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Home bias in portfolio choices: Social learning amongst partially-informed agents

Wen -Lin Wu ( Feng C hia University) Yin- Feng Gau (National Central University). Home bias in portfolio choices: Social learning amongst partially-informed agents. Home Bias: Investors allocate substantial amount of their portfolio investment to domestic assets

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Home bias in portfolio choices: Social learning amongst partially-informed agents

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  1. Wen-Lin Wu (FengChia University) Yin-FengGau (National Central University) Home bias in portfolio choices: Social learning amongst partially-informed agents

  2. Home Bias: Investors allocate substantial amount of their portfolio investment to domestic assets • Potential explanations: Institutional barriers; hedging motivations; asymmetric information and behavioral differences (Lewis (1999), Karolyi and Stulz (2003) and Sercu and Vanpee (2007)) • Several social mechanisms are used in various empirical settings to explain the reasons for the correlation between the investment decisions of investors, such as social influence, social interaction, peer effect, neighborhood effect and word-of-mouth effect (e.g., Hong, Kubik and Stein (2004, 2005), Ivkovic and Weisbenner (2005, 2007), Brown, Ivkovic, Weisbenner and Smith (2008) and Ng and Wu (2010)) • “People who interact with each other regularly tend to think and behave similarly.” --- Robert Shiller (1995) Motivation

  3. Investors’ information environments comprises the effects of public information, private information and information dissemination (Lang, Lins, and Miller (2003)) • Two realities: • Asymmetric informed across country and within country border • Partially informed or Estimation errors in expected returns (see, Merton (1980) and Chopra and Ziemba (1993)) • How they become well informed? • Exploiting all of the available prior beliefs on the private signals of others through their social mechanisms – either social interactions or observational learning (i.e., the social learning) • Methodologies: 1) Exchanging information directly with their ‘smarter’ peers; 2) Carrying out observations of the actions of other investors, or 3) Inferring comments from financial analysts, the media or opinion leaders. Motivation (Cont.)

  4. However, the problems are • Past studies overlook how such social learning effect helps investors to refresh their priors and form new estimates of the true mean returns • Investors reach their portfolio decisions if they are only partially informed, and the asymmetry that exists between them in terms of the quality of the information that they possess. • Therefore, we • Adopt the ‘incomplete information’ model to analyze the effects of social learning on the global portfolio choices of investors. • Highlight the influence of such asymmetry in the quality of the information possessed by partially-informed investors on the foreign investment decisions that they make within their home borders • Determine whether the global portfolio strategies of various types of investors become correlated if information is disseminated across agents Objectives of Paper

  5. Our model setting, based on social learning, conforms to several stylized facts in the field of finance • The social learning amongst partially-informed agents is strongly related to geographical proximity • The social learning is subject to behavioral biases towards foreign assets • Although social learning amplifies the information capacity of investors, they remain only partially informed.

  6. Model structure

  7. Three assets: • Home-based money market account: • Bt: The price of riskless domestic money market account • r: Locally constant riskless rate In the model, we set r = 0, then Bt = 1. • Home equity (Eq. (2)): • Foreign equity (Eq. (3)): • μ1 (μ2): The constant expected return of the domestic (foreign) asset; • σ1 (σ2): The constant standard deviation of the domestic (foreign) asset; • Z1 and Z2: Independent standard Brownian motions, defined on the complete probability space (Ω,F,P) • ρ1,2: Constant instantaneous correlation between home and foreign assets, which is –1< ρ1,2 <1. Two-country Economy

  8. Three types of agent: • Fully-informed: F = {Ft} • Partially-informed leaders: F Pi, X1L = {FtPi, X1L}, where FtPi, X1L = σ((Pi ,s, XL1,s); s  t) and i = 1, 2 • Partially-informed followers: FPi, X1j = {FtPi, X1j}, where FtPi, X1j = σ((Pi,s, Xj1,s); s  t), i = 1,2, and j = L,F • Utility function (Eq. (1)): • Fully-informed agents knows all required parameters - μ1, μ2, σ1, σ2 and ρ1, 2 • Partially-informed leaders and followers only knows σ1, σ2 and ρ1, 2 Two-country Economy (cont.)

  9. Domestic private signal : • Leaders’ private signals (Eq (4)): • Followers’ private signals (Eq. (5): • σLX 1 (σFX 1): The constant standard deviation of the private domestic signal of partially- informed leaders (followers) ; • ZLX 3 (ZFX 1): Standard Brownian motion defined on (Ω,F,P) • ρL,F: Constant instantaneous correlation between dXL1,t/XL1,t and dXF1,t/XF1,t Two-country Economy (cont.)

