HK1058414A - Load aware optimization - Google Patents

Description

Optimization of load knowing

Copyright notice

Contained herein is material that is subject to copyright protection. The copyright owner has no objection to the facsimile reproduction by anyone of the patent disclosure, as it appears in the patent and trademark office patent files or records, but otherwise reserves all rights to the copyright whatsoever.

Technical Field

The present invention relates generally to the field of financial consulting services. More particularly, the invention relates to a process in which an optimized portfolio of financial products (portfolios) may be generated from a universe of financial products carrying a front-end or back-end load.

Background of the invention

From a set of N (N > 1) financial products, an infinite number of portfolios of assets are available for investment. For purposes of this application, the term "financial product" is broadly defined as: a legal representation of the right to provide or receive expected future benefits under certain specified conditions (often expressed as a claim or guarantee). For example, common stocks in domestic or foreign countries, bonds in domestic or foreign countries, real estate, cash equivalents, mutual funds, Exchange Trading Funds (ETF) and other securities or portfolio of securities, etc. are contemplated by the term "financial products".

In any case, existing computer financial analysis systems (also known as "portfolio optimizers") claim to help individuals select portfolios that meet their requirements. These systems generally implement mathematical models based on standard optimization techniques involving mean-variance optimization theory. Asset selection according to the mean square error method may refer to an investor's preferences for different combinations of risk and benefit and portfolio sets (also referred to as active sets or active limits) to identify an optimal portfolio of financial products. FIG. 1 illustrates a feasible set of portfolios, which represent all portfolios that may be formed from a particular set of financial products. Arc ACs represent an active set of portfolios, each of which provides the highest expected revenue for a given risk level. The risk of a portfolio is typically measured by the standard deviation of the revenue.

Generally, the process of portfolio optimization involves determining a portfolio of financial products that maximizes a utility function (utility function) of an investor. In general, the portfolio optimization process assumes that the user has a utility function (i.e., mean-variance utility) that is reasonably estimated by a quadratic utility function, i.e., that person prefers to have more wealth on average and dislikes the volatility of wealth. Based on this assumption and given a user's risk tolerance, an optimized portfolio is calculated that has a mean square error that is valid from the set of financial products available to the user.

The problem of determining an optimized portfolio from a set of N financial products can be represented as a series of one or more Quadratic Programs (QPs)) And (5) problems are solved. QP is a technique for optimizing (minimizing or maximizing) a quadratic function of the decision variables that are affected by linear equality and or inequality constraints on those decision variables. A particular type of QP technique, known as the "activity group" method, has been used in Financial analysis products of Financial engineerines corporation (FEI). The "activity group" method is described in chapter 5 of "Practical Optimization" by Academic Press, Gill, Murray, and Wright, which is incorporated herein by reference. Another frequently used method is the critical line algorithm, published in 1991 by MA, Cambridge, Blackwell, Portfolio Selection 2 by Markowitz^ndDescribed in edition, which is hereby incorporated by reference. In addition, if the optimization problem is properly constrained, it can be solved using the QP gradient method as described in "An Algorithm for Portfolio Improvement" by Sharpe in Advances in chemical programming and Final Planning, published by JAI Press, 1987, which is incorporated herein by reference.

Current QP optimization programs do not have the ability to factor a load payment at the front end or back end of a financial product purchase because including a load significantly changes the form of the optimized function, i.e., the objective function is no longer quadratic. In short, using prior art optimized QP techniques, when an investor's portfolio already contains a portion of the loaded financial product, it is not possible to easily and efficiently determine an optimal portfolio for that investor by reallocating his current portfolio.

Summary of The Invention

A process for facilitating load-aware optimization is described that uses a modification to an input to a standard portfolio optimization. First, the financial product for each load in a set of available financial products is modeled as a loaded portion and an unloaded portion by determining an adjusted benefit for each of the load-bearing financial products based on a predetermined hold time, a current hold in the load-bearing financial product, information about a future desired contribution to or a desired withdrawal from the load-bearing financial product, an expected benefit of the load-bearing financial product, and an amount of load associated with the load-bearing financial product. A recommended portfolio of one or more financial products is then generated from the set of available financial products based on the adjusted returns for each bearing financial product and the expected returns for each non-bearing financial product.

Other features of the present invention will be apparent from the accompanying drawings and from the detailed description that follows.

Brief description of the drawings

The present invention is illustrated by way of example, and not by way of limitation, in the figures of the accompanying drawings and in which like reference numerals refer to similar elements and in which:

FIG. 1 illustrates a portfolio feasible set that can be formed from a set of financial products.

FIG. 2 illustrates a financial consulting system in accordance with one embodiment of the present invention.

FIG. 3 is an example of a computer system upon which an embodiment of the present invention may be implemented.

FIG. 4 is a simplified block diagram illustrating an exemplary analysis module of a financial consulting system in accordance with one embodiment of the present invention.

FIG. 5 is a flow diagram illustrating portfolio optimization in accordance with one embodiment of the present invention.

Detailed Description

The portfolio optimization techniques described herein, with known load, relate to a method of optimizing a portfolio in which one or more financial products in the field of financial products from which the portfolio is to be selected comprise one or more load-bearing financial products. In accordance with an embodiment of the present invention, a mechanism is provided for maintaining performance using QP techniques while solving the load-aware optimization problem.

Embodiments of the present invention include significant changes to prior art optimization methods. In some embodiments, the benefits of the loaded financial product are described in terms of an unloaded financial product for use in solving the optimization problem by adjusting the actual projected benefits of the loaded financial product to account for the load effect on the optimization term. For example, if the optimization cycle is 1 year and the financial product has a 5% load, the actual revenue for the financial product will be reduced by 5% from the projected annual revenue. Similarly, if the optimization cycle is 5 years and the financial product has a 5% load, the actual annual revenue for the financial product will only be reduced by 1% from the projected annual revenue.

Investors using embodiments of the present invention often own portfolios containing previously purchased financial products. Determining an optimized portfolio for such an investor often involves suggesting that the investor redistribute the relative amounts of financial products held in the portfolio before he optimizes. The investor may be advised to sell certain financial products, in whole or in part, or the investor may be advised to increase the number of certain financial products held by the investor. The adjustment of the revenue for the load is different depending on whether the investor is advised to sell the loaded financial product or purchase more of the loaded financial product in order to achieve the best portfolio allocation for the investor. Purchasing more of a previously held financial product is analyzed in terms of revenue ratios adjusted for the load fee paid on the purchase and the fee paid for the product in the future. When a portion of the hold is sold, the remaining portion of the financial product is analyzed at a revenue rate adjusted for a fee charged for future amortization of the product.

To recapture the advantage of being able to solve the optimization problem using QP techniques, embodiments of the present invention double the number of variables associated with previously held, loaded financial products. One set of variables describes a partially loaded financial product to be sold to arrive at the optimal portfolio of financial products and another set of variables describes a partially loaded financial product to be purchased to arrive at the optimal portfolio. After the QP optimization has been run, the two sets of variables are added together to produce the relative portions of each loaded financial product in the optimized (recommended) portfolio of assets.

In the following description, for purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of the present invention. It will be apparent, however, to one skilled in the art that the present invention may be practiced without some of these specific details. In other instances, well-known structures and devices are shown in block diagram form.

