WO2001027844A1  Investment analysis and management system for generating financial advice  Google Patents
Investment analysis and management system for generating financial adviceInfo
 Publication number
 WO2001027844A1 WO2001027844A1 PCT/US2000/028208 US0028208W WO2001027844A1 WO 2001027844 A1 WO2001027844 A1 WO 2001027844A1 US 0028208 W US0028208 W US 0028208W WO 2001027844 A1 WO2001027844 A1 WO 2001027844A1
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 goal
 risk
 user
 system
 portfolio
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 G—PHYSICS
 G06—COMPUTING; CALCULATING; COUNTING
 G06Q—DATA PROCESSING SYSTEMS OR METHODS, SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL, SUPERVISORY OR FORECASTING PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL, SUPERVISORY OR FORECASTING PURPOSES, NOT OTHERWISE PROVIDED FOR
 G06Q40/00—Finance; Insurance; Tax strategies; Processing of corporate or income taxes
 G06Q40/04—Exchange, e.g. stocks, commodities, derivatives or currency exchange
Abstract
Description
INVESTMENT ANALYSIS AND MANAGEMENT
SYSTEM FOR GENERATING FINANCIAL ADVICE
Technical Field
This invention relates to a method and apparatus for identifying a financial objective, identifying current investments and assets and for determining an investment strategy for achieving the financial objective.
Background
Investors in stocks, mutual funds, bonds and other financial instruments have broadened substantially to include many individuals who formerly relied primarily on interest bearing savings accounts. These individuals generally have specific goals, such as saving for retirement, for college tuition, or for a house down payment. Such individuals usually lack the time necessary for learning how to select from the large number of investment opportunities or for conducting a full analysis of alternative investment strategies. One particular need is for a user friendly computer based system which can analyze an individual's current investment position, identify the individual's degree of risk aversion, and, knowing the individual's goals, provide a recommended investment strategy for meeting those goals. Summary of the Invention
It is an object of the present invention to provide a computer based system that a user can access to obtain a recommended investment strategy for meeting specified goals. It is a further object to provide a computer based system which solicits information from an individual on current investments, risk aversion and goals and generates in response a simulation of future returns on various investments and provides recommendations for investments most likely to achieve the goals.
It is a further object to provide a computer based system which can implement the recommendations for achieving the goals, and over time, monitor progress toward meeting those goals, such that new simulations can be conducted periodically to account for changing circumstances and new recommendations made.
These and other objects of the present invention are achieved by an apparatus and method for enabling a user to interactively create an investment strategy comprising: providing an interactive electronic space having a display that generates a user questionnaire; identifying the user's risk tolerance based on answers to the questionnaire; identifying the user's goals based on answers to the questionnaire; identifying the current investment portfolio and assets based on the user's answers to the questionnaire; conducting a goal analysis and identifying a goal forecast; conducting a performance review of the investment portfolio and assets and simulating a potential return at the time the goal is to be met; analyzing a database of investment instruments containing information on degree of risk and past performance; simulating future returns for the existing investment portfolio and selecting risk/goal appropriate investment alternatives and simulating future returns thereof; and generating a recommendation for maintaining or altering existing investments in the portfolio and/or selecting risk/goal appropriate investments for achieving the goal.
Preferably, the computer based system is accessed via a home page format where a user can interactively consult with the computer based system which acts as an investment adviser. This adviser presents the user with the questionnaires which, after completion, are used for the analysis.
In a preferred embodiment, the computer system has access to one or more databases containing past performance characteristics for numerous financial instruments, such as multiple families of mutual funds, as these funds are popular with individual investors.
Preferably, the home page style work space displays information on the goal, and analyzes progress to achieving the goal. The home page is interactive such that the user can view specific details of each investment, obtain additional recommendations, make changes to the investment strategies, and add new goals.
The invention has particular use in analyzing and making recommendations on mutual funds which are a key choice of investment for the individual investor, utilizing a computer simulation computer program to determine likely returns for individual investments to the date of achieving the goal. When there is a shortfall in the existing investment portfolio, the computer searches one or more databases for risk/goal appropriate investments which have a high probability of achieving the goal, making a recommendation for utilizing one or more alternative investments which increases the likelihood of achieving the goal in the time allowed. This is done by using a database containing information on numerous funds including historical performance of the market to simulate future returns relative to risk. Such a database may be created or be available from a vendor of financial information, the system preferably obtaining information via a communication interface through the internet.
Once the analysis is complete, and recommendations are made to the user, the user may accept or reject the recommendations. As an option, the user may utilize the inventive computer based system to execute the recommended changes to the investment portfolio .
Utilizing the present invention, a user can be relieved of the burden of individual fund research and selection, instead utilizing the computer based system to select and weigh various investments depending on an individual's goals, risk tolerance and time frame, so as to recommend risk/goal appropriate investments. The inventive system also allows tracking over time, with the ability to revise the portfolio to take into consideration market changes, with automatic execution to simplify investment management.
The inventive method and apparatus is readily usable with all types of investments such as individual securities, mutual funds of all types, bonds, etc. A key component and object of the invention is to provide long term support and analysis for meeting a defined goal such as saving for retirement, saving for college, buying a house, etc. An important factor in matching recommended portfolios to specific goals is the user defined time frame or "horizon", balanced with the risk level for a specific goal. For example, a short term goal, that is three years or less, would favor a minimum risk portfolio as a first asset allocation, though an aggressive user may override that recommendation and seek advise on higher risk alternatives. A long term goal, such as for retirement or college (over 3 years duration) , allows for more interim risk in the portfolio selection, though an individual user's risk tolerance will alter the recommended portfolio selections.
The system thus seeks to provide a long term strategy for asset allocation and management with periodic updates to track actual progress against the original estimate.
Thus, reliable long term forecasting is a key to the value of the inventive system as it allows simulations with alternative investments to meet the user's needs.
Preferably, a Monte Carlo mathematical simulation is used to forecast a range of likely investment returns, using a quasi random sampling technique that runs simulations statistically equivalent to a lengthy process covering thousands of pathways so that the user may run several forecasts in a matter of minutes covering alternative portfolios. Forecasting is also done of the goal itself. For example, to test different college tuition inflation rates, assumed to be paid out over four years or the retirement goal using a life expectancy formula to take into account that people are living longer and are in retirement longer.
