Abstract:
The present invention provides a method and system for the statistical analysis, display and dissemination of financial data over an information network such as the Internet and WWW. The present invention utilizes resampled statistical methods for the analysis of financial data. Resampled statistical analysis provides a meaningful and reasonable statistical description of financial information, which typically escapes modeling using parametric methods (i.e. assumptions of a Gaussian distribution). The present invention provides at least a GUI that provides functionality for user input of statistical queries, a statistical computation engine that performs statistical analysis of financial data and a graphical rendering engine that generates graphical display of statistical distributions generated by the statistical computation engine. According to one embodiment, the present invention employs a parallel processing architecture to speed generation of the resampled statistics.

Description:
FIELD OF THE INVENTION 
     The present invention relates to the area of electronic information systems. In particular, the present invention relates to a method and system for the delivery of financial information using resampled statistical methods over an information network. 
     BACKGROUND INFORMATION 
     Investors and financial analysts rely upon electronic information systems for the delivery of accurate financial and investment data and analysis in order to devise meaningful investment strategies. The growth of the Internet and World Wide Web (“WWW”) highlights the potential for global distribution of “real time” or “near real time” financial information and analysis. For example, a number of WWW sites provide financial information to clients such as investors and financial analysts. 
     However, conventional financial information sites do not provide meaningful analysis tools to accurately analyze, forecast and predict the behavior of financial markets. Conventional technology for delivery of financial information over information networks such as the Internet typically allows users to track returns for various investments and perform rudimentary statistical analysis (e.g., computation of the mean and standard deviation) for these investments. However, these rudimentary statistical functions are not useful to investors in forecasting the behavior of financial markets because they rely upon assumptions that the underlying probability distribution function (“PDF”) for the financial data follows a normal or Gaussian distribution, which is generally false. 
     The true distribution of returns for any financial market (and thus of a trading strategy) is unknown. It is therefore incorrect to rely upon a statistical model based on assumptions of normality (e.g., standard deviation). Typically, the PDF for financial market data is heavy tailed (i.e., the histograms of financial market data typically involve many outliers containing important information). Thus, statistical measures such as the standard deviation provide no meaningful insight into the distribution of financial data. 
     Providing reasonable methods for the analysis of financial market data is essential for investors. Reasonable statistical analysis of financial data should at a minimum provide an accurate assessment of potential financial risk and reward. However, conventional methods, which rely upon assumptions of a Gaussian distribution, are dangerous to investors because these analyses understate the true risk and overstate potential rewards for an investment or trading strategy. Thus, this information is not generally useful and if relied upon promotes imprudent investment decisions. In general, the heavy tailed nature of financial data presents significant challenges in providing meaningful statistical analysis. 
     SUMMARY OF THE INVENTION 
     The present invention provides a method and system for the statistical analysis, display and dissemination of financial data over an information network such as the Internet and WWW. The present invention utilizes resampled statistical methods for the analysis of financial data. Resampled statistical analysis provides a meaningful and reasonable statistical description of financial information, which typically escapes modeling using parametric methods (i.e., assumptions of a Gaussian distribution). 
     The present invention includes a financial information network node that is coupled to an information network such as the Internet. The financial information network node includes a front end subsystem, a resampled statistical analysis engine (“RSAE”) and a graphics rendering engine (“GRE”). The front end subsystem provides a graphical user interface (“GUI”) that allows clients also coupled to the information network to submit requests for resampled statistical analysis of various financial investments and receive graphical display of the results. The RSAE performs resampled statistical analysis of financial data in response to user queries and incorporates routines to preserve temporal correlation in financial data, which necessarily provides more accurate analysis. In addition, the RSAE provides for user control of a number of parameters to simulate various financial environmental conditions. For example, according to one embodiment, the RSAE allows a user to simulate either bull or bear market conditions by setting a bias parameter that controls a degree of randomness in the resampling process. The GRE generates a graphical display of statistical distributions generated by the RSAE. 
     According to one embodiment, the present invention employs a parallel processing architecture to speed generation of the resampled statistics. The parallel architecture is afforded by the nature of the resampling algorithm itself, which permits the financial data to be vectorized. This parallel processing architecture provides at least two significant advantages. First, the architecture permits the delivery and processing of financial data in compressed time frames, which facilitates “real time” or “near real time” statistical analysis. In addition, the parallel computation scheme provides the ability to perform statistical analysis on a large number of financial entities (e.g., a mutual fund or hedge fund) through a weighting process. 
     According to one embodiment of the present invention for implementation on the Internet, a financial information site is coupled to the Internet via a front end subsystem including a WWW server. The financial information site includes a front end subsystem, a RSAE and a GRE. In addition, the financial information site maintains a database of financial data for any number of financial entities such as companies, mutual funds etc. The financial information site also maintains a database of clients that have registered with the financial information site and desire to obtain statistical analysis of financial data. 
     In order to perform a resampled statistical analysis, a query is received from a client via the front end subsystem. A client may specify a number of parameters including an investment or investments (e.g., a portfolio) to be analyzed, a financial function, a sample size, a period, a type of plot and a bias parameter, which controls the randomness of the resampling process. Based upon the parameters specified by the client, the RSAE performs a resampled statistical analysis of relevant financial data. The GRE then produces a distribution plot based upon the output generated by the RSAE, which is presented to the client via the front end subsystem. 
     According to one embodiment of the present invention, the RSAE performs at least three types of financial functions on financial data. A gross rate of return function provides analysis of the gross rate of returns for an investment over a specified time period. A maximum drawdown function provides analysis of a maximum drawdown for an investment over a specified period. A monitor function provides analysis of a number of “up” and “down” days for a particular investment over a period of time. 
     The financial information site also provides functionality for storing a set of client specified alert rules that are used to automatically monitor the behavior of investments based upon a resampled statistical analysis process and notify clients of the financial information site when the behavior of a particular investment violates a specified rule. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a block diagram of a network architecture that illustrates the relationship between a financial information site and a client according to one embodiment of the present invention. 
