Investor Contagion: A Network Model for

Asset Markets

James LuoELE 381

Mini-project Presentation

Introduction

• Traditional finance models make many assumptions when formulating asset pricing theories

• In reality, many of these assumptions are unrealistic

• New field of Behavioral Finance attempts to relax or redefine assumptions

Information

• Rational investors use some updating rule to weigh information equally• E.g. Bayes’ rule

• Traditional finance largely assumes that the path of information transfer does not matter• In reality, the source of information and how

that information travels matter because different sources have different influence

• Concerned about potential herding and contagion

Relevant Literature

• Bikhchandani and Sharia (2000) argue that herding can be caused by peer influence

• Kodres and Pritsker (2002) show that cross-market contagion can occur when investors rebalance portfolios

A Novel Application of Networks

• Assume that the investors in an asset market can be modeled by a network of N nodes• Three topologies: Watts-Strogatz, Preferential

Attachment, and an Artificial Network• Artificial Network has clusters of roughly size qN, and there exists a central cluster such that exactly one link connects the central cluster to each other cluster

• We test both un-weighted and weighted networks, where a weighted network implies varying influence

Model Setup

• An asset pays a number on [0, 1] at maturity T

• At time 0, each investor receives private information about that payoff, with information distributed i.i.d and normally with mean equal to the true payoff and some variance

• Market maker first sets a price, equal to the expected payoff of the asset (initially 0.5) [Heuristic 1]

Investor Behavior

• First period, investors submit “buy” or “sell” based on their signal, and we assume the market clears due to some large enough mass of “noise” traders

• Each period after, the investors can see the beliefs of their neighbors from the period prior• They update their beliefs by taking a weighted

average of neighbors’ prior beliefs and their own [Heuristic 2]

• Market maker increments/decrements price by 0.01 if there are more buyers/sellers

Assumptions

• Risk-neutral investors• No discounting• Long-run equilibrium, if it exists, should be the

same

• No transaction costs• Should just lower valuations and price

• Endowments of the asset do not matter• Can short sell and liquidity can be provided by

noise traders

Key Results

• Assumed N = 1000, T = 100, and variance = 0.05

• Four sections• Un-weighted networks and random signals• Un-weighted networks and seeding of

negative outlook• Weighted networks and random signals• Weighted networks and seeding of negative

outlook

Un-weighted Networks and Random Signals

Un-weighted Networks and Random Signals

Un-weighted Networks and Random Signals

Un-weighted Networks and 10% seeding

Un-weighted Networks and 10% seeding

Un-weighted Networks and 10% seeding

Weighted Networks with Random Signals

Weighted Networks with Random Signals

Weighted Networks with Random Signals

Weighted Networks with 10% Seeding

Weighted Networks with 10% Seeding

Weighted Networks with 10% Seeding

Weighted Networks with 1% Seeding

Weighted Networks with 1% Seeding

Weighted Networks with 1% Seeding

Conclusion

• Topologies that follow power law are most susceptible to outliers, and those that are small world tend to be the most fragile when exposed

• Small group of investors can have disproportionate effects on the price if they are influential

• Under incomplete and asymmetric information, price can deviate from fundamental value and large mispricings can occur

Future Work

• Alternative model that allows for period-by-period Bayesian updating

• Addition of a bid-ask spread and limit orders• Time-dependent preferences (discounting)• Empirical test of some well-defined investor

network