1 Helsinki University of Technology Systems Analysis Laboratory Robust Portfolio Selection in Robust Portfolio Selection in Multiattribute Capital Budgeting Multiattribute Capital Budgeting Pekka Mild and Ahti Salo Systems Analysis Laboratory Helsinki University of Technology P.O. Box 1100, 02150 HUT, Finland http://www.sal.hut.fi
20
Embed
1 Helsinki University of Technology Systems Analysis Laboratory Robust Portfolio Selection in Multiattribute Capital Budgeting Pekka Mild and Ahti Salo.
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
1
Helsinki University of Technology Systems Analysis Laboratory
Robust Portfolio Selection in Multiattribute Robust Portfolio Selection in Multiattribute
Capital BudgetingCapital Budgeting
Pekka Mild and Ahti SaloSystems Analysis Laboratory
Helsinki University of TechnologyP.O. Box 1100, 02150 HUT, Finland
http://www.sal.hut.fi
Helsinki University of Technology Systems Analysis Laboratory
2
Background Background
Multiattribute capital budgeting– Several projects evaluated w.r.t several attributes (e.g., 6-12 attributes)
– Project value as weighted sum of attribute specific scores
Treats feasible weight region according to fixed portfolios.Defines subsets anddetermines extreme points.
TpQwwpV ),(
Portfolio indicator vector
Attribute weightcoefficients, wS0
Projects’ scorematrix (fixed)
Helsinki University of Technology Systems Analysis Laboratory
9
Determination of potentially optimal portfolios (2/3)Determination of potentially optimal portfolios (2/3)
Splits feasible weight region into disjoint subsets– Each subset is either divided in two or considered done
– New subsets by additional constraints
– Subsets defined explicitly by extreme points
For each (sub)set Sk the basic steps are
1. Calculate optimal portfolio at each extreme point of Sk
2. i) If each extreme point has the same optimal portfolio, conclude that this portfolio is optimal in the entire subset Sk
ii) If some of the extremes have different optimal portfolios, divide the respective subset in two with a hyperplane exhibiting equal value for the two portfolios chosen to define the division
Helsinki University of Technology Systems Analysis Laboratory
10
Determination of potentially optimal portfolios (3/3)Determination of potentially optimal portfolios (3/3)
The portfolios are constructed in descending value– Only feasible portfolios are constructed
No all inconclusive computations– Constructed portfolios are potentially optimal
– No cross-checks and later rejections
Extreme points of the subsets are
generated by utilizing the extremes
of the parent set
V(pk,w) V(pk,w)
w10 1w21 0
pinfeas
p1
p2
Helsinki University of Technology Systems Analysis Laboratory
Core of a non-dominated portfolio– Consists of projects included in all non-dominated portfolios
– Share of non-dominated portfolios in which a project is included
– Measures derived in the portfolio context - and not in isolation
Implications for project choice– Select core projects
– Discard projects that are not included in any non-dominated portfolio
– Reconsider remaining projects
Helsinki University of Technology Systems Analysis Laboratory
19
Uses of methodologyUses of methodology Consensus-seeking in group decision making
– Consideration of multiple stakeholders’ interests (incomplete weights)
– Select a portfolio that best satisfies all views» E.g. no-one has to give up more than 30% of their individual optimum
Robust decision making in scenario analysis– Attributes interpreted as scenarios
– Weights interpreted as probabilities
Sequential project selection– Core projects
– Additional constraints
Sensitivity analysis– Effect of small changes in the weights
– Displaying the emerging potential portfolios at once
Helsinki University of Technology Systems Analysis Laboratory
20
ReferencesReferences
» Arbel, A., (1989). Approximate Articulation of Preference and Priority Derivation, EJOR, Vol. 43, pp. 317-326.
» Carrizosa, E., Conde, E., Fernández, F. R., Puerto, J., (1995). Multi-Criteria Analysis with Partial Information about the Weighting Coefficients, EJOR, Vol. 81, pp 291-301.
» Kim, S. H., Han, C. H., (2000). Establishing Dominance between Alternatives with Incomplete Information in a Hierarchically Structured Value Tree, EJOR, Vol. 122, pp. 79-90.
» Salo, A., Hämäläinen, R. P., (1992). Preference Assessment by Imprecise Ratio Statements, Operations Research, Vol. 40, pp. 1053-1060.
» Salo, A., Hämäläinen, R. P., (1995). Preference Programming Through Approximate Ratio Comparisons, EJOR, Vol. 82, pp. 458-475.
» Salo, A., Hämäläinen, R. P., (2001). Preference Ratios in Multiattribute Evaluation (PRIME) - Elicitation and Decision Procedures under Incomplete Information, IEEE Transactions on SMC, Vol. 31, pp. 533-545.
» Stummer, C., Heidenberg, K., (2003). Interactive R&D Portfolio Analysis with Project Interdependencies and Time Profiles of Multiple Objectives, IEEE Trans. on Engineering Management, Vol. 50, pp. 175 - 183.