Asset allocations are determined by placing customers in appropriate risk points for each goal, the risk points calculated with associated market returns. The highest risk point features a risk/return ratio that represents portfolio exposure to 100% of a representative security market index (such as the Standard & Poor's 500 Index). The lower risk point features a risk/return ratio that represents portfolio exposure to 100% of a representative riskfree rate (such as a U.S. Treasury index). The risk points in between these highest and lowest risk points feature risk/return ratios which complete a progression between the highest and lowest risk points. One preferred model uses a total of 11 risk points.
The system then calculates an asset allocation for each of the 11 risk points. Each allocation has a blend of asset classes that generates the level of risk/return associated with each risk point. These allocations are tested using security market approximations and fund returns for each class. The optimal blend is determined based on quantitative analysis for these asset class representatives. Evaluation and recommendations of mutual funds are determined using a multistage process. The first stage is a quantitative screening process used to specify a fund's market sector and evaluate its riskadjusted performance, among other things. The second stage is style analysis. The next stage is to review publicly available information about the fund. In the final step, the remaining funds are ranked in attractiveness. The funds remaining are used, for example, to make mutual fund recommendations according to each client's risk profile and financial goals.
The inventive apparatus includes a computerized data processing system that has an external data interface for communicating with users preferably via a server based system.
The processing system is linked to one or more relational databases where the various investments are represented, annotated, weighted and evaluated for use by a simulation program for selection of risk appropriateness based on user input. The relational database is continually updated to assure timely information such that each simulation uses current information as well as historic performance data, and real time access via a communication interface to various remote sources of information is one possibility to assure timely advise generation. Once a user inputs a goal, at a given horizon, the current investment portfolio, if any, and data on risk tolerance/aversion, various investments are selected, future returns simulated, and combined to propose a mix of investments reasonably believed to meet the goal at the horizon. The user may repeat the simulation, by varying the goal, or degree of risk, assts available, etc., to arrive at the optimum portfolio. The user may then issue a command and the computerized data processing system may communicate with an investment data processing system to initiate the trades necessary to procure the recommended portfolio. At periodic intervals, normally 36 months, the user may access the computer data processing system to obtain a progress report and based on the reported progress, or changed individual circumstances, may perform a new simulation. The computer based system then reruns the simulation collecting fresh data and, if a shortfall appears, identify alternatives for revising the selection of investments based on current conditions, and allow the user to accept or reject the proposed alternatives.
As the time to the horizon shortens, the computer data processing system will automatically propose modification to the portfolio to address the change in risk tolerance vs. time to goal, again allowing the user to autoimplement any changes to the portfolio, or to customize to reflect the user's preferences. These preferences are simulated to advise the user of their likely effects on meeting the goal. Using the present invention, a user is relieved of conducing exhaustive market research and has a means to use massive amounts of financial information that is processed and presented in a simple form, listing a select group of investments, mathematically believed suitable for meeting a goal, obtaining a diversified portfolio based on the selected list, monitoring progress and performance using again a simulation that forecasts returns vs. risk and adjusting the portfolio to meet changed circumstances over time.
Such a system is quite easy to use, saves significant amounts of time and provides a reasonable, rational basis for long term investing. Such an investment management system provides significant confidence in the selection of risk appropriate investments, though of course, past history is no guarantee of future returns.
In summary, the invention is a computer system for analyzing a plurality of investments comprising: a database containing data on the plurality of investments; means for inputting user data relative to at least one goal; means for inputting user data relative to risk tolerance and existing assets; means for generating a goal projection for quantifying assets needed at a goal date; processing means for forecasting returns for the plurality of investments, and for selecting a list of investments projected to meet the goal, in corespondence to the risk tolerance and existing assets of the user; and, display means for presenting the list to the user.
The system may further include means to execute a user command to effect the transactions necessary for obtaining the selected portfolio.
The system may further include means to monitor the selected portfolio, to update the return forecast and to select alternative investments suitable for meeting the goal.
The system may use a quasiMonte Carlo simulation for forecasting returns.
Of course, a high speed computer processing system may be used with associated data storage capability, and having a user interface via a server preferably accessible over the internet. Data in the database can be updated continually or be accessible via a communication interface on a real time basis, to take into consideration current market conditions and forecasts on factors such as inflation, lending rates, etc.
The investment system is particularly useful in selecting and analyzing mutual funds, though the invention is not limited thereto .
Brief Description Of The Drawings
Fig. 1 is a table of typical investments. Fig. 2 is a table of relevant information for acquisition from a user.
Fig. 3 is a flow chart of the system according to the present invention.
Figs. 4a4d are tables of questions generated by the system for the user seeking financial advise.
Fig. 5 is a table showing the type of information retrieved by the system for the financial analysis.
Figs. 6a and 6b are typical displays generated by the system to acquire information from the user. Fig. 7 is a table of exemplary default asset class compositions used in the goal simulation process.
Fig. 8 is a depiction of distributed market returns. Figs. 9a and 9b show the distributions of the various return paths projected by the simulator for reaching the defined goal.
Fig. 10 shows a typical display for obtaining the user's constraints . Fig. 11 is a table of an exemplary fund candidate list.
Fig. 12 shows a typical display of the resultant recommendations for achieving the goal.
Fig. 13 is a flow chart of the multi goal simulation process . Fig. 14 is a flow chart of the autoexecution of portfolio adjustment m accordance with the recommendations made and accepted by the user.
Figs. 15a and 15b show the initial portfolio and the proposed portfolio in accordance with the system generated advice.
Figs. 16a and 16b illustrate requirements for considering inflation m the recommendations.
Fig. 17 is a table of required and optional information needed by the system for generating financial advice. Fig. 18 shows the effects of risk tolerance on the simulation.
Fig. 19 shows distribution of a risky asset.
Fig. 20 shows the derivation of principle components.
Figs. 21a and 21b shows the effects of quasi random distribution.
Fig. 22 shows convergence using two methodologies.
Fig. 23 shows use of the security market line by the system. Fig. 24 is a table showing the center weights for various exemplary risk levels.
Fig. 25 shows the relaxation parameters for each iteration. Fig. 26 shows the weight ranges increasing with each iteration.
