US 20010014875 A1 Abstract Computer technology for substantially optimizing portfolios of multiple participants is disclosed. Preferably the portfolios of such multiple participants comprise fixed income instruments. The disclosed systems and methods include using at least one computer system for storing digital data representing portfolio holdings of multiple parties and, in particular, for each participant storing in the computer memory data representing constraints with respect to the desired portfolio. The method and system comprise optimizing using an optimization engine portfolio and constraint information of multiple participants so as to generate a set of trades that would substantially optimize participants portfolios with respect to a known objective.
Claims(54) 1. A computer method for adjusting portfolios of fixed income instruments of multiple parties comprising:
storing in memory of at least one computer digital data representing portfolio holdings of multiple parties; storing in the memory of at least one computer digital data representing constraints that define trading requirements of the parties; converting, using at least one computer, the digital data representing the portfolios of multiple parties and the digital data representing the constraints of the multiple parties to optimization digital data adapted for processing by an optimization engine; and optimizing using at least one computer the optimization digital data so as to generate a set of trades among the parties that rebalance the parties' portfolios in accordance with parties' constraints such that the portfolios are substantially optimized with respect to a predetermined objective. 2. The method of claim 1 3. The method of claim 1 4. The method of claim 1 5. The method of claim 1 6. The method of claim 1 7. The method of claim 1 8. The method of claim 7 9. The method of claim 7 10. The method of claim 7 11. The method of claim 7 12. The method of claim 7 13. The method of claim 1 14. The method of claim 13 15. The method of claim 13 16. The method of claim 13 17. The method of claim 13 18. The method of claim 13 19. The method of claim 13 20. The method of claim 1 21. The method of claim 20 22. The method of claim 20 23. The method of claim 22 24. The method of claim 1 25. The method of claim 24 26. The method of claim 24 27. The method of claim 26 28. A computer system for providing an exchange between fixed-income portfolios of multiple participants comprising at least one computer having a processor and a memory, comprising:
means for storing data representing fixed-income portfolios of multiple participants and constraints provided by the participants defining participants' requirements for the portfolio generated by the exchange; and an optimization engine that processes digital data representing fixed-income portfolios and constraints of the multiple participants so as to determine transactions between the participants that substantially optimize the portfolios for a predetermined objective in accordance with the constraints. 29. The system of claim 28 30. The system of claim 28 31. The system of claim 28 32. The system of claim 28 33. The system of claim 28 34. The system method of claim 28 35. The system of claim 28 36. The system of claim 35 37. The system of claim 35 38. The system of claim 35 39. The system of claim 35 40. The system of claim 35 41. The system of claim 28 42. The system of claim 41 43. The system of claim 41 44. The system of claim 41 45. The system of claim 41 46. The system of claim 41 47. The system of claim 41 48. The system of claim 30 49. The system of claim 30 50. The system of claim 49 51. The system of claim 28 52. The system of claim 51 53. The system of claim 51 54. The method of claim 53 Description [0001] This invention relates to computer technology for optimizing portfolios of multiple participants and, in particular, for optimizing portfolios of fixed income instruments. [0002] It is well known that computer technology can be effectively employed for financial applications. It is also known to employ computers that execute optimization programs, such as programs based on linear programming techniques, so as to achieve financial goals. For example, computer technology that analyzes and optimizes a portfolio held by a given entity is known. Computer systems have also been employed as an intermediary in transactions where multiple parties desire to trade specific equity instruments. In such computer applications, optimization may be employed to facilitate trading of an equity of interest. However, inventors are not aware of computer technology developed for trading holdings of multiple participants, where a computer acting as an intermediary processes entire portfolios of the participating entities and generates trades that optimize portfolios for a desired result, particularly for portfolios of fixed income instruments. [0003] Portfolio-based trading, for example, exists in the equities market, where investors may buy or sell a portfolio of stocks on an aggregate