System and method for displaying and analyzing financial correlation data

• US 9,098,877 B2
• Filed: 12/10/2013
• Issued: 08/04/2015
• Est. Priority Date: 01/30/2013
• Status: Active Grant

• Current Assignee: The Capital Group Companies Incorporated (Morgan Stanley)
• Original Assignee: The Capital Group Companies Incorporated (Morgan Stanley)
• Inventors: Phoa, Wesley Kym-Son
• Primary Examiner(s): Johnson, Gregory
• Application Number:
  US14/102,234
• Publication Number:
  US 20140214721A1
• Time in Patent Office: 602 Days
• Field of Search: 705/36.R
• US Class Current: 1/1
• CPC Class Codes: G06Q 40/06 Asset management; Financial planning or analysis
• CPC Class Codes: G06T 11/203 Drawing of straight lines or curves

Abstract

A method for displaying a matrix of correlations or other statistical measures of co-movement associated with a plurality of financial instruments, portfolios, indices, or asset classes is disclosed. The method includes: converting the matrix of correlations or other co-movement measures into a probability transition matrix; defining a corresponding abstract distance measurement between any two of the plurality of financial instruments, portfolios, indices, or asset classes based on the probability transition matrix; assigning coordinates in a Euclidean space to each of the plurality of financial instruments, portfolios, indices, or asset classes, wherein a Euclidean distance between any two financial instruments, portfolios, indices, or asset classes in the Euclidean space corresponds to the corresponding abstract distance measurement; and displaying on a display device the plurality of financial instruments, portfolios, indices, or asset classes based on more significant dimensions of the Euclidean space.

Claims

1. A computer-implemented method for displaying on a display device an N×

N matrix of correlations of N financial instruments, portfolios, indices, or asset classes using M dimensions, N being a large number, M being significantly smaller than N, while closely approximating distances between the N financial instruments, portfolios, indices, or asset classes as defined by the N×

N matrix of correlations, the method comprising;

converting by a computer processor the N×

N matrix of correlations into a probability transition matrix, each of the correlations representing a numerical correlation between two of the N financial instruments, portfolios, indices, or asset classes, the probability transition matrix comprising corresponding normalized versions of the correlations in the N×

N matrix of correlations;

defining by the computer processor a corresponding first distance measurement between any two of the N financial instruments, portfolios, indices, or asset classes based on the probability transition matrix, the first distance measurement measuring a closeness between corresponding said normalized correlations of said any two of the N financial instruments, portfolios, indices, or asset classes;

using by the computer processor a diffusion map to assign coordinates in an M-dimensional Euclidean space to each of the N financial instruments, portfolios, indices, or asset classes corresponding to non-unit eigenvalues of the probability transition matrix such that a Euclidean distance between said any two of the N financial instruments, portfolios, indices, or asset classes in the Euclidean space closely approximates the corresponding first distance measurement; and

displaying on the display device the N financial instruments, portfolios, indices, or asset classes based on the Euclidean space corresponding to a selection of M ones of the eigenvalues.

2. The method of claim 1, wherein N is at least 100 and each of the correlations is derived from the standard correlation coefficient of a corresponding pair of the N financial instruments, portfolios, indices, or asset classes.

3. The method of claim 2, wherein N is at least 500 and each of the correlations is one more than the standard correlation coefficient of the corresponding pair of the N financial instruments, portfolios, indices, or asset classes.

4. The method of claim 1, wherein M is three.

5. The method of claim 4, wherein the M dimensions comprise the dimensions of the Euclidean space corresponding to the three largest ones of the eigenvalues.

6. The method of claim 4, wherein the display device is configured to display 3-dimensional images and the displaying of the N financial instruments, portfolios, indices, or asset classes comprises displaying an identifying label for each of the N financial instruments, portfolios, indices, or asset classes in a 3-dimensional Euclidean representation on the display device.

7. The method of claim 6 further comprising modifying by the computer processor the 3-dimensional Euclidean representation on the display device in response to a user command inputted using a gaming controller configured to rotate, zoom, and pan the 3-dimensional Euclidean representation on the display device.

8. The method of claim 6 further comprising displaying by the computer processor on the display device successive representations of correlation data as observed on successive dates.

9. The method of claim 6 further comprising adjusting by the computer processor a color or size of the identifying label to correspond to a respective value of an additional numerical characteristic being displayed in the 3-dimensional Euclidean representation on the display device for each of the N financial instruments, portfolios, indices, or asset classes.

10. The method of claim 1, wherein M is two.

11. The method of claim 10, wherein the M dimensions comprise the dimensions of the Euclidean space corresponding to the two largest ones of the eigenvalues.

12. The method of claim 10, wherein the displaying of the N financial instruments, portfolios, indices, or asset classes comprises displaying an identifying label for each of the N financial instruments, portfolios, indices, or asset classes in a 2-dimensional Euclidean representation on the display device.

13. The method of claim 1 further comprising generating by the computer processor a measure of diversification of the N financial instruments, portfolios, indices, or asset classes.

