Wen-Lin Wu (Feng Chia University) Yin-Feng Gau (National
Central University)
Slide 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)
Slide 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.
Slide 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
Slide 5
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.
Slide 6
Slide 7
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.
Slide 8
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
Slide 9
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
Slide 10
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
Slide 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.
Slide 12
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
Slide 13
Multi-dimensional Kalman-Bucy filter Linear system: d i = 0, i
is constant Linear observations (Eq. (8)) : where
Slide 14
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 ).
Slide 15
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
Slide 16
Multi-dimensional Kalman-Bucy filter Linear system: d i = 0, i
is constant Linear observations (Eq. (9)) : where
Slide 17
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 ).
Slide 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 1 ( 2 ), to the
learning mechanisms
Slide 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)
Slide 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 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.
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
Slide 25
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
Slide 26
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
Slide 27
Slide 28
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.
Slide 29
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Slide 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.
Slide 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)