Thiago de Oliveira Souza Bradford University School of Management Universite libre de Bruxelles, ECARES Open Seminar at Eesti Pank, October 2013

1. Overview
Introduction
The model
Empirical analysis
Concluding remarks
Strategic asset allocation with heterogeneous
beliefs
Thiago de Oliveira Souza
Bradford University School of Management
Universit` libre de Bruxelles, ECARES
e
t.deoliveirasouza@bradford.ac.uk
Eesti Pank
Open Seminar October 2013

2. Overview
Introduction
The model
Empirical analysis
Concluding remarks
Presentation
The paper in “60” seconds: A summary
How the existence of long-term investors affects the results of the
heterogeneous beliefs models?
Two steps in the answer:
Deriving an intertemporal asset demand
Comparing the results empirically (using stock indices)
Differences are large, especially if agents are very risk averse.

3. Overview
Introduction
The model
Empirical analysis
Concluding remarks
Presentation
Outline
Introduction
Motivation
Long term investors
Heterogeneous agents
The model
Portfolio and consumption choices (Epstein-Zin, 1989)
Approximate demand for assets (Campbell et al, 2003)
Focus on the difference between the intertemporal and myopic
terms
Proportion of agent types (Brock and Hommes, 1998)
Empirical analysis
Value vs. Momentum investors
Demand for assets: Fundamentalists
Demand for assets: Chartists/Momentum
Estimated proportion of traders
Sensitivity to the parameters (noise)
Fluctuation of types over time in each market
Concluding remarks

4. Overview
Introduction
The model
Empirical analysis
Concluding remarks
Motivation
The investment horizon effect
Mean-Variance: Theory
Myopic planning
Consumption is not in the picture
Quadratic utility (u(W ) = W − bW 2 ): Non-monotonicity, etc.
Risk Measures: Application
Moreover: Changing investment set (not iid) ⇒ Hedging

5. Overview
Introduction
The model
Empirical analysis
Concluding remarks
Motivation
Heterogeneous beliefs
“Puzzles” in the representative agent framework
Equity Premium puzzle (Mehra and Prescott, 1985)
Volatility puzzle (Campbell, 1998)
Risk-free puzzle (Weil, 1989)
Conflicting evidence
Momentum effect (Jegadeesh and Titman, 1993)
Mean reversion (De Bondt and Thaler, 1985)
High trading volumes as opposed to a no-trade equilibrium
(e.g., Milgrom and Stokey, 1982)

6. Overview
Introduction
The model
Empirical analysis
Concluding remarks
Portfolio and consumption choices
The investor’s maximization problem
Choosing the asset allocation and stream of consumption:
1− γ
θ
maxU (Ct , Et [Ut+1 ]) = (1 − δ)Ct
αt ,Ct
s.t.
1
1− γ
+ δ(Et (Ut+1 )) θ
θ
1− δ
Wt+1 = (Wt − Ct )(1 + Rp,t+1 ),
n
Rp,t+1 =
∑ αh,i,t (Ri,t+1 − R1,t+1 ) + R1,t+1 .
i=2
Approximate demand for assets (given the consumption policy):
Myopic Demand
1 −1
1
∗
αh,t = Σh,xx Eh,t (xt+1 ) + Varh,t (xt+1 ) + (1 − γ)σh,1x
γ
2
1 −1
θ
+ Σh,xx −
σ
− σh,1,c−w,t ι .
γ
ψ h,c−w,t
Intertemporal hedging demand
* Smooth consumption implies that c/w varies through wealth.

7. Overview
Introduction
The model
Empirical analysis
Concluding remarks
The model’s output
Connecting the dots
Proportion of agents of type h (Brock and Hommes, 1998):
ηht =
exp( βUh,t−1 )
H
∑h=1 exp( βUh,t−1 )
Uh,t =(xt ) • αh,t .
Demand for assets of agents type h (Campbell et al, 2003):
Myopic Demand
∗
αh,t =
1 −1
1
Σh,xx Eh,t (xt+1 ) + Varh,t (xt+1 ) + (1 − γ)σh,1x
γ
2
1 −1
θ
+ Σh,xx − (σh,c−w,t − σh,1,c−w,t ι) .
γ
ψ
Intertemporal hedging demand

8. Overview
Introduction
The model
Empirical analysis
Concluding remarks
Formulation
Overview
Investor in the U.S.A. diversifies using the international stock
markets:
Dow Jones, FTSE, Nikkei and Hang Seng.
Two models/types/strategies:
Fundamentalist (value strategies)
Chartist (momentum strategies)
Factor models: DP and past return
The assumption about the investment horizon impacts:
The estimation of the proportions of investors
The response to noise in observed performances
The demand for assets
A summary next...

9. Overview
Introduction
The model
Empirical analysis
Concluding remarks
Formulation
Summary of the results
If agents are very risk averse, the assumptions about
investment horizon is crucial
IHD dominates for very risk averse agents
The IHD term is significantly large even for less risk averse
agents
The effects are asymmetric for fundamentalist and chartist
types
Noise in the observed performances also has asymmetric
effects on myopic and long-term investors

10. Overview
Introduction
The model
Empirical analysis
The components of the demand for assets
Fundamentalist investors’ demand for assets
Concluding remarks

11. Overview
Introduction
The model
Empirical analysis
The components of the demand for assets
Momentum investors’ demand for assets
Concluding remarks

12. Overview
Introduction
The model
Empirical analysis
Quantifying the differences
Proportion of traders and investment horizons
Concluding remarks

13. Overview
Introduction
The model
Empirical analysis
Quantifying the differences
Noise sensitivity (intensity of choice)
Concluding remarks

14. Overview
Introduction
The model
Empirical analysis
Concluding remarks
Quantifying the differences
Proportion of traders in each market: “Policy implications”

15. Overview
Introduction
The model
Empirical analysis
Concluding remarks
Strategic asset allocation with heterogeneous beliefs
Summary
Empirical exercise shows that the IHD is significantly large
Especially true for very risk averse agents
Or not so important for reasonably risk averse agents?
Considering short- or long-term investors has a large impact on
the results
Changes in the parameters (e.g., noise in the data) have
different effects depending on the investment horizon
considered
The increase in investment horizon has asymmetric effects on
different agent types
Overall, estimating the model involves a joint assumption
about the strategies considered by the agents, and their
investment horizons

16. Overview
Introduction
The model
Strategic asset allocation with heterogeneous beliefs
Thank you!
Empirical analysis
Concluding remarks