Fig. 27 is a flow chart of the optimization process. Fig. 28 is an illustration of the categories and logic used by the pac an system.
Fig. 29 is an exemplary style class portfolio weighing table.
Detailed Description Of The Invention
By way of example, the investments of Jane, a typical user, are depicted in Fig. 1. Jane has two taxsheltered relationships: one through Spacey Sprocket's 401 (k) plan and her husband George's 401 (k). In addition, Jane has opened accounts at a no transaction fee fund platform and at a brokerage and has one direct account. Jane's profile will be used to illustrate the operation of the invention. Jane provides the system with information that the advice "engine" uses to provide investment recommendations to her. For the purposes of this application, the terms "fund advisor" "advisor" "optimizer" etc. refer to the computer based system of the present invention, these terms used to simplify the description and not to limit the scope of the present invention. Fig. 2 illustrates exemplary information that is relevant to the recommendation process, though other information may also be used .
The flowchart of Figure 3 diagrams the initial user experience with the invention. Once the user completes enough of the process to reach the advisor work space, subsequent visits to the advisor will start there. The invention preferably utilizes a centralized approach to identifying customers. This functionality is embodied in the provision of a unitary identifier which combines all of a user' s passwords and personal access codes into a single personal identification number (PIN) , referred to hereafter as the "onepin" .
The onepin provides access to an individualized personal home page which lists a variety of useful functions available to a customer. One function is the display of all of a customer's selected accounts in a single view. When users set up a onepin, they can specify which of their accounts they would like to associate with the onepin.
Onepin allows customers the flexibility to add any or all of their accounts to a single view. One advantage is that a user can set up multiple onepins with different account combinations. For example, Jane could have a onepin home page that contains just her accounts in one fund family and a second onepin home page that includes a mix of accounts.
The user questions fall into four categories: personal financial information, risk tolerance, investment experience and, on a goalbygoal basis, goal horizon questions. The answer to each question is a factor in determining the customer' s appropriate risk level for a particular goal. Typical questions are identified m Figs. 4a4d.
The answers to the risk assessment questionnaire will generate a number that represents the user's base risk score. As users identify their goals, they are given the opportunity to identify the time horizon for each goal. Each time horizon is given a score, a Goal Specific Time Horizon Score, from a table. For each goal, then, its GoalSpecific Risk Assessment Number is determined by the following equation: Risk Assessment Questionnaire Score + GoalSpecific Time Horizon Score = Goal Specific Risk Assessment Number
A user's Goal Specific Risk Assessment Numbers are used to determine which asset class allocations should be used for each goal. The default asset class compositions for each risk score appear later. Jane has four investment goals: her retirement, George's retirement, her soontoarrive child's college and a down payment on their next home.
The Goal Names specified appear as the titles for the pages that will be displayed. There are different questions for different goal types. The Goal Horizon is the single most important factor m determining the risk profile for each goal. Thus, even if the questionnaire answers indicate very aggressive investment tendencies, a very short goal horizon will dictate that she invest conservatively to reach that goal Autopopulation of Customer Data Because onepin facilitates a consolidated view of a user's holdings, onepin enables the autopopulation of user data in the displayed account information tables. To accomplish this, onepin loads account information when a onepin is established that will allow the system to retrieve platformspecific information about the user's holdings, as shown in Fig. 5.
Once a user initiates an advisor session, this information is populated in the appropriate database and reference tables contained within the advisor system. The user may be asked to provide information by manual input to a series of external holdings screens. Samples of the screens are shown in the figs. 6a and 6b. This information is stored in a table with other user information for reference.
The computer based advisor system uses a goalsbased investment philosophy. The mechanism for organizing these goals and assigning assets to reach them is an important function of the system. As users become comfortable with the goalsbased approach, they are better able to review and revise their investment holdings.
A user's goal is more than a simple estimate of how much money they want to have at a future date. The advisor system queries not only that basic question, but requests answers to a series of inquiries.
The goal type has the greatest influence over the number and character of the assumptions and information required from the user. A down payment goal, for example, has relatively few characteristics and needs only a few inputs from the user. In contrast, the retirement goal is much more complicated and requires greater user information. The information obtained is used in the goal simulation process. What follows is an overview of the goal simulation process, described in detail later. The purpose of the goal simulation is to determine the probability of reaching the goal. An optimization process seeks to find the best portfolio to maximize that probability. The goal simulator works by breaking down the analytical process into the following components: what amount, if any, does Jane have toward the goal today; how much time does Jane have to achieve that goal; what is the cost of Jane's goal; given Jane's portfolio risk, what is the likelihood that the goal will be achieved.
The factors considered to answer these questions differ with different types of investment goals. The basic process, however, is the same. The amount available today is simply the amount that Jane has allocated to the goal when she set up her investments. In the example, Jane has $21,000 allocated to the down payment goal. When Jane initially specifies her goal, she is asked to provide a goal horizon number which represents the number of years she has to reach her goal.
The investor's goal must be quantified to simulate the investment performance of a portfolio, to know the amount of money Jane needs and when (e.g., $50,000 five years from today) . The complexity of this calculation depends on the goal type. A down payment goal is the simplest to quantify, while a retirement goal is the most difficult. Calculating the dollar amount needed for a down payment goal can be very simple. Jane could simply say that she wants to have $50,000 five years from now to make a down payment on a house. However, for the advisor system to assist her in making this determination, Jane should provide the following data: how much the kind of house she wants costs today (e.g., $200,000), when she would actually want to purchase this house (e.g., three years), ow large her down payment and closing costs should be (e.g., 10%) .
Jane enters this data in a Goal Profile, and then the advisor system makes assumptions as to home price inflation rate and general inflation rate, both of which affect the goal. Using the example numbers, Jane will need $23,820 after three years.
In a retirement goal, the advisor system must evaluate additional factors that influence the final goal amount: annual income during retirement for each year in retirement, annual social security benefit for each year in retirement, annual pension benefit for each year in retirement, other income during retirement for each year in retirement, cash acquired at start of retirement, estate to leave at end of retirement.
As was the case in the down payment goal, a series of calculations is performed on these requirements and a single number that represents the estimate of the amount of money required on the goal horizon date is determined. Given Jane's portfolio risk, the next step is determining the likelihood that the goal will be achieved.