  10. Let dXL1,t/XL1,t and dP1,t /P1,t are correlated with the constant instantaneous correlation, ρL1,X1, we have Eq. (6) and (7) • ZLX 1: Standard Brownian motion defined on (Ω,F,P), which is assumed to be independent of ZFX 1 and Z1; • Conditional on ρL1,X1, ρL,F and ρ1,2 , we assume that Z2 is independent of ZLX 1 and ZFX 1 in order to simplify our model analysis Two-country Economy (cont.)

  11. The foreign country is geographically distant • The lack of knowledge on foreign firms, • The inability to monitor these firms, and • The poor quality or credibility of the available financial information on the foreign market (Ahearne, Griever and Warnock, 2004) • The partially- informed leaders and followers do not access to any private foreign signals. They only have access to past realizations of the prices of the foreign equities to estimate the true means of the foreign stock returns. Two-country Economy (cont.)

  12. All agents use all available information they have to estimate the expected returnsμi(i=1,2) • The conditional distribution of the unobservable μi: • Conditional mean of μi: mLi,t = E[μi|FtPi, X1L] • Conditional variance of μi: vLi,t= E[(μi – mLi,t)2|FtPi, X1L] • Conditional covariance of μ1 and μ2: vL12,t= vL21,t = E[(μ1 – mL1,t)(μ2 – mL2,t)|FtPi, X1L] • Filtering errors: vLi,t(i=1,2), vL12,tand vL21,t Solving the Filtering Problems of Partially-informed leaders

  13. Multi-dimensional Kalman-Bucy filter • Linear system: dμi = 0, ∵μi is constant • Linear observations (Eq. (8)): where

  14. The updating rules for the conditional means, mLi,t = E[μi|FtPi, X1L] (i = 1, 2) (Eq. (10)): • The conditional variance-covariance matrix of μ1 and μ2(Eq. (11)): • Liptser and Shiryaev (2001, Theorem 12.7) • The posterior distribution of μi : {μi|FtPi, X1L} ~ N(mLi,t, vLi,t).

  15. All agents use all available information they have to estimate the expected returnsμi(i=1,2) • The conditional distribution of the unobservable μi: • Conditional mean of μi: mFi,t= E[μi|FtPi, X1j] • Conditional variance of μi: vFi,t= E[(μi – mFi,t)2|FtPi, X1j] • Conditional covariance of μ1 and μ2: vF12,t = vF21,t = E[(μ1 – mF1,t)(μ2 – mF2,t)|FtPi, X1j] • Filtering errors: vFi,t(i=1,2), vF12,tand vF21,t Solving the Filtering Problems of Partially-informed followers

  16. Multi-dimensional Kalman-Bucy filter • Linear system: dμi = 0, ∵μi is constant • Linear observations (Eq. (9)): where

  17. The updating rules for the conditional means, mFi,t = E[μi|FtPi, X1j] (E.(12)): • The conditional variance-covariance matrix of μ1 and μ2 (eq. (13)): • Liptser and Shiryaev (2001, Theorem 12.7) • The posterior distribution of μi : {μi| FtPi, X1j} ~ N(mFi,t, vFi,t).

  18. The decision processes of the agents: Affected by their own psychological irrationalities • Some agents over-react or under-react to changes in observable state variables • As a result of their overconfidence ( j) in their private domestic signals, agents will tend to overreact immediately on receipt of domestic news (Hirshleifer and Luo, 2001; Nosic, Weber and Glaser, 2011) • Agents tend to exhibit conservative behavior (under-reaction,  j) to foreign news, which gives rise to pessimism with regard to the expected returns of the foreign assets • We add  j ( j), the learning bias factor in the updating of the estimate in μ1 (μ2), to the learning mechanisms The Filtrating Problems of Partially-informed Agents (Cont.)

  19. where  j (j = L, F) refers to the overconfidence bias;  j ≤ 0;  j (j = L, F) is the conservatism bias; 0 ≤  j ≤ 1 Eq. (14) Eq. (15)

  20.  j (j = L, F) < 0: Partially-informed agents who are overconfident in their private domestic signals will tend to over-react to new domestic information in their updating of μ1 •  j = 0: No overconfident bias •  j = 0: No conservative bias • 0 < j < 1: Conservatism in updating m2,t (Under-react to the new arrival of foreign news) •  j = 1: No react to any new foreign information • Both over-reaction and under-reaction reflect the fact that these agents simply place too much weight on their prior beliefs, and insufficient weight on new information.

