SYSTEMS AND METHODS FOR PORTFOLIO ANALYSIS

• US 20090112774A1
• Filed: 07/02/2008
• Published: 04/30/2009
• Est. Priority Date: 10/24/2007
• Status: Active Grant

• Current Assignee: Bloomberg Finance LP (Bloomberg LP)
• Original Assignee: Lehman Brothers Incorporated (Barclays PLC)
• Inventors: Meucci, Attilio
• Granted Patent: US 8,548,884 B2
• Time in Patent Office: Days
• US Class Current: 705/36.R
• CPC Class Codes: G06Q 40/00 Finance; Insurance; Tax strategies; Processing of corporate or income taxes
• CPC Class Codes: G06Q 40/06 Asset management; Financial planning or 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 the specified portfolio. Other aspects and embodiments comprise analogous software and computer systems.

Claims

1. A computer-implemented method comprising:

electronically receiving data describing one or more risk factors driving volatility of each of a plurality of securities comprised in a specified portfolio;

for each of said plurality of securities;

categorizing each of said 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 said security, based on said best fit distributions; and

aggregating said security return distributions to generate a return distribution for said specified portfolio.

2. The method of claim 1, wherein for each security, generating said return distribution comprises sampling a value from each risk factor'"'"'s best fit distribution.

3. The method of claim 1, wherein for each security, generating said return distribution comprises:

(a) sampling a value from each risk factor'"'"'s best fit distribution;

(b) conducting a simulation based on a scenario defined by said sampled values;

(c) incorporating a correlation among said risk factors;

(d) multiplying said sampled values by corresponding factor exposures to obtain a product for each risk factor;

(e) summing said risk factor products for said scenario; and

(f) repeating steps (a)-(e) for a plurality of scenarios.

4. The method of claim 3, further comprising performing steps (a)-(f) for each security in a benchmark portfolio to generate a return distribution for said benchmark portfolio.

5. The method of claim 1, wherein for each of said plurality of securities, generating said return distribution comprises weighting each risk factor'"'"'s more recent historical data, as represented by time series data, more heavily than more distant historical data.

6. The method of claim 4, further comprising generating a tracking error distribution for said specified portfolio by calculating a difference between a return distribution for said specified portfolio and a return distribution for said benchmark portfolio, and aggregating said return distributions.

7. The method of claim 6, further comprising calculating value at risk for said specified portfolio based on said return distribution for said specified portfolio and said tracking error distribution.

8. The method of claim 6, further comprising calculating expected shortfall for said specified portfolio based on said return distribution for said specified portfolio and said tracking error distribution.

9. The method of claim 6, further comprising calculating volatility for said specified portfolio based on said return distribution for said specified portfolio and said tracking error distribution.

10. The method of claim 1, wherein said aggregating step comprises linearly combining systematic, idiosyncratic, and default returns.

11. The method of claim 10, wherein said idiosyncratic return for a portfolio is a linear combination of returns for sub-portfolios related to correlation clusters.

12. The method of claim 1, wherein said aggregating step comprises aggregating an idiosyncratic return component.

13. The method of claim 12, wherein said aggregating an idiosyncratic return component comprises subdividing said portfolio according to correlation clusters and aggregating said clusters according to an entropy-based algorithm.

14. Software stored on a computer readable medium and implemented by a computer system, said software comprising:

software for electronically receiving data describing one or more risk factors driving volatility of each of a plurality of securities comprised in a specified portfolio;

software for, for each of said plurality of securities;

categorizing each of said 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 said security, based on said best fit distributions; and

software for aggregating said security return distributions to generate a return distribution for said specified portfolio.

15. The software of claim 14, wherein for each security, generating said return distribution comprises sampling a value from each risk factor'"'"'s best fit distribution.

16. The software of claim 14, wherein for each security, generating said return distribution comprises:

(a) sampling a value from each risk factor'"'"'s best fit distribution;

(b) conducting a simulation based on a scenario defined by said sampled values;

(c) incorporating a correlation among said risk factors;

(d) multiplying said sampled values by corresponding factor exposures to obtain a product for each risk factor;

(e) summing said risk factor products for said scenario; and

(f) repeating steps (a)-(e) for a plurality of scenarios.

