Factor Risk Models with Multiple Specific Risk Estimates
Construction of factor risk models that more advantageously predict the future volatility of returns of a portfolio of securities such as stocks, bonds, or the like is addressed. More specifically, factor risk models with more than one estimate of specific risk or, alternatively an original specific risk estimate together with a set of specific risk differences derived from more than one estimate of specific risk.
1 . A computer-based method of using a factor risk model to estimate a risk of a portfolio of assets comprising:
electronically receiving by a programmed computer a portfolio to be analyzed defined by a N-dimensional vector for a set of N possible investment opportunities with elements corresponding to investment holdings in said portfolio;
electronically receiving by the programmed computer a factor risk model defined and calibrated for portfolios in the N investment opportunities, said factor risk model comprising a matrix of factor exposures, a matrix of factor covariances, and two or more matrices modelling either specific covariance or specific risk;
electronically receiving by the programmed computer a choice of which specific covariance or specific risk model to use, where more than one choice may be selected;
computing a risk prediction for the portfolio using the factor risk model for each specific covariance or specific risk model selected; and
electronically outputting the modified risk prediction.
2 . The method of claim 1 in which the matrices of specific covariances or specific risk models are diagonal matrices so that the factor risk model need only supply vectors of specific variance or specific risk for each specific covariance model.
3 . The method of claim 2 where the first specific risk model is provided as estimates of specific variance or specific risk while the other specific risk models are specified in terms of differences from the first model.
4 . A computer-based method comprising:
electronically inputting a set of N possible investment opportunities;
defining a vector space of N-dimensional vectors representing portfolios in the N investment opportunities, whose vector elements correspond to investment holdings in any investment portfolio;
electronically receiving by a programmed computer a factor risk model defined and calibrated for portfolios in the N investment opportunities, said factor risk model comprising a matrix of factor exposures, a matrix of factor covariances, and two or more matrices modelling either specific covariance or specific risk;
electronically receiving by the programmed computer a choice of which specific covariance model or specific risk model to use, where more than one choice may be selected;
defining a portfolio optimization strategy for determining an optimized portfolio of investment holdings that utilizes said factor risk model and the choice or choices of which specific covariance or risk models to use;
computing the optimal portfolio using the portfolio optimization strategy utilizing the programmed computer and portfolio optimization software; and
electronically outputting the optimized portfolio.
5 . The method of claim 3 in which the models of specific covariances or specific risk are diagonal matrices so that the factor risk model need only supply vectors of specific variance or specific risk for each model.
6 . The method of claim 5 where the first specific risk model is provided as estimates of specific variance or specific risk while the other specific risk models are specified in terms of differences from the first model.