Abstract: Methods and systems for estimating time-varying factor exposures of either an individual financial instrument or a portfolio of such instruments, through the solution of a constrained multi-criteria dynamic optimization problem, providing an estimation error function and one or more transition error functions to be minimized over a period of time. The factor exposures relay the influence of the factors on the return of the instrument or portfolio. The estimation error function provides the estimation error at each time interval between the return of the asset collection and a sum of products of each factor exposure and its respective factor. Each transition error function provides a transition error of each factor exposure between time intervals. In one embodiment, the constraints can include a budget constraint and non-negativity bounds applying to some or all of the factor exposures.