Bayesian evaluation and selection strategies in portfolio decision analysis
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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

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.


Sports illustrated cover jinx
Sports Illustrated cover jinx decision analysis

  • 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


Sports illustrated cover jinx1
Sports Illustrated cover jinx decision analysis

  • 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


Sports illustrated cover jinx2
Sports Illustrated cover jinx decision analysis

  • 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 


Post decision disappointment in portfolio selection
Post-decision disappointment in portfolio selection decision analysis

= 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


Bayesian analysis in portfolio selection
Bayesian analysis in portfolio selection decision analysis

  • 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) →


Bayesian analysis in portfolio selection1
Bayesian analysis in portfolio selection decision analysis

  • 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


Example
Example decision analysis

  • 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)


Example cont d
Example cont’d decision analysis

= Selected project

= Unselected project

Size proportional to cost

True value = 52

Estimated value = 62

True value = 55

Estimated value = 58


Value of additional information
Value of additional information decision analysis

= 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


Value of additional information1
Value of additional information decision analysis

  • 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


Conclusion
Conclusion decision analysis

  • 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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