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Bayesian evaluation and selection strategies in portfolio decision analysis. E. Vilkkumaa, J. Liesiö, A. Salo INFORMS Annual meeting, Phoenix, Oct 14 th -17 th 2012.
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Bayesian evaluation and selection strategies in portfolio decision analysis E. Vilkkumaa, J. Liesiö, A. Salo INFORMS Annual meeting, Phoenix, Oct 14th-17th 2012 The document can be stored and made available to the public on the open internet pages of Aalto University. All other rights are reserved.
Post-decision disappointment in portfolio selection = Optimal project based on vE = Optimal project based on v Size is proportional to cost • Project portfolio selection is important • Decisions are typically based on uncertain value estimates vE about true value v • If the value of a project is overestimated, this project is more likely to be selected • Disappointments are therefore likely * Brown (1974, Journal of Finance), Harrison and March (1986, Administrative Science Quarterly), Smith and Winkler (2006, Management Science)
Underestimation of costs in public work projects (1/2) • Flyvbjerg et al. 2002 found statistically significant escalation (p<0.001) of costs in public infrastructure projects • This escalation was attributed to strategic misrepresentation by project promoters Frequency (%) Average escalation μ=27,6% Cost escalation (%) Source: Flyvbjerg et al. (2002), Underestimating Costs in Public Work Projects – Error or Lie? Journal of the American Planning Association, Vol. 68, pp. 279-295.
Underestimation of costs in public work projects (2/2) • If projects with the lowest cost estimates are selected, the realized costs tend to be higher even if cost estimates are unbiased a priori • Cost escalation could therefore be attributed to ʻpost-decision disappointment’ as well
Bayesian revision of value estimates (1/2) • Assume that the prior f(v) and the likelihood f(vE|v) are known such that • By Bayes’ rule we have f(v|vE)f(v)·f(vE|v) • Use the Bayes estimates viB for selection • If Vi~N(μi,σi2), ViE=vi+εi, εi~N(0,τi2) , then Vi|viE~N(viB,ρi2), where
Bayesian revision of value estimates (2/2) • Portfolio selection based on the revised estimates viB • Eliminates post-decision disappointment • Maximizes the expected portfolio value given the estimates viE • Using f(v|vE), we show how to: • Determine the expected value of acquiring additional estimates viE • Determine the probability that project i belongs to the truly optimal portfolio (= portfolio that would be selected if the true values v were known)
Example (1/2) • 10 projects (A,...,J) with costs from $1M to $12M • Budget $25M • Projects’ true values Vi ~ N(10,32) • A,...,D conventional projects • Estimation error εi ~ N(0,12) • Two interdependent projects: B can be selected only if A is selected • E,...,J novel, radical projects • These are more difficult to estimate: εi ~ N(0, 2.82)
Example (2/2) = Optimal project based on vE / vB = Optimal project based on v Size proportional to cost * True value = 52$M Estimated value = 62$M True value = 55$M Estimated value = 58$M
Value of additional information (1/2) = Optimal project based on current information • Knowing f(v|vE), we can determine • The expected value (EVI) of additional value estimates VE prior to acquiring vE • The probability that project i belongs to the truly optimal portfolio The probability that the project belongs to the truly optimal portfolio is here close to 0 or 1
Value of additional information (2/2) • Select 20 out of 100 projects • Re-evaluation strategies • All 100 projects • 30 projects with the highest EVI • ʻShort list’ approach (Best 30) • 30 randomly selected projects • Due to evaluation costs, strategy 2 is likely to outperform strategy 1
Conclusions • Uncertainties in cost and value estimates should be explicitly accounted for • Bayesian revision of the uncertain estimates helps • Increase the expected value of the selected portfolio • Alleviate post-decision disappointment • Bayesian modeling of uncertainties guides the cost-efficient acquisition of additional estimates as well