Abstract: Robust methods for determining an investment portfolio are based on investment parameters which are assumed to be error bounded rather than precisely known values. A confidence threshold is input based on the measure of confidence in the resulting worst-case portfolio performance that is desired by an investor. Using historical return data, a nominal value for the mean return for each asset, a nominal factor loading vector for each asset and a nominal factor covariance matrix are determined. Uncertainty sets, which define the region within which a parameter is statistically expected to reside are defined for the mean return vector, factor loading matrix and factor covariance matrix. The uncertainty sets are then applied to a robust investment problem of interest, based on investment objectives, such that the worst case market parameters reside within the applied uncertainty sets with a probability set by the selected confidence threshold.

Abstract: Robust methods for determining an investment portfolio are based on investment parameters which are assumed to be error bounded rather than precisely known values. A confidence threshold is input based on the measure of confidence in the resulting worst-case portfolio performance that is desired by an investor. Using historical return data, a nominal value for the mean return for each asset, a nominal factor loading vector for each asset and a nominal factor covariance matrix are determined. Uncertainty sets, which define the region within which a parameter is statistically expected to reside are defined for the mean return vector, factor loading matrix and factor covariance matrix. The uncertainty sets are then applied to a robust investment problem of interest, based on investment objectives, such that the worst case market parameters reside within the applied uncertainty sets with a probability set by the selected confidence threshold.