Classifications

• • G—PHYSICS
  • G06—COMPUTING; CALCULATING OR COUNTING
  • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
  • G06Q40/00—Finance; Insurance; Tax strategies; Processing of corporate or income taxes
  • G06Q40/04—Trading; Exchange, e.g. stocks, commodities, derivatives or currency exchange
• • G—PHYSICS
  • G06—COMPUTING; CALCULATING OR COUNTING
  • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
  • G06Q40/00—Finance; Insurance; Tax strategies; Processing of corporate or income taxes
  • G06Q40/06—Asset management; Financial planning or analysis

Definitions

• the invention relates generally to the field of financial advisory services. More particularly, the invention relates to a system for advising a user regarding feasible and optimal portfolio allocations among a set of available financial products.
• some prior art programs typically referred to as "retirement calculators," require the user to provide estimates of future inflation, interest rates and the expected return on their investments.
• the user is likely, and is in fact encouraged, to simply increase the expected investment returns until their desired portfolio value is achieved.
• one ofthe problems with this type of program is that the user is likely to create an unattainable portfolio based on an unrealistic set of future economic scenarios. That is, the portfolio of financial products required to achieve the X% growth per year in order to meet the user's retirement goal may not be available to the user.
• the idealistic future economic conditions assumed by the user for example, 0% inflation and 20% interest rates, may not be macroeconomically consistent.
• prior art investment packages simply allow the user to manipulate economic conditions until a desired result is achieved rather than encouraging the user to focus on his/her own decisions regarding investment risk, savings rate, and retirement age within the context of realistic economic assumptions. Consequently, the so called "advice" rendered by many ofthe prior art investment software packages can be misleading and impossible to implement in practice.
• investment advice software in the prior art have various other disadvantages which are overcome by the present invention.
• prior art systems typically do not provide realistic estimates ofthe investment or retirement horizon risk- return tradeoff given a user's specific investments and financial circumstances. This makes informed judgments about the appropriate level of investment risk very difficult. Obtaining the appropriate level of investment risk (and return) is critical to the success of a long-term investment plan.
• a financial advisory system that employs advanced financial techniques to provide financial advice to individuals on how to reach specific financial goals. More specifically, it is desirable to provide a system that automatically generates future- looking realistic economic and investment return scenarios and allows a user to arrive at a feasible portfolio that meets both intermediate and long- term financial goals by a process of outcome-based risk profiling. In this manner, the user can focus on his/her own decisions regarding investment risk, savings, and retirement age while interactively observing the impact of those decisions on the range of possible investment outcomes.
• the financial advisory system create a feasible optimal portfolio that maximizes the utility function ofthe user by selecting financial products that are available to the user and that provides the highest possible utility given the user's risk tolerance, investment horizon and savings level.
• utility what is meant is a function that determines the relative preferences of an individual for different combinations of financial products based on one or more characteristics of the products (e.g., expected return, variance, etc.), and optionally one or more parameters specific to the individual.
• a financial advisory system is described.
• return scenarios for optimized portfolio allocations are simulated interactively to facilitate financial product selection.
• Return scenarios for each asset class of a plurality of asset classes are generated based upon estimated future scenarios of one or more economic factors.
• a mapping from each financial product of an available set of financial products onto one or more asset classes ofthe plurality of asset classes is created by determining exposures ofthe available set of financial products to each asset class of the plurality of asset classes. In this way, the expected returns and correlations of a plurality of financial products are generated and used to produce optimized portfolios of financial products.
• Return scenarios are simulated for one or more portfolios including combinations of financial products from the available set of financial products based upon the mapping.
• Figure 1 illustrates a financial advisory system according to one embodiment of the present invention.
• Figure 2 is an example of a typical computer system upon which one embodiment of the present invention can be implemented.
• Figure 3 is a block diagram illustrating various analytic modules according to one embodiment ofthe present invention.
• Figure 4 is a flow diagram illustrating core asset class scenario generation according to one embodiment ofthe present invention.
• Figure 5 is a flow diagram illustrating factor asset class scenario generation according to one embodiment ofthe present invention.
• Figure 6 is a flow diagram illustrating financial product exposure determination according to one embodiment ofthe present invention.
• Figure 7 is a flow diagram illustrating portfolio optimization according to one embodiment of the present invention.
• Figure 8 is a flow diagram illustrating plan monitoring processing according to one embodiment ofthe present invention.
• a financial advisory system is described.
• a factor model approach is laid on top of a pricing kernel model to simulate returns of a plurality of asset classes, and ultimately financial products, such as securities or portfolios of securities.
• financial products refers to a legal representation ofthe right (often denoted as a claim or security) to provide or receive prospective future benefits under certain stated conditions.
• the forecasts may then be used for purposes of providing financial advisory services to a user. For example, such forecasts are useful for selecting the composition of an optimized portfolio (based on a utility function) from a set of available financial products conditional on decisions and constraints provided by the user.
• the core asset classes in combination with additional asset class estimates that are conditioned on the core asset classes comprise a model (hereinafter "the factor model") of a comprehensive set of asset classes that span the universe of typical investment products.
• a factor model is a return-generating function that attributes the return on a financial product, such as a security, to the financial product's sensitivity to the movements of various common economic factors.
• the factor model enables the system to assess how financial products and portfolios will respond to changes in factors or indices to which financial products are exposed.
• the selection of asset classes may be tailored to address a narrow or broad range of investors.
• asset classes may be chosen that are relevant only to a particular industry or asset classes may be chosen to span the market range of a broad set of possible investments (e.g. all available mutual funds or individual equities).