  21. Portfolio decision (see, Eq.(16)) Optimal portfolio weight (see, Eq.(17)) The Optimal Portfolio Weight for the Fully-informed Agents

  22. Portfolio decision (see, Eq.(18)) Optimal portfolio weight (see, Eq.(19)) The Optimal Portfolio Weight for the Partially-informed Leaders

  23. Portfolio decision (See, Eq. (20)) Optimal portfolio weight (see, Eq. (21)) The Optimal Portfolio Weight for the Partially-informed Followers

  24. Dataset: • MSCI US, WI-ex-US: 01/1970 ~ 12/2011 • MSCI EM: 01/1988 ~ 12/2011 • Summary Statistics for Equity Returns • Correlation Coefficient (ρ) *Sample correlation coefficients are calculated for the period from January 1988 to December 2011. Table 1. Summary Statistics for Equity Returns

  25. Required parameters: • Relative risk aversion parameter: γ= 3 • The overconfidence parameters of partially-informed leaders and followers :  j = –5 • The conservatism parameters of partially-informed leaders and followers: j = 0.95 • The variances in the informative signals : σLX 1 = σFX 1 = 0.5σ1 • US agents have an informational advantage based upon their closer geographical or social proximity (Huberman, 2001; Portes and Rey, 2005) • The informative signal will always be more precise than the past realizations of domestic stock returns Numerical exercises

  26. The correlation between the private domestic signals of partially-informed leaders and the domestic stock returns: 0<ρL1,X1< 1 • Good news always leads to high stock returns (Lundtofte, 2006) • The private signals of agents cannot be perfectly correlated with the stock returns • The correlation between the private domestic signals of partially-informed leaders and the private domestic signals of partially-informed followers: 0<ρL,F<1 • The variance in the knowledgeable priors of partially-informed agents are taken to be the estimate variances: vji,0 = σi2/ Kji (i = 1, 2, and j = L, F)) • Kji: The number of observations, or the period over which they are observed, thereby denoting the precision or their priors. • Starting from January 1988, the partially-informed investors formulate their estimations of the mean returns for the three indices.  K(US/Wi-ex-US) = 216, K(EM) = 0

  27. Figure 1. The 95% Confidence Intervals of the Partially-informed Leaders and Followers’ Estimates of the True Value of Means

  28. Note: The 95% confidence interval are determined by the true parameter values, which are μ1 = 0.0049, σ1 = 0.0455 for the US index, μ2 = 0.0053, σ2 = 0.0505 for the WI-ex-US index, μ2 = 0.0077, σ2 = 0.0714 for the EM index, and σLX 1 = σFX 1 = 0.5σ1 = 0.0228 for the partially-informed leaders and followers. There are three thousand post-initial observations, where the initial date starts from January 1988.

  29. Figure 2. The Partially-Informed Leaders’ Optimal Portfolio Weights

  30. Figure 3. The Partially-Informed Followers’ Optimal Portfolio Weights, As the Partially-informed Leaders Have Better Quality Private Home Signals (L1,X1 = 0.95)

  31. Figure 4. The Partially-informed Followers’ Optimal Portfolio weights, As the Partially-informed Leaders Have Lower Quality Private Home Signals (L1,X1 = 0.01)

  32. Features • The social learning effect helps investors to refresh their priors and form new estimates of the true mean returns • Investors reach their portfolio decisions if they are only partially informed, and the asymmetry that exists between them in terms of the quality of the information that they possess. • Our model confirm that the portfolio choices of investors are a function of their information environment. • The viewpoints of both the transmitters and the receiver are important • Providing an alternative model in line with the dependence of market information efficiency on the structure of a network system(e.g., Ozsoylev (2007) and Colla and Mele (2010)) • Complements the extant empirical evidence on the important role in investment decision-making played by information sharing with peers through social networks. Important Features

  33. Application: • Applying from “central” information source to “sequential” learning from their predecessors; that is, Follower 1 initially learns from the Leader, then Follower 2 learns from Follower 1, and so on. • Applying to partially-informed leaders and followers within foreign country borders • Extended to a framework where partially-informed domestic agents possess private signals on foreign assets through internet social networks (e.g., facebook) Important Features

  34. The end!Thanks for your listings and comments

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