Asset Pricing Implications of Social Networks. Han N. Ozsoylev University of Oxford

Transcription

1 Asset Pricing Implications of Social Networks Han N. Ozsoylev University of Oxford 1

2 Motivation - Communication in financial markets in financial markets, agents communicate and learn from each other this affects their financial decisions any evidence? Shiller and Pound s (1989) survey among institutional investors Hong, Kubik and Stein (2004): stock market participation is influenced by social interaction (data from HRS) 2

3 Motivation - Social network effects in financial decisions Duflo and Saez (2002) empirical study on retirement savings decisions subgroups: gender, status, age, and tenure lines among university staff own-group peer effect on participation and on vendor s choice, but no cross-group peer effects Duflo and Saez (2003) similar results in a randomized experiment 3

4 Motivation - Social network effects during bank runs Kelly and O Grada (2000): behavior of Irish depositors in a New York bank during the panics of 1854 and 1857 social networks determined by place of origin in Ireland and neighborhood in New York social network is the main factor in determination of depositors behaviors 4

5 Motivation - Social network effects in stock markets Hong, Kubik and Stein (2005): parallel portfolio decisions among mutual fund managers located in the same city, no significant correlation across different cities their interpretation: word-of-mouth learning among peer groups Feng and Seasholes (2005): study orders taken in different branches of a Chinese brokerage firm: branches dispersed across different geographic regions significantly high correlation between orders taken in the same branch, no such correlation across different branches 5

6 Objectives an asset pricing model which allows for communication and learning in social networks any asset pricing implications of social networks? is social influence a determinant in pricing? any network effects on asset demand correlations? could social networks account for the observed high volatility ratio of price to fundamentals? social network effects on informational efficiency 6

7 What does literature say? DeMarzo, Vayanos, Zwiebel (2003) boundedly-rational model of opinion formation in social networks (work in progress for financial markets) assumes persuasion bias: double counting of repeated information social influence is effective in opinion formation [bounded rationality, no market interaction] 7

8 Bisin, Horst, Ozgur (2006) a model of rational agents interacting locally utility is dependent on neighbor s action one-sided interaction and each agent has one neighbor local preferences for conformity and habit persistence does not study financial markets where asset prices convey information [no market interaction, limited social interaction pattern] 8

9 Ozsoylev (2004) a financial market model where agents infer information from neighbors actions both price and social interactions convey information analysis mainly confined to one-sided interactions but allows for differing numbers of neighbors across agents social influence affects asset pricing social network effects on asset demands (in stylized networks) social interaction can impair informational efficiency of price [restrictions on social interaction patterns, silent on excess volatility] 9

10 Model - Economic environment n agents 2 periods: trade in 1st period, consumption in 2nd period traded assets: one risk-free and one risky X is the random payoff of risky asset and realizes in 2nd period prices: 1 for risk-free, p for risky asset 10

11 Model - Preferences & parametric specifications CARA preferences; a common risk aversion coefficient ρ (0, ) agent i observes the realization of a private random signal θ i := X + ɛ i, which communicates the risky payoff X perturbed by noise ɛ i net supply (i.e., liquidity) of risky asset is L, which is a realization of random variable L X, L, ɛ, i = 1,..., n are jointly normally distributed and mutually independent 11

12 Model - Social learning agents learn, i.e. gain information, from other agents about the risky payoff X whom an agent learns from is determined by a social network, which is modelled by a simple directed graph vertices: agents directed edges: direction of learning (i j: i learns from j) given a social network N Ω, S(N, i) := {k {1,..., n} : i k} {i} k S(N, i): information source of i (S(N, 1), S(N, 2),..., S(N, n)) fully captures the interactions among agents imposed by the social network N 12

13 Model - Social learning learning takes place for agent i through the observation of E [ ] X {θ k } k S(N,i) that is, agent i observes the expectation of risky payoff X conditional on her information sources private signals E [ ] X {θ k } k S(N,i) : agent i s social inference

