1. Investor Contagion: A Network Model for Asset Markets James Luo ELE 381 Mini-project Presentation

2. 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

3. 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

4. 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

5. 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

6. 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]

7. 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

8. 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

9. 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

10. Un-weighted Networks and Random Signals

13. Un-weighted Networks and 10% seeding

16. Weighted Networks with Random Signals

19. Weighted Networks with 10% Seeding

22. Weighted Networks with 1% Seeding

25. 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

26. 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