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. - PowerPoint PPT PresentationTRANSCRIPT
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
0 2 4 6 8 10 12 14 16 180
2
4
6
8
10
12
14
16
18
J
E
D
C
H
A
F
I
B
G
True value v
Est
ima
te vE
0 2 4 6 8 10 12 14 16 180
2
4
6
8
10
12
14
16
18
True value v
Ba
yes
est
ima
te vB
A
FI
E
J
B
DC
G
H
Prior mean
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 vE
• 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 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) →
dvvvvfvVv )|(]|[E EEB
.,22
42
22
2
22
2
EB vv
Bayesian analysis in portfolio selection
• 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
• 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
True value = 52Estimated value = 62
True value = 55Estimated value = 58
= Selected project = Unselected project Size proportional to cost
0 2 4 6 8 10 12 14 16 180
2
4
6
8
10
12
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16
18
J
E
D
C
H
A
F
I
B
G
True value v
Est
ima
te v
E
0 2 4 6 8 10 12 14 16 180
2
4
6
8
10
12
14
16
18
True value vB
aye
s e
stim
ate
vB
A
FI
E
J
B
DC
G
H
Prior meanPrior mean
Value of additional information
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
A
B
DI
J
CG
H E
Probability of being in the optimal portfolio
EV
I (M
EU
R)
F
• Knowing f(V|vE), we can compute – Expected value (EVI) of
additional information VE
– Probability that project i is included in the optimal portfolio
Probability of being in the optimal portfolio close to 0 or 1
EV
I fo
r si
ngle
pro
ject
re-
eval
uatio
n
= Selected project = Unselected project Size proportional to cost
Value of additional information
1 2 3 491
92
93
94
95
96
97
Number of evaluation rounds
Por
tfolio
val
ue (
% o
f the
opt
imum
)
k=100
k=30
Best 30
Random 30
1 2 3 464
66
68
70
72
74
76
78
Number of evaluation rounds
Sha
re o
f cor
rect
cho
ices
(%
)
k=100
k=30
Best 30
Random 30
• Selection of 20 out of 100 projects
• Re-evaluation strategies1. 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