Optimal strategies for selecting project portfolios using uncertain value estimates

Transcription

1 Optmal strateges for selectng project portfolos usng uncertan alue estmates. Vlkkumaa, J. Lesö, A. Salo Unersty of Venna, Noember 6th 013 The document can be stored and made aalable to the publc on the open nternet pages of Aalto Unersty. All other rghts are resered.

2 Post-decson dsappontment n portfolo selecton stmate ($M) = Optmal project based on = Optmal project based on Sze s proportonal to cost A F J I True alue ($M) D H C G Project portfolo selecton s mportant Decsons are typcally based on uncertan alue estmates about true alue If the alue of a project s oerestmated, ths project s more lkely to be selected Dsappontments are therefore lkely rown (1974, Journal of Fnance), Harrson and March (1986, Admnstrate Scence Quarterly), Smth and Wnkler (006, Management Scence)

3 Frequency (%) Underestmaton of costs n publc work projects (1/) Cost escalaton (%) Aerage escalaton =7,6% Flybjerg et al. 00 found statstcally sgnfcant escalaton (p<0.001) of costs n publc nfrastructure projects Ths escalaton was attrbuted to strategc msrepresentaton by project promoters Source: Flybjerg et al. (00), Underestmatng Costs n Publc Work Projects rror or Le? Journal of the Amercan Plannng Assocaton, Vol. 68, pp

4 Underestmaton of costs n publc work projects (/) Dstrbuton of maxmal escalaton among 3 projects, =17% Dstrbuton of escalaton for each project, =0%, =0% Cost escalaton (%) Dstrbuton of maxmal escalaton among 6 projects, =5% If projects wth the lowest cost estmates are selected, the realzed costs tend to be hgher een f cost estmates are unbased a pror Cost escalaton could therefore be attrbuted to post-decson dsappontment as well

5 Assume that the pror f() and the lkelhood f( ) are known such that y ayes rule we hae f( ) f() f( ) Use the ayes estmates for selecton If V ~N( ), V =, ~N(0, ), then V ~N( ), where ayesan reson of alue estmates (1/) d f V V ) ( ] [., 4 d f V V ) ( ] [

6 ayesan reson of alue estmates (/) Portfolo selecton based on the resed estmates lmnates post-decson dsappontment Maxmzes the expected portfolo alue gen the estmates Usng f( ), we show how to: 1. Determne the expected alue of acqurng addtonal estmates. Determne the probablty that project belongs to the truly optmal portfolo (= portfolo that would be selected f the true alues were known)

7 xample (1/) 10 projects (A,...,J) wth costs from $1M to $1M udget $5M Projects true alues V ~ N(10,3 ) A,...,D conentonal projects stmaton error ~ N(0,1 ) Two nterdependent projects: can be selected only f A s selected,...,j noel, radcal projects These are more dffcult to estmate: ~ N(0,.8 )

8 xample (/) = Optmal project based on / = Optmal project based on Sze proportonal to cost stmate ($M) Pror mean A F J I D H C G ayes estmate ($M) Pror mean A F 1 J I D H C G True alue ($M) True alue = 5$M stmated alue = 6$M True alue ($M) True alue = 55$M stmated alue = 58$M

9 Value of addtonal nformaton (1/) VI for a sngle project ealuaton = Optmal project based on current nformaton G F H A Probablty that the project belongs to the truly optmal portfolo D I C J Knowng f( ), we can determne The expected alue (VI) of addtonal alue estmates V pror to acqurng The probablty that project belongs to the truly optmal portfolo The probablty that the project belongs to the truly optmal portfolo s here close to 0 or 1

10 Value of addtonal nformaton (/) Portfolo alue - ealuaton cost Complete re-ealuaton 30 hghest VI hghest expectaton Random Number of ealuaton rounds Select 0 out of 100 projects aluaton cost 3% of a project s cost Re-ealuaton strateges 1. All 100 projects. 30 projects wth the hghest VI 3. Short lst approach (est 30) randomly selected projects

11 Conclusons Uncertantes n cost and alue estmates should be explctly accounted for ayesan reson of the uncertan estmates helps Increase the expected alue of the selected portfolo Alleate post-decson dsappontment ayesan modelng of uncertantes gudes the costeffcent acquston of addtonal estmates as well