Systems and Methods for Portfolio Analysis

Abstract

In one aspect, the invention comprises a computer-implemented method comprising: (i) electronically receiving data describing one or more risk factors driving volatility of each of a plurality of securities comprised in a specified portfolio; (ii) for each of the plurality of securities, categorizing each of the risk factors as a random variable and identifying a distribution that best fits each risk factor's historical behavior; and generating a return distribution for the security, based on the best fit distributions; and (iii) aggregating the security return distributions to generate a return distribution for in the specified portfolio. Other aspects and embodiments comprise analogous software and computer systems.

1 .- 39 . (canceled) 
     
     
         40 . A computer-implemented method comprising:
 electronically receiving, at a computer processor, data describing one or more risk factors associated with volatility of each of a first plurality of securities in a first portfolio;   for each of the first plurality of securities, using a computer processor,
 categorizing each of said one or more risk factors as a random variable and identifying a distribution that best fits data regarding historical behavior of each of the one or more risk factors; 
 generating a first return distribution based on the best fit distribution; and 
   aggregating the first return distribution for each of the first plurality of securities to generate an aggregated security return for the first portfolio, wherein said aggregating includes aggregating an idiosyncratic return component of the first portfolio.   
     
     
         41 . The method of  claim 40 , wherein the aggregating further comprises linearly combining a systematic return component, the idiosyncratic return component, and a default return component of the first portfolio. 
     
     
         42 . The method of  claim 40 , wherein the idiosyncratic return of the first portfolio is a linear combination of returns for sub-portfolios related to correlation clusters. 
     
     
         43 . The method of  claim 40 , wherein the aggregating the idiosyncratic return component comprises subdividing the first portfolio according to correlation clusters and aggregating the clusters according to an entropy-based algorithm. 
     
     
         44 . The method of  claim 40  wherein generating said first return distribution for each of the first plurality of securities comprises:
 (a) sampling a value from each of the one or more risk factor's best fit distribution; 
 (b) conducting a simulation based on a scenario defined by said sampled values; 
 (c) incorporating data regarding a correlation among each of the one or more risk factors; 
 (d) multiplying the sampled value from each of the one or more risk factor's best fit distribution by a risk factor exposure corresponding to each of the one or more risk factors to obtain a risk factor product for each of the one or more risk factors; and 
 (e) summing the risk factor product for each of the one or more risk factors to generate the return distribution. 
 
     
     
         45 . The method of  claim 44 , further comprising performing steps (a)-(e) for each of a second plurality of securities in a second portfolio to generate a second distribution for said second portfolio. 
     
     
         46 . The method of  claim 45 , further comprising generating a tracking error distribution for said first portfolio by calculating a difference between the first return distribution for the first portfolio and the second return distribution for the second portfolio, and aggregating the first return distribution and the second return distribution. 
     
     
         47 . The method of  claim 46 , further comprising calculating value at risk for the first portfolio based on the first return distribution for the first portfolio and the tracking error distribution. 
     
     
         48 . The method of  claim 46 , further comprising calculating expected shortfall for the first portfolio based on the first return distribution for the first portfolio and the tracking error distribution. 
     
     
         49 . The method of  claim 46 , further comprising calculating volatility for the first portfolio based on the first return distribution for the first portfolio and said tracking error distribution. 
     
     
         50 . A non-transitory computer readable storage medium having computer-executable instructions recorded thereon that, when executed on a computer, configure the computer to perform a method comprising:
 electronically receiving data describing one or more risk factors associated with volatility of each of a first plurality of securities in a first portfolio;   for each of the first plurality of securities,
 categorizing each of said one or more risk factors as a random variable and identifying a distribution that best fits data regarding historical behavior of each of the one or more risk factors; and 
 generating a first return distribution based on the best fit distribution; and 
   aggregating the first return distribution for each of the first plurality of securities to generate an aggregated security return for the first portfolio, wherein said aggregating includes aggregating an idiosyncratic return component of the first portfolio.   
     
     
         51 . The non-transitory computer readable storage medium of  claim 50 , wherein the aggregating further comprises linearly combining a systematic return component, the idiosyncratic return component, and a default return component of the first portfolio. 
     
     
         52 . The non-transitory computer readable storage medium of  claim 50 , wherein the idiosyncratic return of the first portfolio is a linear combination of returns for sub-portfolios related to correlation clusters. 
     
     
         53 . The non-transitory computer readable storage medium of  claim 50 , wherein the aggregating the idiosyncratic return component comprises subdividing the first portfolio according to correlation clusters and aggregating the clusters according to an entropy-based algorithm. 
     