The present invention includes various steps that will be described below. The steps of the present invention may be embodied in the form of machine-executable instructions. These instructions can be used to cause a general-purpose or special-purpose processor that is programmed with the instructions to perform the steps of the present invention. Alternatively, the steps of the present invention might be performed by specific hardware components that contain hardwired logic for performing the steps of the present invention, or by any combination of programmed computer components and custom hardware components.

The present invention may be provided as a computer program product which may include a machine-readable medium having stored thereon instructions which may be used to program a computer (or other electronic devices) to perform a process according to the present invention. The machine-readable medium may include, but is not limited to, floppy diskettes, optical disks, CD-ROMs, and magneto-optical disks, ROMs, RAMs, EPROMs, EEPROMs, magnetic or optical cards, or other type of media/machine-readable medium suitable for storing electronic instructions. The present invention may also be downloaded as a computer program product, wherein the program may be transferred from a remote computer (e.g., a server) to a requesting computer (e.g., a client) by way of data signals embodied in a carrier wave or other propagation medium via a communication link (e.g., a modem or network connection).

Although embodiments of the present invention will be described with reference to a financial consulting system, the methods and apparatus described herein are equally applicable to other types of asset allocation applications, financial planning applications, investment consulting services, financial product selection services, automated financial product screening tools such as electronic personal shopping agents, and the like. Further, although the portfolio optimization problem is discussed herein in terms of financial products, any type of financial product, such as stocks and bonds, may be specified.

Overview of the System

The present invention may be incorporated into a client-server based financial consulting system 200 such as the one illustrated in figure 2. According to the embodiment described in FIG. 2, the financial consulting system 200 includes a financial segmentation server 220, a broadcasting server 215, a contents server 217, an AdviceServer^TM210(AdviceServer is a trademark of finarial enginees, inc., the assignee of the present invention), and a client 205.

The financial segmentation server 220 may function as a main segmentation and verification area for financial content distribution. In this manner, the financial segmentation server 220 functions as a data repository. Raw source data, typically time series data, may be refined and processed at the financial segmentation server 220 into analytically useful data. On a monthly basis, or may be any batch processing interval basis, the financial segmentation server 220 converts raw time series data obtained from the data supplier from a vendor-specific format to a standard format that can be used throughout the financial consulting system 200. Various financial engines may also be operated to generate data for validating and quality assurance data received from suppliers. Any calibration of the analysis data required by the financial engine may be performed prior to publishing the final analysis data to the broadcast server 215.

The broadcast server 215 is a database server. Thus, it runs a program such as Microsoft Windows^TM SQL Server、Oracle^TMAnd the like, a relational database management system (RDBMS). The broadcast server 215 provides a single point of access to all financial product information and analysis data. When suggestion servers, such as AdviceServer210, require data, they may query information from the broadcast server database. The broadcast server 215 may also populate a content server, such as the content server 217, so that remote execution of the AdviceServer210 does not require direct communication with the broadcast server 215. The AdviceServer210 is the primary provider for the client 205 services. The AdviceServer210 also functions as a proxy between an external system, such as the external system 225, and the broadcast server 215 or the content server 217.

According to the described embodiment, the user may interact with and receive feedback from the financial consulting system 200 using client software that may run within a browser application or as a stand-alone desktop application on the user's personal computer 205. The client software communicates with an AdviceServer210 that acts as an HTTP server.

An example computer system

Having briefly described an exemplary financial consulting system 200 in which various features of the present invention may be employed, a computer system 300 representing an exemplary client 105 or server in which features of the present invention may be implemented will now be described with reference to FIG. 3. Computer system 300 includes a bus or other communication means 301 for communicating information, and a processing device such as processor 302 coupled with bus 301 for processing information. Computer system 300 further includes a Random Access Memory (RAM) or another dynamic storage device 304 (referred to as main memory), coupled to bus 301 for storing information and instructions to be executed by processor 302. Main memory 304 also may be used for storing temporary variables or other intermediate information during execution of instructions by processor 302. Computer system 300 also includes a Read Only Memory (ROM) and/or other static storage device 306 coupled to bus 301 for storing static information and instructions for processor 302.

A data storage device 307 such as a magnetic disk or optical disk and its corresponding drive may also be coupled to computer system 300 for storing information and instructions. Computer system 300 may also be coupled via bus 301 to a display device 321, such as a Cathode Ray Tube (CRT) or Liquid Crystal Display (LCD), for displaying information to a computer user. For example, a graphical depiction of the desired portfolio performance, asset allocations for an optimal portfolio, charts indicating short-term and long-term financial risk, icons indicating likelihood of achieving various financial goals, and other data types may be presented to the user on the display device 321. Generally, an alphanumeric input device 322, including alphanumeric and other keys, is coupled to bus 301 for communicating information and/or command selections to processor 302. Another type of user input device is cursor control 323, such as a mouse, a trackball, or cursor direction keys for communicating direction information and command selections to processor 302 and for controlling cursor movement on display 321.

A communication device 325 is also connected to the bus 301 for accessing a remote server, such as the AdviceServer210 or other server, for example, via the Internet. The communication device 325 may comprise a modem, a network interface card, or other well-known interface devices, such as those used to connect to ethernet, token ring, or other types of networks. In any event, in this manner, computer system 300 may be connected to a number of servers via a conventional network infrastructure, such as a company's intranet and/or the Internet, for example.

Example analysis Module

FIG. 4 is a simplified block diagram illustrating exemplary analysis modules of the financial consulting system 200 in accordance with one embodiment of the present invention. According to the described embodiments, the following modules are provided: a pricing module 405, a factors module 410, a financial product mapping module 415, a tax adjustment module 420, an annual calculation module 425, a simulation processing module 430, a portfolio optimization module 440, a User Interface (UI) module 445, and a plan monitoring module 450. It should be understood that: the functionality described herein may be implemented with more or fewer modules than those discussed below. In addition, the modules and functions may be distributed in various configurations among a client system, such as client 205, and one or more server systems, such as financial segmentation server 220, broadcast server 215, or AdviceServer 210. The function of each example module will now be briefly described.

A "metric-economic model" is a statistical model that provides a means of predicting the level of some variable, called an "endogenous variable", over some other level of the variable, called an "exogenous variable", and sometimes it previously determines the value of the endogenous variable (called a hysteresis strain number). Pricing module 405 is a balanced metric economic model for predicting prices and benefits (also referred to herein as "core asset solutions") for a set of core asset classes. The pricing module provides current level estimates and predictions of economic factors (also known as state variables) and then estimates the revenue for the core asset class based thereon. According to one embodiment of the invention, the economic factor may be represented by three external state variables: price expansion, a real short term interest rate, and dividend growth. The three external state variables may be fitted with an autoregressive time series model to match the historical instants of the corresponding monitored economic variables, as described further below.

In any event, the core asset classes generated are the basis for portfolio modeling and are designed to provide a set of related and internally consistent (e.g., non-arbitrage) benefits. Arbitrage means an opportunity to create a favorable trading opportunity involving non-net investments and positive values in all states of the world.

According to one embodiment, the core asset classes comprise short term US government bonds, long term US government bonds, and US stocks. To extend the core asset class to cover the entire range of possible investments that people typically have access to, additional asset classes may be incorporated into the pricing module 405, or the additional asset classes may be included in the factor model 410 and may depend on the core asset class, as discussed further below.

