Diversification measurement and analysis system

Abstract

This disclosure details methods for measuring and analyzing diversification of portfolio of assets. A dimension is a logical and quantitative means to measure diversification. As the number of dimensions increases so does diversification. Strong asset correlations among each other detract from the notion of independence. A positive correlation increases risks and is therefore undesirable. Assets are embedded into a high dimensional Euclidean vector space. The entire portfolio is interpreted as a set of points whose ambient dimension is the number of assets in the portfolio. The Karhunen-Loève expansion is used to quantify the KL dimension of the geometric object induced by a portfolio. The associated dimension is taken as the measure of diversification accounts for both the number of assets and the commonality within them. This ensures that measuring diversification as a dimension accounts for the complete diversification affect of the portfolio and is thus a valuable portfolio management tool.

1 . A machine comprising:
 (a) a means for calculating a diversification value for a portfolio based on at least one dimension derived from a Karhunen-Loève expansion for the portfolio; and   (b) a means for publishing the diversification value.   
     
     
         2 . The machine of  claim 1  wherein the means for calculating the diversification value for the portfolio is configured to:
 (a) receive the portfolio as input, wherein the portfolio comprises a plurality of assets; 
 (b) obtain a set of weight data by weighting each of the plurality of assets within the portfolio according to an investment value allocated to each of said assets; 
 (c) obtaining relationships between each of the plurality of assets and the set of weight data; and 
 (d) model the portfolio in a geometric space based on asset relationship and the set of weight data. 
 
     
     
         3 . The machine of  claim 1  wherein the means for calculating the diversification value for the portfolio is configured to:
 (a) receive the portfolio as input, wherein the portfolio comprises a plurality of assets; 
 (b) weight each of the plurality of assets within the portfolio according to an investment value allocated to each of said assets; 
 (c) obtain relationships between each asset from the plurality of assets and at least one other asset from the plurality of assets by performing an act taken from the set of acts comprising:
 calculating the relationships between each asset from the plurality of assets and at least one other asset; and, 
 receiving the relationships between each asset from the plurality of assets and at least one other asset; 
 
 (d) model the portfolio in a geometric space based on asset relationship and weight data. 
 
     
     
         4 . The machine of  claim 1 , wherein the means for calculating the diversification value for the portfolio is configured to create a rolling time series of the at least one dimension. 
     
     
         5 . The machine of  claim 1 , wherein the means for publishing the diversification value is configured to create a chart based on combining the diversification value with a set of portfolio statistical data. 
     
     
         6 . The machine of  claim 1 , wherein the means for calculating the diversification value for the portfolio is configured to create ratios of dimensions at one or more confidence intervals. 
     
     
         7 . The machine of  claim 1 , wherein the means for calculating the diversification value for the portfolio is configured to determine relative contributions of each asset in the portfolio to the diversification value for the portfolio, based on measuring the portfolio dimensionality with and without each asset. 
     
     
         8 . The machine of  claim 1 , wherein the means for calculating the diversification value for the portfolio is configured to create a ratio of a dimension at a selected confidence interval to the portfolios' ambient dimension. 
     
     
         9 . A system for measuring the diversification of a portfolio, the system comprising a computer processor and a set of computer-executable instructions configuring the system to perform a set of steps, the set of steps comprising:
 i. receiving, as input, a portfolio comprising a plurality of assets, asset relationship and weight data;   ii. modeling the portfolio in a geometric space using the asset relationships and weight data;   iii. computing one or more dimensions for the portfolio based on a Karhunen Loeve expansion for the portfolio; and   iv. producing a diversification metric using the one or more dimensions.   
     
     
         10 . The system of  claim 9  wherein the set of steps further comprises:
 (a) creating a rolling time series of the one or more dimensions; and 
 (b) using the rolling time series to detect changes in one or more elements taken from the set consisting of:
 i. diversification; 
 ii. systematic risk; and 
 iii. idiosyncratic risk. 
 
 
     
     
         11 . The system of  claim 9 , wherein the set of steps further comprises:
 (a) combining the diversification metric with portfolio statistical data; and   (b) creating a 3d contour surface, with the 3 dimensions depicting values for portfolio risk, portfolio return and the diversification metric.   
     
     
         12 . The system of  claim 9 , wherein the set of steps further comprises creating a ratio of dimensions taken from the Karhunen-Loève expansion. 
     
     
         13 . The system of  claim 9 , wherein the set of steps further comprises determining relative contributions of each asset in the portfolio to the diversification metric, based on measuring the one or more dimensions with and without each asset. 
     
     
         14 . The system of  claim 9 , wherein the set of steps further comprises comparing the one or more dimensions for the portfolio versus portfolio dimension data taken from the set consisting of:
 (a) a second portfolio;   (b) a sample of other portfolio diversification metrics;   (c) a population of other portfolio diversification metrics; and   (d) a variation of a conditioning system applied to the portfolio.   
     
     
         15 . The system of  claim 9 , wherein the set of steps further comprises the application of a conditioning system to input data. 
     
     
         16 . The system of  claim 9 , wherein the set of steps further comprises creating one or more ratios of dimensions, wherein a ratio is determined from the ratio set and is taken as the diversification metric. 
     
     
         17 . A holistic portfolio diversification analysis system which comprises a computer processor and is operable to produce an analytical framework for evaluating integrated risks from both systemic and non-systemic sources, the system configured according to a set of computer executable instructions encoded on a computer readable medium to perform a set of steps comprising:
 i. receiving, as input, a portfolio comprising a plurality of assets;   ii. obtaining a set of asset relationship and weight data for the portfolio;   iii. modeling the portfolio in a geometric space using the asset relationship and weight data; and   iv. computing an array of dimensions for the portfolio based on a Karhunen-Loève expansion for the portfolio.   
     
     
         18 . The system of  claim 17  wherein the set of steps further comprises:
 (a) creating a rolling time series of the array of dimensions; and 
 (b) using the rolling time series of the array of dimensions to detect changes in diversification. 
 
     
     
         19 . The system of  claim 17 , wherein the set of steps further comprises:
 (a) creating a rolling time series of the array of dimensions; and   (b) using the rolling time series of the array of dimensions to detect changes in systematic risk.   
     
     
         20 . The system of  claim 17 , wherein the set of steps further comprises creating ratios of dimensions. 
     
     
         21 . The system of  claim 17 , wherein the set of steps further comprises determining relative contributions of each asset in the portfolio to a diversification value for the portfolio, based on measuring the array of dimensions with and without each asset.