Factors to Assets: Mapping Factor Exposures to Asset Allocations

The authors develop a methodology that maps a given set of factor exposures to a group of asset classes. When there are fewer factors than asset classes, which is the case in most practical situations, the mapping is not unique. The authors show how one can express a given set of factor exposures as a particular combination of assets subject to real-world investor preferences and constraints: leverage, minimum and maximum asset class positions, illiquid versus liquid proportions, active risk, turnover, and other constraints. Formally, the authors find the set of asset classes that has the minimum distance in terms of factor exposures from the desired set, subject to these constraints.