• asset classes selected as factors for the factor model have been chosen to span the range of investments typically available to individual investors in mainstream mutual funds and defined contribution plans.
• financial products available to an investor may be mapped onto the factor model. To assure that a portfolio recommended by the system is attainable, it is preferable to generate investment scenarios that include only those financial products that are available to the investor.
• the available financial products may include, for example, a specific set of mutual funds offered by an employer sponsored 401(k) program.
• this mapping of financial products onto the factor model is accomplished by decomposing the returns of individual financial products into exposures to the asset classes employed by the factor model. In this manner, the system learns how each of the financial products available to the user behave relative to the asset classes employed by the factor model. In so doing, the system implicitly determines the constraints on feasible exposures to different asset classes faced by an investor given a selected subset of financial products. Given this relationship between the user's available financial products and the factor model, the system may generate feasible forward-looking investment scenarios.
• the system may further advise the user regarding actions that may be taken (e.g., save more money, retire later, take on additional investment risk, seek opportunities to expand the investment set) to achieve certain financial goals, such as particular retirement standard of living, accumulating a down payment for the purchase of a house, or saving enough money to send a child to college.
• actions that may be taken e.g., save more money, retire later, take on additional investment risk, seek opportunities to expand the investment set
• certain financial goals such as particular retirement standard of living, accumulating a down payment for the purchase of a house, or saving enough money to send a child to college.
• the present invention includes various steps, which will be described below.
• the steps ofthe present invention may be embodied in machine-executable instructions.
• the instructions can be used to cause a general-purpose or special-purpose processor that is programmed with the instructions to perform the steps ofthe present invention.
• the steps ofthe present invention may be performed by specific hardware components that contain hardwired logic for performing the steps, 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, magnet or optical cards, flash memory, 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 to a requesting computer 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).
• the present invention may be included within a client-server transaction based financial advisory system 100 such as that illustrated in Figure 1.
• the financial advisory system 100 includes a financial staging server 120, a broadcast server 115, a content server 117, an AdviceServerTM 1 10 (AdviceServerTM is a trademark of Financial Engines, Inc., the assignee ofthe present invention), and a client 105.
• AdviceServerTM is a trademark of Financial Engines, Inc., the assignee ofthe present invention
• the financial staging server 120 may serve as a primary staging and validation area for the publication of financial content.
• the financial staging server 120 acts as a data warehouse.
• Raw source data typically time series data
• the financial staging server 120 converts raw time series data obtained from data vendors from the specific vendor's format into a standard format that can be used throughout the financial advisory system 100.
• Various financial engines may be run to generate data for validation and quality assurance ofthe data received from the vendors. Additional engines may be run to generate module inputs, model parameters, and intermediate calculations needed by the system based on raw data received by the vendors. Any calibrations ofthe analytic data needed by the financial engines may be performed prior to publishing the final analytic data to the broadcast server 115.
• the broadcast server 1 15 is a database server. As such, it runs an instance of a Relational Database Management System (RDBMS), such as Microsoft SQL-ServerTM, OracleTM or the like.
• RDBMS Relational Database Management System
• the broadcast server 115 provides a single point of access to all fund information and analytic data. When advice servers such as AdviceServer 110 need data, they may query information from the broadcast server database. The broadcast server 115 may also populate content servers, such as content server 1 17, so remote implementations ofthe AdviceServer 110 need not communicate directly, with the broadcast server 115.
• the AdviceServer 1 10 is the primary provider of services for the client 105.
• the AdviceServer 110 also acts as a proxy between external systems, such as external system 125, and the broadcast server 115 or the content server 1 17.
• the AdviceServer 110 is the central database repository for holding user profile and portfolio data. In this manner, ongoing portfolio analysis may be performed and alerts may be triggered, as described further below.
• the user may interact with and receive feedback from the financial advisory system 100 using client software which may be running within a browser application or as a standalone desktop application on the user's personal computer 105.
• the client software communicates with the AdviceServer 110 which acts as a HTTP server.
• the user may provide information regarding risk preferences, savings preferences, current age, gender, income, expected income growth, current account balances, current financial product holdings, current savings rate, retirement age goal, retirement income goals, available financial products, intermediate and long-term goals, constraints on fund holdings, liabilities, expected contributions, state and federal tax bracket (marginal and average).
• the user may provide information for themselves and each profiled person in their household. This information may be saved in one or more files in the financial advisory system 100, preferably on one ofthe servers to allow ongoing plan monitoring to be performed. In other embodiments ofthe present invention additional information may be provided by the user, for example, estimates of future social security benefits or anticipated inheritances.
• the system may forecast a retirement income and graphically depict the current portfolio's projected growth and range of possible values over time.
• the system may also provide the user with statistics regarding the likelihood that they will be able to retire when they would like, given the projected returns on the user's current portfolio based upon the data input by the user, including the user's current savings rate, retirement age goal, and investment holdings.
• the financial advisory system 100 may provide an initial diagnosis based upon the user's risk preference, savings rate, and desired risk-return tradeoffs. This diagnosis can result in a series of suggested actions including: (1) rebalance the portfolio, (2) increase savings, (3) retire later, or (4) adjust investment risk.
• An iterative process may then begin in which the user may adjust his/her investment risk, savings rate, and/or retirement age and have the financial advisory system 100 evaluate the projected performance of an optimized portfolio given the financial products available to the user based on the currently selected risk tolerance, investment horizon and savings rate decisions.
