wen-lin wu (feng chia university) yin-feng gau (national central university)

Wen-Lin Wu (Feng Chia University) Yin-Feng Gau (National Central University)

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)

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.

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

Our model setting, based on social learning, conforms to several stylized facts in the field of finance 1. The social learning amongst partially-informed agents is strongly related to geographical proximity 2. The social learning is subject to behavioral biases towards foreign assets 3. Although social learning amplifies the information capacity of investors, they remain only partially informed.

Three assets: Home-based money market account: B t : The price of riskless domestic money market account r: Locally constant riskless rate In the model, we set r = 0, then B t = 1. Home equity (Eq. (2)) : Foreign equity (Eq. (3)) : 1 ( 2 ): The constant expected return of the domestic (foreign) asset; 1 ( 2 ): The constant standard deviation of the domestic (foreign) asset; Z 1 and Z 2 : Independent standard Brownian motions, defined on the complete probability space (, F, P) 1,2 : Constant instantaneous correlation between home and foreign assets, which is 1 < 1,2 < 1.

Three types of agent: Fully-informed: F = {F t } Partially-informed leaders: F Pi, X1L = {F t Pi, X1L }, where F t Pi, X1L = ((P i,s, X L 1,s ); s t) and i = 1, 2 Partially-informed followers: F Pi, X1j = {F t Pi, X1j }, where F t Pi, X1j = ((P i,s, X j 1,s ); s t), i = 1, 2, and j = L, F Utility function (Eq. (1)) : Fully-informed agents knows all required parameters - 1, 2, 1, 2 and 1, 2 Partially-informed leaders and followers only knows 1, 2 and 1, 2

Domestic private signal : Leaders private signals (Eq (4)) : Followers private signals (Eq. (5): L X 1 ( F X 1 ): The constant standard deviation of the private domestic signal of partially- informed leaders (followers) ; Z L X 3 (Z F X 1 ): Standard Brownian motion defined on (, F, P) L,F : Constant instantaneous correlation between dX L 1,t / X L 1,t and dX F 1,t / X F 1,t

Let dX L 1,t / X L 1,t and dP 1,t / P 1,t are correlated with the constant instantaneous correlation, L 1,X1, we have Eq. (6) and (7) Z L X 1 : Standard Brownian motion defined on (, F, P), which is assumed to be independent of Z F X 1 and Z 1 ; Conditional on L 1,X1, L,F and 1,2, we assume that Z 2 is independent of Z L X 1 and Z F X 1 in order to simplify our model analysis

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.

All agents use all available information they have to estimate the expected returns i (i = 1, 2) The conditional distribution of the unobservable i : Conditional mean of i : m L i,t = E[ i | F t Pi, X1L ] Conditional variance of i : v L i,t = E[( i m L i,t ) 2 | F t Pi, X1L ] Conditional covariance of 1 and 2 : v L 12,t = v L 21,t = E[( 1 m L 1,t )( 2 m L 2,t ) | F t Pi, X1L ] Filtering errors: v L i,t (i = 1, 2), v L 12,t and v L 21,t

Multi-dimensional Kalman-Bucy filter Linear system: d i = 0, i is constant Linear observations (Eq. (8)) : where

The updating rules for the conditional means, m L i,t = E[ i | F t Pi, X1L ] (i = 1, 2) (Eq. (10)) : The conditional variance-covariance matrix of 1 and 2 (Eq. (11)) : Liptser and Shiryaev (2001, Theorem 12.7) The posterior distribution of i : { i | F t Pi, X1L } ~ N(m L i,t, v L i,t ).

All agents use all available information they have to estimate the expected returns i (i = 1, 2) The conditional distribution of the unobservable i : Conditional mean of i : m F i,t = E[ i | F t Pi, X1j ] Conditional variance of i : v F i,t = E[( i m F i,t ) 2 | F t Pi, X1j ] Conditional covariance of 1 and 2 : v F 12,t = v F 21,t = E[( 1 m F 1,t )( 2 m F 2,t ) | F t Pi, X1j ] Filtering errors: v F i,t (i = 1, 2), v F 12,t and v F 21,t

Multi-dimensional Kalman-Bucy filter Linear system: d i = 0, i is constant Linear observations (Eq. (9)) : where

The updating rules for the conditional means, m F i,t = E[ i | F t Pi, X1j ] (E.(12)) : The conditional variance-covariance matrix of 1 and 2 (eq. (13)) : Liptser and Shiryaev (2001, Theorem 12.7) The posterior distribution of i : { i | F t Pi, X1j } ~ N(m F i,t, v F i,t ).

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 1 ( 2 ), to the learning mechanisms

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)

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 1 j = 0: No overconfident bias j = 0: No conservative bias 0 < j < 1: Conservatism in updating m 2,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.

Portfolio decision (see, Eq.(16)) Optimal portfolio weight (see, Eq.(17))

Portfolio decision (see, Eq.(18)) Optimal portfolio weight (see, Eq.(19))

Portfolio decision (See, Eq. (20)) Optimal portfolio weight (see, Eq. (21))

Dataset: MSCI US, WI-ex-US: 01/1970 ~ 12/2011 MSCI EM: 01/1988 ~ 12/2011 Summary Statistics for Equity Returns Correlation Coefficient ( ) *Sample correlation coefficients are calculated for the period from January 1988 to December 2011. USWI-ex-USEM Mean ( ) 0.00490.00530.0077 Std. Dev. ( ) 0.04550.05050.0714 Kurtosis2.38811.58863.0673 Skewness-0.6463-0.5894-1.0398 Sharpe Ratio0.10830.10490.1078 Number of Observations504 288 USWI-ex-USEM US1 WI-ex-US0.64571 EM0.6785 * 0.7144 * 1

Required parameters: Relative risk aversion parameter: = 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 : L X 1 = F X 1 = 0.5 1 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

The correlation between the private domestic signals of partially-informed leaders and the domestic stock returns: 0 < L 1,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 < L,F < 1 The variance in the knowledgeable priors of partially- informed agents are taken to be the estimate variances: v j i,0 = i 2 / K j i (i = 1, 2, and j = L, F)) K j i : 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

Note: The 95% confidence interval are determined by the true parameter values, which are 1 = 0.0049, 1 = 0.0455 for the US index, 2 = 0.0053, 2 = 0.0505 for the WI-ex-US index, 2 = 0.0077, 2 = 0.0714 for the EM index, and L X 1 = F X 1 = 0.5 1 = 0.0228 for the partially-informed leaders and followers. There are three thousand post-initial observations, where the initial date starts from January 1988.

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.

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)

wen-lin wu (feng chia university) yin-feng gau (national central university)

Documents