basis. The investor provides a statistical description of the portfolio, usually including how closely it tracks the S&P 500 index, the sector distribution of the portfolio, and a measure of the diversification of the portfolio. The broker then commits to trade the portfolio of unknown stocks for a fixed fee at the prevailing market price at a pre-arranged point in time, typically the market daily close. Because the broker only knows the “statistical” composition of the portfolio, the investor feels more comfortable that the broker is unable to affect the closing prices. Because of the statistical relationship between the portfolio and the index, the broker feels comfortable that the investor cannot unload a portfolio of unattractive securities. An important component of such a transaction is the independent price of equities contributed by the public transaction records of the equity markets. [0004] The vast majority of fixed income transactions are performed on a principal basis where the broker takes the opposite side of the transaction from the investor. The lack of adequate fixed income transaction records and the broad range of structures and maturities of fixed income instruments creates a significant barrier to developing the confidence on either side of the transaction that pricing is fair. Thus, it is desirable to provide a system that employs unbiased pricing and reassures the investors that the transaction is a fair deal. Further, it is desirable to provide computer technology that supports such fixed income transactions and, in particular, enables multiple parties to participate in the transactions. In particular, it is desirable to develop computer technology that would allow multiple investors to specify constraints on their portfolio holdings and, within those constraints, allocate by the optimization computer process fixed income holdings to individual investors participating in the transaction. [0005] As noted, in general, optimization techniques for financial applications are known. For example, Adamidou et al., [0006] Optimization methodologies relating to financial applications are surveyed in H. Dahl, A. Meeraus, and S. A. Zenios, [0007] Such publications on financial engineering do not teach computer technology that enables multi-party portfolio trading in fixed income instruments, wherein computer-driven optimization aids in rebalancing portfolios of multiple participants. Yet, there is a need for such technology. For example, there is a need to provide computer technology that enables multiple investors to recognize the economic benefits of selling bonds at a price below the price originally paid thereby obtaining a tax deduction. Accordingly, there is a need to develop technology that would enable investors to exchange portfolio holdings so as to substantially maximize the tax deductible loss. It is believed that technology for such portfolio trading between multiple parties that enables them to substantially optimize trades so as to substantially maximize tax advantages has not been developed by others. [0008] Although the system and method of the present invention relates to computer technology applicable to a wide array of portfolio optimizations in trading among diverse parties, the preferred embodiment relates to a computer system and method that provide a capability of taking advantage of refunds on taxes paid within the previous three years by maximizing book losses on trades of multiple participants. The preferred embodiment provides technology that enables trades as swaps among multiple parties while keeping the trades out of the market. The advantage of swapping between portfolios of participating firms versus transacting in the open market is that large scale trades can be executed without adversely affecting the market trading. In addition, the specific preferred embodiment enables swap members to buy discount bonds as replacements, which may be problematic in the open market but provides further, two advantages. [0009] The computer technology of the preferred embodiment facilitates a solution to a multi-party book-loss optimization. In general, the input to the computer system of the preferred embodiment comprises a set of bond portfolios owned by a group of firms, and the output comprises the set of trades which substantially maximizes the participant firms' total book losses. The implementation of the preferred embodiment avoids churning (i.e., buying and selling the same security) and wash sales (i.e., buying and selling a sufficiently similar security) and, therefore, reduces a risk of degeneracy in the process of maximizing book losses. [0010] In addition, individual firms typically have portfolio composition constraints that must remain satisfied in any intermediated transaction implemented by the system. Such constraints may include fixed market value of holdings within given sectors and maximum holdings of given names. The implementation of the preferred embodiment provides means for satisfying such constraints. [0011] Although a