     FIG. 2 is a detailed block diagram of a financial information site according to one embodiment of the present invention. 
     FIG. 3 depicts the structure of a client record that is stored in a client database at a financial information site according to one embodiment of the present invention. 
     FIG. 4 depicts the structure of an investment record that is stored in an investment database at a financial information site according to one embodiment of the present invention. 
     FIG. 5 a  depicts the structure of an alert rule record that is stored in an alert rules database at a financial information site according to one embodiment of the present invention. 
     FIG. 5 b  depicts the structure of a rule object record according to one embodiment of the present invention. 
     FIG. 6 a  depicts a data structure for storing financial data in a financial database according to one embodiment of the present invention. 
     FIG. 6 b  depicts a data structure for storing a financial return according to one embodiment of the present invention. 
     FIG. 7 depicts a data structure for storing a function prototype in a function database at a financial information site according to one embodiment of the present invention. 
     FIG. 8 depicts a data structure for storing plot information in a plot database at a financial information site according to one embodiment of the present invention. 
     FIG. 9 a  (reprinted from Efron and Tibshirani) depicts the underlying theory of the bootstrap method. 
     FIG. 9 b  depicts a procedure for performing a bootstrap method to generate a distribution of bootstrap replications according to one embodiment of the present invention. 
     FIG. 10 is a flowchart of steps for performing a resampled analysis of an investment and generating a graphical output according to one embodiment of the present invention. 
     FIG. 11 is a flowchart that depicts a set of steps to initiate a resampled statistical analysis of financial data using a parallel processing architecture according to one embodiment of the present invention. 
     FIG. 12 is a flowchart of a parallel processing control process according to one embodiment of the present invention. 
     FIG. 13 is a flowchart of a set of steps for performing a resampled statistical analysis according to one embodiment of the present invention. 
     FIG. 14 is a flowchart of a set of steps for performing a biasing procedure according to one embodiment of the present invention. 
     FIG. 15 is an exemplary plot of a resampled statistical analysis comparing two investment strategies with respect to gross rate of returns according to one embodiment of the present invention. 
     FIG. 16 is an exemplary plot of a resampled statistical analysis comparing two investment strategies with respect to maximum drawdown returns according to one embodiment of the present invention. 
     FIG. 17 is an exemplary plot of a resampled statistical analysis comparing multiple investment strategies with respect to a monitor function according to one embodiment of the present invention. 
    
    
     DETAILED DESCRIPTION 
     Although the embodiments described herein utilize the Internet and WWW, the present invention is compatible with any type of information network public or private and thus, the embodiments described herein are not intended to limit the scope of the claims appended hereto. For example, the present invention could be implemented using a private Intranet, local area network (LAN), metropolitan area network (MAN), wide area network (WAN) or even a wireless network 
     FIG. 1 is a block diagram of a network topology that illustrates the relationship between the Internet, a financial information site and various clients according to one embodiment of the present invention. Based upon queries submitted by clients, financial information site  119  performs resampled statistical analysis of financial data and provides a graphical display of distribution results. Details of the functionality provided by financial information site  119  are described below. 
     Clients  105   a-   105   c  communicate with financial information site  119  via Internet  114 . According to the embodiment depicted in FIG. 1, financial information site  119  is coupled to Internet  114  via T1 line  130   b.  Client  105   a  illustrates a typical narrowband client coupled to Internet  114  via a dial-up connection described in more detail below. Client  105   b  illustrates a typical broadband client coupled to Internet  114  via a cable modem. Client  105   c  illustrates a corporate client that is coupled to Internet via T1 line  130   c  and server  151 . Corporate client  105   c  includes three network nodes  171   a - 171   c  that share bandwidth on Ethernet  161 . Although FIG. 1 illustrates three clients ( 105   a - 105   c  ), it is to be understood that financial information site  119  may serve any arbitrary number of clients  105  limited only by the processing power and bandwidth available. 
     As illustrated in FIG. 1, client  105   a  communicates with financial information site  119  via personal computer  112   a,  modem  115   a,  POTS telephone line  117  and Internet service provider  120   a . Internet service provider  120   a  includes modem bank  121  and router  135   a  that routes packets received from modem bank  121  onto Internet  114  via T1 line  130   a.  Packets are routed over Internet  114  to client gateway server  140   a  at financial information site  119  via T1 line  130   b.    
     Client  105   a  utilizes personal computer  112   a  to navigate Internet/World-Wide-Web (WWW  114  via browser software (not shown) and display device (not shown). The browser software permits navigation between various file servers connected to Internet  114 , including client gateway server  140   a  at financial information site  119 . The browser software also provides functionality for rendering of files distributed on the Internet (i.e., through plug-ins or Active X controls). 
     In order to transmit data to financial information site  119 , personal computer  112   a  transmits signals through a dial-up connection utilizing modem  115   a.  Modem  115   a  performs modulation of digital signals generated by personal computer  112   a  onto an analog carrier signal for transmission over the public switched telephone network (“PSTN”) (not shown). Modem  115   a  also performs demodulation of signals received over local lines (e.g., 117) from the PSTN extracting digital byte codes from a modulated analog carrier. 
     Signals are received at ISP  120   a , which is connected to the PSTN through modem bank  121 . Digital IP packets are then transmitted via Internet  114  and various routers (not shown) to WWW server  140   a.  IP packets are also transmitted in the reverse direction from WWW server  140   a  to personal computer  112   a.    
     Client  105   b  is coupled to Internet  114  via a broadband cable connection. In particular, personal computer  112   b  transmits packets via cable modem  115   b  to ISP  120   b  where the packets are routed over Internet  114  to client gateway server  140   a.  Packets from financial information site  119  traverse a reverse path to client  105   b  . Similar to client  105   a,  client  105   b  utilizes browser software to navigate Internet  114  and WWW. 
