Reconciling Factor Optimization with Portfolio Constraints

Allocation between factor portfolios can bring significant advantages over traditional portfolio optimization performed among individual assets or asset classes. One such advantage is a substantial dimension reduction when one’s attention turns from many assets to few factors. This, however, comes at the cost of decreased flexibility in satisfying portfolio constraints.To address this problem, we suggest a natural approach inspired by a geometric interpretation of quadratic programming: among all feasible constrained portfolios, the optimal one minimizes tracking error with respect to the optimal unconstrained portfolio. Thus we obtain an optimal solution by "projecting" an optimal unconstrained factor portfolio onto a set of all feasible portfolios using tracking error as a distance measure. Doing so helps align alpha and risk factors in portfolio optimization.