• This process ofthe financial advisory system 100 providing advice and/or feedback and the user adjusting risk, savings, and retirement age parameters may continue until the user has achieved a desired portfolio forecast and performance distribution. At this time, the user may chose to implement the optimal portfolio. The parameters and portfolio allocation may then be saved by the financial advisory system 100 for future user sessions.
• the financial advisory system 100 may evaluate the user's portfolio against one or more financial goals and may notify the user if progress towards any of the goals has changed in a material way.
• the user's data e.g., the user's profile information, account holdings, plan parameters, and tax information
• the current forecast for the one or more goals may be presented to the user.
• the ongoing plan monitoring has generated any alerts, they may be presented to the user at this time.
• alerts may be generated proactively by the system and transmitted to the user via a telephone, email, fax, or standard mail messaging system.
• the user may again begin the iterative process of adjusting the decision variables described above (e.g., risk level, savings rate, and retirement age) until the user is satisfied with the likelihood of meeting his/her goal(s).
• the decision variables described above e.g., risk level, savings rate, and retirement age
• the user may simply modify the data upon which the financial advisory system's assumptions are based. For example, if the user's salary increases, this information should be updated in the user's profile. Additionally, if the user's employer adds a new mutual fund to the company's 401 (k) program, then the user should update the list of available financial products in the user profile information.
• the financial advisory system 100 may be connected to external record-keeping systems at the user's employer that can provide automatic updates to selected user information.
• the user is never asked to predict the future with regard to interest rates, inflation, expected portfolio returns, or other difficult to estimate economic variables and parameters.
• the optimal portfolio generated by the financial advisory system 100 is guaranteed to be attainable. That is, the optimal portfolio has been determined based upon the specific financial products that are available to the user.
• Computer system 200 representing an exemplary client 105 or server in which features ofthe present invention may be implemented will now be described with reference to Figure 2.
• Computer system 200 comprises a bus or other communication means 201 for communicating information, and a processing means such as processor 202 coupled with bus 201 for processing information.
• Computer system 200 further comprises a random access memory (RAM) or other dynamic storage device 204 (referred to as main memory), coupled to bus 201 for storing information and instructions to be executed by processor 202.
• Main memory 204 also may be used for storing temporary variables or other intermediate information during execution of instructions by processor 202.
• Computer system 200 also comprises a read only memory (ROM) and/or other static storage device 206 coupled to bus 201 for storing static information and instructions for processor 202.
• a data storage device 207 such as a magnetic disk or optical disc and its corresponding drive may also be coupled to computer system 200 for storing information and instructions.
• Computer system 200 can also be coupled via bus 201 to a display device 221, such as a cathode ray tube (CRT) or Liquid Crystal Display (LCD), for displaying information to a computer user.
• a display device 221 such as a cathode ray tube (CRT) or Liquid Crystal Display (LCD)
• CTR cathode ray tube
• LCD Liquid Crystal Display
• graphical depictions of expected portfolio performance, asset allocation for an optimal portfolio, charts indicating retirement age probabilities, and other data types may be presented to the user on the display device 221.
• an alphanumeric input device 222 may coupled to bus 201 for communicating information and/or command selections to processor 202.
• cursor control 223, such as a mouse, a trackball, or cursor direction keys for communicating direction information and command selections to processor 202 and for controlling cursor movement on display 221.
• a communication device 225 is also coupled to bus 201 for accessing remote servers, such as the AdviceServer 1 10, or other servers via the Internet, for example.
• the communication device 225 may include a modem, a network interface card, or other well known interface devices, such as those used for coupling to an Ethernet, token ring, or other types of networks.
• the computer system 200 may be coupled to a number of clients and/or servers via a conventional network infrastructure, such as a company's Intranet and/or the Internet, for example.
• FIG. 3 is a simplified block diagram illustrating exemplary analytic modules of the financial advisory system 100 according to one embodiment ofthe present invention. According to the embodiment depicted, the following modules are provided: a pricing module 305, a factor module 310, a financial product mapping module 315, a tax adjustment module 320, an annuitization module 325, a simulation processing module 330, a portfolio optimization module 340, a user interface (UI) module 345, and a plan monitoring module 350. It should be appreciated that the functionality described herein may be implemented in more or less modules than discussed below.
• modules and functionality may be distributed in various configurations among a client system, such as client 105 and one or more server systems, such as the financial staging server 120, the broadcast server 115, or the AdviceServer 1 10.
• client system such as client 105
• server systems such as the financial staging server 120, the broadcast server 115, or the AdviceServer 1 10.
• the functionality of each ofthe exemplary modules will now be briefly described.
• An “econometric model” is a statistical model that provides a means of forecasting the levels of certain variables refe ⁇ ed to as “endogenous variables,” conditional on the levels of certain other variables, known as “exogenous variables,” and in some cases previously determined values ofthe endogenous variables (sometimes referred to as lagged dependent variables).
• the pricing module 305 is an equilibrium econometric model for forecasting prices and returns (also referred to herein as “core asset scenarios”) for a set of core asset classes.
• the pricing module provides estimates of current levels and forecasts of economic factors (also known as state variables), upon which the estimates of core asset class returns are based.
• the economic factors may be represented with three exogenous state variables, price inflation, a real short-term interest rate, and dividend growth.
• the three exogenous state variables may be fitted with autoregressive time series models to match historical moments ofthe corresponding observed economic variables, as described further below.