     Corporate client  105   c  includes network nodes  171   a - 171   c,  which are coupled to Internet via Ethernet  161 , server  151  and T1 line  130   c . Network nodes  171   a - 171   c  may communicate with financial information site  119  via Ethernet, server  151 , T1 line  130   c , Internet  114  and T1 line  130   b.  Similar to clients  105   a - 105   b  , it is assumed that users at network nodes  171   a - 171   c  utilize browser software to navigate Internet  114  and WWW. 
     The specific nature of clients  105   a - 105   c  and the methods through which they are coupled to Internet  114  depicted in FIG. 1 are merely exemplary. The present invention is compatible with any type of Internet client and/or connection (broadband or narrowband). In general, it is to be understood that clients  105  may connect to Internet  114  using any potential medium whether it be a dedicated connection such as a cable modem, T1 line, DSL (“Digital Subscriber Line”), a dial-up POTS connection or even a wireless connection. 
     FIG. 2 is a detailed block diagram of a financial information site according to one embodiment of the present invention. Financial information site  119  includes front end subsystem  129 , RSAE  139 , GRE  149 , back end server  140 , client database  150   g  and alert rules database  150   c.    
     Front end subsystem  129  includes client/gateway server  140   a,  which is coupled to GUI database  150   a.  Front end subsystem  129  provides a GUI, which allows clients  105  to transmit information to and receive information from financial information site  119 . According to one embodiment GUI database  150   a  stores HTML (“Hypertext Markup Language”) code (i.e., WWW pages) relating to various information and functions provided by financial information site  119 . For example, GUI database  150   a  may store a HTML “home page” for financial information site  119  or HTML pages including forms, which allow the input of data at financial information site  119 . 
     Front end subsystem  129  also includes SMTP (“Simple Mail Transport Protocol”) server  140   f  SMTP server  140   f  performs transmission of e-mail messages to clients  105  associated with financial information site  119  in order to provide notification regarding various events (as described in more detail below). 
     Client gateway server  140   a  communicates with back end server  140   b,  which controls and orchestrates the large-scale processing of data at financial information site  119 . In particular, back end server  140   b  handles responses to requests from clients  105  for resampled statistical analysis of investments. For example, back end server  140   b  submits requests to RSAE for resampled statistical analysis of financial data and submits requests to GRE for graphical rendering of output generated by RSAE. Back end server  140   b  communicates with control server  140   c  at RSAE  139 , graphics rendering server  140   e  at GRE  149  and SMTP server  140   f  at front end 1 subsystem  29 . 
     RSAE  139  includes control server  140   c,  parallel process control server  140   d , parallel processors  112   a - 112   e  (each including local respective cache  112   a   1 - 112   e   1 ), financial database  150   d,  investment database  150   e,  function database  150   f,  shared memory area  160   a  and output data area  160   b.  Note that RSAE  139  depicted in FIGS. 1-2 utilizes a parallel processing architecture. This parallel scheme is merely exemplary and is not intended to limit the scope of the claims appended hereto. Other embodiments may not rely upon a parallel processing architecture at RSAE  139 . 
     Control server  140   c  provides communication functions between back end server  140   b  and RSAE  139  and controls the overall operation of a resampled statistical analysis process. Control server  140   c  is coupled to parallel process control server  140   d  and shared memory area  160   a.  Shared memory area  160   a  stores sample data for financial investments currently being analyzed by RSAE  139 . As described in detail below, control server  140   c  receives requests for parallel processing computations from back end server  140   b,  performs certain initialization functions, loads appropriate data into shared memory  160   a  and forwards these requests to parallel process control server  140   d  for performance. Control server  140   c  then waits for a completion signal from parallel process control server  140   d  and provides the output results to back end server  140   b  for further processing (e.g., graphical rendering via GRE  149 ). 
     Control server  140   c  is also coupled to financial database  150   d,  investment database  150   e,  function database  150   f  and shared memory area  160   a.  Financial database  150   d  (described in more detail below) stores financial sample data relating to particular investments. Investment database  150   e  (described in more detail below) stores financial data regarding investments for which clients may be interested in performing resampled statistical analysis (i.e., stocks, mutual finds, etc.). Function database  150   f  (described in more detail below) stores function prototypes for functions to be performed on financial data. 
     Parallel process control server  140   d  is coupled to parallel processors  112   a - 112   e  and output data memory area  160   b.  Parallel processors  112   a - 112   e,  which are each coupled to a respective local cache  112   a   1 - 112   e   1  and shared memory area  160   a , perform resampled statistical analysis of sample data stored in shared memory area  160   a  (i.e., resampled statistical computations). Parallel process control server  140   d  (described in more detail below) orchestrates and controls parallel computation processes running on parallel processors  112   a - 112   e.  In particular, parallel process control server  140   d  requests initialization of resampled statistical analysis of data stored in shared memory area  160   a  from individual processors  112   a - 112   e.  Upon completion of all parallel processes running on processors  112   a - 112   e,  parallel process control server  140   d  retrieves the results stored in local caches  112   a   1 - 112   e   1  and stores the aggregate data in output data area  160   b  where it can be processed further (e.g., in GRE  149 ). 
     GRE  149  performs graphical rendering (e.g., plots) of output data generated by RSAE  139 . GRE  149  includes graphics rendering engine server  140   e,  which is coupled to plot database  150   b.  As described in detail below, plot database  150   b  stores data regarding the rendering and formatting of distribution plots generated by graphics rendering engine server  140   e.    
     Back end server  140   b  is also coupled to client database  150   g  and alert rules database  150   c.  Client database  150   g  stores information related to clients that have registered with financial information site  119 . Alert rules database  150   c  stores data pertaining to client specified rules for alerting clients to near real time behavior of investments. According to one embodiment of the present invention, clients are alerted to rule violations by e-mail via SMTP server  140   f,  which is also coupled to back end server  140   b.    
