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 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 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

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

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

Bayesian analysis in portfolio selection Idea: instead of v E, use the Bayes estimate v B =E[V|v E ] as a basis for selection Given the distributions for V and V E |V, Bayes’ rule states E.g., V~N(μ,σ 2 ), V E =v+ε, ε~N(0,τ 2 ) → V|v E ~N(v B,ρ 2 ), where f(V|V E )  f(V)·f(V E |V) →

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

Example 10 projects (A,...,J) with costs from 1 to 12 M$ Budget 25M$ Projects’ true values V i ~ N(10,3 2 ) A,...,D conventional projects –Estimation error ε i ~ N(0,1 2 ) –Moreover, B can only be selected if A is selected E,...,J novel, radical projects –More difficult to estimate: ε i ~ N(0, )

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

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

Value of additional information Selection of 20 out of 100 projects Re-evaluation strategies 1.All 100 projects 2.30 projects with the highest EVI 3.’Short list’ approach (Best 30) 4.30 randomly selected projects

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