Constraints are now an integral part of the portfolio construction process. With constraints comes the challenge of understanding how they cause the optimal portfolios to deviate from a trade-off dictated by the forecasts of risk and return. We describe the theory and application of a technique able to quantify the impact of individual constraints in several different ways. This includes decomposing the difference between the optimal constrained and unconstrained portfolios and the difference between alphas and implied alphas as described in earlier work by Grinold and others. Furthermore, we introduce a new technique that applies these decompositions on an ex-post basis, providing on understanding of how constraints actually impact realized risk and return.

Axioma Research Paper No. 014

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