     FIG. 3 depicts the structure of a client record that is stored in a client database  150   g  at a financial information site  119  according to one embodiment of the present invention. Each client record  305  includes client ID field  310 , client password field  315 , portfolio* pointer field  320 , alert rules* pointer field  325 , e-mail address field  330 , billing parameter field  335  and preference parameter fields  340 (1)- 340 (N). 
     Client ID field  310  stores a unique 16-byte character array or pointer to a character array of a client that has registered with financial information site  119 . Client password field  315  stores a unique 16-byte character array or pointer to a character array of a password associated with a client  105 . Clients  105  may establish a client ID and password upon registration with financial information site  119 . 
     Portfolio* pointer field  320  stores a pointer to a linked list of investments that a client  105  has selected for tracking using financial information site  119 . According to one embodiment of the present invention, each link in the linked list stores an identifier of an investment entity as described in more detail below. Alert rules* pointer field  340  stores a linked list of alert rule record IDs (discussed in more detail below) that specify particular financial alert rules that are monitored by financial information site  119  and associated with individual clients  105 . These rules are used to notify individual clients  105  of the occurrence of particular events they wish to follow based upon a resampled statistical analysis of financial data. E-mail address field  330  stores a 32-byte character array or pointer to a character array of an e-mail address of a client  105 . Billing parameter field  335  stores a pointer to billing object record that includes billing information for a client  105 . Preference parameters  340 (1)- 340 (N) store preference parameters related to customization functions associated with financial information site  119 . 
     FIG. 4 depicts the structure of an investment record that is stored in an investment database  150   e  at a financial information site  119  according to one embodiment of the present invention. Investments may represent stocks, mutual funds, etc. Each investment record  405  includes investment ID field  410 , investment name field  415  and investment data pointer  420 . Investment ID field  410  stores a unique 32-bit value corresponding to a particular investment. Investment name field  415  stores a 16-byte character array of a name of an investment. Investment data pointer  420  stores a pointer to a linked list of financial data records related to an investment, which are stored in financial database  150   d  (described in more detail below). 
     FIG. 5 a  depicts the structure of an alert rule record that is stored in an alert rules database  150   c  at a financial information site  119  according to one embodiment of the present invention. According to one embodiment of the present invention, each alert rule specifies a percentile constraint of a resampled distribution for which a client  105  desires notification. Clients  105  of financial information site  119  may desire to be notified if the occurrence of a current event is extremely unlikely. As described in detail below, financial information site  119  executes a process to notify clients if a threshold percentile of a resampled statistical distribution is either below or above a current value of a financial event, indicating that the event is unlikely. For example, a client  105  may desire to be alerted if the gross rate of returns for a specified investment over a 200-day period assumes an improbable value. In this case, each day (or at a frequency specified by a client  105 ), financial information site  119  calculates the actual gross rate of returns for the investment over the last 200 days. Then, financial information site  119  executes a resampled statistical process to evaluate the gross rate of returns for 200-day periods described in detail below) to determine whether a percentile value of the distribution is above or below the current value. If so, the current value is highly unlikely and the client  105  is notified via e-mail. 
     Each alert rule record  505  includes rule ID field  510  and rule function object* pointer field  515 . Rule ID field  510  stores a unique 32-bit integer value pertaining to an alert rule, which is used for identification purposes. Rule function object pointer field  515  stores a reference to a rule object (described with reference to FIG. 5 b ) relating to the occurrence of a financial event for which a client desires notification. 
     FIG. 5 b  depicts the structure of an alert rule object according to one embodiment of the present invention. Each rule alert rule record  507  includes investment ID field  520 , function field  525 , periods field  530 , operator field  535 , percentile value field  540 , sample size field  545  and replications field  550 . Investment ID field stores a 32-bit integer value identifying an investment, as described below with respect to FIG. 6 a . Function field  525  stores a 32-bit function ID of a function record as described below with respect to FIG.  7 . Periods field  530  stores a number of periods (i.e., days) for which the client  105  desires to evaluate the investment. Operator field  535  stores a 4-bit field indicating an operator such as ‘&lt;’ or‘&gt;.’ Percentile value field  540  stores an integer representing a percentile value. Sample size field  545  stores a 32-bit integer value representing a sample size for which to conduct a resampled statistical analysis. Replications field  550  stores a 32-bit integer value representing a number of replications to perform in conducting a resampled statistical process. 
     As described in detail below, the resampled process is conducted based upon parameters stored in fields  520 ,  525 ,  530 ,  545  and  550 . Based upon operator filed  535 , it is then determined whether the distribution results for a resampled statistical process above or below the current value exceed the percentile value stored in percentile value field  540 . If so, the client is notified 
     FIG. 6 a  depicts a data structure for storing financial data in a financial database according to one embodiment of the present invention. Each financial data record  605  includes investment ID field  610 , and one or more return objects  625 (1)- 625 (N). Investment ID field  610  stores a 32-bit integer value uniquely identifying a financial record. Return objects  625  (as described in FIG. 6 b ) store actual data values of returns associated with the investment represented by investment ID field  610 . 
     FIG. 6 b  depicts a data structure for storing a return object according to one embodiment of the present invention. Each return object  625  includes a date field  630  and a value field  635 . Date field  630  stores a data object corresponding to the data of a return and value field  635  stores the value (dollar amount or otherwise) of the investment on the date stored in date field  630 . 
