Patent ID: 7617142
Filing Date: 2009-11-10
Classification: G06Q

Abstract:
1. A method of estimating time-varying factor exposures at each time interval in a period of time, through a dynamic optimization of a model relating an influence of at least one factor on a return of an asset collection, the method comprising the steps of: receiving data related to the return of the asset collection for the plurality of time intervals, the asset collection including at least one asset; receiving data related to the at least one factor for the plurality of time intervals; for each of the plurality of time intervals, determining, by a computer, at least one factor exposure minimizing a value of an objective function while meeting at least one constraint on possible values for the at least one factor exposure, wherein each of the at least one factor exposures relays the influence of a respective factor on the return of the asset collection, wherein the objective function includes an estimation error term representing an estimation error at each time interval between the return of the asset collection and a sum of products of each of the at least one factor exposure and its respective factor, wherein the objective function includes at least one transition error term representing a transition error at each time interval after a first time interval for each of the at least one factor exposure between the time interval and a prior time interval, and wherein the determining step includes the step of: formulating the objective function as a parameter-weighted sum, the parameter-weighted sum being a sum of a quadratic norm of the estimation error term and a parameter-weighted quadratic norm of each of the at least one transition error term; and at each of the plurality of time intervals, determining a structural breakpoint ratio for each factor exposure, the structural breakpoint ratio being a ratio of a minimum of the parameter-weighted sum over all the time intervals to a minimum of a modified parameters weighted sum, the modified parameter-weighted sum being a sum of a quadratic norm of the estimation error and a parameter-weighted quadratic norm of the at least one transition error over all the time intervals, the modified parameter-weighted sum excluding at least part of a transition error term representing a transition error for the factor exposure between the time interval and a prior time interval.