Though assets are difficult to estimate, the advisor system generates a distribution of potential future wealth by forecasting portfolio return. What follows is a simplified illustrative description of the goal simulation process. A typical more detailed description is shown m Fig. 7. The goal simulation can be run for both Jane's current and recommended portfolios .
The advisor system must make certain assumptions about the range of potential returns that a portfolio, given its risk characteristics, could achieve on a periodic basis. The system determines this range of potential returns by assuming the existence of a Security Market Line (SML) . This is a widely accepted and supported approach to forecasting. A key assumption is that market returns, over time, are normally distributed. This is consistent with empirical data studies. A depiction of market returns is shown m Fig. 8. Each "ball" represents a potential return for a given time period. There are fewer balls representing high and low returns. The width of this distribution varies depending upon the risk level of the portfolio. The representation shown is for a less risky portfolio, since most of the potential returns are withm a tight range . The goal simulator then performs a "Monte Carlo simulation" of forecasted returns. The goal simulator starts at current assets (i.e. $21,000) and selects a ball from the graph and uses it as the simulated return for that year. The goal simulator then puts the ball back and selects another ball to represent the return for the next year and the next, etc. until the horizon date is reached. In this simplified example, it stops after three years. The resulting asset numbers form a "path" that represents one possible path that Jane' s down payment goal portfolio may take, as shown m Fig. 9a.
The goal simulator then draws this path again and again, simulating returns many times, for example, over 200 times, to develop a distribution of likely returns. The result is depicted m Fig. 9b. The resulting range of possible outcomes is normally distributed. In other words, more of the paths end at the center of the range than at the top or the bottom. In this example, if the ending values of more than 85% of the paths are greater than the cost of the goal, the goal is likely to be reached.
Optimizing the user's portfolio is a complicated process that, like the goal simulation, cannot be described accurately without a highly technical discussion. This discussion appears m a later section on portfolio optimization. What follows is a simplified overview of the factors that influence the optimization and how the realtime optimizer accommodates them.
Before performing the optimization, the computer based advisor system gives Jane the opportunity to add constraints. These constraints appear on the screen in Fig. 10. Each constraint has a default setting that appears as the current value when the user first arrives at the screen. Any changes that the user makes on the optimization parameters are added to a list of constraints that the optimizer considers in building the recommended portfolio. The realtime optimizer seeks to simultaneously accomplish two basic goals: maximum return and minimum risk. This is a complex process that involves a number of cycles. The key steps to a cycle are summarized here.
Step 1. User goal specific risk. The goalspecific risk score determined by the scored questionnaire placed the goal in one of 10 target risk categories. The optimizer seeks to construct a portfolio that has a risk profile that matches this risk level.
Step 2. Asset allocation. Each of the risk categories has a target asset allocation assigned to it. These asset allocations are described later in relation to asset class portfolio composition. The purpose of this target asset allocation is to set a starting point for the optimizer in its pursuit of maximum return.
Step 3. Narrow the universe of investments. The optimizer system has the capability of referring to many funds, yet it is preferred to review and examine all of the funds available in each of a select set of platforms from various financial providers. For example, analysts may review all of the funds in one program, and select a number of "best" funds in each asset category. These funds comprise a fund candidate list. There are various ways to do this and one example is described in more detail later. In any event, the optimizer has a candidate list for each selected financial provider.
Step 4. Determine maximum return objective. To determine the maximum return objective, the Security Market Line (SML) is used. The SML is a representation of the overall risk/return ratios of market performance. The SML is based on historical performance of the market over many years and is an accepted concept in modern portfolio theory. The realtime optimizer uses this security market line to calculate the expected return for each of the funds on the candidate lists that it considers for recommendation, using the return on the SML that corresponds to a fund's risk level, represented by its variance.
In addition to the fund candidate lists, the system keeps a current record of all mutual funds and their performance characteristics, or has access via a communication interface with a database containing such information. Among these records are, for example, 1, 3, 5 and 10year performance numbers, etc, as well as the variance (or risk level) for each fund. This is used to map expected returns on the SML. A list of the typical records that can be used is shown in Fig. 11.
The system advisor then reviews Jane's GoalSpecific Risk
Assessment Number and identifies various combinations of funds that have the highest expected return for a given level of risk. However, this would not result in an optimum solution; there are some additional constraints that should be considered.
The system advisor establishes a list of requirements that increases the difficulty of solving for an appropriate maximum return/minimum risk solution, to take into account real world factors. Examples of some constraints are: asset class weighing; number of fund candidates available in each asset class; diversification requirements (maximum percent of portfolio for any one investment) ; rules for compensating for missing asset classes; do not sell requirements imposed; amounts of money held at each financial provider, etc..
With input on these constraints, the optimizer may generate a solution. The optimizer cycles, or iterates, through a series of possible solutions. If a solution cannot be found at the end of a cycle, the portfolio optimizer has a series of procedures that allow it to "relax" constraints until a solution can be found.
The constraint relaxation process is unique and is based on infeasible problem analysis routines. Not all constraints are relaxed, as some constraints are fixed and cannot be relaxed. The amount a constraint may be relaxed can vary from constraint to constraint. Details about the constraint relaxation process appear later. At the end of this process, however, the optimizer will have a specific list of investments that comprise an optimum portfolio. These investments are shown to the user on a recommendation screens. The recommendation screen (fig. 12) is generated in response to the selection of an optimized portfolio.
It should be stated that when the fund candidate list is created for the portfolio optimizer, proxies for each of the candidates can be generated. These proxies are chosen by selecting funds statistically correlated with each candidate. In other words, the proxies are good substitutes to those funds that are estimated to behave most like the candidate chosen, though there will not always be a substitute fund. These proxies increase the choices available to the user without regenerating a new optimum portfolio. The asset classes are generally consistent with the Morningstar classifications. The predetermmed proxies will be displayed below the fund chosen by the optimization process. Thus, the process which generates the recommendation screen will "look up" the proxies on a database table and list those funds below each fund chosen by the optimizer, so the user may select a preferred investment, without affecting the optimized portfolio displayed.
