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Optimal revision of uncertain estimates in project portfolio selection

Explore the importance of using Bayesian revised estimates in project portfolio selection to eliminate the optimizer's curse caused by unbiased estimates, leading to more accurate project prioritization.

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Optimal revision of uncertain estimates in project portfolio selection

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  1. Optimal revision of uncertain estimates in project portfolio selection Eeva Vilkkumaa, Juuso Liesiö, Ahti Salo Department of Mathematics and Systems Analysis, Aalto University School of Science and Technology

  2. Contents Project portfolio selection Optimizer’s curse Revised estimates Discussion

  3. Project portfolio selection Estimates Portfolio selection Values t Select a subset of projects within a budget, e.g., k out of n projects with the aim of maximizing the sum of the projects’ values μi, i=1,...,n The values μiare generally unknown, whereby decisions about which projects to select are made based on estimates Viabout μi.

  4. Optimizer’s curse in portfolio selection Assume that the estimates are unbiased Portfolio maximization selects, on average, overestimated projects → the value of the portfolio is less than expected based on the estimation information (optimizer’s curse; cf. Smith and Winkler, 2006): where is the index set of the selected projects.

  5. Optimizer’s curse in portfolio selection µi ~ N(0,12) Portfolio value Vi = µi + εi, εi ~ N(0,σ2) Standard deviation of estimation error Choosing 10 projects out of 100 Values i.i.d with Unbiased estimates The larger the estimation error variance, the harder it is to identify the best projects, and the larger the difference between the estimated and realized portfolio value

  6. Optimal revision of the estimates where Estimates do not account for the uncertainties Use Bayesian revised estimates instead as a basis for project selection For instance, with µi ~ N(mi,σi2), Vi ~ N(µi,τi2): The estimate V and the prior information m are weighted according to their uncertainty.

  7. Optimal revision of the estimates Portfolio value µi ~ N(0,12) Standard deviation of estimation error Vi = µi + εi, εi ~ N(0,σ2) With revised estimates the optimizers’ curse is eliminated, that is where is the index set of the projects selected using revised estimates Previous example • Choosing 10 projects out of 100 • True values i.i.d. with • Unbiased estimates

  8. Revised estimates and portfolio composition In the previous example, the projects’ values were identically distributed, and the estimation errors had equal variances Then, prioritization among the projects remains unchanged when the estimates are revised, because In general, using revised estimates may result in a different project prioritization than estimates

  9. Revised estimates and portfolio composition Same error variances Different error variances Project value Project value Vi = µi + εi, εi ~ N(0,0.52) Vi = µi + εi, εi ~ N(0,12) Estimate Revised estimate Estimate Revised estimate Choosing 3 projects out of 8 True values i.i.d. With µi ~ N(0,12) On the left, estimates with equal error variance for all projects On the right, four projects (dashed) more difficult to estimate

  10. Revised estimates and portfolio composition Same error variances Different error variances Project value Project value Estimate Revised estimate Estimate Revised estimate On the left, equal error variances → estimates are shifted towards the common prior mean (zero) in the same proportion On the right: the revised estimates of the ”dashed” projects are more drawn towards zero, because the estimation information is less reliable Selection of 3 projects leads to different portfolios depending on whether the estimates are revised or not

  11. Revised estimates and portfolio value Optimal Portfolio value Revised estimates Estimates • 1) εi ~ N(0,0.12) - small error variance • 2) εi ~ N(0,12) - large error variance Share of projects with large error variance [%] The use of revised estimates yields at least as high overall portfolio value as the use of initial estimates, i.e. Example: • Selection of 10 out of 100 projects with values µi ~ N(3,12) • Population contains two types of projects: • Revised estimates yield higher portfolio value for any non-trivial division between projects with small and large estimation error variances

  12. Revised estimates and correct choices Share of correct choices [%] Share of projects with large error variance [%] The share of correctly selected projects increases with revised estimates in the normally distributed case, i.e., where K is the index set of the projects in the optimal portfolio In the previous example, the difference between the two portfolios is statistically significant (α=0.05), when the share of projects with large error variance is between 25-55%

  13. Discussion Selection based on project prioritization resulting from estimates • The value of the portfolio will, on average, be lower than expected • If there are differences in the projects’ estimation error variances, too many projects with large error variance will be selected Suggestions for improving the selection process • Accounting for the uncertainties by using revised estimates • Sorting the projects in terms of estimation error variances by, e.g., budget division

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