Identifying and Compensating for Model Mis-Specification in Factor Risk Models

Abstract

Techniques for more accurately estimating the risk, or active risk, of an investment portfolio when using factor risk models are disclosed. This improved accuracy is achieved by identifying and compensating for the inherent “modeling error” present when risk is represented using a factor risk model. The approach adds one or more factors that depend on the investment portfolio and that explicitly compensate for factors that are unspecified or unattributed in the original factor risk model. These unspecified factors of the original factor risk model lead to modeling error in the original factor risk model. The approach can be used with a variety of different factor risk models, such as, fundamental, statistical and macro risk models, for example, and for a variety of securities, such as equities, international equities, composites, exchange traded funds (ETFs), or the like, currencies, and fixed-income, for example. The risk associated with modeling error in a factor risk model relative to a particular portfolio is identified and quantified. Knowledge of this risk associated with modeling error can be utilized when estimating risk, or active risk, using factor risk models or when constructing optimal portfolios by mean-variance optimization or other portfolio construction strategies and procedures that make use of factor risk models.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a computer-based system which may be suitably utilized to implement the present invention;

FIG. 2A illustrates a flowchart of a first process in accordance with the present invention;

FIG. 2B illustrates a flowchart of a second process in accordance with the present invention;

FIG. 3 illustrates a flowchart of a third process in accordance with the present invention; and

FIGS. 4A and 4B are tables each of which illustrates a comparison of an exemplary risk factor model not utilizing the present invention with an exemplary modified risk factor model in accordance with the present invention.

Claims

1. A computer-based method of modifying a fully specified factor risk model whose elements are known deterministically or probabilistically, comprising: computing a correction to the fully specified factor risk model that depends only on the matrix of factor exposures;determining a correction magnitude;adding the correction times the magnitude to the fully specified factor risk model to produce a modified factor risk model; andutilizing the modified factor risk model to calculate an adjusted risk estimate for the portfolio.

2. The computer based method of claim 1 further comprising the step of: determining a correction magnitude specific to the portfolio whose risk is to be estimated.

3. The computer based method of claim 1 further comprising the step of: determining a correction magnitude specific to a portfolio construction strategy.

4. A computer-based method of modifying a fully specified factor risk model whose elements are known deterministically or probabilistically, comprising: selecting a portfolio whose risk is to be estimated;determining a new factor and factor exposure for the factor risk model that cannot be estimated without knowledge of the portfolio;adding this new factor and factor exposure to the fully specified factor risk model to produce a modified factor risk model; andutilizing the modified factor risk model to calculate an adjusted risk estimate for the portfolio.

5. The computer based method of claim 4 wherein the step of determining a new factor and factor exposure for the factor risk model further comprises: calculating the new factor so that its projection into the null space of the transpose of a rectangular matrix of factor exposures or factor loadings has a magnitude greater than or equal to a predetermined percentage of the new factor's magnitude.

6. The computer based method of claim 4 further comprising the step of: determining a new investment portfolio utilizing the modified factor risk model.

7. The computer based method of claim 4 further comprising the step of: backtesting the modified factor risk model.

8. The computer based method of 7 wherein a sequence of backtests are performed using alternative strategies for determining the new factor and factor exposure.

9. A computer-based method comprising: determining a model uncertainty metric defined on a space of portfolios, said portfolios being vectors with elements corresponding to holdings in said portfolios; said model uncertainty metric depending on the null space of the transpose of a matrix of factor loadings or factor exposures; anda particular portfolio to be analyzed; andutilizing the model uncertainty metric to adjust a measure of portfolio performance.

10. The method of claim 9 wherein said measure of portfolio performance is a risk or tracking error of the portfolio.

11. The method of claim 9 wherein said measure of portfolio performance is an expected return of the portfolio.

12. The method of claim 9 wherein said measure of portfolio performance is a utility of the portfolio.

13. The method of claim 9 wherein said measure of portfolio performance is a value at risk for the portfolio.

14. The method of claim 9 further comprising the step of utilizing the model uncertainty metric in conjunction with a factor risk model and portfolio optimization software to determine an optimized portfolio.

15. A computer implemented system for modifying a fully specified factor risk model whose elements are known deterministically or probabilistically, the system comprising: a memory for storing data for an investment portfolio whose risk is to be estimated; anda processor cooperating with the memory and with software to operate so as to determine a new factor and factor exposure for the factor risk model that cannot be estimated without knowledge of the investment portfolios adding this new factor and factor exposure to the fully specified factor risk model to produce a modified factor risk model; and calculating an adjusted risk estimate for the investment portfolio utilizing the modified factor risk model.

16. The computer implemented system of claim 15 further comprising a portfolio optimization program for utilizing the modified risk model to determine a new investment portfolio; and an output device to output data describing the new investment portfolio.

17. The computer implemented system of claim 15 further comprising: a database of historical data, wherein said processor further operates to retrieve and utilize historical data from said database to back test the modified factor risk model.

18. The computer implemented system of claim 17 wherein a sequence of back tests is performed using alternative strategies for determining the new factor and factor exposure.

19. The computer implemented method of claim 15 wherein said processor further operates to compute the new factor by calculating the new factor so that its projection into the null space of the transpose of a matrix of factor exposures or factor loadings has a magnitude greater than or equal to a predetermined percentage of the new factors magnitude.

20. Computer software stored on a storage medium, said software operating to modify a fully specified factor risk model whose elements are known deterministically or probabilistically, by: selecting a portfolio whose risk is to be estimated;determining a new factor and factor exposure for the factor risk model that cannot be estimated without knowledge of the portfolio;adding this new factor and factor exposure to the fully specified factor risk model to produce a modified factor risk model; andutilizing the modified factor risk model to calculate an adjusted risk estimate for the portfolio.

21. The computer software of claim 20 further operating to: calculate the new factor so that its projection into the null space of the transpose of a matrix of factor exposures or factor loadings has a magnitude greater than or equal to a predetermined percentage of the new factor's magnitude.