particular implementation of the preferred embodiment relates to producing tax deductions, a person skilled in the art will realize that it can be generalized to allow different participants to have different objectives and still produce multi-party portfolio-based optimized transaction. Furthermore, as will be understood by a person skilled in the art, extensions are possible where the participants provide prices at which they would be willing to buy or sell rather than using uniform prices provided by the intermediary entity, as in the preferred embodiment. In general, a person skilled in the art will appreciate that the invention can be extended to accommodate differing views among the participants on the economic attributes of the fixed-income instruments in their portfolios. [0012] The invention will be better understood when taken in conjunction with the following detailed description and accompanying drawings, in which: [0013]FIG. 1 illustrates computer architecture and organization of the preferred embodiment; [0014]FIGS. 2 and 3 illustrate the flowchart of the operation of the system of the preferred embodiment. [0015]FIG. 4 illustrates the flowchart of the optimization interface software. [0016] The following detailed description of the preferred embodiments is organized as follows: first, computer architecture of the preferred embodiment is disclosed. Next, a specific illustrative application addressed by the technology of the preferred embodiment is described. Thereafter, software programming developed for implementing the illustrative application of the preferred embodiment is disclosed. [0017] Computer architecture of the preferred embodiment is depicted in FIG. 1. In general, the system depicted in FIG. 1 receives data representing portfolios of fixed income instruments owned by multiple investors (also referred to as clients, firms, and participants) and constraints associated with the portfolio as inputs. The system then generates a set of trades so that the resultant portfolios of the investors are substantially optimized with respect to a given economic benefit. [0018] The data representing portfolio information and specific client constraints is provided by the clients participating in the transaction to the workstation [0019] Client portfolio data and their constraints are then translated into a uniform format discussed below and entered into a front end module, symbolically illustrated as [0020] The workstation [0021] In the preferred embodiment, data obtained from external sources includes: bond indicatives (e.g., coupon, maturity, etc.) from EJV, Electronic Joint Venture (EJV) Capital Markets Services (http://www.ejv.com) 1996, and Bloomberg, Bloomberg L.P. 499 Park Ave., NY, N.Y. 10022 (http://www.bloomberg.com) 1996, databases, insurance company holdings from the Capital Access FINCOM database, Capital Access Corp. Mountain Heights Center, 430 Mountain Ave. Murray Hill, N.J. 07974 (http://www.interactive.net/˜cac) 1996, sector descriptions from EJV and Fact Set, FactSet Research Systems Inc., One Greenwich Plaza, Greenwich, Conn. 06830 (http://www.factset.com) 1996. [0022] The data stored in the front end [0023] The CPLEX optimization engine of the preferred embodiment is a linear optimizer for solving linear programming problems encountered in a wide variety of resource allocation programs. CPLEX provides several solvers for different problem environments. See http:\\www.cplex.com. The CPLEX Linear Optimizer Base System provides a basic linear programming environment using continuous variables and employing algorithms mainly based on a well-known Simplex method. It also supports a variety of input/output formats such as MPS files, known in the art. This system can handle problems with millions of constraints and variables. The CPLEX Mixed Integer Solver (MIP) is an addition to the CPLEX Linear Optimizer Base system. It employs various heuristic algorithms such as a branch-and-bound technique to handle the difficult optimization problems involving integers. The CPLEX Barrier/QP Solver is an optimizer for solving linear and quadratic problems. CPLEX can be run on various computer platforms. The CPLEX programs are also available as parallel versions so that they can be run on multiple-CPU systems for increased performance. [0024] The optimization engine [0025] The optimization engine [0026] It should be noted that the computers of the disclosed embodiment are, in general, known devices that include a central processing unit, primary and secondary memory, and network interfaces, as well as other well known hardware components. As discussed, these computers are configured for the special purpose of providing substantial optimization of multi-party trades using software discussed herein. [0027] In another embodiment, the system of FIG. 1 can be enhanced to allow participants to enter their own data directly to the front end over the Internet. The system can also be enhanced by posting recommended transactions continuously on the Internet. [0028] Tax law allows