Investor Contagion: A Network Model for Asset Markets

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

11. Un-weighted Networks and Random Signals

12. Un-weighted Networks and Random Signals

13. Un-weighted Networks and 10% seeding

14. Un-weighted Networks and 10% seeding

15. Un-weighted Networks and 10% seeding

16. Weighted Networks with Random Signals

17. Weighted Networks with Random Signals

18. Weighted Networks with Random Signals

19. Weighted Networks with 10% Seeding

20. Weighted Networks with 10% Seeding

21. Weighted Networks with 10% Seeding

22. Weighted Networks with 1% Seeding

23. Weighted Networks with 1% Seeding

24. 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