Based on the asset schemas produced by the pricing module 405, the factor module 410 generates revenue schemas (also referred to herein as "factor model asset schemas") for a set of factor asset classes, which are used for exposure analysis such as style analysis and simulation of portfolio revenue. The additional asset class, referred to as factors, described in the factor model is conditionally dependent on the core asset class revenue scheme generated by the pricing module 405. According to one embodiment, these additional factors may correspond to a set of asset classes or indices selected in such a way as to cover the range of investments typically available to individual investors in mainstream corporate financial products and defined amortization programs. For example, the factors may be divided into the following groups: cash, mortgage, stock, and foreign stock. The stock group may be further broken down into two different abbreviated categories (1) to grow on the comparative (2) market capitalization. Growing stocks are essentially stocks that have a relatively high price (e.g., a high price/book ratio) relative to their underlying book value. In contrast, standard stocks have a relatively low price relative to their underlying book value. With respect to market capitalization, stocks may be divided into large, medium,and a set of small capital sums. An example set of factors is listed in table 1 below.

Group of	Factors of the fact
		Cash:	short term US bond (core class)
And (3) bond:	middle-term US bond (core class)
			Long term US bond (core class)
	Bond of US company
			US mortgage support certificate
	non-US government bond
		Stock:	large market value stock-value
	Stock growth of large market value
			Stock-value of Chinese market
	Stock growth of Chinese and urban values
			Stock-value of small market value
	Stock-growth of small market value
		Foreign countries:	international stock-europe
	International stock-pacific
			International stock-emerging market

TABLE 1 example factor sets

In this connection, it is important to point out: completely different factors may be used depending on the particular implementation. The factors listed in table 1 are given merely as an example of a set of factors that achieve the goal of covering the range of investments generally available to individual investors in mainstream corporate financial products and defined amortization programs. It will be apparent to one of ordinary skill in the art that alternative factors may be used. In particular, it is possible to construct factors representing the functionality of the underlying asset class for pricing securities that are non-linearly related to the price of certain asset classes (e.g., derived securities). In other embodiments of the invention, additional factors may be relevant to cover a large number of financial alternatives, such as industry-specific stock indexes.

The financial product mapping module 415 maps financial product benefits onto the factor models on a periodic basis. Importantly, financial product revenue need not represent a fixed allocation of a single financial product. Within the context of the optimization problem, any personal asset returns may consist of a static or dynamic policy involving one or more financial products. For example, an asset itself may represent a constant rebalancing strategy across a set of financial products. In addition, any dynamic policy that can be formulated as an algorithm can be incorporated into the portfolio optimization. For example, an algorithm can be implemented that specifies that the risk tolerance decreases with the age of the user. It is also possible to include path-related algorithms (e.g., portfolio insurance). In one embodiment, the process of mapping financial product benefits onto the factor model includes decomposing financial product benefits into exposure to the factor. The mapping, in effect, indicates how the financial product benefits behave relative to the benefits of the factors. According to one embodiment, the financial product-mapping module 415 resides on a server (e.g., financial segmentation server 220, broadcast server 215, or adviceServer 210). In an alternative embodiment, the financial product-mapping module 415 may be located on the client 205.

In one embodiment of the invention, an external method known as "revenue-based style analysis" is used to determine the exposure of a financial product to the factor. The method is referred to as external because it does not rely on information that is only available from sources internal to the financial product. Conversely, in this embodiment, a typical exposure of a financial product to the factor may be established based simply on the revenue realized by the financial product, as described further below. For more background on revenue-based style analysis, see Investment Management Review 59-69, 12 months 1988, "Determining a Fund's Effective AssetMix", by Sharpe, William F, and The Journal of Portfolio Management, 18, No.2 (winter 1992), pages 7-19, "AssetAllocation: management Style and Performance Measurement "(" Sharpe [1992] ").

An alternative method of determining factor exposure to a financial product involves examining underlying assets maintained in a financial product (e.g., a mutual fund) via an information file having a managing entity, classifying exposure based on standard industry classification rules (e.g., SIC rules), identifying factor exposure based on analysis of the product structure (e.g., stock index options, or mortgage-backed securities), and obtaining exposure information from an asset manager of the financial product based on the target benchmark. In each method, the primary function of the process is to determine the set of exposure factors that best describe the performance of the financial product.

The tax adjustment module 420 takes into account the tax implications of the financial product and the user's financial environment. For example, the tax adjustment module 420 may provide methods to adjust taxable revenues and accumulations, as well as to estimate future tax liability associated with early allocations from pension and defined amortization plans, and to estimate deferred taxes from investments in qualifying plans. In addition, financial product revenue for retention in a taxable investment instrument (e.g., a standard brokerage account) may be adjusted to account for expected tax accounting effects for accumulation and distribution. For example, the revenue component attributable to dividend income should be taxed at the income tax rate of the user, and the revenue component attributable to capital income should be taxed at an appropriate capital income tax rate depending on the holding time.

Additionally, the tax module 420 may predict a future component of the total return for the financial product due to the dividend income versus the portion due to the capital income based on one or more characteristics of the financial product. Wherein the characteristics of the financial products include, for example, active or passive characteristics of the financial product management, renewal rates, and categories of financial products. This allows for accurate calculations to be made in conjunction with specific tax effects based on the financial product and the financial environment of the investor. Finally, the tax module 420 facilitates tax-effective investments by determining optimal asset allocation among taxable accounts (e.g., broker accounts) and non-taxable accounts (e.g., personal retirement accounts (IRA), or employer funding 401(k) plans). In this manner, the tax module 420 is designed to estimate tax impact for a particular user with reference to the resulting tax rate, capital profitability, and available financial products for that user. Finally, the tax module 420 generates tax adjusted revenue and tax adjusted allocations for each available financial product.

The portfolio optimization module 440 computes a utility maximization set of financial products under a set of constraints defined by the user and the available feasible investment sets. In one embodiment, the calculation is based on a mean-variance optimization of the financial product. The constraints defined by the user may include limits on the class of assets and/or the holding of a particular financial product. In addition, the user can specify intermediate goals such as purchasing a house or passing a child through a college, which can be incorporated into the optimization. In any event, the optimization explicitly takes into account the impact of future dispatches and anticipated withdrawals on the optimal asset allocation. In addition, a factor covariance matrix used during optimization is calculated based on a prediction of expected revenue for the factors generated by the factors module 410 over the investment time horizon. Thus, the portfolio optimization module 440 can explicitly consider the impact of different investment ranges, including range impacts from intermediate dispatches and withdrawals.

The simulation processing module 430 provides additional analysis for processing the originally simulated revenue scheme into statistical data that may be displayed to the user via the UI 445. In one embodiment of the invention, these analyses generate statistics such as the likelihood of achieving a certain goal or the projected time required to reach a certain asset level with a certain probability. The simulation processing module 430 also incorporates methods to adjust the simulation scheme for effects caused by sampling errors in relatively small examples. The simulation processing module 430 provides the user with the ability to interact in real-time with the portfolio scenario generated by the portfolio optimization module 440.