     FIG. 7 depicts a data structure for storing data in a function database  150   f  at a financial information site  119  according to one embodiment of the present invention. Function database  150   f  stores various function prototypes for functions to be performed on investment data, which are used in performing resampled statistical analysis of financial data. For example, according to one embodiment function database  150   f  stores function prototypes for gross rate of return, maximum drawdown and/or a monitor function. Each function record  705  includes function prototype ID  710  and function prototype object  715 . Function prototype ID field  710  stores a unique 32-bit integer value pertaining to a function prototype, which is used for identification purposes. Function prototype object field  715  stores a 1024-byte character array of a function prototype. The syntax for representing a function prototype stored in function prototype object field  715  is variable. Practitioners skilled in the art will recognize that many data structures and techniques may be utilized to represent function prototypes. According to one embodiment of the present invention, a maximum drawdown function prototype is stored in function database  150  based upon the following equation: For a set of returns (r 1 -r n ):          Max   .              Drawdown     =     1   -     Min                   (             1   +     r   1       1               (     1   +     r   1       )          (     1   +     r   2       )       1               (     1   +     r   1       )          (     1   +     r   2       )          (     1   +     r   3       )       1         ⋯             (     1   +     r   1       )          (     1   +     r   2       )          (     1   +     r   3       )                   …                   (     1   +     r   n       )       1             0             (     1   +     r   1       )          (     1   +     r   2       )         (     1   +     r   1       )                 (     1   +     r   1       )          (     1   +     r   2       )          (     1   +     r   3       )         (     1   +     r   1       )           ⋯             (     1   +     r   1       )          (     1   +     r   2       )          (     1   +     r   3       )                   …                   (     1   +     r   n       )         (     1   +     r   1       )               0       0             (     1   +     r   1       )          (     1   +     r   2       )          (     1   +     r   3       )           (     1   +     r   1       )          (     1   +     r   2       )             ⋯             (     1   +     r   1       )          (     1   +     r   2       )          (     1   +     r   3       )                   …                   (     1   +     r   n       )           (     1   +     r   1       )          (     1   +     r   2       )                 ⋮       ⋮       ⋮       ⋯       ⋮           0       0       0       ⋯             (     1   +     r   1       )          (     1   +     r   2       )          (     1   +     r   3       )                   …                   (     1   +     r   n       )           (     1   +     r   1       )          (     1   +     r   2       )          (     1   +     r   3       )                   …                   (     1   +     r     n   -   1         )               )                                
     According to one embodiment of the present invention, a gross rate of returns function prototype is stored in function database  150   f  based upon the follow equation: For a set of returns (r 1 -rn):          Gross                 Rate                 of                 Return     =       [       ∏   i          (     1   +     r   i       )       ]     -   1                            
     According to one embodiment of the present invention, a monitor function calculates a number of ‘up’ or ‘down’ days for a given investment over a certain period. Thus, the following equation describes a monitor function:          ∑   i   N          δ                   (       r   i     =   up     )                              
     Thus, for example, according to one embodiment, the maximum drawdown function, the gross rate of return function (as described above) and the monitor function are coded according to a predefined syntax and stored as a function prototype in function database  150   f.    
     FIG. 8 depicts a data structure for storing plot information in a plot database at a financial information site according to one embodiment of the present invention. Each plot type record  805  stores plot type ID field  810  and one or more plot parameter fields  825 (1)- 825 (N). Plot ID field stores a unique 32-bit integer identifying a particular plot type. Plot parameter fields  825 (1)- 825 (N) store various parameters relating to formatting of plots. 
     FIG. 9 a  (reprinted from Efron and Tibshirani) depicts the underlying theory of the bootstrap method. Ideally statistical inferences are based on a known probability distribution F. A parameter is a function of a known probability distribution F. 
     
       
         θ= t ( F ) 
       
     
     Furthermore, generally financial data may not be modeled parametrically because it is heavy tailed (i.e., non-Gaussian) and therefore, F is not known or ascertainable. For example, with respect to financial data, an investor may desire to study a specific parameter of a financial investment such as the gross rate of return of a stock over a certain period of time that is dependent upon knowledge of the true probability distribution function for the investment. However, generally neither the PDF for an investment, nor the PDF for a parameter such as the gross rate of return over a specified time period for the investment (which is dependent upon the underlying PDF) is known. 
     Resampled statistical methods such as the bootstrap attempt to estimate the PDF of an unknown distribution using sampled data. Typically, sample data is available for an investment that is dependent upon an unknown PDF F. 
     
       
           F→x= ( x   1   ,x   2   , . . . x   n ) 
       
     
     The empirical distribution function {circumflex over (F)} is defined to be the discrete distribution that puts probability 1/n on each value x i , i=1,2, . . . n. {circumflex over (F)} assigns to a set A in the sample space of x its empirical probability Prob{A}=#{x i εA}/n, In, the proportion of the observed sample x=(x 1 , 2 , . . . ,x n ). 
     The plug-in principle is a method of estimating parameters from samples. The plug-in estimate of a parameter θ=t(F) is defined to be {circumflex over (θ)}=t({circumflex over (F)})  910 . These statistics are referred to as summary statistics, estimates or estimators. Resampled statistical methods attempt to determine the distribution of {circumflex over (θ)}, an estimator of θ, derived from a sample x. 
     Bootstrap methods depend on the notion of a bootstrap sample. If {circumflex over (F)} is an empirical distribution with probability of 1/n for each of the observed values x i , i=1,2, . . . n, a bootstrap sample is defined to be a random sample of size n drawn from {circumflex over (F)}, x*=(x 1 *,x 2 *, . . . ,x n *), where {circumflex over (F)}→(x 1 *,x 2 *, . . . ,x n *). The star notion indicates that x* is not the actual data set x, but rather a randomized, or resampled version of x. The bootstrap data points x 1 *,x 2 *, . . . ,x n * are a random sample of size n drawn with replacement from the population of n objects (x 1 , x 2 , . . . , x n ). Corresponding to a bootstrap data set x* is a bootstrap replication of {circumflex over (θ)}, {circumflex over (θ)}*=s(x*)  915 . The quantity s(x*) is the result of applying the same function s(·) to x* as was applied to x (i.e., the statistical function of interest). For example, s(·) may be the gross rate of return of an investment over a specific period of time. 