The system may solve multiple goals simultaneously. The system includes a multigoal solver (see Fig. 13) that helps investors allocate their assets towards their goals by allowing them to prioritize their goals into different categories according to importance. The solver then calculates whether existing assets can reach stated goals by category. If goals cannot be reached with existing assets within a category, the solver will allocate the existing assets to stated goals m the way that will give highest return rate while making sure that short horizon goals are sufficiently funded. The solver will also calculate the shortfalls to the stated goals and suggest extra deposits accordingly.
When an investor deposits an asset, it is divided into two main types, tax deferred (retirement oriented) account and taxable (nonretirement oriented) account. The tax deferred asset goes only to retirement goals. Taxable asset can be used for any goals with the exception of UTMA accounts and the like. One of the advisor system's key features is the ability to execute recommended trades automatically. Once the user has reviewed the recommendations and is satisfied with them, the system can automatically arrange for the execution of the trades at the click of an authorization button.
The process flow in Fig. 14 is a depiction of the autoexecution process for a brokerage platform. While this process can be completely automated, it is preferably not completely automated to allow monitoring and control of the complex business rules that will be involved with the trades. This compromise is a good balance of safety and minimum time out of market.
Suppose Jane's brokerage account was as shown in Fig. 15a. The recommended portfolio is shown in 15b. The interplay between the settlement dates and cutoff times of the funds impacts how to autoexecute the recommended transactions.
The order should be sent in 2 days (31) before 3:00 p.m. (the earliest BUY cutoff time) , to accommodate the time to transact, thus there is builtin additional time to act as a cushion to ensure that the trade can and will be executed.
Investors tend to focus on the obvious risks of shortterm fluctuations in returns, but the risk of slowly decreasing purchasing power is also important to consider. Inflation, even at a relatively low rate, can significantly reduce purchasing power. All investment plans, even the most conservative, should seek to maintain real value or buying power. Fig. 16a illustrates the declining value of $1,000 of savings over a ten year period at various rates of inflation. The real rate of return to an investment is the return after taking into account the effects of tax and inflation. It is used to determine whether an investment is maintaining its purchasing power. The combined effects of inflation and taxation m the following example provide a very small positive return.
Fig. 16b illustrates the gross returns an investor would need to receive at various rates of tax and inflation just to break even (i.e. to achieve a real return of 0%) . These examples show that over time, inflation's effects, especially for people on a fixed income, are a cause for concern. Individuals can find their buying power is reduced year after year. As shown, to stay even with a 4% average inflation rate, a taxpayer m the 28% marginal tax bracket needs to earn an average of 5.5% on savings and investments. Suppose an investor retires at age 67 and expects to live m retirement for 20 years. A $100,000 annual income at retirement would need to grow to $219,112 by age 87, just to stay even with 4% inflation.
To overcome the effects of inflation, the system will seek investments that outperform inflation, and attempt to diversify the portfolio to spread the risk m case one of the asset class underperforms . Academics have studied data taken from broad stock market indexes such as the S&P 500 and the Dow Jones Industrial Average and determined that over long periods of time, the return from common stocks is higher than the eroding effects of inflation. Fixedincome asset classes, which have provided the least amount of shortterm volatility, have historically had the lowest chance of beating inflation and of increasing the investor's purchasing power. Stocks as an asset class have been able to maintain their value much better and are one of the best investments to overcome inflation for long term investors. These factors are used by the advisor system preparing a recommended portfolio. Key Assumptions for Portfolio Composition Design
Low risk portfolios need higher current income. Low risk portfolios have a value style bias index for a combination of case and Lehman Aggregate, producing higher yields for the same. This leads to a substitution of the Lehman risk, and to a greater emphasis on risk management rather than longterm accumulation. Intermediate portfolios are style neutral. Higher risk portfolios have a growth style bias due to a greater emphasis on longterm accumulation. Ideal or optimal international exposure is the 15%25% range. No benefit is believed derived from a style bias m small cap.
The simulator calculates the likelihood that a financial goal will be met. At the top level, this likelihood is found by considering the difference between financial assets, which are modeled as stochastic, and liabilities, which are modeled as deterministic. This can be written as a very general formula: prob success  P(assets ≥ liabilities)
For this calculation, whether a cash flow is stochastic or deterministic defines it as an asset or liability. In the Goal Simulator, the asset side of the equation consists of the distribution of wealth at the goal horizon date. The liability side is the number of dollars needed at the horizon date m order to achieve the goal, which may be for example, having the funds to live comfortably m retirement, or pay for college. To illustrate the goal simulator algorithm, the calculation for a retirement case is chosen because it is the most complicated; all other goals, from an algorithmic standpoint, can be considered subsets thereof. To calculate the probability of a client achieving their retirement goal, the total values are compared at the goal horizon date.
In order to estimate each quantity, the user is asked to provide information, shown m Fig. 17. Some fields are required, while others may use default values.
A single number estimating the amount of money required for the goal on the goal horizon date is computed, using compound or discounted dollar amounts entered by the user. The total liability has several parts: during retirement annual income for each year in retirement, annual social security benefit for each year in retirement, annual pension benefit for each year in retirement, other income during retirement for each year in retirement, cash acquired at start of retirement, estate to leave at end of retirement. To calculate each of these elements, define the following variables :
To begin the calculation, find the horizon salary rate by continuously compounding current salary over time to horizon by the expected rate of salary increase
S_{H} = Sexp(r,t_{R} )
Calculate the social security benefit. If the client does not expect to receive social security, then set S_{s} to zero immediately. Otherwise, beginning from horizon date salary, continuously discount back to today using the inflation rate, to find the salary in today's dollars.
S_{l} = S_{H} exp(r,t_{R})
Determine the annual benefit amount in today's dollars.
If retirement age is less than 66, scale benefit by 0.8. At the same time, scale the benefit amount by client's expected weight. This gives the final answer for social security.
Calculate the horizon date annual value of retirement income. (Recall the value was entered in today's dollars.) 0 = S_{0},*_{e} exp(r,t_{Λ})
Combine these elements to produce the horizon year total funds required.
F_{h} will be needed for each year in retirement, continuously compounded appropriately for inflation, and then similarly discounted by r_{R}, the return on investment during retirement.
= J _{Λ} exp[(r, r_{i?}>]rit Discount the estate dollars by inflation from the end of retirement to the beginning, then compound by return on investments in retirement.
