Information Immobility and the Home Bias

Transcription

1 Information Immobility and the Home Bias Stijn Van Nieuwerburgh and Laura Veldkamp Discussed by Urban Jermann July 2006 Discussed by Urban Jermann () Information Immobility July / 15

2 Contribution: Model with endogenous information asymmetry to study portfolio home bias Key model features: CARA-normal (mean-variance) portfolio choice Private signals about asset payo s Information acquisition subject to capacity constraint (Sims 2003) Noisy rational expectations equilibrium (Admati 1985) Discussed by Urban Jermann () Information Immobility July / 15

3 Main ndings: Learning ampli es initial information asymmetry With enough learning capacity can explain US home bias Discussed by Urban Jermann () Information Immobility July / 15

4 Portfolio Choice with Asymmetric Information With information advantage, optimal share holdings are given by q 1 = bσ 1 (bµ pr) ρ Without information advantage 1 q no adv = Σ 1 (µ ρ pr) For uncorrelated assets, for asset i q i = 1 bµi ρ bσ 2 i p i r Discussed by Urban Jermann () Information Immobility July / 15

5 Portfolio Choice with Asymmetric Information Assuming information advantage is from private signal and bσ 2 i known is Discussed by Urban Jermann () Information Immobility July / 15

6 Portfolio Choice with Asymmetric Information Assuming information advantage is from private signal and bσ 2 i known Expected holding (conditional on public information) is E [q i ] = 1 E [bµi p i r] ρ bσ 2 i = 1 ρ µi bσ 2 i p i r clearly with bσ 2 i < σ 2 i then je (q i )j > E q no adv i :! Home Bias Discussed by Urban Jermann () Information Immobility July / 15

7 Portfolio Choice with Asymmetric Information Assuming information advantage is from private signal and bσ 2 i known Expected holding (conditional on public information) is E [q i ] = 1 E [bµi p i r] ρ bσ 2 i = 1 ρ µi bσ 2 i p i r clearly with bσ 2 i < σ 2 i then je (q i )j > Actual holding q i Eq i = E q no adv i 1 (bµi p i r) E (bµ i p i r) ρ bσ 2 i :! Home Bias 0 Discussed by Urban Jermann () Information Immobility July / 15

8 Portfolio Choice with Asymmetric Information Informed agent has higher expected returns Eq i (f i p i r) = than non-informed agent 1 [E (µi p i r)] 2 + cov ( bµ i, f i ) ρ bσ 2 i 1 [E (µi p i r)] 2 ρ σ 2 i Discussed by Urban Jermann () Information Immobility July / 15

9 How much information asymmetry for (expected) home bias? De ne domestic portfolio share w h = Eq h Eq h + Eq f, (p = 1) Discussed by Urban Jermann () Information Immobility July / 15

10 How much information asymmetry for (expected) home bias? De ne domestic portfolio share w h = Eq h Eq h + Eq f, (p = 1) assume 2 uncorrelated assets and symmetry, with bσ 2 h = (1 τ) bσ 2 f Discussed by Urban Jermann () Information Immobility July / 15

11 How much information asymmetry for (expected) home bias? De ne domestic portfolio share w h = Eq h Eq h + Eq f, (p = 1) assume 2 uncorrelated assets and symmetry, with then bσ 2 h = (1 τ) bσ 2 f w h = 1 2 τ Discussed by Urban Jermann () Information Immobility July / 15

12 How much information asymmetry for (expected) home bias? De ne domestic portfolio share w h = Eq h Eq h + Eq f, (p = 1) assume 2 uncorrelated assets and symmetry, with then w h =.9 requires bσ 2 h = (1 τ) bσ 2 f w h = 1 2 τ τ =.89 Discussed by Urban Jermann () Information Immobility July / 15

13 Information asymmetry with correlated assets (with µ i p i r = 0.08, σ 2 i = ) Discussed by Urban Jermann () Information Immobility July / 15

14 Information asymmetry with correlated assets (with µ i p i r = 0.08, σ 2 i = ) Is Home Bias still a Puzzle with a 0.8 correlation? Discussed by Urban Jermann () Information Immobility July / 15

15 Actual positions with information advantage Actual position depends on additional information q 1 = bσ 1 (bµ pr), with Var (bµ) = Σ bσ ρ Discussed by Urban Jermann () Information Immobility July / 15