The year calculation module 425 provides a meaningful way of expressing the portfolio value of the user at the end of the investment range item. Rather than simply indicating to the user the total projected portfolio value, a standard method of communicating information to the user is to convert the projected portfolio value into a number of retirement revenues. By dividing the projected portfolio value by the retirement length, the projected portfolio value at retirement may be distributed over the retirement length. More sophisticated techniques may involve determining how much the portfolio value of the design will grow during retirement and otherwise taking into account the impact of inflation. In either case, however, these approaches erroneously assume that the length of the retirement period is known in advance.

Therefore, it is desirable to indicate to the user an amount of retirement revenue that is more representative of the actual living level that can not easily change during the user's retirement. According to one embodiment, this amount of retirement revenue represents the adjusted revenue of inflation, which would be created synthetically by a real annuity guarantee purchased from an insurance company or via a trading strategy involving liberal bond securities indexed by inflation. In this way, the mortality risk is excluded from the assumption, since the user will be guaranteed a certain actual annual income no matter how long the length of the retirement period is. To determine this amount of retirement revenue, the annualization standard method used by insurance companies may be used. In addition, the probability of personal death for a given age, risk profile, and gender may be based on standard insurance statistics used in the insurance industry. For more information, see The Society of Actuaries, Illinois, Itasca, pages 52-59 1986, Bowers, Newton L.J., et al, "Actuarial Mathesics" and Society of Actuaries Group evaluation Table Force, Transactions of The Society of Actuaries, 1994 volume XLVII, Group evaluation Table and 1994Group evaluation testing Table ". Calculating a value for a currency expansion adjusted annuity value may involve estimating the appropriate value for the true liability for each maturity. The pricing module 405 generates real treasury prices that are used to calculate the underlying real annuity values for the portfolio at the investment horizon.

Referring now to the plan monitor module 450, a mechanism is provided for alerting the user to the occurrence of various predetermined conditions relating to the characteristics of the recommended portfolio. Because the data on which the portfolio optimization module 440 depends changes often, it is important to re-evaluate the characteristics of recommended portfolios on a periodic basis to notify the user in a timely manner, such as when positive action is required by the user. According to one embodiment, the schedule monitoring module 450 resides on the AdviceServer 410. In this manner, the schedule monitoring module 450 has constant access to the user profile and portfolio data.

In one embodiment, the occurrence of two basic conditions may cause the schedule monitoring module 450 to trigger a notification or alert to the user. The first condition that may trigger an alert to the user is that the current probability of achieving a goal is outside a predetermined tolerance range of the expected probability of achieving that particular goal. Generally, one goal is a financial goal, such as a certain retirement income or the accumulation of a certain amount of money for a child to pass through the college. Additionally, the plan monitor module 450 may alert the user if a measure of the utility of the currently recommended portfolio has fallen below a predetermined tolerance level, even if the current odds of achieving the financial goal is within a predetermined tolerance range. Various other conditions are considered that may result in the generation of an alert. For example, if the financial product attribute in the currently recommended portfolio has changed such that the portfolio's risk rate is outside the user's risk tolerance range, the user may receive an indication that he should rebalance the portfolio.

The UI module 445 provides a mechanism for data input and output to provide the user with a means to interact with the financial consulting system 200 and receive feedback from the financial consulting system 200, respectively. Further description of one UI that may be used in accordance with one embodiment of the present invention is disclosed in U.S. Pat. No. 5918,217 entitled "USER INTERFACE FOR FINENCIAL ADVISORY," the contents of which are incorporated herein by reference.

Other modules that may be included in the financial consulting system 200 such as a pension module and a social security module. The pension module may be provided to estimate pension benefits and revenues. The social security module may provide an estimate of expected social security revenue that a person will receive when retired. The estimation may be based on calculations used by the Social Security Administration (SSA) and a probability distribution for simplification in the current level of benefits.

Portfolio optimization

Portfolio optimization is the process of determining a set of financial products that maximize a user utility function. According to an embodiment, the portfolio optimization process assumes that the user has a utility function (i.e., mean-variance utility) that is reasonably approximated by a quadratic utility function, i.e., people like to have more average wealth on average and dislike the volatility of wealth. Based on this assumption and given a user's risk tolerance, portfolio optimization module 440 calculates the effective mean-variance portfolio from the set of financial products available to the user. As described above, the constraints defined by the user may also be taken into account by the optimization process. For example, the user may indicate a desire to have a certain percentage of his portfolio allocated to a particular financial product. In this example, the optimization module 440 determines allocations among the unconstrained financial products such that the recommended portfolio as a whole accommodates the constraint(s) of the user and optimizes the risk tolerance level of the user.

Prior art mean-variance portfolio optimization traditionally treats this problem as a single cycle optimization and uses only the single cycle attributes (expected return and variance of return) of the financial product to be optimized as parameters in the optimization. Importantly, in the embodiments described herein, the portfolio optimization problem for a loaded financial product is structured in such a way that it can explicitly take into account the effects of different investment ranges and the effects of intermediate deployments and withdrawals. Furthermore the problem is built so that it can be solved with the QP method, however the optimized parameters will have the property of multiple cycles, which is quite different from their single cycle counterparts.

Referring now to FIG. 5, a method for portfolio optimization in accordance with one embodiment of the present invention will now be described. At step 505, information is received regarding the set of financial products to be considered in the optimization. In particular, if the user holds any of these financial products in their current portfolio, any held dollar amount is received. At step 510, information regarding the anticipated retrieval is received. This information may contain the dollar amount and time expected to be withdrawn. At step 520, information is received regarding an anticipated future dispatch. According to one embodiment, this information may be in the form of an accumulation rate expressed as a percentage of the user's total revenue, or alternatively in the form of a constant or variable dollar value that may be specified by the user.

At step 530, information regarding the relevant investment time horizon is received. For example, in an implementation designed for a retirement plan, the time range may represent the user's desired retirement age.

At step 540, information regarding the user's risk tolerance, Tau, is received.

At step 550, a portfolio is determined for which the average variance is valid, while accounting for front-end and/or back-end loads associated with one or more financial products in the set of available financial products. According to one embodiment, the expected utility of the portfolio in real dollars as measured at time T is substantially maximized by determining a portfolio proportion that maximizes a quadratic function. This problem can be solved using the QP method.

First, an initial portfolio is identified as the starting point for solving the optimization problem. Typically, the initial portfolio is specified by an investor and may contain available financial products and/or financial products currently held by the investor. For example, if the investor is optimizing his 401(k) plan, the initial portfolio will be the financial product he is currently maintaining in the plan. The initial set of financial products will be all of the financial products that the investor can invest as part of an optimized portfolio. For example, if the 401(k) investor has 20 financial products selected in his 401(k) plan, then the 20 group representations can be in the sameThe investor's optimization 401(k) is all possible financial products allocated in the portfolio. Each loaded financial product within the set of financial products is modeled as an equivalent, presumably unloaded financial product having a projected return adjusted by the load value factored into the optimization term and accounting for future dispatches and withdrawals of each loaded financial product. Generally, an adjusted revenue for the hypothetical equivalent unloaded financial product is generated as follows: a predetermined hold time is divided into T time intervals, which are marked with integers from 1 to T. This interval generally corresponds to a period equal to one year, and T therefore represents the duration of the retention time measured in years. If R represents the simple return of the loaded financial product in the t-th time interval, then the total return in this interval is equal to (1+ R) by definition_t). Adjusted simple revenue r_tI.e. the simple gain of the assumed unloaded equivalent, is given by the following expression:

Γ_t＝[(1-γ)·(1+R_t)]-1 (Eq.1)

The total revenue of this adjustment is thus equal to (1+ r |)_t). In equation (1), the variable y is called the tuning number and gives a fixed scheme benefit R1, R2, …, RT during the hold time, assuming it is the same over all time intervals during the hold time. However, the number of adjustments typically varies with the recipe. By equating the final wealth of the loaded financial product with the final wealth of the equivalent unloaded financial product, an equation can be derived that determines the adjustment number. This equation can be solved approximately (either numerically or analytically) for the adjustment number. The adjustment amount will depend on the load cost, initial investment wealth, amortization and takeout, hold time, and random earning schedule of the financial product during the hold time. Thus, the adjustment number is a random variable with respect to the set of revenue random scenarios on the loaded financial product.