     Thus the bootstrap attempts to estimate a parameter of interest θ=t(F) from an unknown distribution F using a random sample x=(x 1 ,x 2 , . . . ,x n ). Given a random sample x=(x 1 ,x 2 , . . . ,x n ) and a statistic {circumflex over (θ)}=s(x,F) that depends on the sample and possibly the underlying distribution F, the distribution of {circumflex over (θ)}, 
     
       
         ζ F ({circumflex over (θ)}= s (x, F )) 
       
     
     is estimated by that of 
     
       
         ζ {circumflex over (F)} ({circumflex over (θ)}*= s (x*, {circumflex over (F)} ) 
       
     
     FIG. 9 b  depicts a process for performing a bootstrap method (a resampled statistical method) to generate a distribution of bootstrap replications according to one embodiment of the present invention. In step  920 ,  a  sample space x is selected. In step  925 ,  a  statistical function based on the sample space data is computed {circumflex over (θ)}=t({circumflex over (F)}). In step  930 , bootstrap samples x*=(x 1 *,x 2 *, . . . ,x n *), are generated from the sample space using a resampling process. In step  935 ,  a  bootstrap replication {circumflex over (θ)}=s(x*) is computed for each bootstrap sample using a desired function. In step  940 , a plot of the distribution of bootstrap replications (s(x* 1 ),s(x* 2 ) . . . s(x* B )) is generated in order to estimate the distribution of {circumflex over (θ)}. 
     FIG. 10 is a flowchart of steps for initializing a resampled statistical analysis of financial data at a financial information site  119  according to one embodiment of the present invention. In step  1005 , the process is initiated upon receipt of a request for a resampled statistical analysis of financial data, which is received via front end subsystem  129  (e.g., via an HTML form). In step  1010 , input parameters relating to a resampled statistical analysis are received via client/gateway server  140   a  and transmitted to back end server  140   b.  According to one embodiment, the following parameters are solicited from a client  105 : investment; 
     function; 
     periods (Q); 
     bias; 
     sample_size; 
     replications; and 
     plot_type. 
     The ‘investment’ parameter specifies an identifier of an investment (i.e.,  410 ) stored in investment database  150   e . The ‘function’ parameter specifies a function prototype identifier (i.e.,  710 ) stored in function database  150   f  . For example, according to one embodiment, the function prototype may correspond to a function for maximum drawdown, gross rate of return or a monitor function as described above. The ‘periods’ parameter specifies a number of periods for which a client  105  desires to evaluate an investment. For example, a client  105  may desire to perform a resampled statistical analysis for the gross rate of returns of an investment over a 253-day period. The ‘bias’ parameter is a decimal value that is either −1 or between 0 and 1 that specifies the degree of randomness in the resampling process. A value of −1 indicates that the resampling process should be conducted purely randomly. As described in more detail below, if the ‘bias’ parameter is between 0 and 1, sampling is performed so that b% of the samples are ‘up’ days and 1−b% of the samples are ‘down’ ‘days, where b=bias. Thus, if b=1, only ‘up’ days will be selected and if b=0 only ‘down’ days are selected. The ‘sample_size’ parameter specifies a number of samples to use in the resampling process (the size of the x). The ‘replications’ parameter specifies a number of bootstrap samples to be used in the resampling process. The ‘plot_type’ parameter specifies a plot type identifier (i.e.,  810 ) pertaining to formatting parameters to be used in generating a plot of distribution results. 
     In step  1015 , back end server  140   b  requests the initiation of a resampled statistical analysis process at RSAE  139 . In particular, according to one embodiment of the present invention, back end server  140   b  transmits the following vector to control server  140   c  at RSAE  139 : 
     request_resampling process (investment, function, periods (Q), bias, sample_size, replications, plot_type) 
     Back end server  140   b  then waits for completion of the resampled statistical analysis task. In step  1020 , back end server  140   b  determines whether RSAE  139  has completed the resampling process. According to one embodiment, upon completion of the resampling process, control server  140   c  transmits a completion signal to back end server  140   b  and an address in output data area  160   b  where output data of a resampled statistical process is stored. If the resampling process is not completed (‘no’ branch of step  1020 ), back end server  140   b  continues to wait for notification. If the resampling method is completed (‘yes’ branch of step  1020 ), in step  1025 , back end processor  140   b  requests a graphics plot from GRE  129 . In particular, according to one embodiment, back end processor  140   b  transmits the following vector to graphics rendering server  140   e  at GRE  149 : 
     plot(OutAddr, plot_type, plot_parameters). 
     OutAddr specifies an address in output data area, which stores results of a resampled statistical process previously conducted by RSAE  139 , plot_type specifies a plot type requested by a client  105  and plot_parameters specifies additional plotting parameters that may be required by GRE  129 . Back end server  140   b  then waits for completion of the plot. In step  1027 , back end processor  140   b  determines whether graphics rendering server  140   e  has completed the requested plot (i.e., whether graphics server has transmitted a completion signal to back end processor). According to one embodiment, upon completion of a plot, graphics rendering server  140   e  transmits a completion signal to back end processor  140   b.  Graphics rendering server  140   e  also transmits results of the plotting process in the form of plot data, which may be used to dynamically create an HTML page for transmission to a client  105 . If the plot is not finished (‘no’ branch of step  1027 ), back end processor  140   b  continues to wait for the completion signal. If the plot has been completed (‘yes’ branch of step  1027 ) in step  1029  and back end processor  140   b  transmits the plot data results (e.g., HTML page) to client/gateway server  140   a  for transmission to client  105 . The process ends in step  1030 . 
     FIG. 11 is a flowchart that depicts a set of preparation steps performed by a control server  140   c  at a financial information site  119  to initialize a resampled statistical analysis of financial data using a parallel processing. In step  1105 , the process is initiated upon the receipt of a request_resampling_process vector from back end server  140   b  as described above with reference to FIG.  10 . 