16 Actual positions with information advantage Actual position depends on additional information q 1 = bσ 1 (bµ pr), with Var (bµ) = Σ bσ ρ How likely is a short position in domestic holdings? Discussed by Urban Jermann () Information Immobility July / 15

17 Actual positions with information advantage Actual position depends on additional information q 1 = bσ 1 (bµ pr), with Var (bµ) = Σ bσ ρ How likely is a short position in domestic holdings? With ρ =.8 and τ =.42, we have bµ N (1.36, 4.2) Probability of negative position is 37% Discussed by Urban Jermann () Information Immobility July / 15

18 Endogenous Information Acquisition Having substituted optimal share holdings, the learning problem with 2 uncorrelated assets can be written as max fbσ 1,bσ 2 g 1 + θ 2 1 σ θ2 2 bσ 2 1 bσ 2 2 σ2, with θ 2 i (µ i pr) 2 σ 2 i s.t. bσ 1 bσ 2 σ 1 σ 2 exp ( K) : capacity constraint bσ 1 σ 1 : no negative learning bσ 2 σ 2 Discussed by Urban Jermann () Information Immobility July / 15

19 Main result of paper Rewrite problem max fs 1,S 2 g L 1 S 1 + L 2 S 2 with S i = 1 bσ 2 i, "precision" s.t. S 1 S 2 exp (2K) σ 1 σ 2 : "production possibility set" S 1 1 σ 1, S 2 1 σ 2 Discussed by Urban Jermann () Information Immobility July / 15

20 Main result of paper Rewrite problem max fs 1,S 2 g L 1 S 1 + L 2 S 2 with S i = 1 bσ 2 i, "precision" s.t. S 1 S 2 exp (2K) σ 1 σ 2 : "production possibility set" S 1 1 σ 1, S 2 1 σ 2 Linear indi erence curves + convex production possibilities frontier! multiple/corner solutions Discussed by Urban Jermann () Information Immobility July / 15

21 Reasons for a more "concrete" capacity constraint Variety of information problems: Why same constraint? Discussed by Urban Jermann () Information Immobility July / 15

22 Reasons for a more "concrete" capacity constraint Variety of information problems: Why same constraint? Limited capacity for processing (freely available) information (Sims) Discussed by Urban Jermann () Information Immobility July / 15

23 Reasons for a more "concrete" capacity constraint Variety of information problems: Why same constraint? Limited capacity for processing (freely available) information (Sims) Costly Investigation Discussed by Urban Jermann () Information Immobility July / 15

24 Reasons for a more "concrete" capacity constraint Variety of information problems: Why same constraint? Limited capacity for processing (freely available) information (Sims) Costly Investigation Exact functional form is crucial here Discussed by Urban Jermann () Information Immobility July / 15

25 Reasons for a more "concrete" capacity constraint Variety of information problems: Why same constraint? Limited capacity for processing (freely available) information (Sims) Costly Investigation Exact functional form is crucial here Useful for quantitative analysis Discussed by Urban Jermann () Information Immobility July / 15

26 Another capacity constraint: Un-Learnable Risk Consider the following capacity constraint from VNV (2005) bσ 2 1 ασ 2 1 bσ 2 2 ασ 2 2 (1 α) 2 σ 2 1 σ 2 1 exp ( 2K) Discussed by Urban Jermann () Information Immobility July / 15

27 Another capacity constraint: Un-Learnable Risk Consider the following capacity constraint from VNV (2005) bσ 2 1 ασ 2 1 bσ 2 2 ασ 2 2 (1 α) 2 σ 2 1 σ 2 1 exp ( 2K) ασ 2 i un-learnable risk, 0 α 1 Discussed by Urban Jermann () Information Immobility July / 15

28 Another capacity constraint: Un-Learnable Risk Consider the following capacity constraint from VNV (2005) bσ 2 1 ασ 2 1 bσ 2 2 ασ 2 2 (1 α) 2 σ 2 1 σ 2 1 exp ( 2K) ασ 2 i un-learnable risk, 0 α 1 Eliminating all learnable risk, bσ 2 i capacity ασ 2 i! 0, requires in nite Discussed by Urban Jermann () Information Immobility July / 15

29 Discussed by Urban Jermann () Information Immobility July / 15

30 Overall Very nice model, very nice analysis! I would like more concreteness on the capacity constraint more detailed quantitative analysis Discussed by Urban Jermann () Information Immobility July / 15