• the resulting core asset classes are the foundation for portfolio simulation and are designed to provide a coherent and internally consistent (e.g., no arbitrage) set of returns. By arbitrage what is meant is an opportunity to create a profitable trading opportunity that involves no net investment and positive values in all states ofthe world.
• the core asset classes include short-term US government bonds, long-term US government bonds, and US equities.
• additional asset classes may be incorporated into the pricing module 305 or the additional asset classes may be included in the factor model 310 and be conditioned on the core asset classes, as discussed further below.
• the factor module 310 Based upon the core asset scenarios generated by the pricing module 305, the factor module 310 produces return scenarios (also refe ⁇ ed to herein as "factor model asset scenarios") for a set of factor asset classes that are used for both exposure analysis, such as style analysis, and the simulation of portfolio returns.
• the additional asset classes, refe ⁇ ed to as factors, represented in the factor model are conditional upon the core asset class return scenarios generated by the pricing module 305.
• these additional factors may co ⁇ espond to a set of asset classes or indices that are chosen in a manner to span the range of investments typically available to individual investors in mainstream mutual funds and defined contribution plans.
• the factors may be divided into the following groups: cash, bonds, equities, and foreign equities.
• the equities group may further be broken down into two different broad classifications (1) value versus growth and (2) market capitalization.
• Growth stocks are basically stocks with relatively high prices relative to their underlying book value (e.g., high price-to-book ratio).
• value stocks have relatively low prices relative to their underlying book value.
• market capitalization stocks may be divided into groups of large, medium, and small capitalization. An exemplary set of factors is listed below in Table 1.
• Table 1 At this point it is important to point out that more, less, or a completely different set of factors may be employed depending upon the specific implementation.
• the factors listed in Table 1 are simply presented as an example of a set of factors that achieve the goal of spanning the range of investments typically available to individual investors in mainstream mutual funds and defined contribution plans. It will be apparent to those of ordinary skill in the art that alternative factors may be employed.
• factors that represent functions ofthe underlying asset classes for pricing of securities that are nonlinearly related to the prices of certain asset classes (e.g., derivative securities).
• additional factors may be relevant to span a broader range of financial alternatives, such as industry specific equity indices.
• the financial product mapping module 315 maps financial product returns onto the factor model.
• the process of mapping financial product returns onto the factor model comprises decomposing financial product returns into exposures to the factors.
• the mapping indicates how the financial product returns behave relative to the returns ofthe factors.
• the financial product mapping module 315 is located on one ofthe servers (e.g., the financial staging server 120, the broadcast server 115, or the AdviceServer 110). In alternative embodiments, the financial product mapping module 315 may be located on the client 105.
• an external approach refe ⁇ ed to as "returns-based style analysis” is employed to determine a financial product's exposure to the factors.
• the approach is refe ⁇ ed to as external because it does not rely upon information that may be available only from sources internal to the financial product. Rather, in this embodiment, typical exposures ofthe financial product to the factors may be established based simply upon realized returns of a financial product, as described further below.
• returns-based style analysis see Sharpe, William F. "Determining a Fund's Effective Asset Mix,” Investment Management Review, December 1988, pp. 59-69 and Sharpe, William F. “Asset Allocation: Management Style and Performance Measurement," The Journal of Portfolio Management, 18, no. 2 (Winter 1992), pp. 7-19 (“Sharpe [1992]”).
• Alternative approaches to determining a financial product's exposure to the factors include surveying the underlying assets held in a financial product (e.g. a mutual fund) via information filed with regulatory bodies, categorizing exposures based on standard industry classification schemes (e.g. SIC codes), identifying the factors exposures based on analysis ofthe structure ofthe product (e.g. equity index options, or mortgage backed securities), and obtaining exposure information based on the target benchmark from the asset manager ofthe financial product.
• the primary function ofthe process is to determine the set of factor exposures that best describes the performance ofthe financial product.
• the tax adjustment module 320 takes into account tax implications of the fmancial products and financial circumstances ofthe user.
• the tax adjustment module 320 may provide methods to adjust taxable income and savings, as well as estimates for future tax liabilities associated with early distributions from pension and defined contribution plans, and defe ⁇ ed taxes from investments in qualified plans.
• the returns for financial products held in taxable investment vehicles e.g. a standard brokerage account
• the component of returns attributable to dividend income should be taxed at the user's income tax rate and the component of returns attributable to capital gains should be taxed at an appropriate capital gains tax rate depending upon the holding period.
• the tax module 320 may forecast future components ofthe financial products total return due to dividend income versus capital gains based upon one or more characteristics ofthe financial products including, for example, the active or passive nature ofthe financial product's management, turnover ratio, and category of financial product. This allows precise calculations incorporating the specific tax effects based on the financial product and financial circumstances ofthe investor.
• the tax module 320 facilitates tax efficient investing by determining optimal asset allocation among taxable accounts (e.g., brokerage accounts) and nontaxable accounts (e.g., an Individual Retirement Account (IRA), or employer sponsored 401(k) plan). In this manner the tax module 320 is designed to estimate the tax impact for a particular user with reference to that particular user's income tax rates, capital gains rates, and available financial products.
• taxable accounts e.g., brokerage accounts
• nontaxable accounts e.g., an Individual Retirement Account (IRA), or employer sponsored 401(k) plan
• the tax module 320 produces tax-adjusted returns for each available financial product and tax-adjusted distributions for each available financial product.
• the portfolio optimization module 340 calculates the utility maximizing set of financial products under a set of constraints defined by the user and the available feasible investment set. In one embodiment, the calculation is based upon a mean-variance optimization ofthe financial products.