     In steps  1115 - 1119 , control server  140   c  reserves appropriate memory in shared memory area  160   a  and output data area  160   b  and stores appropriate sample data for processing in shared memory area  160   a.  In particular, in step  1115 ,  a  sample space is determined using the sample_size parameter received in step  1105 . Because financial database  150   d  may store samples for investments for many different time periods, in step  1115 ,  a  set of relevant samples for the resampled statistical analysis requested by the client  105  is determined. In step  1117 , based upon the sample_size parameter, control server  140   c  determines an amount of memory required for storage of samples in shared memory area  160   a  and allocates an appropriate memory block in shared memory area  160   a  for storage of the samples. Further, based upon the replications parameter, server  140   c  also determines an amount of memory to reserve in output data memory area  160   b  for storage of results of the resampling process. In step  1119 , based upon the sample_size parameter, server  140   c  retrieves financial data samples from financial database  150   d  and stores these samples in shared memory area  160   a  in the memory block previously reserved in step  1117 . In step  1120 , process server  140   c  computes {circumflex over (θ)} from the sample data stored in shared memory area  160   a.  In particular, a statistical function such as the mean, median or standard distribution is calculated by dividing the sample space into appropriate length periods. 
     In steps  1125 - 1160 , control server  140   c  executes a series of steps to format and prepare the data for processing. Specifically, in step  1125 , autocorrelation of the sample space data stored in shared memory area  160   a  is analyzed. Specifically, control server  140   c  executes a process to calculate the autocorrelation and partial autocorrelation functions on the data stored in shared memory area  160   a  for a number of different lag periods (a) and stores the results in temporary storage. According to one embodiment, the following equations are utilized to calculate the autocorrelation and partial autocorrelation functions for the data stored in shared memory area  160   a:    
     ∀a&lt;n and 1≦x&lt;a: 
     Samples in the sample space are defined as: 
     r=(r 1 , ,r 2 , . . . ,r n ) 
     Shifted versions of the sample space are defined: 
     Z 1 ≡(r 1 ,r 2 , . . . ,r n−a ) 
     Z 2 ≡(r a+1 ,r 2 , . . . ,r n ) 
     Z x ≡(r a+1−x , . . . ,r n−x ) 
     The autocorrelation function is defined as:          ACF        (   a   )       =         S        (   a   )           Z   1          Z   2               S        (   a   )         Z   1              S        (   a   )         Z   2                                  
     The partial autocorrelation function is defined as:          PACF        (     x   ,   a     )       =           S        (   a   )           Z   1          Z   2         -         S        (   a   )           Z   2          Z   x                S        (   a   )           Z   1          Z   x                   1   -       (       S        (   a   )           Z   2          Z   x         )     2                           1   -       (       S        (   a   )           Z   1          Z   x         )     2                                    
     The following are intermediate calculations:                  S        (   a   )           Z   1          Z   2         =         (       Z       1   i     -              Z   1     _       )                     (       Z       2   i     -              Z   2     _       )         n   -   a   -   1                       S        (   a   )         Z   1       =           ∑     i   =   1       n   -   a              (       Z     1   i       -       Z   1     _       )     2         n   -   a   -   1                         S        (   a   )         Z   2       =           ∑     i   =     a   +   1       n            (       Z     2   i       -       Z   2     _       )     2         n   -   a   -   1                         Z     1   i       _     =       ∑     i   =   1       n   -   a              Z     2   i         n   -   a                         Z     2   i       _     =       ∑     i   =     a   +   1       n            Z     2   i         n   -   a                                      
     In step  1130 , the autocorrelation and partial autocorrelation data calculated is analyzed to determine a minimum lag factor (N) that minimizes the autocorrelation (a). The minimum lag factor (a) corresponds to the number of consecutive periods that are selected at one time during the resampling process. 
     In step  1135 , the bias parameter received in step  1105  is analyzed. If no bias is selected (i.e., bias=−1 and data is to be selected randomly), control passes to step  1045  (‘no’branch of step  1035 ). If bias&lt;&gt;0, in step  1040 , a bias initialization algorithm is performed as described in detail below. In step  1145 , it is determined whether the sample space data should be transformed. This determination is based upon the precise function requested by the client  105  (i.e., specified by function parameter). For example, if the function is gross rate of return over a specified period, no transformation step is required. However, if for example, the function type is the monitor type, the sample data is transformed to represent the sign of the returns only (i.e., −1 and +1). Other variations will exist depending upon the type of functions implemented. If no transformation is necessary (‘no’ branch of step  1145 ), control is transferred to step  1160 . Otherwise (‘yes’ branch of step  1045 ) in step  1150 , the data is transformed and restored in shared memory area  160   b  in step  1150 . 
     In step  1160 , the variable M=Int(Q/N) is determined. The variable ‘M’ specifies the number of samples to select for each resampling. In step  1165 , server  140   c  executes a request for parallel processing of data stored in shared memory area  160   a  by transmitting a vector to parallel processing control server  140   d  using the prototype: Request_Parallel_Process(input_addr, input_range, output_addr, output_range, M, N function, bias, replications). The parameters ‘input_addr’, ‘input_range’, ‘output_addr’ and ‘output_range’ correspond respectively to the start address and range in shared memory area  160   a  and output memory area  160   b  that were determined in step  1117 . The parameters M and N correspond to the variables determined in steps  1130  and  1160  respectively. The parameters ‘bias’ and ‘replications’ correspond to the same parameters received in step  1105 . 
     In step  1170 , control server  140   c  determines whether it has received a signal from parallel process control server  140   d  indicating the completion of parallel processing. If not (‘no’ branch of step  1070 ), control server  140   c  continues to wait for the completion signal. If a completion signal has been received (‘yes’ branch of step  1170 ), in step  1175 , control server  140   c  transmits a completion signal to back end server  140   b  along with a memory address in output data area  160   b  where the output data for the resampled method is stored. 