E = S_{Btale} &φl(r_{J}  r_{R})T_{R} ]
The total liabilities are the combination of the total salary related expenses, the estate, and any cash inflow at retirement. Cash acquired at retirement is already valued at the proper time, so we simply add it to the total. liabilities = F +E C
where
F = total funds required,
E = estate goal,
C = cash acquired at horizon date.
The assets in the goal simulation equation are modeled as a stochastic variable. This means that at the goal horizon date, a distribution of possible wealth levels is obtained. The actual stochastic variable is portfolio return. To generate a distribution of wealth at the horizon, forecasts of future portfolio returns must be made. Once a model of portfolio returns has been constructed, draw returns from the distribution for each time step during the investment period. This produces a time series of simulated returns starting today and ending one period before the horizon date. From these returns, calculate the growth of wealth along a path. At the horizon, obtain the dollar wealth for one particular path, then repeat the process, each time obtaining another value of horizon wealth, until a distribution of ending wealth has been generated such that the addition of more paths does not change the basic characteristics of the distribution.
To calculate wealth along one simulation path, say path n, generate a time series of returns,
Over a short period of time, the increase in portfolio wealth comes from two components, the return the portfolio makes itself, which is random, as well as the contributions injected into the portfolio, which is not random. Denoting this
ΔR increase in wealth at time t by ' , we have for path n
AP_{t} = r;P_{t} +C_{t}
where P' is the value of the portfolio at time t and C' is the
"injected" contribution. Here, assume that new contributions are put into the portfolio "evenly" rather than at specific r" points in time. Replacing the individual returns ' with the
"internal rate of return" ^{r} , it is shown that the final wealth
T at the planning horizon T satisfies the ordinary
differential equation P_{τ} = P_{0}e^{rT} +C_{0}e^{rT} ζe^{(}'^{~r)t}dt
The algorithm generates paths until the simulation converges,
and there is a "weakly stationary" distribution, <■ • > of horizon
wealth,
assets = * ' ' .
The probability, once again, to be calculated is prob _ success = P(αssets ≥ liabilities)
Compounding returns generates horizon wealth values. These returns are assumed to come from a normal distribution, the justification and consequences of which are discussed below. The result is that the distribution of horizon wealth is log normal. The final answer produced is the probability that assets will be greater than liabilities at the horizon. The easiest way to do this is to calculate probabilities by transforming into normal space. The liability amount is also transformed, which modifies the equation: prob_success = P ( log (assets) > log (liabilities) ) . This probability is exactly the same as the probability for the original dollardenominated variables, since logarithm is a strictly monotonic function.
The stochastic model of returns currently implemented starts by assuming the existence of the Capital Market Line (CML) . Assume the riskier the asset, the higher its expected return. Further assume that any investment strategy can be modeled as a linear combination of a risky asset (the market) and a riskfree asset. By finding a user's risk level, via the fifteen questions discussed previously, determine characteristics of the distribution from which to sample return values at each period. These returns are modeled normally. The riskless and risky assets have expected returns of 3.5% and 10.9%, respectively, and standard deviations of 0% and 16%, respectively. The mean returns are arithmetic. The higher a user's risk tolerance, the higher their mean return and standard deviation (See Fig 18) .
Figure 19 shows the empirical (historical) distribution of the risky asset. In the parlance of MPT, this is the market. In the system, the market is a linear combination of US and international equity indices. Superimposed over the empirical distribution is a normal distribution with the same mean and variance. Over this long time period, the distribution of market returns is very nearly normal.
Using the CML to find a return distribution for a user's recommended risk level allows constructing a time series of returns which depend on one random variable: the risky asset. Stochastic systems of this type are called onefactor models. Therefore, the mechanisms for modeling and predicting returns are consistent.
A factor analysis on the returns of core asset types could also be undertaken. The goal of factor analysis is to take a group of time series, such as historical returns of some indices, and find their uncorrelated, underlying factors. That is, given a group of correlated time series, for example six, find two or three (or more) underlying uncorrelated time series, from which the original time series movements can be reconstructed. See Figure 20. The new, uncorrelated series are called principal components. The advantages of working with principal components are that it is unnecessary to use six time series, and four at most may be satisfactory. Also, correlations between random factors can be disregarded which makes path generation much faster computationally. Once a model of the stochastic variable has been constructed, produce time series of returns for each path using a quasiMonte Carlo (QMC) algorithm. QMC is far more computationally efficient than the classic Monte Carlo (MC) method The reason that a wellconstructed QMC algorithm converges so much more quickly than an MC algorithm is that a Monte Carlo simulation samples random numbers, usually uniformly distributed on the interval [0,1), which are then mapped to the appropriate space using the stochastic equation. The difficulty with random sampling is that there is nothing to prevent "clumping" of the pseudorandom samples. That is, if the last number drawn was .52, it is just as likely that the next number will be very close to .52 as any other number. Since the process of path generation requires so many draws, it is inevitable that clumps appear. The end result is that the simulation has a lot of paths that nearly repeat, and are thus redundant to the calculation.
QMC draws are completely different, and in fact are not random, but successive numbers in a numerical sequence specially constructed to "stay away" from previous elements of the sequence. Several different sequences have been used as draws in simulations, the most widely cited being Halton, Faure, and Sobol' sequences, the last considered the most robust. In Figs. 21a and 21b, two dimensional pseudorandom and Sobol' draws are plotted. Each sequence contains 1000 draws. The clumping in the pseudorandom sequence is clearly visible. Consequently the QMC algorithm covers the probability envelope in far fewer paths, thus obtaining convergence much more quickly. Fig. 22 shows convergence in mean return using the two methodologies. The actual mean value is 11.0. Each path consists of thirty time steps (draws) . The QMC method has an error of less than 0.001% after 421 paths, while the classic MC method is showing little sign of convergence after 2500 paths.
