43% floating interest rate projections. Compared to the 27% floating case, the range of median IE nearly doubles from $20 Million to $36 million, creating a range of $465-501 million. 
       FIGS. 67-70  depict 43% relative to current. The increase in standard deviation of annual IE is $26-38 million—double the increase of the 27% scenario. 
       FIGS. 71-74  depict IE based on 60% floating interest projections. Compared to the 43% case, the range in median IE is relatively unchanged at $455-501 million. 
       FIGS. 75-78  depict 60% relative to current. Although the range of median IE is relatively unchanged from the 43% case, the standard deviation increases about 30% across scenarios. 
     Forward Curves 
     Implied LIBOR Forward rates are not accurate predictors of actual future LIBOR settings.  FIG. 79  depicts historical implied LIBOR Forward Curves at various points dating back to 1990. Historically, forwards tend to over-predict where rates actually go. Forward curves historically tend to be flat to upward sloping regardless of the prevailing Fed bias to raise or lower interest rates. But the forward curve has over-predicted where 3 mL (3-month LIBOR) would be in 3 years by over 250 basis points on average (see TABLE 11). 
     
       
         
           
               
             
               
                 TABLE 11 
               
             
            
               
                   
               
               
                 LIBOR Forward Curves vs. Actual 3 mL 
               
            
           
           
               
               
               
               
               
            
               
                 Statistics in bps 
                   
                   
                   
                   
               
               
                 Overprediction 
                 Average 
                 Median 
                 Max 
                 Min 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                  3 m 
                 21 
                 14 
                 144 
                  −41 
               
               
                  6 m 
                 50 
                 32 
                 265 
                  −84 
               
               
                  9 m 
                 84 
                 57 
                 309 
                 −116 
               
               
                 1.0 y 
                 120 
                 89 
                 381 
                 −178 
               
               
                 1.5 y 
                 182 
                 138 
                 534 
                 −179 
               
               
                 2.0 y 
                 233 
                 188 
                 546 
                 −163 
               
               
                 2.5 y 
                 248 
                 182 
                 589 
                  −72 
               
               
                 3.0 y 
                 259 
                 199 
                 616 
                  −44 
               
               
                 3.5 y 
                 268 
                 220 
                 608 
                  −46 
               
               
                 4.0 y 
                 275 
                 264 
                 611 
                  −15 
               
               
                 4.5 y 
                 284 
                 305 
                 574 
                  −63 
               
               
                 5.0 y 
                 301 
                 314 
                 535 
                  −31 
               
               
                   
               
            
           
         
       
     
     Swap to Floating Analysis 
       FIGS. 80-81  depict annual NPV savings from a 5- and 7-year swap to floating. 
     Observations: (1) Since 1988, an issuer would have averaged 1.69% NPV annual savings by swapping to floating for 5-years; a 5-year swap to floating would have lowered interest expense 92% of the time on an NPV basis since 1988. And (2) Since 1988, an issuer would have averaged 1.85% NPV annual savings by swapping to floating for 7-years; a 7-year swap to floating would have lowered interest expense 97% of the time on an NPV basis since 1988. 
       FIGS. 82-83  depict ABC&#39;s “efficient frontier.” Dotted lines show efficient frontiers with increasing floating rate percentage. 
     Examples of risk management strategies are depicted in  FIGS. 84A-84B ,  85 A- 85 B and  86 A- 86 B. For  FIGS. 84A-84B , the efficient cap strategy is a participating swap. For  FIGS. 85A-85B , the efficient cap strategy is a combination of participating swap and unhedged, depending on risk/return preference. For  FIGS. 86A-86B , the efficient cap strategy is a combination of vanilla swap and unhedged, depending on risk/return preference. 
     This description generally refers to risk distribution and either interest expense or net interest margin. But as explained above, the invention also encompasses charts, displays, and methods that characterize risk in present value (“PV”) terms. Analogous displays are used, but the variable is PV instead of interest expense. Those skilled in the art will recognize that the invention may also be applied to displays of other variables, as appropriate. 
     Also, although the term “accounting performance” is used herein, those skilled in the art will recognize that economic performance data could be substituted without departing from the spirit and scope of the invention. 
     Embodiments of the present invention comprise computer components and computer-implemented steps that will be apparent to those skilled in the art. For ease of exposition, not every step or element of the present invention is described herein as part of a computer system, but those skilled in the art will recognize that each step or element may have a corresponding computer system or software component. Such computer system and/or software components are therefore enabled by describing their corresponding steps or elements (that is, their functionality), and are within the scope of the present invention. 
     For example, all calculations preferably are performed by one or more computers. Moreover, all notifications and other communications, as well as all data transfers, to the extent allowed by law, preferably are transmitted electronically over a computer network. Further, all data preferably is stored in one or more electronic databases.