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FRM Part II · FRM Exam Part II · Portfolio Construction

An asset owner imposes a maximum 5% weight on any single position and a maximum tracking error of 4% versus its benchmark. The optimizer reports that the tracking error constraint is binding while the 5% position cap is not binding for any asset. What does a binding tracking error constraint imply?

A binding tracking error constraint means the portfolio would improve if the limit were relaxed, and the shadow price measures the extra expected active return per unit of added tracking error. The non-binding position cap has no marginal value, and tightening the limit would reduce expected active return.

  1. ARelaxing the tracking error limit would allow a higher expected active return, and its shadow price measures the marginal gainCorrect
  2. BRelaxing the position cap would raise expected return, because the cap is the binding constraint
  3. CThe constraint has no effect on the optimal portfolio, since only binding position caps matter
  4. DTightening the tracking error limit would raise expected active return

Explanation

A binding constraint restricts the optimum; loosening it permits higher objective value, and the shadow price gives the marginal improvement per unit of relaxation. A non-binding cap has zero shadow price. Tightening the limit would lower, not raise, expected active return.

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