corporations to apply losses realized in a given year against gains incurred within the previous three years to receive tax rebate for previous taxes paid. See 1996 [0029] A tax swap is beneficial if tax refunds received today have positive economic value considering the present values of the bonds swapped to achieve the refund. If two firms own underwater bonds (i.e., bonds which values have dropped in comparison to their original values), swapping such bonds for bonds owned by others may enable the firms to take advantage of the tax refund. Tax-related advantages can, for example, result from swapping an underwater bond with a par bond and with a discount bond as discussed below. [0030] Swapping an underwater bond with a par bond that would produce the same yield as the underwater bond requires that the par bond necessarily has a higher coupon. Accordingly, the tax refund received today as a result of a swap is offset by higher future taxes paid on the greater coupons of the par bond. Also, the principal par amount invested in the underwater bond is necessarily larger than the principal amount of the par bond purchased as a result of the swap. Accordingly, some protected principal is lost due to the swap. The net of these effects depends on the discount factor, so that for reasonable discount factors, as illustrated below, the net effect favors doing the swap. [0031] For example, consider a swap of a $100MM par amount of a 6.750% coupon underwater bond, having a current market price of 97.411% yielding 7.750%, for par bonds of equal yield, i.e., 7.750% coupon. Thus the owner of the underwater bonds obtains after the swap $97.411MM par amount of the new bonds with 7.750% coupon. For the purposes of this illustration, it is assumed that all coupons are paid annually, that both bonds mature in three years from the day of the swap, and the tax rate is 35%. [0032] The net economic benefit of swapping the bonds is determined as follows. The seller of the underwater bonds receives $97.411MM plus a tax refund of 35%×(100%−97.411%)×$100MM=$0.906MM. The same entity then uses the $97.411MM to buy new par bonds, netting the tax refund. On three successive years, it receives, after taxes, a coupon of (100%−35%)×7.750%×$97.411MM=$4.907MM. On the third year, it also receives the return of the $97.411MM principal. The opportunity cost of foregoing owning the underwater bond includes its coupons and return principal. The after-tax coupons would have been (100%−35%)×6.750%×$100MM=$4.388MM. The return principal would have been $100MM. [0033] This analysis is summarized in Table 1, which uses a discount factor of 65%×7.75%=5.0375%.
[0034] The breakeven discount rate that makes the swap beneficial is 2.8%. The profitability of the swap increases with increasing maturity of the bonds, decreasing price of the underwater bonds, and increasing discount rate. [0035] Alternatively, one may swap for market-discount bonds, i.e., bonds currently trading at a discount. Normally, securities are taxed on an effective-yield basis; however, market-discount securities have different taxation. If the income from the bond exceeds the financing cost for the bond (which is assumed to be true in this example), the investor may elect to pay tax on cash flow rather than yield. For a discount bond, tax on cash flow is always lower than tax on yield. If the investor makes this election, there is an additional tax due on excess of sale or redemption proceeds over cost. This election may be made on a bond by bond basis. [0036] Swapping to a market-discount bond achieves greater economic benefit than swapping to a par bond, as illustrated in the example below. For simplicity, consider that the underwater bond, discussed in the previous example, is swapped with a bond of identical attributes (but different issuer to avoid a wash sale). The only modifications to the previous analysis are the cash flows of the new discount bonds. As a result of the swap, the new bonds are bought for $97.411MM, netting the tax refund. On three successive years, the investor receives, after taxes, a coupon equal to the coupon foregone. On the third year, the investor also receives the return principal of $100MM, however, we are required to pay tax on the accrual from the discount price. Thus, we receive $100MM plus $4.388MM minus 35% of ($100MM−$97.411MM)=$103.48MM. This analysis is summarized in Table 2 below, which illustrates that the resulting profit is greater than that of the previous scenario.
[0037] Software Implementation [0038] In general, a multi-party book loss optimization problem of the exemplary application described above is well-suited to linear programming, a known optimization technique. Book loss is defined as the par sold multiplied by the difference in book price and market price for the securities available in the secondary market at the time of the transaction. [0039] Table 2 below defines variables used in the following discussion, where indexes i, j, k correspond to the set of all bonds, firms, and sectors, respectively.