14 Model - Rational expectations agent i conditions her expectation of X, on private signal θ i, social inference E [ ] X { θ k } k S(N,i) and price p that is, both social inference and price convey information across agents in the economy agents have rational expectations: agent i knows the joint distribution of the random vector ( X, θ i, E [ ] ) X { θ k } k S(N,i), p. 14

15 Equilibrium An equilibrium consists of a risky asset price function P (θ 1,..., θ n, L) and demand functions { ( z i θi, E [ ] X {θ k } k S(N,i), p such that for )}i=1,...,n all realizations (θ 1,..., θ n, L) of ( θ 1,..., θ n, L) ( (a) agent i s demand z i θi, E [ ] ) X {θ k } k S(N,i), p maximizes her expected utility of final wealth E for all i = 1,..., n, [ u i ( w 1i ) θ i, E [ ] X {θ k } k S(N,i), p = P (θ1,..., θ n, L) ] (b) market clears, i.e., ( n i=1 z i θi, E [ ] ) X {θ k } k S(N,i), p = L. 15

16 Linear Equilibrium Analysis P ( θ 1,..., θ n, L) = π 0 + informational content {}}{ n i=1 π i θ i γ L }{{} liquidity component (noise) 16

17 existence of equilibrium Proposition 1 If the liquidity variance σl 2 is sufficiently large, then for any given social network N Ω there exists a linear equilibrium price of the form p N = P ( θ 1,..., θ n, L) = π N 0 + n with price coefficients that satisfy i=1 π N i θ i γ N L (1) 0 < lim σ 2 L γ N <, 0 < lim σ 2 L π N i <, i = 1,..., n. (2) The remainder of the analysis is restricted to linear equilibrium prices satisfying (1) and (2). 17

18 price and social influence Proposition 2 Given social network N Ω, consider a set of agents {i, i } {1,..., n} such that S(N, i) {i} and S(N, i ) {i }. If n m=1 S(N, m) {i} n > m=1 S(N, m) {i }, then π N i > π N i for sufficiently large liquidity variance σ 2 L. If (a) the liquidity variance is sufficiently large, (b) both agents, i and i, learn from others, (c) compared to agent i, agent i is an information source for a higher number of agents, then agent i s private signal has a higher impact on price compared to signal of i. 18

19 demand correlations and tight-knit social clusters recall empirical evidence: Hong, Kubik and Stein (2005), Feng and Seasholes (2005) these studies suggest that demands from the same tight-knit social cluster are highly correlated whereas demands from disjoint social clusters have insignificant correlation 19

20 we categorize a social cluster as tight-knit if (i) everyone in the cluster learn from all of the agents in that cluster and no one else, (ii) everyone in the cluster is an information source for each of the agents in that cluster and no one else formally, a social cluster C {1,..., n} is tight-knit if S(N, i) = {m : S(N, m) {i} = } = C, i C 20

21 C 1 C 2 Tight-Knit Social Clusters 21

22 Proposition 3 Given social network N Ω, let z N i := z i ( θ i, E [ ] X { θ k } k S(N,i), p N ), i = 1,..., n, denote the equilibrium demand at p. Choose two tight-knit social clusters C 1 {1,..., n} and C 2 {1,..., n} such that C 1 C 2 = and C 1 = C 2 > 1. If the liquidity variance σ 2 L is sufficiently large and i C 1, then for any h C 1 and h C 2 corr( z N i, z N h ) > corr( zn i, z N h ). This proposition compares demand correlations within and across the social clusters which are (a) tight-knit, (b) non-degenerate, (c) identical, and (d) disjoint. The proposition says that the correlation of demands within the same social cluster is larger than the correlation of demands across different social clusters if the liquidity variance is sufficiently large. 22