     
         54 . The non-transitory computer readable storage medium of  claim 50  wherein generating said first return distribution for each of the first plurality of securities comprises:
 (a) sampling a value from each of the one or more risk factor's best fit distribution; 
 (b) conducting a simulation based on a scenario defined by said sampled values; 
 (c) incorporating data regarding a correlation among each of the one or more risk factors; 
 (d) multiplying the sampled value from each of the one or more risk factor's best fit distribution by a risk factor exposure corresponding to each of the one or more risk factors to obtain a risk factor product for each of the one or more risk factors; and 
 (e) summing the risk factor product for each of the one or more risk factors to generate the return distribution. 
 
     
     
         55 . The non-transitory computer readable storage medium of  claim 54 , the method further comprising performing steps (a)-(e) for each of a second plurality of securities in a second portfolio to generate a second distribution for said second portfolio. 
     
     
         56 . The non-transitory computer readable storage medium of  claim 55 , the method further comprising generating a tracking error distribution for said first portfolio by calculating a difference between the first return distribution for the first portfolio and the second return distribution for the second portfolio, and aggregating the first return distribution and the second return distribution. 
     
     
         57 . The non-transitory computer readable storage medium of  claim 56 , the method further comprising calculating value at risk for the first portfolio based on the first return distribution for the first portfolio and the tracking error distribution. 
     
     
         58 . The non-transitory computer readable storage medium of  claim 56 , the method further comprising calculating expected shortfall for the first portfolio based on the first return distribution for the first portfolio and the tracking error distribution. 
     
     
         59 . The non-transitory computer readable storage medium of  claim 56 , the method further comprising calculating volatility for the first portfolio based on the first return distribution for the first portfolio and said tracking error distribution. 
     
     
         60 . A system comprising:
 memory operable to store at least one program; and   at least one processor communicatively coupled to the memory, in which the at least one program, when executed by the at least one processor, causes the at least one processor to:   electronically receive, at a computer processor, data describing one or more risk factors associated with volatility of each of a first plurality of securities in a first portfolio;   for each of the first plurality of securities,
 categorize each of said one or more risk factors as a random variable and identifying a distribution that best fits data regarding historical behavior of each of the one or more risk factors; and 
 generate a first return distribution based on the best fit distribution; and 
   aggregate the first return distribution for each of the first plurality of securities to generate an aggregated security return for the first portfolio, wherein said aggregating includes aggregating an idiosyncratic return component of the first portfolio.   
     
     
         61 . The system of  claim 60 , wherein the aggregating further comprises linearly combining a systematic return component, the idiosyncratic return component, and a default return component of the first portfolio. 
     
     
         62 . The system of  claim 60 , wherein the idiosyncratic return of the first portfolio is a linear combination of returns for sub-portfolios related to correlation clusters. 
     
     
         63 . The system of  claim 60 , wherein the aggregating the idiosyncratic return component comprises subdividing the first portfolio according to correlation clusters and aggregating the clusters according to an entropy-based algorithm. 
     
     
         64 . The system of  claim 60  wherein generating said first return distribution for each of the first plurality of securities comprises:
 (a) sampling a value from each of the one or more risk factor's best fit distribution; 
 (b) conducting a simulation based on a scenario defined by said sampled values; 
 (c) incorporating data regarding a correlation among each of the one or more risk factors; 
 (d) multiplying the sampled value from each of the one or more risk factor's best fit distribution by a risk factor exposure corresponding to each of the one or more risk factors to obtain a risk factor product for each of the one or more risk factors; and 
 (e) summing the risk factor product for each of the one or more risk factors to generate the return distribution. 
 
     
     
         65 . The system of  claim 64 , wherein the processor is further caused to perform steps (a)-(e) for each of a second plurality of securities in a second portfolio to generate a second distribution for said second portfolio. 
     
     
         66 . The system of  claim 65 , wherein the processor is further caused to generate a tracking error distribution for said first portfolio by calculating a difference between the first return distribution for the first portfolio and the second return distribution for the second portfolio, and aggregating the first return distribution and the second return distribution. 
     
     
         67 . The system of  claim 66 , wherein the processor is further caused to calculate value at risk for the first portfolio based on the first return distribution for the first portfolio and the tracking error distribution. 
     
     
         68 . The system of  claim 66 , wherein the processor is further caused to calculate expected shortfall for the first portfolio based on the first return distribution for the first portfolio and the tracking error distribution. 
     
     
         69 . The system of  claim 66 , wherein the processor is further caused to calculate volatility for the first portfolio based on the first return distribution for the first portfolio and said tracking error distribution.