[0040] In the following discussion it is assumed that PRICE [0041] The objective function representing total book loss, optimized by the system, is expressed as follows:
[0042] This function is optimized subject to the following constraints: [0043] Bond conservation: for a given bond, the par amounts bought and sold over all participating firms must net to zero, i.e., there is a closed universe of bonds.
[0044] Precess neutrality: for every firm, the total of all trades must be present-value neutral.
[0045] Duration neutrality: the total of all trades must leave the dollar-duration within a reasonable tolerance. This is a relaxed form of dollar-duration-neutral trading. The constraints are applied on a per party (j) basis.
[0046] These constraints bound the permissible change in dollar duration around a given target range ($DUR [0047] Convexity neutrality: These constraints are similar to the above constraint, except that $DUR [0048] Other market-value weighted attributes: Yield and rating are constrained in an identical manner as duration and convexity. In other embodiments, other portfolio characteristics can be defined in a manner similar to duration and convexity. [0049] Par-value weighted attributes: Maturity and coupon are constrained in a manner similar to duration and convexity; however, par-value rather than market-value is used for weighing. As noted, in other embodiments, other characteristics can be similarly defined. [0050] Proceeds bounding within sectors: The total of all trades must leave the present value (within every sector) between reasonable (predefined) bounds. These constraints can enforce present-value-neutral trading, possibly weakened to provide additional flexibility. Alternately, the use of these constraints may provide an opportunity to employ the transaction in order to reallocate the portfolio. These constraints, expressed below, are applied on a per party (j) basis.
[0051] These constraints bound the permissible change in proceeds within a sector around a given target range (SPV [0052] The sectors include an industry sector type, such as Financials, Utilities, Industrials and Sovereign/Agencies, as well as other types of sectors including rating, broad maturity, fine maturity, duration, convexity, EJV sector, EJV subsector, EJV subsubsector, holdings, issuer, SIC code, and other sectors customized to specific firms. Another category of sectors is a specification of bonds that cannot be sold to a given firm. [0053] Non-negativity and boundedness: the amount bought and sold must be non-negative, and the amount sold must not be greater than the original par amount owned. Additionally, the amount bought must not exceed the total amount owned by all other firms.
[0054] If the right-hand-side of the buy equation is zero, then no variable BUY [0055] In the model defined by the above objective function and constraints, churning and wash sales may occur when more than one party owns the same bond. Churning refers to buying and selling of the same security to generate spurious book loss. Churning involves swapping bonds with the same CUSIP (Committee of Uniform Security Identification Procedure) code. A wash sale involves bonds that satisfy the following three similarity conditions: 1) the same issuer, 2) maturities within five years of each other, and 3) coupons within 25 bp. [0056] To eliminate churning and wash sales, the results obtained by employing the above continuous model may then be modified by computing net sales of each bond for each firm. The net sales would then be presented as a resultant portfolio produced by the transaction. However, it is unlikely that the resultant allocation of bonds would be substantially optimal with respect to the goal of book loss maximization, and therefore this is not the preferred approach. For example, if each of two firms hold two bonds A and B, co-members of a given sector, the objective function may be maximized by a wash sale of bonds A and B: each sells the other both A and B. If only net sales are taken into account these sales would net zero for each bond, and, therefore, no trades and book losses would be produced. The optimal solution, however, is for one firm to sell A and the other to sell B, allowing each to achieve a book loss. [0057] The formulation of the objective function, provided above, maximizes achieved book loss. In an alternative embodiment, this function can be generalized as follows to include the economic value of tax deferral:
[0058] A person skilled in the art, based on this discussion, can also implement optimization with respect to this function. However, given that variables are defined as bought and sold amounts, churning and wash sales still remain an issue. However, if variables were to be defined as the net change in the amount bought and sold, the churning/wash sales problem would be avoided, but the objective function becomes problematic. This happens because there is a benefit only from a net sale, not from a net gain,