• the constraints defined by the user may include bounds on asset class and/or specific financial product holdings.
• users can specify intermediate goals such as buying a house or putting a child through college, for example, that are incorporated into the optimization. In any event, importantly, the optimization explicitly takes into account the impact of future contributions and expected withdrawals on the optimal asset allocation.
• the covariance matrix used during optimization is calculated based upon the forecasts of expected returns for the factors generated by the factor module 310 over the investment time horizon.
• the portfolio optimization module 340 may explicitly take into account the impact of different investment horizons, including the horizon effects impact from intermediate contributions and withdrawals.
• the simulation processing module 330 provides additional analytics for the processing of raw simulated return scenarios into statistics that may be displayed to the user via the UI 345. In the one embodiment ofthe present invention, these analytics generate statistics such as the probability of attaining a certain goal, or the estimated time required to reach a certain level of assets with a certain probability.
• the simulation processing module 330 also incorporates methods to adjust the simulated scenarios for the effects induced by sampling e ⁇ or in relatively small samples.
• the simulation processing module 330 provides the user with the ability to interact with the portfolio scenarios generated by the portfolio optimization module 340 in real-time.
• the annuitization module 325 provides a meaningful way of representing the user's portfolio value at the end ofthe term of the investment horizon. Rather than simply indicating to the user the total projected portfolio value, one standard way of conveying the information to the user is converting the projected portfolio value into a retirement income number.
• the projected portfolio value at retirement may be distributed over the length of retirement by dividing the projected portfolio value by the length of retirement. More sophisticated techniques may involve determining how much the projected portfolio value will grow during retirement and additionally consider the effects of inflation. In either event, however, these approaches e ⁇ oneously assume the length of the retirement period is known in advance.
• this retirement income number represents the inflation adjusted income that would be guaranteed by a real annuity purchased from an insurance company or synthetically created via a trading strategy involving inflation-indexed treasury bond securities. In this manner, the mortality risk is taken out ofthe picture because regardless of the length of the retirement period, the user would be guaranteed a specific annual real income.
• standard methods of annuitization employed by insurance companies may be employed. Additionally, mortality probabilities for an individual of a given age, risk profile, and gender may be based on standard actuarial tables used in the insurance industry.
• Calculating the value of an inflation- adjusted annuity value may involve estimating the appropriate values of real bonds of various maturities.
• the pricing module 305 generates the prices of real bonds used to calculate the implied real annuity value ofthe portfolio at the investment horizon.
• plan monitoring module 350 a mechanism is provided for alerting the user of the occu ⁇ ence of various predetermined conditions involving characteristics ofthe recommended portfolio. Because the data upon which the portfolio optimization module 340 depends is constantly changing, it is important to reevaluate characteristics ofthe recommended portfolio on a periodic basis so that the user may be notified in a timely manner when there is a need for him/her to take affirmative action, for example.
• the plan monitoring module 350 is located on the AdviceServer 1 10. In this manner, the plan monitoring module 350 has constant access to the user profile and portfolio data.
• the occu ⁇ ence of two basic conditions may cause the plan monitoring module 350 to trigger a notification or alert to the user.
• the first condition that may trigger an alert to the user is the current probability of achieving a goal falling outside of a predetermined tolerance range ofthe desired probability of a achieving the particular goal.
• a goal is a financial goal, such as a certain retirement income or the accumulation of a certain amount of money to put a child though college, for example.
• the plan monitoring module 350 may alert the user even if the cu ⁇ ent probability of achieving the financial goal is within the predetermined tolerance range if a measure ofthe currently recommended portfolio's utility has fallen below a predetermined tolerance level.
• Various other conditions are contemplated that may cause alerts to be generated.
• the user may receive an indication that he/she should rebalance the portfolio.
• Plan monitoring processing exemplary real world events that may lead to the above-described alert conditions, and additional alert conditions are described further below.
• the UI module 345 provides mechanisms for data input and output to provide the user with a means of interacting with and receiving feedback from the financial advisory system 100, respectively. Further description of a UI that may be employed according to one embodiment ofthe present invention is disclosed in U.S. Patent Nos. 5,918,217 and 6,012,044, both entitled "USER INTERFACE FOR FINANCIAL ADVISORY SYSTEM," the contents of which are hereby incorporated by reference.
• Other modules may be included in the financial advisory system 100 such as a pension module and a social security module.
• the pension module may be provided to estimate pension benefits and income.
• the social security module may provide estimates ofthe expected social security income that an individual will receive upon retirement. The estimates may be based on calculations used by the Social Security Administration (SSA), and on probability distributions for reductions in the cu ⁇ ent level of benefits.
• SSA Social Security Administration
• Figure 4 is a flow diagram illustrating core asset class scenario generation according to one embodiment ofthe present invention.
• core assets include short-term US government bonds, long-term US government bonds, and US equities.
• the state variables may include general economic factors, such as inflation, interest rates, dividend growth, and other variables.
• state variables are described by econometric models that are estimated based on observed historical data.
• these parameters are used to generate simulated values for the state variables.
• the process begins with a set of initial conditions for each ofthe state variables. Subsequent values are generated by iterating the state variable function to generate new values conditional on previously determined values and a randomly drawn innovation term.
• the state variable functions may be deterministic rather than stochastic.
• the randomly drawn innovation terms for the state variable functions may be co ⁇ elated with a fixed or conditional covariance matrix.
• returns for core asset classes are generated conditional on the values ofthe state variables.