Using one for the adjustment number yApproximate expression, we can get the information for r_tAssume a statistical moment of the yield of an equivalent unloaded product. The adjusted expected value of revenue is used for mean variance portfolio optimization. The expected value of a random variable X will be defined by E [ X ]]And (4) showing. Here, the expected value is calculated relative to a random revenue generation process for the loaded financial product. One for E [ f ] is derived from equation (1)_t]Expression (c):

E[Г_t]＝E[(1-γ)·R_t]-E[γ](equation 2)

Can be numerically calculated for E [ Γ using Monte Carlo simulation_t]To an approximation of (a).

The variance of the returns between two financial products is also used in mean-variance portfolio optimization. Variance cov [ X, Y ] of two random variables X and Y]Equal to the expected value of their product minus their expected value. Consider the variance of two financial products with a load. The product is labeled A and B, and has a color represented by R_A，tAnd R_B，tExpressed, unregulated revenue. The corresponding financial product with no load is assumed to have income of r_A，tAnd r_B，tExpress, and adjust the number gamma according to them_AAnd gamma_BDefined by equation (1). The variance of these two adjusted gains is established from the variance of the unadjusted gain function using the following equation:(equation 3)

Here, the expected value based on this variance is relative to two random processes that generate random returns for the loaded financial product. The approximation for the covariance can be calculated numerically using the monte-carlo method.

In the preferred embodiment, the magnitude of the adjustment number γ is small compared to 1, since it is of the same order as the load cost parameter divided by the holding time, which is typically less than a few percent. In this case, any term of the form (1- γ) can be well approximated by the value 1 only. This approximation is used to simplify the equations for the statistical moments. In particular, equation (2) for the adjusted expected value of revenue reduces to:

E[Г_t]＝E[R_t]-E[γ](equation 4)

Similarly, equation (3) for adjusting the variance of the benefit reduces to:(equation 5)

The variance of the adjusted benefit is therefore approximately equal to the variance of the unadjusted benefit, and the latter can be used for the former. Furthermore, it is clear that: the main effect of load on mean variance optimization is via adjustment to the expected revenue. These approximations are confirmed by testing using the Monte-Carlo method.

The process of calculating the adjusted number and the statistical moment of the adjusted benefit is illustrated by the following equations for the case of a financial product having a front end load cost given by the parameter λ. Let C be_tFor a booth at the beginning of the tth interval (take is a negative booth), W is the initial property in the financial product, and aw is any change to the initial property at the beginning of the hold time. The final property of the loaded financial product with a load fee X is equal to the final property of the equivalent unloaded financial product to obtain the following equation:(equation 6) where | X | max (X, 0) and the total revenue of the loaded financial product over all intervals from T to T, G (T, T), is given by:(equation 7)

As can be seen from the left hand side of equation (6): the load fee is paid only on positive start increments of property and on amortization, but not on takeout.

Continuing the description, by using equation (6) to calculate the coefficients for a two-term McClaurin series expansion of γ as a function of λ, an approximate analytical expression for the adjustment number can be obtained as a linear function of the load cost. It can be noted that: when the load charge is set equal to zero in equation (6), the value of the adjustment number satisfying equation (6) is zero. Using the implicit differential technique on equation (6), an equation can be obtained that adjusts the derivative of the number γ with respect to the load cost λ. This equation yields a derivative value when the load cost is zero. Substituting these values into the formula for the two term McClaurin series gives the following approximation for the adjustment number:(equation 8)

This approximation ignores the second and all higher powers of the load cost. Because the actual load cost is much less than 10%, the size of the ignored term is much less than 1%.

The adjusted expected value of revenue is of particular importance in portfolio optimization problems. For this illustrative example, the simplified expression given by equation (4) is valid, and the expected adjusted benefit is equal to the expected unadjusted benefit minus the expected value of the tuning number. The value of the desired tuning number can be calculated numerically, however, in one embodiment, the benefit R_tIs sufficiently small that R_tIs determined by the expected value of a well-behaved function at E, E R_t]At the expected value, the calculated function is well approximated. In this case, equations (4) and (8) are simplified to the following analytical formulae:(equation 9)

Again, these approximations are confirmed by testing using the Monte-Carlo method. As can be seen from equation (9): the expected value of return for the equivalent unloaded financial product is dependent on the expected value of return for the financial product with front-end load, hold time, initial property, and future and current amortizations and withdrawals, and load costs.

In the preferred embodiment, multiple financial products with (and without) load fees are combined into one portfolio at a constant relative property ratio. These proportions, referred to as target compounds, are approximately maintained over time by periodically selling and purchasing products to achieve the proportions of the properties of the target compound. Such a policy is called a constant-proportion policy and has the property that: portfolio risk rates, measured by variances of their returns, remain approximately constant over time. In calculating the adjusted revenue for a constant-mix portfolio, the initial property, the increase in property, and the contribution can be written as a function of the portfolio property total, the contribution, an initial contribution, and a target contribution, as shown by the following equations:

W_i＝x_o，i·W_p

ΔW_i＝(x_i-x_o，i)·W_p

C_i，t＝x_i·C_p，t

(equation 10)

Here, W_pStarting property representing the total number of portfolios, W is the starting property for the ith financial product, and x_o，iIs the beginning of the portfolio property in the ith financial product. Similarly, x_iIs the target property segment for the ith financial product. The sum of the start portion and the target portion is equal to 1. The starting property increment for the ith financial product is Δ W_i. Because an initial dispatch or removal can be made at the beginning of the first cycle, the increments in the portfolio property can be taken to be zero in value as a whole without loss of generality. Finally, C_i，tIs the dispatch (or take) of the ith financial product at the beginning of the t-th cycle. As an approximation, this quantity is taken as the product of the target portion and the contribution to the portfolio as a whole, where the overall contribution is represented by C_p，tAnd (4) showing. This approximation ignores any increased amortization and removal that occurs during a periodic rebalancing due to the transfer of property between products.

