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Thiago de Oliveira Souza. Strategic asset allocation with heterogeneous beliefs

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

Published in: Economy & Finance, Business
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Thiago de Oliveira Souza. Strategic asset allocation with heterogeneous beliefs

  1. 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. 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. 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. 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. 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. 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. 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. 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. 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. 10. Overview Introduction The model Empirical analysis The components of the demand for assets Fundamentalist investors’ demand for assets Concluding remarks
  11. 11. Overview Introduction The model Empirical analysis The components of the demand for assets Momentum investors’ demand for assets Concluding remarks
  12. 12. Overview Introduction The model Empirical analysis Quantifying the differences Proportion of traders and investment horizons Concluding remarks
  13. 13. Overview Introduction The model Empirical analysis Quantifying the differences Noise sensitivity (intensity of choice) Concluding remarks
  14. 14. Overview Introduction The model Empirical analysis Concluding remarks Quantifying the differences Proportion of traders in each market: “Policy implications”
  15. 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. 16. Overview Introduction The model Strategic asset allocation with heterogeneous beliefs Thank you! Empirical analysis Concluding remarks

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