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Bayesian evaluation and selection strategies in portfolio decision analysis

Bayesian evaluation and selection strategies in portfolio decision analysis. E. Vilkkumaa, J. Liesiö, A. Salo EURO XXV, 8-11 July, Vilnius, Lituhania. The document can be stored and made available to the public on the open internet pages of Aalto University. All other rights are reserved.

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Bayesian evaluation and selection strategies in portfolio decision analysis

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  1. Bayesian evaluation and selection strategies in portfolio decision analysis E. Vilkkumaa, J. Liesiö, A. Salo EURO XXV, 8-11 July, Vilnius, Lituhania The document can be stored and made available to the public on the open internet pages of Aalto University. All other rights are reserved.

  2. Sports Illustrated cover jinx • Apr 6, 1987: The Cleveland Indians • Predicted as the best team in the American League • Would have a dismal 61–101 season, the worst of any team that season

  3. Sports Illustrated cover jinx • Nov 17, 2003: The Kansas City Chiefs  • Appeared on the cover after starting the season 9-0 • Lost the following game and ultimately the divisional playoff against Indianapolis

  4. Sports Illustrated cover jinx • Dec 14, 2011: The Denver Broncos • Appeared on the cover after a six-game win streak • Lost the next three games of the regular season and ultimately the playoffs Teams are selected to appear on the cover based on an outlier performance 

  5. Post-decision disappointment in portfolio selection = Selected project = Unselected project Size proportional to cost • Selecting a portfolio of projects is an important activity in most organizations • Selection is typically based on uncertain value estimates vE • The more overestimated the project, the more probably it will be selected • True performance revealed → post-decision disappointment

  6. Bayesian analysis in portfolio selection • Idea: instead of vE, use the Bayes estimate vB=E[V|vE] as a basis for selection • Given the distributions for V and VE|V, Bayes’ rule states • E.g., V~N(μ,σ2), VE=v+ε, ε~N(0,τ2) → V|vE~N(vB,ρ2), where f(V|VE)f(V)·f(VE|V) →

  7. Bayesian analysis in portfolio selection • Portfolio selected based on vB • Maximizes the expected value of the portfolio given the estimates • Eliminates post-decision disappointment • Using f(V|VE), we can • Compute the expected value of additional information • Compute the probability of project i being included in the optimal portfolio

  8. Example • 10 projects (A,...,J) with costs from 1 to 12 M$ • Budget 25M$ • Projects’ true values Vi ~ N(10,32) • A,...,D conventional projects • Estimation error εi ~ N(0,12) • Moreover, B can only be selected if A is selected • E,...,J novel, radical projects • More difficult to estimate: εi ~ N(0, 2.82)

  9. Example cont’d = Selected project = Unselected project Size proportional to cost True value = 52 Estimated value = 62 True value = 55 Estimated value = 58

  10. Value of additional information = Selected project = Unselected project Size proportional to cost • Knowing f(V|vE), we can compute • Expected value (EVI) of additional information VE • Probability that project i is included in the optimal portfolio EVI for single project re-evaluation Probability of being in the optimal portfolio close to 0 or 1

  11. Value of additional information • Selection of 20 out of 100 projects • Re-evaluation strategies • All 100 projects • 30 projects with the highest EVI • ’Short list’ approach (Best 30) • 30 randomly selected projects

  12. Conclusion • Estimation uncertainties should be explicitly accounted for because of • Suboptimal portfolio value • Post-decision disappointment • Bayesian analysis helps to • Increase the expected value of the selected portfolio • Alleviate post-decision disappointment • Obtain project-specific performance measures • Identify those projects of which it pays off to obtain additional information

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