The use of the formula in equation (10) is illustrated by calculating the expected adjusted revenue for the ith financial product with front-end load in a constant-mix portfolio. The revenue, expected revenue, and load cost parameters of the ith financial product in the t-th interval are respectively represented by R_i，t，e_i＝[R_i，t]And λ_iAnd (4) showing. Adjusted revenue of corresponding hypothetical unloaded financial product is defined by_i，tIs represented by having an integer gamma_iIs given by equation (1) of (a). Using equation (10) in equation (9) and rearranging the terms yields the following system of equations for the adjusted revenue expectation value:

x_i·E[Г_i，t]＝(e_i-δ_i)·x_i-p_i·‖x_i-x_o，iII (equation 11) where the parameter δ_iAnd p_iComprises the following steps:(equation 12)

Parameter delta_iAnd p_iReferred to as the reduction parameter and the penalty parameter, respectively. These parameters are a function of load costs, initial portfolio properties, future and current portfolio dispatches and withdrawals, expected unregulated returns, and hold times. Reduction parameter delta_iAnd a target ratio x_iThe product of (a) represents the cost in expected revenue due to load payments made via the amortization. Penalty parameter p_iAnd any increment of the target ratio on the initial ratio | x_i-x_o，iThe product of |, represents the cost in the expected revenue due to the initial asset rebalancing from the initial mix to the target mix.

The expected value formula for the adjusted revenue for a financial product with back-end load is also given by equation (11), albeit with a different formula for the curtailment and penalty parameters. Because both front-end or back-end load fees withdraw cash from the possession of a financial product, the adjusted revenue will never be greater than the unadjusted revenue of a financial product. Thus, it can be seen that the reduction parameter is always non-negative. This result is confirmed for the front-end load by the first of equation (12). Similarly, all things being equal, any additional purchase of a loaded financial product is no more advantageous than the current hold in that product. Thus, it follows that the penalty parameter is always non-negative. This result is confirmed for the front-end load by the second of equation (12).

From equation (12) it can be learned that: when the load cost is lambda_iIs zero, delta_iAnd p_iAre all equal to zero and the adjusted expected revenue is equal to the unadjusted expected revenue e_i. Thus, assuming that the load cost for an unloaded product takes a value equal to zero, the portfolio of financial products with and without load can be processed by the same formula. A similar observation applies to the variance term.

It is known that: given the expected revenue for each of a portfolio of unloaded financial products and the variance terms among the portfolio members, a mean square error optimization can be performed to approximately maximize the expected utility of a user. This problem leads to a secondary programming problem whose solution can be handled using any of a number of known secondary programming techniques. A typical constant-mix, portfolio optimization design has the following vector matrix form:

maximizing phi (x) e^Tx-(x^TCx)/τ

So that i^Tx＝1

l≤x≤u

(equation 13)

In equation (13), the superscript T represents a vector transpose. The parameter τ is a specified risk tolerance parameter, x is a target ratio vector, e is an expected revenue vector, i is a 1 vector, 1 is a lower limit vector, and u is a vector at the upper limit of the target ratio. All vectors are N-dimensional column vectors, where N is the number of financial products considered for the portfolio. The ith cell of each vector corresponds to the ith financial product. The (N) covariance matrix C has the revenue covariance between the ith and jth financial products as cells in its ith row and jth column. In the first equation, an optimal target ratio x is calculated from the set of all feasible target ratio vectors x^*The objective function phi (x) is maximized. The objective function is one two of the target ratioObjective function and expected profit (e) of portfolio^Tx, linear in x) and the profit variance (x) of the portfolio^TCx, quadratic in x). The second equation, a feasible constraint, requires that the sum of the target proportioning units be equal to 1. This equation is referred to as a budget constraint. This boundary allows an investor to specify the minimum and maximum number of a financial product he wishes to hold in his portfolio. The investor can also specify a specific amount of hold by setting the upper and lower limits to the same explicit value. One typical value for the lower limit is zero; this is a non-short term sell constraint. It is assumed that the upper and lower limits are feasible with respect to each other, and with respect to budget constraints.

A general overview of the exemplary portfolio optimization would allow the portfolio to have M accounts, and one budget constraint per account. Equation (13) is modified for this summary by replacing the second equation with M equations of the form below.(equation 14)

In equation (14), vector i_jIs an N-dimensional column vector with 1 for the cell corresponding to the financial product in the jth account and 0 elsewhere. Account part f_jIs given and represents the number of total portfolio assets assigned to the jth account. The sum of the account portions is generally equal to 1. Note that: when there is only a single account number, equation (14) reduces to the personal account formula given previously in equation (13). This typical portfolio optimization problem with multiple accounts has the following attributes. The objective function is a quadratic function of the N decision variables (units of x). There are simple upper and lower bounds (vectors l and u) on the decision variables. At blockThere are exactly M equal (budget) constraints on the feasible set of policy variables.

The portfolio optimization problem for a loaded financial product has an objective function φ (x) that is substantially different from the objective function in equation (13). Formally, this modification is obtained by replacing the expected revenue vector e, and the covariance matrix C, with their load-adjusted statistical moments. In the preferred embodiment that includes load-adjusted numbers for expectation values rather than for covariance matrices, the objective function for a constant-ratio portfolio optimization has the form:

maximize phi (x) ═ e-delta)^Tx-p^T‖x-x_oII- (xCx)/τ (equation 15)

In equation (15), the N-dimensional column vectors δ and p are referred to as reduction and penalty vectors, respectively. Generally, these vectors depend on load costs, retention periods, initial portfolio properties, and present and future portfolio dispatches and withdrawals. Furthermore, the cells of these vectors are non-negative. In one embodiment of block 615, the units of these vectors are calculated using the formula for the front-end load given by equation (12). Note that: due to the penalty term, the objective function is no longer a quadratic function of the target ratio x, and depends on x_oAn N-dimensional column vector of initial match values.

The portfolio optimization problem for a loaded financial product has a non-quadratic objective function of the form given by equation (15), one or more budget constraints of the form given by equation (14), and upper and lower limits on the target mix ratio given by the last of equation (13). To reproduce a quadratic program, a change in the decision variable can be made. One variation, well known to those skilled in the art of portfolio optimization, will introduce "buy" and "sell" variables defined by the following equations:

b＝‖x-x_o‖

s＝‖x_o-x‖

(equation 16)

In equation (16), the "buy" variable b represents the portion of the target mix that was purchased except for any current hold. Similarly, the "sell" variable s represents the fraction of the target mix that is sold from any current hold. The following three properties of vectors b and s are the result of equation (16) and the maximum and minimum bounds on vector x:

0≤b≤‖u-x_o‖

0≤s≤‖x_o-l‖

b^Ts＝0

(equation 17)

The first two attributes are simple bounds on the b and s tolerance values. Note that: the units of the lower limit limits b and s are non-negative values. The third attribute is a complementarity condition. Together with the non-negative constraint, the complementarity condition requires that at least one of the ith cells of b and s be zero. The financial meaning of this constraint is to prevent simultaneous sale and purchase of the same location in a portfolio. The last attribute of equation (16) is a function of x_oB, and s, formula for the original vector x of the decision variables:

x＝x_o+ b-s (equation 18)

Using equation (18) and a feasible pair of buy-sell vectors, an allowable value for the target ratio vector can be constructed. In particular, if b^*And s^*Is the optimal feasible vector for the design in b and s, the optimal portfolio match x can be calculated^*。

There are two ways to reproduce a secondary design using the buy and sell variables. In thatIn both methods, the penalty term p appearing in the objective function of equation (15)^T‖x-x_oIs represented by the formula (p)^Tb) Instead. Further, b and s are required to satisfy equation (17). Using the first approach, the remaining occurrences of x in the objective function, budget constraint, upper bound, and lower bound are replaced by the right hand side of equation (18). This results in a design with 2N decision variables with simple bounds, M linear equality constraints (budget constraints), and 2N linear inequality constraints (simple bounds on x). The objective function is a quadratic function of b and s. With the second approach, there is no substitution for x, and the three vectors x, b, and s are all treated as decision variable vectors linked by equation (18). This results in a design with 3N decision variables with simple bounds and (M + N) equality constraints. In this case, the objective function is a quadratic function of x, b, and s. It can be shown that: because the penalty vector p is non-negative, the compliancy condition need not be explicitly enforced. This is a result of the field of separable programming, John Wiley, New York, NY 1999&Sons publication, Model building chemical Programming, 4th edition, by h.p. williams, which is incorporated herein by reference. Both approaches thus reproduce a quadratic design.