[0059] which is nonlinear. Alternatively, the churning and wash sales can be avoided by introducing non-linearities into the constraints rather than the objective function:
[0060] The implementation of the preferred embodiment for the exemplary application considered here, enhances the continuous model discussed above by employing mixed-integer techniques. The enhancement of the preferred embodiment effectively addresses the issue of churning and wash sales (including taking into account bonds owned by the subsidiaries of the same parent). [0061] In the preferred embodiment, SELL [0062] where θ is the set of subsidiaries owned by the parent of firm j and M is a suitably large number. The Boolean variables δ [0063] Two or more affiliated parties (e.g., subsidiaries of the same parent firm) cannot trade with each other, yet may require different constraints in order to not be treated as a single entity. In the preferred embodiment this requirement is modeled in the following manner. If a bond i is originally held by at least one of the affiliated parties θ, two cases are possible: (1) i is not held by any party outside of θ; or (2) at least one party outside of θ holds i. Accordingly, in the first case, the constraint BUY [0064] The above constraints do not guarantee that no trades between affiliated parties would occur, but these constraints drastically reduce such trades. The system of the preferred embodiment automatically checks for trades slipping through these constraints for manual correction after optimization. [0065] Although mixed-integer programs such as presented before are difficult to solve optimally for large data sets, sufficiently satisfactory solutions can be obtained using the method of the preferred embodiment as described herein. Results that are not strictly optimal, but are sufficiently optimized to be acceptable, may also be referred to as optimal in this discussion. [0066]FIGS. 2 and 3 illustrate the processing performed by the preferred embodiment with respect to the illustrative tax swap application. Initially, workstation [0067] The front end [0068] User and System constraints can be specified and stored in the front end [0069] Constraints on sectors specify (1) which sectors are constrained; (2) over what statistic the constraint is defined; and (3) the bounds of the constraint. The sectors within a constraint are defined either as an individual identifier or any number of identifiers connected with logical operators. [0070] The following grammar for name expressions is used to specify sectors. [0071] letter: one of [0072] a b c d e f g h i j k l m n o p q r s t u v w x y z [0073] A B C D E F G H I J K L M N O P Q R S T U V W X Y Z [0074] digit: one of [0075] 0 1 2 3 4 5 6 7 8 9 [0076] number: [0077] digit [0078] digit number [0079] char: [0080] letter [0081] digit [0082] op: [0083] | & [0084] identifier: [0085] char [0086] identifier char [0087] unary: [0088] identifier [0089] ˜identifier [0090] sector: [0091] unary [0092] (unary) [0093] unary op binary [0094] (unary op binary) [0095] An identifier is either a full CUSIP, a name (a six character CUSIP), or an alpha-numeric string previously defined as a sector of a certain bond. For example “˜(AAA/AA)” specifies all bonds rated lower than AA. The “|” operator is logical OR; “&” is logical AND; and “˜” means NOT. Parenthesis are used in a conventional manner. A full CUSIP specifies an exact bond issue, whereas a name specifies an issuer. For example “912827T6 & 312911” specifies a single Treasury bond and a group of mortgages. A client firm, for example, may specify names it refuses to buy, e.g., “˜369856”. [0096] The following grammar is used for constraint specification: [0097] applies-to: one of [0098] or-applies [0099] and-applies [0100] or-applies: one of [0101] number [0102] number|or-applies [0103] and-applies: one of [0104] number [0105] number & and-applies [0106] value: one of [0107] #PV [0108] #LOSS [0109] #DUR [0110] #CONV [0111] #MAT [0112] #COUPON [0113] #RATING [0114] variable: one of [0115] #ALL [0116] #SECTOR [0117] #FINAL [0118] #BUY [0119] #SELL [0120] #NET [0121] #CURR [0122] #AVG [0123] numerator-value: [0124] value [0125] value numerator-value [0126] numerator-variable: [0127] variable [0128] variable numerator-variable [0129] numerator: [0130] numerator-value numerator-variable [0131] denominator-value: [0132] value [0133] value denominator-value [0134] denominator-variable: [0135] variable [0136] variable denominator-variable [0137] denominator: [0138] denominator-value denominator-variable [0139] fraction: [0140] numerator [0141] numerator-denominator [0142] method: one of [0143] #REL [0144] #ABS [0145] #PROP [0146] constraint: [0147] applies-to print-name sector fraction method [0148] bounds [0149] In the above grammar, “print-name” is an optional string that provides textual representation of the constraint for summary purposes. The “Or-applies” expressions specify a group of firms in which a given constraint applies individually to each firm. The “And-applies” expressions specify a group of firms to which the constraint applies collectively. [0150] In general, a constraint is of the form:
[0151] A pair of numbers (L, U) represents the lower and upper bounds placed on the constraint. The numerators and (optional) denominators define the statistic. The numerator represents the base statistic, and the denominator can be used to normalize the base statistic. [0152] The base statistic is defined by both variable and value specifications. For example, if a firm is interested in constraining the market-value-weighted dollar duration of all bonds it buys, the numerator is set to #PV#DUR#BUY. The variable #BUY specifies that the set of bonds bought should be considered. The values #PV#DUR specify that the desired statistic is present value times duration times par amount. [0153] Other variables that can be used are #SELL (bonds sold), #NET (buys minus sells), #SECTOR (pay attention to the sectors specified in the constraint), #ALL (ignore sectors), #FINAL (original plus buys minus sells), and #AVG (buys plus sells divided by two). These variables can also be combined as in the example above. The values include #CONV (convexity), #MAT (maturity), #COUPON (coupon), #RATING (rating) and #LOSS (book price minus price), as well as other values defined by the user, as will be understood by one skilled in the art. [0154] As mentioned, the denominator is used to optionally normalize the base statistic. For example the previous numerator #PV#DUR#BUY needs to be normalized by the denominator #PV to compute a valid duration. All the variables specified above can be used in the denominator. In addition the variables used in the denominator include #CURR (current portfolio) and #NONE (denominator equals one). [0155] Commonly used constraints may also be specified as macros. Constraints can be bound with respect to #ABS (absolute value of bounds), #REL (a value relative to a base value, i.e., base value±percentage points), and #PROP (proportional values, i.e., base value multiplied by percentages; the base value is always computed from the incoming portfolios). [0156] For example, suppose firms
[0157] Here the zero lower bound guarantees that the original convexity cannot be lower than the resulting convexity. The large upper bound indicates that convexity is allowed to increase up to 1000% of the original value (essentially unlimited). [0158] At step [0159] Next at [0160] The optimization engine at step [0161] After the optimizer has completed its processing, a transaction proposal is generated at step [0162] If all clients agree on the proposed transactions, as illustrated in FIG. 3, the system accepts at step [0163] First the yields of currently traded US Treasuries are determined as known in the art. Instead of using all US Treasury prices, only the on-the-run prices are used. First, the closing prices of every UST and the market prices of all the on-the-runs are collected. Second, a butterfly portfolio for each UST is constructed using the two on-the-runs with the closest durations as barbells. Third, the change in the current present value of each UST is determined by that of the two ends of the barbell, taking into account the butterfly weights. [0164] Subsequently, the prices of the bonds used in a transaction are easily computed based on the spreads quoted by the traders. The yield of a bond is the yield of the benchmark plus the spread. The spread quoted may be based on yield to maturity, yield to call, yield to put, or yield to average life. The date corresponding to settlement of the final transaction has to be used when converting the bond yield to the final bond price. [0165] Upon receiving the actual trading prices from the traders, the optimization is repeated at step [0166] Alternatively in another preferred embodiment, the actual prices provided by traders may be entered into the system before the complete agreement of the parties on the final transaction has been reached. Specifically, in such an embodiment, the actual prices are introduced when the parties are in substantial but not complete agreement with respect to the proposed swap, so that several final iterations involving optimization are performed with the actual prices obtained from the traders. This embodiment modifies flowcharts of FIGS. 2 and 3 in the following manner. The decision [0167] The Optimization interface module [0168] or [0169] where a [0170] At step [0171] At step [0172] If the numerator variable is #ALL then the program does not check for sector inclusion: this bond will have non-zero coefficients. If the numerator variable is #SECTOR then the interface program [0173] If the bond is constrained, the program determines the proper coefficient a [0174] The program also accounts for an optional denominator. To save MPS file preparation time, the program generates the denominator only once for both the upper and lower bounds. This is done by generating a new linear programming variable and creating an equality constraint for the denominator.