17. The software of claim 16, further comprising software for performing steps (a)-(f) for each security in a benchmark portfolio to generate a return distribution for said benchmark portfolio.

18. The software of claim 14, wherein for each of said plurality of securities, generating said return distribution comprises weighting each risk factor'"'"'s more recent historical data, as represented by time series data, more heavily than more distant historical data.

19. The software of claim 17, further comprising software for generating a tracking error distribution for said specified portfolio by calculating a difference between a return distribution for said specified portfolio and a return distribution for said benchmark portfolio, and aggregating said return distributions.

20. The software of claim 19, further comprising software for calculating value at risk for said specified portfolio based on said return distribution for said specified portfolio and said tracking error distribution.

21. The software of claim 19, further comprising software for calculating expected shortfall for said specified portfolio based on said return distribution for said specified portfolio and said tracking error distribution.

22. The software of claim 19, further comprising software for calculating volatility for said specified portfolio based on said return distribution for said specified portfolio and said tracking error distribution.

23. The software of claim 14, wherein said software for aggregating comprises software for linearly combining systematic, idiosyncratic, and default returns.

24. The software of claim 23, wherein said idiosyncratic return for a portfolio is a linear combination of returns for sub-portfolios related to correlation clusters.

25. The software of claim 14, wherein said software for aggregating comprises software for aggregating an idiosyncratic return component.

26. The software of claim 25, wherein said software for aggregating an idiosyncratic return component comprises software for subdividing said portfolio according to correlation clusters and software for aggregating said clusters according to an entropy-based algorithm.

27. A computer system comprising:

a processor that electronically receives data describing one or more risk factors driving volatility of each of a plurality of securities comprised in a specified portfolio;

a processor that, for each of said plurality of securities;

categorizes each of said risk factors as a random variable and identifies a distribution that best fits each risk factor'"'"'s historical behavior; and

generates a return distribution for said security, based on said best fit distributions; and

a processor that aggregates said security return distributions to generate a return distribution for said specified portfolio.

28. The system of claim 27, wherein for each security, generating said return distribution comprises sampling a value from each risk factor'"'"'s best fit distribution.

29. The system of claim 27, wherein for each security, generating said return distribution comprises:

(a) sampling a value from each risk factor'"'"'s best fit distribution;

(b) conducting a simulation based on a scenario defined by said sampled values;

(c) incorporating a correlation among said risk factors;

(d) multiplying said sampled values by corresponding factor exposures to obtain a product for each risk factor;

(e) summing said risk factor products for said scenario; and

(f) repeating steps (a)-(e) for a plurality of scenarios.

30. The system of claim 29, further comprising a processor that performs steps (a)-(f) for each security in a benchmark portfolio to generate a return distribution for said benchmark portfolio.

31. The system of claim 27, wherein for each of said plurality of securities, generating said return distribution comprises weighting each risk factor'"'"'s more recent historical data, as represented by time series data, more heavily than more distant historical data.

32. The system of claim 30, further comprising a processor that generates a tracking error distribution for said specified portfolio by calculating a difference between a return distribution for said specified portfolio and a return distribution for said benchmark portfolio, and aggregates said return distributions.

33. The system of claim 32, further comprising a processor that calculates value at risk for said specified portfolio based on said return distribution for said specified portfolio and said tracking error distribution.

34. The system of claim 32, further comprising a processor that calculates expected shortfall for said specified portfolio based on said return distribution for said specified portfolio and said tracking error distribution.

35. The system of claim 32, further comprising a processor that calculates volatility for said specified portfolio based on said return distribution for said specified portfolio and said tracking error distribution.

36. The system of claim 27, wherein aggregating comprises linearly combining systematic, idiosyncratic, and default returns.

37. The system of claim 36, wherein said idiosyncratic return for a portfolio is a linear combination of returns for sub-portfolios related to correlation clusters.

38. The system of claim 27, wherein aggregating comprises aggregating an idiosyncratic return component.

39. The system of claim 38, wherein said aggregating an idiosyncratic return component comprises subdividing said portfolio according to correlation clusters and aggregating said clusters according to an entropy-based algorithm.