Diversification measurement and analysis system
First Claim
1. A system for measuring the diversification of a portfolio comprising:
- a computer processor;
wherein said processor;
(i) receives, as input, a portfolio comprising a plurality of assets;
(ii) weights each of the plurality of assets within the portfolio according to an investment value allocated to each of said assets;
(iii) defines a relationship between each of the plurality of assets by correlating each of the plurality of assets within the portfolio;
(iv) models the portfolio in a geometric space by stretching a vector length associated with each of said plurality of assets in the portfolio in proportion to its concentration and contribution to the portfolio while retaining a set of orientations associated with said correlating step;
(v) determines a polytope based on the modeling step associated with the portfolio; and
(vi) compares said polytope to a symmetrical model to determine a diversification value;
wherein the polytope represents the portfolio whose assets are associated with the vector lengths which are stretched in the modeling step.
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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.
76 Citations
11 Claims
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1. A system for measuring the diversification of a portfolio comprising:
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a computer processor; wherein said processor; (i) receives, as input, a portfolio comprising a plurality of assets; (ii) weights each of the plurality of assets within the portfolio according to an investment value allocated to each of said assets; (iii) defines a relationship between each of the plurality of assets by correlating each of the plurality of assets within the portfolio; (iv) models the portfolio in a geometric space by stretching a vector length associated with each of said plurality of assets in the portfolio in proportion to its concentration and contribution to the portfolio while retaining a set of orientations associated with said correlating step; (v) determines a polytope based on the modeling step associated with the portfolio; and (vi) compares said polytope to a symmetrical model to determine a diversification value; wherein the polytope represents the portfolio whose assets are associated with the vector lengths which are stretched in the modeling step. - View Dependent Claims (2)
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3. A method comprising:
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a) receiving a portfolio defined by a set of asset data input through an input device, wherein the portfolio defined by the set of asset data comprises a plurality of assets; b) performing a step taken from a set of steps consisting of; i) computing relationships within the set of asset data; ii) receiving relationships within the set of asset data; c) weighting each of the plurality of assets within the portfolio according to an investment value allocated to each of said assets; d) modeling the portfolio in a geometric space with vectors representing each of the plurality of assets, the vectors having lengths stretched based on the weights for each of the plurality of assets; e) via a processor, applying a Karhunen-Loè
ve expansion process to the portfolio;f) determining a dimension of the portfolio based on applying the Karhunen-Loè
ve expansion process; andg) determining a diversification value for the portfolio based on the determined dimension for the portfolio. - View Dependent Claims (4, 5, 6, 7, 8, 9, 10, 11)
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Specification