Abstract I investigate the effect of financial innovation on portfolio risks when traders have belief disagreements. I decompose traders’ average portfolio risks into two components: the uninsurable variance, defined as portfolio risks that would obtain without belief disagreements, and the speculative variance, defined as portfolio risks that result from speculation. My main result shows that financial innovation always increases the speculative variance through two distinct channels: by generating new bets and by amplifying traders’ existing bets. When disagreements are large, these effects are sufficiently strong that financial innovation increases average portfolio risks, decreases average portfolio comovements, and generates greater speculative trading volume relative to risk-sharing volume. Moreover, a profit-seeking market maker endogenously introduces speculative assets that increase average portfolio risks.

Belief disagreements have been suggested as a major contributing factor to the recent subprime mortgage crisis. This paper theoretically evaluates this hypothesis. I assume that optimists have limited wealth and take on leverage so as to take positions in line with their beliefs. To have a significant effect on asset prices, they need to borrow from traders with pessimistic beliefs using loans collateralized by the asset itself. Since pessimists do not value the collateral as much as optimists do, they are reluctant to lend, which provides an endogenous constraint on optimists' ability to borrow and to influence asset prices. I demonstrate that the tightness of this constraint depends on the nature of belief disagreements. Optimism concerning the probability of downside states has no or little effect on asset prices because these types of optimism are disciplined by this constraint. Instead, optimism concerning the relative probability of upside states could have significant effects on asset prices. This asymmetric disciplining effect is robust to allowing for short selling because pessimists that borrow the asset face a similar endogenous constraint. These results emphasize that what investors disagree about matters for asset prices, to a greater extent than the level of disagreements. When richer contracts are available, relatively complex contracts that resemble some of the recent financial innovations in the mortgage market endogenously emerge to facilitate betting.

I illustrate the effect of financial innovation on portfolio risks by using an example with risk-sharing needs and belief disagreements. I consider two types of innovation: product innovation, formalized as an expansion of new financial assets; and process innovation, formalized as a reduction in transaction costs. When belief disagreements are large, both types of innovation increase portfolio risks. Moreover, endogenous financial innovation is directed towards speculative assets that increase portfolio risks.

ABSTRACT We present a model of financial crises that stem from endogenous complexity . We conceptualize complexity as banks' uncertainty about the financial network of cross exposures. As conditions deteriorate, cross exposures generate the possibility of a domino effect of bankruptcies. As this happens, banks face an increasingly complex environment since they need to understand a greater fraction of the financial network to assess their own financial health. Complexity dramatically amplifies banks' perceived counterparty risk, and makes relatively healthy banks reluctant to buy risky assets. The model also features a novel complexity externality .