Upload
eesti-pank
View
566
Download
0
Tags:
Embed Size (px)
DESCRIPTION
Thiago de Oliveira Souza Bradford University School of Management Universite libre de Bruxelles, ECARES Open Seminar at Eesti Pank, October 2013
Citation preview
Overview Introduction The model Empirical analysis Concluding remarks
Strategic asset allocation with heterogeneousbeliefs
Thiago de Oliveira Souza
Bradford University School of ManagementUniversite libre de Bruxelles, ECARES
Eesti PankOpen Seminar October 2013
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 theheterogeneous beliefs models?
Two steps in the answer:
Deriving an intertemporal asset demandComparing the results empirically (using stock indices)
Differences are large, especially if agents are very risk averse.
Overview Introduction The model Empirical analysis Concluding remarks
Presentation
Outline
IntroductionMotivation
Long term investorsHeterogeneous agents
The modelPortfolio and consumption choices (Epstein-Zin, 1989)Approximate demand for assets (Campbell et al, 2003)
Focus on the difference between the intertemporal and myopicterms
Proportion of agent types (Brock and Hommes, 1998)Empirical analysis
Value vs. Momentum investorsDemand for assets: FundamentalistsDemand for assets: Chartists/MomentumEstimated proportion of tradersSensitivity to the parameters (noise)Fluctuation of types over time in each market
Concluding remarks
Overview Introduction The model Empirical analysis Concluding remarks
Motivation
The investment horizon effect
Mean-Variance: TheoryMyopic planningConsumption is not in the pictureQuadratic utility (u(W) = W− bW2): Non-monotonicity, etc.
Risk Measures: Application
Moreover: Changing investment set (not iid) ⇒ Hedging
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)
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:
maxαt,Ct
U(Ct, Et[Ut+1]) =
[(1− δ)C
1−γθ
t + δ(Et(U1−γt+1 ))
1θ
] θ1−δ
s.t. Wt+1 = (Wt − Ct)(1 + Rp,t+1),
Rp,t+1 =n
∑i=2
αh,i,t(Ri,t+1 − R1,t+1) + R1,t+1.
Approximate demand for assets (given the consumption policy):
α∗h,t =
Myopic Demand︷ ︸︸ ︷1γ
Σ−1h,xx
[Eh,t(xt+1) +
12
Varh,t(xt+1) + (1− γ)σh,1x
]+
1γ
Σ−1h,xx
[− θ
ψ
(σh,c−w,t − σh,1,c−w,tι
)]︸ ︷︷ ︸
Intertemporal hedging demand
.
* Smooth consumption implies that c/w varies through wealth.
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)
∑Hh=1 exp(βUh,t−1)
Uh,t=(xt) • αh,t.
Demand for assets of agents type h (Campbell et al, 2003):
α∗h,t =
Myopic Demand︷ ︸︸ ︷1γ
Σ−1h,xx
[Eh,t(xt+1) +
12
Varh,t(xt+1) + (1− γ)σh,1x
]+
1γ
Σ−1h,xx
[− θ
ψ(σh,c−w,t − σh,1,c−w,tι)
]︸ ︷︷ ︸
Intertemporal hedging demand
.
Overview Introduction The model Empirical analysis Concluding remarks
Formulation
Overview
Investor in the U.S.A. diversifies using the international stockmarkets:
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 investorsThe response to noise in observed performancesThe demand for assetsA summary next...
Overview Introduction The model Empirical analysis Concluding remarks
Formulation
Summary of the results
If agents are very risk averse, the assumptions aboutinvestment horizon is crucial
IHD dominates for very risk averse agents
The IHD term is significantly large even for less risk averseagents
The effects are asymmetric for fundamentalist and chartisttypes
Noise in the observed performances also has asymmetriceffects on myopic and long-term investors
Overview Introduction The model Empirical analysis Concluding remarks
The components of the demand for assets
Fundamentalist investors’ demand for assets
Overview Introduction The model Empirical analysis Concluding remarks
The components of the demand for assets
Momentum investors’ demand for assets
Overview Introduction The model Empirical analysis Concluding remarks
Quantifying the differences
Proportion of traders and investment horizons
Overview Introduction The model Empirical analysis Concluding remarks
Quantifying the differences
Noise sensitivity (intensity of choice)
Overview Introduction The model Empirical analysis Concluding remarks
Quantifying the differences
Proportion of traders in each market: “Policy implications”
Overview Introduction The model Empirical analysis Concluding remarks
Strategic asset allocation with heterogeneous beliefs
Summary
Empirical exercise shows that the IHD is significantly largeEspecially 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 onthe results
Changes in the parameters (e.g., noise in the data) havedifferent effects depending on the investment horizonconsidered
The increase in investment horizon has asymmetric effects ondifferent agent types
Overall, estimating the model involves a joint assumptionabout the strategies considered by the agents, and theirinvestment horizons
Overview Introduction The model Empirical analysis Concluding remarks
Strategic asset allocation with heterogeneous beliefs
Thank you!