This paper formalizes the idea that more hedging instruments or derivative securities may destabilize a market when traders are heterogeneous and learn from experience based on realized returns. Here is a sketch of the idea. Consider a heterogeneous agent intertemporal asset market where risk averse agents are learning the structure of asset prices in the economy by using, for example, different prediction strategies of future asset prices under some kind of reinforcement or evolutionary learning, for instance as in Brock and Hommes (1997).
Let there be S states of the world and a finite number n of contingent claims or risk hedging instruments available. If n < S − 1 the market is incomplete. We model the risk hedging instruments as “Arrow” securities for state s, 1 s n < S − 1, each paying 1 if state s occurs and 0 otherwise. Elementary Arrow securities are used here as a convenient analytical device, and a suitable combination of Arrow securities may serve as a proxy of more realistic financial instruments such as futures, derivatives or recently introduced collateralized debt obligations. Now
suppose that n < S − 2 and that a new risk hedging instrument, that is, a new Arrow
security, is added for state n + 1 < S − 1. Then, since agents are risk averse, and
since they can use the new Arrow security to hedge out “extra” risk, they will now
tend to place bigger positions on the market. Thus if an agent’s forecasting tool turns out to be on the “right side” of the market, it will return a larger profit (because a larger position has been placed on the market), and therefore it will receive a stronger reinforcement and more individuals will switch to using that particular forecasting tool. This, in turn, implies that the learning system is now more likely to “overshoot”, i.e. to become unstable, and consequently market volatility increases. This intuitive idea will be formalized in a stylized model.
On the other hand it has been argued that an increasing multitude of derivative securities has made it possible for rational speculators to help stabilize markets since they can take bets on market imperfections and hedge their risk. A second contribution of our paper is to investigate the potential stabilizing role of rational traders in a market with co-existing non fully rational traders. Can a perfectly rational trader employ a growing number of hedging instruments to stabilize the market? It turns out that, when the information gathering costs for full rational expectations are large, rational traders can not prevent destabilization.
In the mortgage context, information gathering is expensive. One either needs to set up a good underwriting model, which can take years of experience, or at least to careful loan-by-loan due diligence. Many of us believed that hedges (such as Credit Default Swaps) helped distribute risk better and mitigate against systemic risk. How I wish we had this paper then. (BTW, I took two classes in grad school from Brock. I learned maybe 1/3 of what he was trying to teach, because I am not that good at math. I still learned more from him than pretty much anyone).