• Returns of core asset classes may be described by a function of a constant, previously determined core asset class returns, previously determined values of the state variables, and a random innovation term. Subsequent values are generated by iterating a core asset class function to generate new values conditional on previously determined values and a random draws ofthe innovation term.
• the core asset class functions may be deterministic rather than stochastic. In general, the randomly drawn innovation terms for the core asset class functions may be correlated with a fixed or conditional covariance matrix. In alternative embodiments, steps 410 and 420 may be omitted and the core asset class returns may be generated directly in an unconditional manner.
• a simple example of such a model would be a function consisting of a constant and a randomly drawn innovation term.
• a prefe ⁇ ed approach would jointly generate core asset class returns based on a model that incorporates a stochastic process (also refe ⁇ ed to as a pricing kernel) that limits the prices on the assets and payoffs in such a way that no arbitrage is possible.
• a stochastic process also refe ⁇ ed to as a pricing kernel
• a scenario in this context is a set of projected future values for factors.
• US_Stocks is a core asset class representing the returns estimated by the pricing module 305 for US stocks at time t.
• a j is a constant representing the average returns of factor asset class i relative to the core asset class exposures ("factor alpha").
• ⁇ . is a residual random variable representing the returns of factor asset class i that are not explained by the core asset class exposures ("residual variance").
• the beta coefficients (also refe ⁇ ed to as the loadings or slope coefficients) for each of the core asset classes are determined.
• a regression is run to estimate the values ofthe beta coefficients.
• the regression methodology may or may not include restrictions on the sign or magnitudes of the estimated beta coefficients.
• the coefficients may be restricted to sum to one. However, in other embodiments, there may be no restrictions placed on the estimated beta coefficients.
• the alpha estimated by the regression is not used for generating the factor model asset scenarios. Estimates of alpha based on historical data are extremely noisy because the variance ofthe expected returns process is quite high relative to the mean. Based on limited sample data, the estimated alphas are poor predictors of future expected retums.
• a novel way of estimating the alpha coefficients that reduces the probability of statistical e ⁇ or is used in the calibration ofthe factor model. This process imposes macroconsistency on the factor model by estimating the alpha coefficients relative to a known efficient portfolio, namely the Market Portfolio. Macroconsistency is the property that expected returns for the factor asset classes are consistent with an observed market equilibrium, that is estimated returns will result in markets clearing under reasonable assumptions.
• the Market Portfolio is the portfolio defined by the aggregate holdings of all asset classes. It is a portfolio consisting of a value- weighted investment in all factor asset classes. Therefore, in the present example, macroconsistency may be achieved by setting the proportion invested in each factor equal to the percentage ofthe total market capitalization represented by the particular factor asset class.
• a reverse optimization may be performed to determine the implied factor alpha for each factor based upon the holdings in the Market Portfolio. This procedure determines a set of factor alphas that guarantee consistency with the observed market equilibrium.
• Quadratic Programming QP is employed to maximize the following utility function:
• E(r) represents expected retums for the asset classes
• C(r) represents the covariance matrix for the asset class returns
• T Tau
• X is a matrix representing the proportionate holdings of each asset class of an optimal portfolio comprising the asset classes, and u is a vector of all ones.
• C(r) may be estimated from historical returns data or more advantageously may be estimated from projected returns generated by a pricing kernel model.
• Quadratic Programming is a technique for solving an optimization problem involving a quadratic (squared terms) objective function with linear equality and or inequality constraints.
• QP Quadratic Programming
• Equation #2 when QP is called for, an approach refe ⁇ ed to as an "active set” method is employed herein.
• the active set method is explained in Gill, Mu ⁇ ay, and Wright, “Practical Optimization,” Academic Press, 1981, Chapter 5.
• the first order conditions for the optimization of Equation #2 are:
• E(r) 2 C(r )- + Ku (EQ #3) r
• K is a Lagrange multiplier
• factor returns may be generated based upon the estimated alphas from step 520 and the estimated beta coefficients from step 510.
• factor model asset scenarios as are desired may be generated using Equation #1 and random draws for the innovation valuer .
• a random value fors is selected for each evaluation of Equation #1.
• ⁇ t is distributed as a standard normal variate. In other words ⁇ _ is drawn from a standard normal distribution with a mean of 0 and a standard deviation of 1.
• the financial product exposure determination module 315 computes the factor asset class exposures for a particular fund via a nonlinear estimation procedure.
• the exposure estimates, Sf n are called style coefficients, and are generally restricted to the range [0,1] and to sum to one. In other embodiments, these restrictions may be relaxed (for example, with financial products that may involve short positions, the coefficients could be negative).
• Alpha may be thought of as a measure ofthe relative under or over performance of a particular fund relative to its passive style benchmark.
• the goal is to take any individual group of assets that people might hold, such as a group of mutual funds, and map those assets onto the factor model, thus allowing portfolios to be simulated forward in time.
• this mapping is achieved with what is referred to as "returns-based style analysis” as described in Sharpe [1992], which is hereby incorporated by reference.
• style analysis refers to determining a financial product's exposure to changes in the returns of a set of major asset classes using Quadratic Programming or similar techniques.
• Figure 6 is a flow diagram illustrating a method of determining a financial product's exposures to factor asset class returns according to one embodiment ofthe present invention.
• the historical returns for one or more financial products to be analyzed are received.
• the financial product exposure module 315 may reside on a server device and periodically retrieve the historical return data from a historical database stored in another portion ofthe same computer system, such as RAM, a hard disk, an optical disc, or other storage device.
