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

t.deoliveirasouza@bradford.ac.uk

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!