In the preferred embodiment, the quadratic design is reproduced from a different and non-obvious change in the decision variables. The decision variable vector x is replaced by two decision variable vectors, an "unaffected" variable, v, and a "penalized" variable, w, which are defined by the following equation:

v＝‖x_o-l‖-‖x_o-x‖

＝min[x，x_o]-min[l，x_o]

w＝‖x-x_o‖-‖l-x_o‖

＝max[x，x_o]-max[l，x_o]

(equation 19)

Vector min [ x, y](max[x，y]) Is equal to the ith element of vectors x and y, x_iAnd y_iMinimum (maximum) value of (c). Note that: v denotes the number of target matches x above the lower limit and unaffected by the load penalty term, and w denotes the number of target matches x above the lower limit and responded to by the penalty term. The following three properties of vectors v and w are the result of equation (16) and the maximum and minimum bounds on vector x:

0≤v≤min[u，x_o]-min[l，x_o]

0≤w≤max[u，x_o]-max[l，x_o]

(v-‖x_o-l‖)^T(w+‖l-x_o‖)＝0

(equation 20)

The first two attributes are simple bounds on the v and w tolerances. Note that: the lower limit limits the unit of v and w to non-negative values. The third attribute is a complementarity condition. Again, the financial meaning of this constraint is to prevent simultaneous sale and purchase of the same location in a portfolio. The last attribute of equation (20) is a formula for the original vector x of decision variables based on l, v, and w:

x ═ l + v + w (equation 21)

Using equation (21) and a feasible pair of unaffected-penalty vectors, an allowable value for the target proportioning vector can be constructed. In particular if v^*And w^*Is the optimal feasible vector for a design, denoted by v and w, the optimal portfolio match x can be calculated^*。

The unaffected and penalized variables are used to againA quadratic design for portfolio optimization for which the load is known is now available. Penalty term p appearing in the objective function of equation (15)^T‖x-x_oThe second base using equation (19) is written in terms of w. Instead of the expression for the vector x given by equation (21) in the non-penalty term, an expression for the objective function is produced as a function of v and w:(equation 22)

Note that: the objective function is a quadratic function of the 2N decision variables given by the elements of the vectors v and w. Term phi_oIs a constant with respect to the optimization and can be neglected. Similarly, x can be eliminated from the multi-account budget constraint given by equation (14):(equation 23)

Further note that: the limit on x is automatically met if the limits on v and w given by equation (22) are met. Again, it can be shown that: because the penalty vector p is non-negative, the compliancy condition need not be explicitly enforced. Thus, equations (22) and (23), along with the bounds from equation (20), contain a quadratic design in 2N decision variables with simple bounds and M linear equation constraints.

It should be noted that: it may not be necessary to use all 2N of the unaffected-penalty decision variables. If the ith financial product is not loaded, the penalty variable w corresponding to this product_iCan always be set equal to zero and eliminated from the problem. Also, the same applies toIf the ith financial product has a load and its lower limit is greater than or equal to its starting mix ratio (/)_i≥x_o，i) If so, the unaffected variable v corresponding to this product_iAlways equal to zero and can be eliminated from the problem. This is the case for a financial product that is not currently held in a portfolio, but is being considered for purchase. Similarly, if the ith financial product has a load and its upper bound is less than or equal to its starting mix (u)_i≤x_o，i) Then the penalty variable w corresponding to this product_iAlways equal to zero and can be eliminated from the problem. The latter two results are a direct consequence of the simple bounds in equation (20).

Using the unaffected-penalty variable has two advantages over using the buy-sell variable. The first advantage is that the unaffected-penalty formula is always of a smaller size, i.e., it has fewer constraints or fewer variables than either of the buy-sell formulas. This unaffected-penalty variable is preferable because memory and computation time increase with increasing number of variables and limits.

When two questions have the same form, their solutions can be computed using the same computer software. It is to be noted that: although the two questions may have different sizes, parameter values, and hence different solutions, they can still have the same form. The difference is handled by specifying different values for the input-output parameters of the computer software code. It is to be noted that: the objective function in equation (22), without the constant term, has the same form as the unloaded objective function in equation (13). Furthermore, the budget constraint given by equation (23) and the multi-account budget constraint for the no-load equation given by equation (14) have the same form. A second advantage of the unaffected-penalized quadratic design is that it happens to be in the same form as the unloaded portfolio optimization and can be implemented using the same standard software code that is currently used for an unloaded portfolio optimization.

It should be noted that: there are other decision variable transformations that have similar properties and advantages to the unaffected-penalized decision variables. Although a pair of vectors v and w are defined in terms of the lower bound 1, one obvious equivalent is to define a pair of vectors in terms of the upper bound u. It should be noted that: the transformation techniques described above are applied to portfolio optimization problems with generally linear equality and inequality constraints in addition to budget constraints. Any additional constraints are handled in the same spirit as the budget constraints.

In the preferred embodiment, the assignments to a portfolio are different for different accounts. For example, one user IRA account may have a amortization of $2,000 per year, while his SEP-IRA account may have an amortization of $10,000 per year, on a keep time basis. For a constant proportion portfolio consisting of one account, equation (10) is used to model the initial property, property increment, and amortization to the ith financial product. For multiple accounts with different amortization rates, by using (K) on the right hand side of the third equation_j，t/f_j) To replace C_p，tEquation (10) can be modified where j represents the account number containing the jth financial product, f_jIs part of the jth account, and K_j，tIs the assignment of the nth account to the tth account at the beginning of the tth time interval. The penalty and reduction terms for a loaded financial product then follow using equation (9) and these modified equations.

Alternative embodiments:

in the foregoing specification, the invention has been described with reference to specific embodiments thereof. It will, however, be evident that various modifications and changes may be made thereto without departing from the broader spirit and scope of the invention. Accordingly, the specification and drawings are to be regarded in an illustrative rather than a restrictive sense.

For example, while the embodiments discussed herein are primarily concerned with performing portfolio optimization in which one or more financial products in a set of available financial products carry a front end load, it should be understood that: the invention is equally applicable to portfolio optimization involving one or more back-end load bearing financial products or a group of financial products including one or more front-end load bearing financial products and one or more back-end load bearing financial products. Additionally, in some embodiments, the teachings provided herein can be utilized in a portfolio rebalancing process involving one or more loaded financial products; where no new financial product becomes available and only the relative portion of each product held in the portfolio is changed. In addition, embodiments of the invention have been discussed herein with reference to financial products, but the invention is not limited to any particular type of financial product. Embodiments of the present invention are applicable to any type of financial product that charges a load or the equivalent of a load.

