Journal of Investment Strategies

Reconciling factor optimization with portfolio constraints

Boris Gnedenko and Igor Yelnik

  • We show how to optimally account for asset constraints in factor optimization
  • Solution is obtained by projecting an optimal unconstrained portfolio onto a feasible portfolio set
  • This also gives way to aligning alpha factors and risk factors in portfolio optimization
  • Our approach is inspired by a geometric interpretation of quadratic programming


Allocation between factor portfolios can bring significant advantages over traditional portfolio optimization performed among individual assets. Substantial dimension reduction when one's attention turns from many assets to few factors is an important example. This, however, comes at the cost of decreased flexibility in satisfying portfolio constraints. To address this problem, we suggest an approach inspired by a geometric interpretation of quadratic programming. 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.


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