The preferred implementation solves each goal separately, and there is no mechanism for "communication" between goals. This is an issue because a user may have two goals, one greatly overfunded, and the other slightly underfunded. The advisor cannot recommend that currently held or future periodic contributions be reallocated to ensure full funding of both goals. Different rules applying to different folios would have to be examined to check whether reallocation was possible, for instance. If a goal has a shortfall, the dollar amount of future periodic contributions required to meet the goal can be calculated with approximately 85% certainty (expected value minus one standard deviation) . This is done using the return paths generated during the simulation runs, by calculating the shortfall, U, and finding
the level of new periodic contributions, —* °, such that
This equation can be solved for additional future contribution amounts, and can be used with no direct modification by replacing the normal distribution of returns with an empirical,, to recommend contribution shifts between goals, or to introduce a multifactor model of returns. Portfolio Optimizer
The system optimizer constructs the best possible portfolio for a client given the following: a fund universe that may be a subset of all available funds, and preferably is a screened list of recommended funds, screened as described previously, for a brokeragetype account; a family of funds in a 401 (k) plan, etc; client imposed restrictions, which may restrict the sale of an asset via a "do not sell" and "do not sell/okay to buy more" buttons in the optimizer user displays; client additions to the fund universe, where the client adds select funds to the list of optimization candidates, though system generated statistics are used in the optimization algorithm; constraints given by the system or which are userdefined or defined by Jo circumstance (e.g., only available funds) .
The optimizer preferably uses a quadratic optimization formulation, which means that the objective function is a second order polynomial (e.g., y = x^{2} + 3x  6), and the constraints are linear (e.g., y = 3x  6) .
The quasilinear formulation is preferred as linear and nonlinear optimizers have weaknesses. For example, a linear optimizer maximizes return, but is unable to account for risk, nor is there a way to iterate a linear optimization problem to obtain a particular risk value. The linear formulation is not sufficiently useful in this application.
The nonlinear formulization maximizes return, and has risk level as one of its constraints, but has two significant limitations : There is no "utility tradeoff", that is, the optimizer won't find a solution that gives a little more risk for a lot more return and if a fund family from which the optimizer chooses funds does not smoothly span all of risk space, it can give incorrect answers. For example, assuming a user has a target risk level of 10, and the choices in his 401 (k) plan are a money market fund, a short bond fund, a balanced fund, two conservative large cap value funds, and an international equity fund, if the two domestic equity funds are themselves at risk level 7, the optimizer is going to give more weight to the international equity fund in order to meet the risk constraint. A properly applied quasilinear formulation will reduce the risk level for this client, since the extra risk does not justify the additional expected return.
The system assigns an alpha of zero to all optimization candidates. The forecasted risk/return estimates for each candidate are based on the candidates historical risk, and a fitted return point on the same security Market Line (SML) . Given the standard deviation of a candidate holding, the return is the corresponding return point on the SML (see Figure 23) . The standard deviations are calculated using as many as 36 monthly returns, and as few as twelve depending on data availability. The system preferably has the capability to modify the security market line (SML) , such as according to a haircut matrix.
The optimizer in one embodiment uses a single period, i.e. it assumes that all holdings will remain in the portfolio until the horizon.
The general portfolio optimization problem has the goal of maximizing expected return while simultaneously minimizing absolute risk, subject to a set of optimization constraints. Usually these constraints are meant to ensure diversification of the optimized portfolio.
The objective function for the portfolio optimization problem is
max T ω„R„  λCov(R_{m} , R_{n} )
where N is the number of optimization candidates, ω_{n} is the weight to include of candidate n in the portfolio, R_{n} is the expected return of candidate n, which comes from the 36 months of historical data
A is a parameter dialing the relative importance of risk aversion,
Cov (R_{m},R_{n}) is the covariance matrix of the returns of the candidates .
It is possible that the problem will be over constrained, which means that the constraints are too tight, two or more are incompatible, or both. This is called an infeasible optimization problem. In its most basic implementation, when a problem is found to be infeasible, all constraints can be relaxed by a preset percentage. The optimization is run again, with the constraints relaxed again if necessary until a solution is obtained. Alternatively, the computer based optimizer component of the system includes an ability to review an infeasible problem and selectively determine which constraint or constraints are causing the infeasibility . Logic is used so that, given this information, an appropriate subset of constraints is relaxed. The system may provide value by in effect connecting A with a more intuitive risk level calculated and provided by the client via the questionnaire, by using logic and iterating on A until a solution with the proper risk level is obtained. The iteration is preferably via the secant method, which estimates the objective as a function of A, finds the derivative of that function, and uses this to determine an estimated value of A yielding the selected risk level. If a solution exists, it usually takes no more than four iterations. Constraint Details
Constraints can be classified as being either "hard" or "soft". Soft constraints are defined as those that can be relaxed or changed if a problem is infeasible. Hard constraints are defined as those that can not be changed. If a problem is infeasible, hard constraints are not relaxed and no solution is given. Similarly, if the soft constraints have been relaxed as far as possible, the problem will not have a solution.
Hard constraints may include, but are not limitd to, the following : client entered "do not sell" or "do not sell/okay to buy more" commands; no fund may have weight less than zero (no short positions); no fund may represent more than 25% of the entire dollar holdings designated for a particular investment goal (An exception may be made when there are less than five optimization candidates, since then the maximum weight will be less than one for total weight) ; and, weights in each folio can not be changed.
Soft constraints are more complicated, being assigned different ranks. The rank of a constraint determines how and when that constraint will relax.
In one embodiment, there are three levels of constraints, corresponding to rank: overall stock/bond/cash ( S/B/C) weights; equity style weight constraints (large cap growth, large cap value, small/mid cap, international) ; sector weights (utilities, tech, etc.).
The process relaxes (3) faster, and more, than (2) , which can relax faster, and more, than (1) . Constraint rank (1) may allow drift without warning for example, of one risk point away from the initially recommended mix, and with a warning two risk point drift. For example, assume a client has a recommended risk level of 7. The (S/B/C) target is ( .70/ .25/ .05) . Without a warning, the optimal asset mix can be anywhere in the range of a 68 risk level, or (.60 .80/.10.35/0.05) . In the above example, the resulting optimized portfolio may well have a risk level of 7, and a (S/B/C) mix corresponding to risk level 6, ( .65/ .35/ .05) . This simply indicates that the funds in this particular optimization candidate list, taken together, are riskier than usual. In this context, risk depends not only on the variance of each particular candidate, but also on the covariance between each pair of candidates.
Constraint set (2) may relax for example, large cap stocks differently than small/mid cap and international. Generally, large cap growth and value are considered similar. Small/mid cap and international are riskier, and the optimal weights may be allowed to vary farther down than up.