Claims (19)

1. A method of selecting a recommended portfolio of one or more financial products, the method comprising:

determining an adjusted benefit for each of the supported financial products in the set of financial products based on a predetermined hold time, current holds in the supported financial products, information about future trips to or anticipated withdrawals from the supported financial products, expected benefits for each supported financial product, and an amount of load associated with each supported financial product; and

a recommended portfolio of one or more financial products is generated from the set of financial products in varying proportions based on the adjusted returns for each supported financial product and the expected returns for each unsupported financial product.

2. The method of claim 1, wherein: one or more risk rating levels may be specified by a user to indicate the user's risk tolerance, and wherein the generating of the recommended portfolio is additionally based on the user's risk tolerance.

3. The method of claim 1, wherein: the generating the portfolio is additionally based on a variance of revenue associated with the set of financial products.

4. The method of claim 3, wherein: generating the portfolio includes using quadratic programming techniques to determine a proportion of loaded and unloaded financial products that maximize the expected value of the utility from the portfolio, wherein the utility function is sufficiently approximated by a linear combination of expected returns and variances of returns for the portfolio.

5. The method of claim 2, wherein: the risk level corresponds to a measure of variability in the monetary value of a financial product or a portfolio in response to changes in market conditions.

6. A method of redistributing a portfolio of one or more financial products, the method comprising:

determining whether the portfolio contains a loaded financial product;

decomposing a portion relating to the relative amount of the loaded financial product currently held in the portfolio into three items, a first item being a variable representing a portion of the loaded financial product currently held in the portfolio, a second item being a variable representing a portion of the loaded financial product that can be sold to produce a recommended portfolio from the portfolio, and a third item being a variable representing a portion of the loaded financial product that can be purchased to produce a recommended portfolio from the portfolio and from a set of available financial products;

determining an adjusted revenue for each loaded financial product of the set of available financial products and each loaded financial product contained within the portfolio based on a predetermined time period, expected revenue for each loaded financial product, and an amount of load associated with each loaded financial product;

generating a recommended portfolio of one or more financial products from the available set of financial products and from one or more financial products in the portfolio based on a predetermined time period, current holds in each of the carried financial products, information about future trips to the intended amortization of the carried financial product or anticipated withdrawals from the carried financial product, and expected returns for each non-carried financial product.

7. The method of claim 6, wherein: a portion relating to the relative quantity of loaded financial products that are suggested to be held in the recommended portfolio is broken down into three items, the first item being a known portion of the loaded financial products that is a designated lower/upper limit portion representing a minimum/maximum portion of the loaded financial products that are suggested to be available in the recommended portfolio; the second term is a variable representing the portion of the loaded financial product that is above/below the lower/upper limit and unaffected by an initial loading fee; and a third term is a variable representing the portion of the financial product loaded above/below the lower/upper limit and subject to an initial loading fee.

8. The method of claim 7, wherein: the first item associated with the recommended portfolio is based on a user-specified minimum or maximum allowable portion of a loaded financial product.

9. The method of claim 6, wherein: generating a new portfolio includes using quadratic programming techniques to determine a proportion of loaded and unloaded financial products that maximize the expected value of the utility from the portfolio, wherein the utility function is sufficiently approximated by a linear combination of expected returns and variances of the portfolio.

10. The method of claim 9, wherein: the generating a new portfolio is additionally based on a variance of revenue associated with a set of financial products.

11. The method of claim 9, wherein: one or more risk rating levels may be specified by a user to indicate the user's risk tolerance, and wherein the generating of the recommended portfolio is otherwise based on the user's risk tolerance.

12. A method of redistributing a portfolio of one or more financial products, the method comprising:

modeling each loaded financial product of the one or more financial products according to at least one of a loaded portion and an unloaded portion;

calculating an adjusted benefit for each of the supported financial products based on the expected benefit for each of the supported financial products, a predetermined hold time, current holds in each of the supported financial products, information regarding expected spreads to or expected withdrawals from each of the supported financial products in the future, and an amount of load associated with each of the supported financial products; and

the reallocated portfolio of assets is generated based on the adjusted revenue and expected revenue.

13. A method of financial product selection comprising:

calculating adjusted returns for the loaded financial products in the set of financial products, the adjusted returns describing performance of the loaded financial products taking into account a load applied to the loaded financial products;

simulating each loaded financial product of the other financial products in an optimal portfolio of assets in accordance with at least one of a loaded component and an unloaded component, performance of the loaded component in accordance with a correlated expected return description of the plurality of expected returns, and performance of the unloaded component in accordance with a correlated adjusted return description of the plurality of adjusted returns; and

generating an portfolio of one or more financial products from the set of financial products in varying proportions based on a plurality of expected returns for the unloaded portion of the set of financial products, expected returns for the unloaded portion, adjusted returns for loaded financial products in the set of financial products, and adjusted returns for the loaded portion.

14. The method of claim 13, wherein: one or more risk rating levels may be specified by a user to indicate the user's risk tolerance, and wherein the generating of the recommended portfolio is otherwise based on the user's risk tolerance.

15. The method of claim 14, wherein: the generating of the one or more portfolios of financial products further comprises using secondary programming techniques to determine, in varying proportions, the portfolio of financial products, the loaded portion of loaded financial products, and the unloaded portion of loaded financial products that have the highest expected return for a given risk level.

16. The method of claim 13, wherein: the generating one or more portfolios of financial products is additionally based on variance information associated with a set of financial products.

17. The method of claim 13, wherein: the simulating each loaded financial product further comprises representing at least one of the loaded financial products of the other financial products as a sum of three terms, one of which indicates a minimum or maximum fraction that each financial product should contribute to the optimal portfolio.

18. A machine-readable medium having stored therein data representing sequences of instructions which, when executed by a processor, cause said processor to perform the following:

determining an adjusted benefit for each of the carrier financial products of the set of available financial products based on a predetermined hold time, current holds in the carrier financial product, information about future trips to or anticipated withdrawals from the carrier financial product, expected benefits for each of the carrier financial products, and an amount of load associated with each of the carrier financial products; and

a recommended portfolio of one or more financial products is generated from a set of available financial products in varying proportions based on the adjusted returns for each bearing financial product and the expected returns for each non-bearing financial product.

19. A computer system, comprising:

a processor; and

a computer readable medium containing instructions that, when executed, cause a processor to:

calculating adjusted returns for the loaded financial products of the set of financial products, the adjusted returns describing performance of the loaded financial products taking into account a load applied to the loaded financial products,

representing each of the other financial products in an optimal portfolio of assets each loaded financial product according to at least one of a loaded portion and an unloaded portion, performance of the loaded portion described in terms of an associated expected return of the expected returns, and performance of the unloaded portion described in terms of an associated adjusted return of adjusted returns, and

one or more portfolios of financial products are generated from the set of financial products in varying proportions based on a plurality of expected benefits of the unloaded portion of the set of financial products, the expected benefits of the unloaded portion, the adjusted benefits of the loaded financial products in the set of financial products, and the adjusted benefits of the loaded portion.