Methods and Apparatus for Improving Factor Risk Model Responsiveness
Construction of factor risk models that better predict the future volatility of returns of a portfolio of securities such as stocks, bonds, or the like is addressed. More specifically, improved factor-factor covariance estimation is made even when the covariances change rapidly over time. Methods and techniques for achieving better accuracy, responsiveness, and stability of factor risk models are addressed.
1 . A computer-based method of estimating the variance of a factor in a factor risk model comprising the steps of:
storing data for the factor in a memory;
determining a time series history of factor returns for the factor over a set of historical times by a programmed processor cooperating with the memory and with software;
calculating a set of exponentially decaying weights with a fixed half life corresponding to the time series history of factor returns by the programmed processor cooperating with the memory and with software;
computing a metric of volatility for each historical time by the programmed processor cooperating with memory and with software;
calculating a set of volatility adjustment multipliers by the programmed processor cooperating with the memory and with software as the ratios of most recent volatility metric to the computed volatility metric;
determining when at least one volatility adjustment multiplier is outside a predetermined range;
adjusting the at least one volatility adjustment multiplier to a value in the predetermined range;
computing the factor-factor covariance for the time series of factor returns using the volatility adjustment multipliers within the range and any adjusted volatility adjustment multipliers for any volatility adjustment multipliers determined to be outside the range by the programmed processor cooperating with the memory and with software; and
outputting the factor variance as part of a factor risk model as an electronic output by an output device.
2 . The method of claim 1 where the output factor variance is used in the computation of the volatility of a portfolio of assets.
3 . The method of claim 1 where the output factor variance is used to rebalance an investment portfolio.
4 . The method of claim 1 where the output factor variance is used in a performance attribution analysis.
5 . A computer-based apparatus for estimating the variance of a factor in a factor risk model comprising:
a programmed processor cooperating with memory and with software to:
determine a time series history of factor returns over a set of historical times selected utilizing an input device;
calculate a set of exponentially decaying weights with a fixed half life corresponding to the time series history of factor returns;
compute a metric of volatility for each historical time;
calculate a set of volatility adjustment multipliers that is the ratio of most recent volatility metric to the measured volatility metric;
determine at least one volatility adjustment multiplier is outside a predetermined range;
adjust the at least one volatility adjustment multiplier to a value in the predetermined range;
compute the factor variance for the time series of factor returns using the set of exponentially decaying weights, and volatility adjustment multipliers within the range and any adjusted volatility adjustment multiplier for any volatility multiplier determined to be outside the range; and
an output means for outputting the factor variance as part of a factor risk model as an electronic output.
6 . The apparatus of claim 5 where the output factor variance is used in the computation of the volatility of a portfolio of assets stored in a database.
7 . The apparatus of claim 5 where the output factor variance is used by the programmed processor to rebalance an investment portfolio.
8 . The apparatus of claim 5 where the output factor variance is used by the programmed processor to perform a performance attribution analysis.