Strategy, Structure and Selection
David Bowie
Motivation
• Investment advice
– Risk and reward
– Implementation
• Optimal vs. practical?
Conventional Advice
• Hierarchical approach
– Strategy: benchmark vs. liabilities
– Structure: nature and number of managers
– Selection: individual portfolios
Risk budgeting
• Risk Budget
– Magnitude
– Attribution
Selection
Structure
• Motivated by
– ‘importance’ of risks
– ease of explanation
Strategy
Model
• Model:
– Strategy: k
– Structure: ϕ
– Selection: Ractive
[
]
R fund = k ϕR passive + (1 − ϕ ) Ractive + (1 − k )rf
Model
• Investors maximise (approximate) expected
utility function
• E[U(Rfund)] = E[Rfund] - τ/2 Var[Rfund]
Hierarchical: strategy
• Determine systematic risk, k
• Assume +ve active contribution
• Depends on:
– risk tolerance
– market return and risk
k=
Rmkt − rf
σ
2
mkt
τ
−1
Strategy and risk aversion
E[ Rmkt ] = 10%
Var[ Rmkt ] = 20%
150%
rf = 5%
Mismatch
125%
100%
75%
50%
25%
0%
0
1
2
3
Risk aversion
4
5
Hierarchical: structure
• For optimal k, choose proportion active to
maximise utility
α active
1−ϕ = 2
σ active
 Rmkt − rf

2
 σ mkt



• Inevitable overlap with selection …
Structure and selection
100.00
75.00
Propn active
50.00
25.00
1
0.5 IR
0.00
0%
1.50%
Active risk
3%
0
4.50%
Hierarchical: structure
• Structure then selection
– House structures
• Selection then structure
– Often preferred in practice
• Require ‘style neutrality’ (β = 1)
– But permit matching asset (cash)
Portfolio structure
Strategic matching
assets
Risky assets:
•Passive
•Active
•Matching assets
Sufficient degrees of freedom
Hierarchical: structure first
• Effectively extra constraint
• Risky assets ~ appraisal ratios and
systematic risk(s)
 1  α i   1  β i 
xi = π    + ν   
 σ i  σ i   σ i  σ i 
Example
A
B
C
α
0.15
0.25
0.25
β
0.8
1.1
1.0
σ
3.0
4.0
4.0
IR
0.05
0.06
0.06
AR
1.7
1.6
1.6
xi
13%
40%
47%
IR hurdle
0.250
0.200
0.150
0.100
0.050
5.0%
10.0%
Active risk
2.0%
1.0%
0.000
0.5%
Minimum IR
100%
75%
50%
25%
0% Proportion in
risky portfolio
Hierarchical: selection first
• Well-known result (Black & Treynor)
• Risky assets ~ appraisal ratios,
i.e. IR/active risk
 1  α i 
xi = π   
 σ i  σ i 
Example
A
B
C
α
0.15
0.25
0.25
β
0.8
1.1
1.0
σ
3.0
4.0
4.0
IR
0.05
0.06
0.06
AR
1.7
1.6
1.6
xi
35%
33%
33%
Insights
• Strategy, selection, structure
– Sufficient degrees of freedom
• Strategy:
– determines level of matching
• Selection:
– Appraisal ratios
– Independent of risk tolerance
• Structure:
– A consequence
– Independent of risk tolerance