[0175] The equality coefficients are generated in a manner similar to the inequality coefficients previously discussed. [0176] The new linear programming variable is then appended to the end of upper and lower bounds inequalities. The coefficient of the new linear programming variable is the negative upper or lower bound, respectively, as illustrated below.
[0177] Next, at step [0178] As noted at step [0179] The previously described preferred embodiment is neutral with respect to multiple firms, i.e., no firm is given an advantage over another. However, the resultant trades may distribute gains among the firms not completely evenly. Although, completely fair distribution of gains is difficult, the fairness of the distribution can be improved by utilizing one of the techniques discussed below, or other techniques known in the art. Although the solution which does not attempt to achieve a fair distribution is sufficient for the implementation of the preferred embodiment, alternative embodiments may include additional processing that addresses fairness as discussed below. [0180] One such approach to achieving fairness that may be used in an alternative embodiment is to employ a method developed by Shapley for constructing a “fair” solution to the classic coalition problem in game theory. See H. Raiffa, [0181] In formulating a tax swap as a coalition problem, the majority of a subgroup's utility is attributed by its tax loss, which can be evaluated with the optimizer for each subgroup. Two additional factors contributing to utility include: 1) a consideration that discount securities (priced below par), purchased in the swap, have a smaller future tax burden than par or premium securities, so that all players wish to swap in discount securities; and 2) by swapping among themselves, the firms have less total transaction costs than the market would charge, especially considering premiums due to the inelasticity of supply of discount bonds. Once these considerations are factored into the subgroup utilities, Shapley values can be computed, to determine a fair division of proceeds. [0182] In some alternative embodiments, it may also be desirable to tilt the objective function. Since the objective function thus far is to maximize total loss, it may be achieved through one firm receiving a disproportionate share of the tax loss relative to other firms. One method of rectifying the immediate book-loss and concomitant tax advantage bias is with the following objective function:
[0183] where a [0184] To negotiate an actual deal it is important for the entity acting as an intermediary to standardize security prices in the resulting trades in accordance to the market prices of the corresponding investments. As discussed above, the benchmark pricing module manages such a pricing. The standardized pricing gives the multiple parties to the swap confidence in the impartiality of the intermediary entity. Payment for the services of the intermediary may for example, come from a fixed percentage of realized tax deduction, or using another compensation scheme. [0185] Individual parties must be prevented or at worst dissuaded from “cherry picking” prices or securities, i.e., viewing the optimized trades and selectively committing to only certain trades. For example, a party which avoids an assigned buy trade that is perceived as too expensive is hoping to engage in a form of arbitrage. That party wants to buy at no worse than fair value, but of course does not identify the bonds it is selling above fair value. [0186] The intermediary entity must tightly control the timing of the swap, not allowing individual parties to stretch the target trade date. With time slippage comes the risk that the market will rally. If the market rallies, there will be fewer underwater securities in the pool and less losses embedded in each security. One technique of controlling timing is to limit participation and plan a series of swaps. [0187] The present invention is not to be limited in scope by the specific embodiments described herein. Indeed, modifications of the invention in addition to those described herein will become apparent to those skilled in the art from the foregoing description and accompanying figures. Doubtless, numerous other embodiments can be conceived that would not depart from the teaching of the present invention, which scope is defined by the following claims. Referenced by
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