23 excess price volatility and social networks empirical studies, including Shiller (1981) and Mankiw, Romer and Shapiro (1985, 1991), reveal that stock prices are more volatile compared to stock fundamentals Campbell and Kyle (1993) suggest that noise trading can be the factor creating excess volatility * this argument works in our setup as well (fundamental=risky payoff, noise=liquidity variance) it is difficult to justify excess volatility only by large noise can social networks provide an alternative justification for excess volatility? 23

24 Given an equilibrium price of the form p N = π0 N + n i=1 πi N the price volatility is delivered by θ i γ N L, var( p N ) = var I ( p N ) (information driven volatility component) { }}{ 2 n πj N σ 2 n x + (πj N )2 σɛ 2 j=1 j=1 + (γ N ) 2 σ 2 L }{{} var L ( p N ) (liquidity driven volatility component) 24

25 N 1 N Social network N 1 is more centralized than social network N 2. Agent 1 is the central node in N 1. 25

26 Proposition 4 Let p N 1 and p N 2 be equilibrium prices for social networks N 1 Ω and N 2 Ω, respectively. Suppose that S(N 1, i) {i} and S(N 2, i) {i} for all i = 1,..., n. For sufficiently large liquidity variance σl 2, (a) var L ( p N 1) < var L ( p N 2) if ni=1 S(N1, i) > n S(N2 i=1, i), ni=1 S(N1, i) (b) var I ( p N 1) > var I ( p N 2) if ( ni=1 nm=1 S(N1, m) {i} (c) var( p N 1) < var( p N 2) if = n i=1 S(N2, i) 2 ( ) > ni=1 nm=1 S(N2, m) {i} ni=1 S(N1, i) > n S(N2 i=1, i). and 2 ), 26

27 all studies on price volatility to date assume that agents are socially isolated then Proposition 4 seems to enhance the excess volatility puzzle any hope for a social network justification of excess volatility? N N o Centralization vs. Isolation 27

28 Remark 1 Suppose σ 2 L = s n2 for some s R ++. Then var ( p N ) > var ( p N o) (3) for sufficiently large number of agents n. Moreover, for any given constant C > 0 there exist N Z ++ and σ 2 ɛ (N) R ++ such that for all n > N and for all σ 2 ɛ < σ2 ɛ (N) var ( p N ) > C var ( p N o) and var ( p N ) > C σ 2 x. (4) (3) says that price volatility in a star network is larger than that in a trivial network imposing complete social isolation (4) says that price volatility in the star network can be made arbitrarily large relative to the volatility of risky payoff by making private signals sufficiently precise 28

29 informational efficiency and social networks Social network N 1 is informationally dominated by social network N 2 for the set of equilibrium prices { p N 1, p N 2} if var ( X θ i, E [ ) ( X { θ k } k S(N1,i)], p N 1 var X θ i, E [ ] ) X { θ k } k S(N2,i), p N 2 for all i = 1,..., n and var ( X θ h, E [ ) ( X { θ k } k S(N1,h)], p N 1 > var X θ h, E [ ] ) X { θ k } k S(N2,h), p N 2 for some h {1,..., n}. Social network ˆN is informationally efficient for the set of equilibrium prices { p N : N Ω } if ˆN is not informationally dominated by any social network N Ω for the equilibrium prices { p ˆN, p N }. 29

30 Proposition 5 For sufficiently large liquidity variance σ 2 L, (a) social network N 1 is informationally dominated by social network N 2 for the set of equilibrium prices { p N 1, p N 2} if S(N 1, i) < S(N 2 ), i for all i = 1,..., n, (b) social network ˆN is informationally efficient for the set of equilibrium prices { p N : N Ω} if S( ˆN, i) = {1,..., n} for all i = 1,..., n. 30

31 Concluding Remarks asset pricing implications of social networks: social influence is an important determinant in asset pricing there are social network effects on demand correlations learning from common and central sources can be the cause of excess volatility when liquidity is highly volatile, social learning enhances informational efficiency 31