14. The method of claim 13, wherein the generating of the measure of diversification of the N financial instruments, portfolios, indices, or asset classes comprises generating the measure of diversification using the M dimensions of the Euclidean space.

15. The method of claim 13, wherein the measure of diversification comprises a global concentration, a relative global concentration, or a largest local concentration.

16. The method of claim 15, wherein

the measure of diversification comprises a global concentration, and

the generating of the global concentration comprises:

assigning by the computer processor a weight to each of the N financial instruments, portfolios, indices, or asset classes; and

weighting by the computer processor a contribution of each of the N financial instruments, portfolios, indices, or asset classes by its respective said weight in the global concentration.

17. The method of claim 16 further comprising generating by the computer processor a portfolio diversification measure by:

identifying by the computer processor ones of the N financial instruments, portfolios, indices, or asset classes;

assigning by the computer processor second weights to respective said ones of the N financial instruments, portfolios, indices, or asset classes; and

generating by the computer processor the global concentration by only using the ones of the N financial instruments, portfolios, indices, or asset classes in place of each of the N financial instruments, portfolios, indices, or asset classes, and using the second weights in place of the weight of each of the N financial instruments, portfolios, indices, or asset classes.

18. The method of claim 1 further comprising generating by the computer processor a sequence of successively less significant local concentrations of the N financial instruments, portfolios, indices, or asset classes.

19. The method of claim 1 further comprising generating by the computer processor a plurality of relative local concentrations of the Euclidean space.

20. The method of claim 1 further comprising generating by the computer processor a numerical summary measure of accuracy with which the Euclidean distance as measured in the M dimensions of the Euclidean space approximates the corresponding first distance measurement.

21. The method of claim 1 further comprising changing by the computer processor a sign of one of the coordinates for improving consistency of the displaying of the N financial instruments, portfolios, indices, or asset classes over a period of time.

22. The method of claim 1 further comprising re-ordering by the computer processor the coordinates for improving consistency of the displaying of the N financial instruments, portfolios, indices, or asset classes over a period of time.

23. The method of claim 1, wherein the financial instruments comprise publicly traded equity securities, publicly traded fixed income securities, publicly available mutual funds, exchange-traded funds, publicly traded currencies, exchange-traded futures, or options on exchange-traded futures.

24. The method of claim 1 further comprising:

in response to the displaying on the display device, receiving by the computer processor a user command to modify an attribute for a selected one of the N financial instruments, portfolios, indices, or asset classes; and

modifying by the computer processor the attribute in response to the user command.

25. The method of claim 24, wherein the attribute corresponds to an investment amount.

26. The method of claim 1, wherein the correlations correspond to financial returns.

27. A system for displaying an N×

N matrix of correlations associated with N financial instruments, portfolios, indices, or asset classes using M dimensions, N being a large number, M being significantly smaller than N, while closely approximating distances between the N financial instruments, portfolios, indices, or asset classes as defined by the N×

N matrix of correlations, the system comprising;

a processor;

a display device coupled to the processor;

a gaming controller configured to rotate, zoom, and pan an image displayed on the display device; and

a nonvolatile storage device coupled to the processor and storing instructions that, when executed by the processor, cause the processor to;

convert the N×

N matrix of correlations into a probability transition matrix, each of the correlations representing a numerical correlation between two of the N financial instruments, portfolios, indices, or asset classes, the probability transition matrix comprising corresponding normalized versions of the correlations in the N×

N matrix of correlations;

define a corresponding first distance measurement between any two of the N financial instruments, portfolios, indices, or asset classes based on the probability transition matrix, the first distance measurement measuring a closeness between corresponding said normalized correlations of said any two of the N financial instruments, portfolios, indices, or asset classes;

use a diffusion map to assign coordinates in an M-dimensional Euclidean space to each of the N financial instruments, portfolios, indices, or asset classes corresponding to non-unit eigenvalues of the probability transition matrix such that a Euclidean distance between said any two of the N financial instruments, portfolios, indices, or asset classes in the Euclidean space closely approximates the corresponding first distance measurement;

display on the display device the N financial instruments, portfolios, indices, or asset classes based on the Euclidean space corresponding to a selection of M ones of the eigenvalues; and

rotate, zoom, or pan the image displayed on the display device in response to a user'"'"'s input with the gaming controller.

28. The system of claim 27, wherein M is three, the image is a 3-D image, and the instructions, when executed by the processor, further cause the process to display the N financial instruments, portfolios, indices, or asset classes as the 3-D image on the display device.

29. The system of claim 28, wherein the instructions, when executed by the processor, further cause the processor to control the display device to display the N financial instruments, portfolios, indices, or asset classes by displaying an identifying label for each of the N financial instruments, portfolios, indices, or asset classes in a 3-dimensional Euclidean representation on the display device.

30. The system of claim 29, wherein the processor is further configured to receive a user command and the instructions, when executed by the processor, further cause the processor to modify the 3-dimensional Euclidean representation on the display device in response to the user command.