Sector constraints are the most flexible, as they are typically only on the equity portion of holdings. This can have a range of 25%250% of market weight m that sector, which can be relaxed considerably on the second iteration.
To quantify the constraints, the following definitions are used: g : large cap growth v : large cap value n : small and mid cap i : international equities
S : al .l. equit.ies, S = g^{6} + v + m + i
B : bonds
C : cash O : other For any given risk level, r, which is a number from zero to ten, the target, or center, weights are:
0
^{S}O
B
C
o
Figure 24 shows center weights for each risk level. The overall S/B/C weightings are different for each risk level. The constraints on these move in units of risk levels, defined as: r\
ΔS tower  $0 ^0
^uppppeerr  S ' o So rl
A^{B} er =^{B}0 ^{B}l
rl From here on, superscript r is dropped. For any quantities that change with iteration, a superscript j is added to signify iteration number .
For bonds and cash weights, another parameter is added, since
AD p^{per} _{^ e} c. can be zero. An absolute quantity is added to the risk
level derived upper bound. These parameters are relaxation parameters, which change depending on the iteration. Since other weight targets are always zero, this is done for them aw well.
In order to keep the small/mid and international balanced with the large cap numbers , first define :
rTj * 0 ^ lower ^*^ lower lower r
S_{n}+S' AS„
S uipper
g_{0}+v m_{0}m_{u} ^{J} _{pper}i_{0}i_{pper} ' lower ~
_{CVj} _ g_{0} +^{v} +m_{0}m_{l} ^{]} _{over} +i_{0}i _{er}
^ upper ?0+V_{0} The constraints follow. After the constraints, a table listing the iterative parameters is given.
^O *> lowe_{r} ^ 'lower ≤ <> <  + _{upper}ΔZ> _{upper}
: stocks
B_{0}  B[_{ower}t±B t_{wer} <B≤B_{0} + + B_{f} bonds
^{J} 0 cash
o≤O≤o other
c. l^{i}oner _{+} ^s lo^{j}wer ^{■} GV ' lo^{J}wero vQ <σ<G upper +S u^{J}ppe G ^V u^{J}pperG e large cap growth
V ' lo^{J}wer + 'Sl,^{3}ower G^{J}V ' l,o^{J}wer v ^{r} _{n}0 —<v —<V ' uu^{}}ppppeerrS z„ 0O+ 'S *" uuppppeerr G^{J}V ' uu^{J}ppper large cap value
S _{r}GV^ (g_{0}+v_{0})≤g + v≤ S' GV^{>} (g_{0} + v_{0} ) large cap (growth and
value)
S er∞O 0  wer )<™≤ S ^{'} ' ^{m}00 + Kpper) small/mid cap
J ^{•}>
S er 0  slower )≤'≤ Sapper' 00 + ' ',upper int' equities
If any combination of parameters leads to a lower bound less than zero, or an upper bound greater than one, then that bound is reset to zero or one, respectively.
Fig. 25 shows the relaxation parameters for each iteration. A maximum of sixteen iterations is typically performed, as it is unlikely that after sixteen iterations no feasible solution can be found. This may occur when a client has put an unreasonable "do not sell" constraint on one or more holdings. Another would be where the user's 401 (k) choices can not produce a portfolio with an appropriate risk level .
If a fund family does not contain enough of any asset class, that weight may be redirected into another asset class as follows: if no small cap, then put weight in large cap; if no international, then put weight in large cap; if no bonds, then put weight in cash.
The rightmost column of Fig. 26 shows that little rigor is applied to sector constraints. With good fund screening and using the covariance matrix as part of the objective function, reasonably good sector weights may be obtained. Postoptimization processing may introduce semicontinuous constraints. These are like normal constraints: lower_bound <_&>_ < uppeτ_bound, but also allow ω_= 0. The fund advisor system may be configured to conduct multiperiod optimizations, as well as include tax effects in arriving at the recommendations. A optimizer flow chart is shown in Fig. 27.
An alternative to portfolio optimization is to use a PacMan system to select appropriate funds from a Registered Investment Advisor constructed "Buy List", in a percentage suitable to the user's risk level. Any needed bond funds and/or money market funds are determined by what state a client' lives in and his/her tax bracket. If the user's portfolio has a balance less than $25,000, a single fund solution can be provided as an alternative.
For 401k plans where no "Buy List" is available, PacMan will seek to categorize each fund by using various formulas and Morning Star data, and then recommend specific investment percentages for each fund that is available in the client's 401k plan.
Fig. 28 is a graphical representation of the categories and search logic used by PacMan. Starting in the first category box "Large Cap Value", PacMan logic looks by platform, and chooses the highest rated available fund. If a fund is not available in the desired category, the system will look in the next numbered category, and so on and so on until a portfolio with a LCV, LCG, and SMID fund is chosen. If a portfolio requires holdings in the International and Fixed Income asset classes, funds representing those groups, or other groups, are added.
PacMan does not perform a portfolio optimization, as the amount of money allocated to each asset class in a portfolio is determined by a Style Class Portfolio Weighting table (see Fig. 29). Using this, the asset class weightings are mapped to a user via their pre assigned risk level.
While preferred embodiments of the present invention have been shown and described, it will be understood by those skilled in the art that various changes and modifications can be made without varying from the scope of the present invention. I particular, the choice of security, and algorithm for identifying appropriate investments can be altered to selected from any subset of the universe of investments existing or available in the future, and thus be available for selection by a user of the system. What is claimed is :
Claims
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WO2003005254A1 (en) *  20010705  20030116  Estubroker Agencia De Valores, Sa  Computerassisted method for realtime consultation in relation to the acquisition of financial assets and for the automatic management of the sale thereof 
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WO2017024039A1 (en) *  20150803  20170209  Finmason, Inc.  Financial risk management assessment system and method for assessing financial risk 
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WO2003005254A1 (en) *  20010705  20030116  Estubroker Agencia De Valores, Sa  Computerassisted method for realtime consultation in relation to the acquisition of financial assets and for the automatic management of the sale thereof 
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WO2017223247A1 (en) *  20160621  20171228  Wittkotter Erland  Realtime probability determination based on technical indicators in a financial instrument environment 
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