Abstract: Investment portfolios undergo a calibration procedure to improve their efficiency and stability. Any set of portfolios could be selected for calibration. If said portfolios represent a result of a portfolio optimization or asset allocation, then using original model inputs, an optimization procedure is performed to compute an original efficient frontier and a set of frontier portfolios is selected for calibration. A plurality of random samples of modified optimization inputs based on the original inputs is generated. For each random sample of inputs a modified efficient frontier is computed using the portfolio optimization model with modified inputs. Each portfolio selected for calibration is projected on the modified efficient frontier to create a corresponding modified calibration portfolio. Calibrated portfolio is created by averaging its calibrations. Calibrated efficient frontier is created by averaging all calibration portfolios for each selected portfolio on the original frontier.

Abstract: A method is for determining a factor exposure of an asset collection for each of time intervals in a period of time, the asset collection including at least one asset. An objective function which includes an estimation error term or at least one transition error term is determined. The estimation error term represents an estimation error at each time interval between a performance of the asset collection and a sum of products of each of the factor exposure and its respective factor. The transition error term represents a transition error at each time interval after a first time interval for each of the factor exposure between the time interval and a prior time interval. At least one hedging or leveraging constraint on the factor exposure for at least one of the time intervals is defined. The factor exposure by optimizing a value of the objective function is determined.

Abstract: A method is for determining a factor exposure of an asset collection for each of time intervals in a period of time. For each of time intervals, an objective function which includes an estimation error term or at least one transition error term is determined. The estimation error term represents an estimation error at each time interval between a performance of the asset collection and a sum of products of each of the at least one factor exposure and its respective factor. The at least one transition error term represents 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. For each of time intervals, the at least one factor exposure by optimizing a value of the objective function is determined.

Abstract: Described is a system including a memory arrangement and a processor for graphically representing in a space data representing at least one portfolio. The memory arrangement stores a Multi-Criteria Financial Optimization (“MCFO”). The processor solves the MCFO to generate data corresponding to a set of portfolios. The processor selects vertex points corresponding to a set of components of the portfolios. The processor defines coordinates of the vertices on a chart and plots the vertices as points on the chart. The processor defining a projection vector-function using coordinates of the vertices and selecting a subset of the portfolios on the chart. The processor computing coordinates for the portfolios in the subset using the projection vector-function and a weighting corresponding to the portfolios. The processor plotting points corresponding to the portfolios in the subset on the chart using the computed coordinates.

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.

Abstract: A system and method for factor-based measuring of similarity between financial instruments are described. The method including selecting a model for factor intersection calculation of a two or more of financial instruments, the model including a plurality of factors; determining factor exposure values for first and second financial instruments on each of the factors; determining a proximity between the factor exposure values based on the selected model; and calculating a factor intersection result between the factor exposure values, wherein the factor intersection result includes at least one of an overlap amount and a non-overlap amount.

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.

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.