• the financial product exposure module 325 may reside on a client system and receive the historical return data from a server device as needed.
• factor asset class returns are received.
• step 630 QP techniques or the like are employed to determine estimated exposures (the S coefficients) to the factor asset class returns.
• expected future alpha is determined for each subperiod ofthe desired scenario period.
• mutual funds or related financial products for example, historical alpha alone is not a good estimate of future alpha. That is, a given mutual fund or related financial product will not continue to outperform/under perform its peers indefinitely into the future. Rather, empirical evidence suggests that over performance may partially persist over one to two years while under performance may persist somewhat longer (see for example, Carhart, Mark M. "On Persistence in Mutual Fund Performance.” Journal of Finance, March 1997, Volume 52 No. l- pp.57-82).
• future alpha may depend upon a number of factors, such as turnover, expense ratio, and historical alpha.
• factors such as turnover, expense ratio, and historical alpha.
• one or more of these factors may be more or less important for particular types of funds.
• it is much more costly to buy and sell in emerging markets as compared to the market for large capitalization US equities.
• bond turnover can be achieved at a much lower cost, therefore, turnover has much less affect on the future alpha of a bond fund than an equity fund. Consequently, the penalty for turnover may be higher for emerging market funds compared to large cap U.S. equities and bond funds.
• Improved results may be achieved by taking into account additional characteristics ofthe fund, such as the fact that the fund is an index fund and the size ofthe fund as measured by total net assets, for example.
• a more sophisticated model is employed for determining future alpha for each fund: where, hast is the baseline prediction for future Alpha ofthe fund p , Rho, governs the speed of decay from a hlslonca , to a base a h ⁇ x i o n ca i ls Alpha estimated in Equation #4
• a b0se C+ ⁇ ] Expense_Ratio + ⁇ 2 Turnover + ⁇ i Fund_Size (EQ #6) where the parameters are estimated separately for each of four different classes of funds: US equity, foreign equity, taxable bond, nontaxable bond.
• These parameters may be estimated using conventional econometric techniques, such as ordinary least squares (OLS).
• Rho is estimated by first calculating historical deviations from a base ("residual alpha") and then estimating Rho as the first order serial co ⁇ elation ofthe residual alpha series.
• Portfolio optimization is the process of determining a set of financial products that maximizes the utility function of a user.
• portfolio optimization processing assumes that users have a mean-variant utility function, namely, that people like having more wealth and dislike volatility of wealth. Based on this assumption and given a user's risk tolerance, the portfolio optimization module 340 calculates the mean-variance efficient portfolio from the set of financial products available to the user.
• constraints defined by the user may also be taken into consideration by the optimization process. For example, the user may indicate a desire to have a certain percentage of his/her portfolio allocated to a particular financial product.
• the optimization module 340 determines the allocation among the unconstrained financial products such that the recommended portfolio as a whole accommodates the user's constraint(s) and is optimal for the user's level of risk tolerance.
• Prior art mean-variant portfolio optimization traditionally treats the problem as a single period optimization.
• the portfolio optimization problem is structured in such as way that it may explicitly take into account the impact of different investment horizons and the impact of intermediate contributions and withdrawals. Further the problem is set up so that it may be solved with QP methods. Refe ⁇ ing now to Figure 7, a method of portfolio optimization according to one embodiment ofthe present invention will now be described.
• information regarding expected withdrawals is received. This information may include the dollar amount and timing ofthe expected withdrawal.
• information regarding expected future contributions is received. According to one embodiment, this information may be in the form of a savings rate expressed as a percentage ofthe user's gross income or alternatively a constant or variable dollar value may be specified by the user.
• step 730 information regarding the relevant investment time horizon is received.
• the time horizon might represent the user's desired retirement age.
• step 740 information regarding the user's risk tolerance, Tau, is received.
• the mean- variance efficient portfolio is determined.
• Xi represents the recommended constant proportion of each net contribution that should be allocated to financial product i. represents the net contribution at time t
• Rji represents the expected returns for financial product i in year j
• n is the number of financial products that are available for optimization
• g is the value of constrained assets for a given scenario
• any individual asset return may be composed of a static or dynamic strategy involving one or more financial products.
• one ofthe assets may itself represent a constant rebalanced strategy over a group of financial products.
• any dynamic strategy that can be formulated as an algorithm may be incorporated into the portfolio optimization. For example, an algorithm which specifies risk tolerance which decreases with the age ofthe user could be implemented. It is also possible to incorporate path dependent algorithms (e.g., portfolio insurance).
• Equation #8 contributions are made from the cu ⁇ ent year to the year prior to retirement. Typically, a contribution made at time t will be invested from time t until retirement. An exception to this would be if a user specifies a withdrawal, in which case a portion ofthe contribution may only be held until the expected withdrawal date.
• the pre- and post-settlement, total values are governed by the pair of equations:
• W + (t) W-(t) + C(t) + D(t) - L(t) - S(t), O ⁇ t ⁇ T.
• C(t) is the nominal contribution to the account at time "t”
• D(t) is the total of all distributed "dividends”
• L(t) is the "leakage”
• S(t) is the "shrinkage”
• W + (T) is the final horizon wealth after all taxes have been paid.
• D(t) the total of all distributed dividends, is the sum ofthe positive distributions:
• L(t) is the total amount of dollars paid in loads
• L;(t) is the number of dollars paid in loads on just the i-th asset.
• the equation for the "shrinkage" S(t), the total amount paid in taxes, has two terms.
