Considering a Risk Constrained Portfolio

Project selection is made more difficult when it is constrained. Risk can be constrained on each individual project else on the total portfolio. 7 min read.


Our previous blog Advantages of Constructing a Portfolio explained that it is constraints that makes it difficult to choose the best set from the full set of potential projects.

Project Portfolio – List

Consider 20 possible projects, which reflects anticipated gains in thousands of dollars per annum, an expected total project cost and an estimate of the risk associated with the project. Risk has been assessed by the project manager and represents the likelihood that the project gains and costs will not be achieved as they are captured in the proposal.

Project Portfolio List

Constrained Project Portfolio: Individual Project Risk

Lets examine the portfolio by constraining it by risk. Risk can be constrained either on each individual project else on the total portfolio. In general, current selection methods do not treat projects as an integrated portfolio and instead apply risk constraints on each project. Often this constraint is imposed by simply filtering out any project that does not meet a pre-established risk threshold. Assuming a risk constraint of 40 percent on each project then this implies that projects 6, 10 and 13 above are no longer acceptable and are not considered in the portfolio.

Project portfolio results with individual project constraints,

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Individual Risk Constrained Project Portfolio - Results

The imposition of risk constraints for each individual project reduces value by,

  • Random $786k ($1,420-634) – Representing a 55% reduction. 
  • Ranking $1,550 ($6,182-4,632) – Representing a 25% reduction
  • Mathematical $1,390 ($6,358-4,968) – Representing a 22% reduction

It is much more difficult to optimize a portfolio when there are sets of constraints that must be respected. As in the previous blog, ranking outperforms random and mathematical outperforms ranking. Generally, as more constraints are added the mathematical method extends its advantage more fully over the ranked method.

Constrained Project Portfolio: Integrated Portfolio Risk

A better way to manage risk is to impose a risk constraint on the average or total risk of the portfolio rather than on each individual project as is done in the standard method. If a target is set for the average risk of 40 percent, then the total risk should be .40 * 20 = 8.0. This very concept implies that the natural unit of performance is the portfolio rather than the individual project, which is not usually considered in standard project selection approaches. If this approach is applied to the mathematical method it is able to generate a much better portfolio by considering gains over the full set of 20 potential projects.

Project portfolio results with portfolio project constraints,

Integrated Risk Constrained Project Portfolio - Mathematical

Integrated Risk Constrained Project Portfolio - Results

The imposition of risk constraints on the total portfolio improves value by,

  • Ranking $1,726 ($6,358-4,632) – Representing a 37% improvement
  • Mathematical $1,390 ($6,358-4,968) – Representing a 28% improvement


Constraints limit portfolio value. Instead of considering risk at the individual project level far better outcomes can be achieved if instead risk is considered at the portfolio level. In general, this allows all of the projects within the portfolio to be considered rather than have individual high risk projects excluded from consideration.

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