     FIG. 12 is a flowchart of a parallel processing control process according to one embodiment of the present invention. Although only 5 parallel processors ( 112   a - 112   e ) are depicted in FIG. 1, this number is arbitrary and any number P of parallel processors may be used to perform the resampling technique. Furthermore, although the method described herein utilizes a parallel processing architecture, the present invention does not require a parallel processing scheme. According to one embodiment of the present invention, the process depicted in FIG. 12 is implemented by parallel process control server  140   d  at financial information site  119 . 
     In step  1205 , parallel process control server  140   d  receives a vector requesting a parallel process as described in step  1165 . In step  1210 , parallel process control server  140   d  performs a load balancing step. In step  1220 , parallel process control server  140   d  requests the initiation of processes on individual parallel processors  112   a - 112   e  by transmitting a begin_process vector to each respective parallel processor  112   a - 112   e . According to one embodiment of the present invention the vector is transmitted to each processor  112   a - 112   e  to initiate parallel processing: begin_process(input_addr, input_range, M, N, function, bias, replications/P). The parameters ‘input_addr’, ‘input_range’, correspond respectively to the start address and range in shared memory area  160   a  that were received in step  1205 . The parameters ‘periods’, ‘bias’and ‘replications’, ‘M’ and ‘N’ correspond to the same parameters received in step  1205 . P specifies the number of parallel processors. Thus, each parallel processor computes replications/P replications. 
     In step  1230 , parallel process control server  140   d  checks to determine whether all parallel processors  112   a - 112   e  have completed processing. Upon completion of a processing task, each parallel processor executes a step of notifying control server  140   c  of completion. In particular, according to one embodiment, upon completion each parallel processor  112  sends parallel process control server a notification message defining a memory block where output results have been stored on the respective local cache  112   a   1 - 112   e   1 . If notifications have not been received from all processors  112   a - 112   e , parallel process control server  140   c  continues waiting (‘no’ branch of step  1120 ). Upon receipt of all completion notifications (‘yes’ branch of step  1230 ), parallel process control server  140   d  retrieves the data output for each parallel processor stored on local cache  112   a   1 - 112   a   5 . 
     In step  1240 , parallel process control server assembles all output data from each respective local cache  112   a   1 - 112   e   1  in output data area  160   b.  In step  1250 , parallel process control server  140   d  notifies server control  140   c  that the parallel processing is completed. The process ends in step  1260 . 
     FIG. 13 is a flowchart of set of steps for performing a resampled statistical method according to one embodiment of the present invention. The steps shown in FIG. 13 are executed on each parallel processor  112   a - 112   e  upon the request for a parallel process by server  140   d.  In step  1305 , the process is initiated and each parallel processor receives a begin_process vector as described above with reference to step  1220  of FIG.  12 . In step  1310  each respective processor  112   a - 112   e  determines a range of output memory in local cache  112   a   1 - 112   e   1  for storage of output results. In step  1320 , the parallel processor  112  determines a random start location in shared memory area  160   a  to begin sampling. In step  1325 , it is determined whether all replications (Q) have been completed. If not (‘no’ branch of step  1325 ) processing continues with steps  1330 - 1345 . Steps  1330 - 1345  correspond to the selection of a bootstrap sample x* Replication . In step  1330 , a temporary variable ‘Count’ is set to zero. In step  1335 , N consecutive periods of sample points are selected from shared memory area. The degree of randomness in selection is determined by the variable ‘bias’. If bias=−1, the beginning of each consecutive period is selected purely randomly. If the ‘bias’ parameter is set to any value other than −1, sampling is performed so that bias percent of the samples are “up” days for the investment and 1-bias percent of the samples are “down” days for the investment as described in detail below. Thus, if bias=1, only “up” days will be selected. In step  1340 , the temporary ‘Count’ variable is increment. A biasing process is described in detail below with reference to FIG.  14 . In step  1345 , it is determined whether Count=M. If not (‘no’ branch of step  1345 ), flow continues with step  1335  (i.e., another N consecutive periods are selected). If so (‘yes’ branch of step  1345 ), flow continues with step  1350 , and a bootstrap replication s(x *eplication ) is computed corresponding to the function s(.) received in step  1305 . In step  1355 , the bootstrap replication s(x *replication ) is stored in local cache (e.g.,  120   a   1 ). Flow continues with step  1325 . When all replications have been completed (‘yes’ branch of step  1325 ), in step  1360 , the parallel processor  112  notifies parallel process control server  140   d  that processing has been completed and also notifies parallel process control server  140   d  of the memory block in local cache (i.e.,  112   a-   112   e   1 ) where the output data is stored. 
     FIG. 14 is a flowchart of a set of steps for conducting a bias algorithm according to one embodiment of the present invention. The process is initiated in step  1405 . In step  1410 , the sample space is separated into two sets, a first set including only ‘up’ days and a second set including only ‘down’ days. In step,  1420   a  random number r, between 0 and 1 is selected. In step  1430 , it is determined whether the random number r&lt;=b (the bias parameter specified by the client). If so (‘yes’ branch of step  1430 ), in step  1440 , an up day is selected. If nor (‘no’ branch of step  1440 ), in step  1450 ,  a  down day is selected. The process ends in step  1460 . The process depicted in FIG. 14 is repeated for each bootstrap sample. 
     FIG. 15 is an exemplary plot of a resampled statistical analysis comparing two investment strategies with respect to gross rate of returns. As depicted in FIG. 15, investment strategy  1510  outperforms investment strategy  1520 . 
     FIG. 16 is an exemplary plot of a resampled statistical analysis comparing two investment strategies with respect to maximum drawdown. As depicted in FIG. 16, investment strategy  1610  outperforms investment strategy  1620 . 
     FIG. 17 is an exemplary plot of a resampled statistical analysis comparing two investment strategies with respect to a monitor function. As depicted in FIG. 17, investment strategies  1720  outperforms investment strategy  1710 .