• the first term is the tax on distributions and is multiplied by the marginal tax-rate; the second term is the tax on capital gains and is multiplied by the capital gains tax-rate.
• non-taxable accounts we choose non-taxable accounts as a baseline. If all the funds in a non-taxable account were converted to an annuity, and the annuity payments were taken as withdrawals, then the withdrawals would mimic a salary subject to income taxes. This is precisely the client's pre-retirement situation. Before aggregating a taxable account, we scale its "after-tax" value to this baseline using the formula:
• the baseline equivalent is obtained by grossing up values using the average tax-rate.
• Eq.(24a) is the evolution equation for a single asset with the effective return.
• Eq.(24b) is an implicit equation for the effective return R e (t) in terms ofthe asset retums R j (t).
• V ⁇ (W, , ⁇ ) E 0 W* T ) - E 0 (W, ,T ) 2 but
• W r ⁇ .T 2 exp ⁇ ⁇ a + bX j+ + c ⁇ j+l + d ⁇ J+l + eX j + fTL j + g ⁇ j
• the same technique can be used with a simple redefinition ofthe constants to be twice their original values.
• the covariance between any two core assets can be calculated by simply adding co ⁇ esponding constants and repeating the same technique.
• the effective annual covariance between returns on asset i and returns on asset j are calculated as: (Note, the weights, ⁇ > ⁇ , are between zero and one, and sum to one.)
• this annualizing technique could be personalized for a given user's situation.
• the user's horizon could specify T, and their level of cu ⁇ ent wealth and future contributions could specify the relevant weights.
• the real world events include the following: (1) a financial product's style exposure changes, (2) the market value ofthe user's assets have changed in a significant way, (3) new financial products become available to the user, (4) the risk characteristics ofthe user's portfolio have deviated from the desired risk exposure, or (5) the currently recommended portfolio no longer has the highest expected return for the cu ⁇ ent level of portfolio risk (e.g., the portfolio is no longer on the mean-variance efficient frontier).
• An efficient frontier is the sets of assets (portfolios) that provide the highest level of return over different levels of risk. At each point on the efficient frontier, there is no portfolio that provides a higher expected return for the same or lower level of risk.
• the inefficiency is greater than a predetermined tolerance or if the inefficiency will substantially impact one ofthe user's fmancial goals, such as his/her retirement income goal, then the user is notified that he/she should rebalance the portfolio.
• the plan monitoring module 350 may not alert the user.
• the predefined tolerance depends upon the impact ofthe inefficiency on expected wealth.
• the tolerance could depend upon relevant transaction costs.
• a significant change in the market value ofthe user's assets may affect one or both ofthe probability of achieving a financial goal and the cu ⁇ ent risk associated with the portfolio.
• the portfolio may no longer be within a predetermined probability tolerance of achieving one or more financial goals.
• the risk associated with the portfolio may also have changed significantly. Either of these conditions may cause the user to be notified that changes are required in the portfolio allocation or decision variables to compensate for the reduction in market value ofthe portfolio.
• a large increase in the value ofthe user's portfolio could trigger an alert due to the increase in the probability of achieving one or more financial goals or due to the altered risk associated with the newly inflated portfolio.
• the user may be alerted by the plan monitoring module 350 if, for example, a higher expected return may be possible at lower risk as a result of diversifying the cu ⁇ ent portfolio to include one or more ofthe newly available financial products.
• exemplary plan monitoring processing will now be described with respect to Figure 8.
• the data needed for reevaluating the cu ⁇ ent portfolio and for determining a cu ⁇ ent optimal portfolio is retrieved, such as the user profile and portfolio data which may be stored on the AdviceServer 110, for example.
• the user profile may include investment plan profile information stored during a previous session, such as the probability of reaching one or more financial goals, the risk ofthe portfolio, and the like.
• selected user information on the AdviceServer 1 10 may be kept up to date automatically if the financial advisory system 100 has access to the record-keeping systems ofthe user's employer. Alternatively, selected user information may be updated manually by the user.
• a cu ⁇ ent optimal portfolio is determined, as described above.
• changes to the user database and/or portfolio data are taken into consideration. For example, if one or more new financial products have become available to the user, portfolios including the one or more new financial products are evaluated.
• the cu ⁇ ent portfolio is evaluated in a number of different dimensions to determine if any trigger conditions are satisfied. For example, if the increase in expected wealth, or the increase in the probability of reaching one or more investment goals resulting from a reallocation to the cu ⁇ ent optimal portfolio is above a predetermined tolerance, then processing will continue with step 840. Additionally, if the risk ofthe cu ⁇ ent portfolio is substantially different from the investment plan profile or if the probability of achieving one or more financial goals is substantially different from the investment plan profile, then processing continues with step 840.
• advice processing is performed.
• the system may offer advice regarding which decision variable should be modified to bring the portfolio back on track to reach the one or more financial goals with the desired probability.
• the system may recommend a reallocation to improve efficiency ofthe portfolio.
• An alert may be generated to notify the user ofthe advice and/or need for affirmative action on his/her part. As described above, the alert may be displayed during a subsequent user session with the financial advisory system 100 and/or the alerts may be transmitted immediately to the user by telephone, fax, email, pager, fax, or similar messaging system.
• the plan monitoring module 350 performs ongoing portfolio evaluation to deal with the constantly changing data that may ultimately affect the exposure determination process and the portfolio optimization process.
• the user may receive timely advice instructing him/her how to most efficiently achieve one or more financial goals and/or maintain one or more portfolio characteristics based upon the available set of financial products.

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