Our paper provides a complete characterization of leverage and default in binomial economies with financial assets serving as collateral.First, our Binomial No-Default Theorem states that any equilibrium is equivalent (in real allocations and prices) to another equilibrium in which there is no default.Thus actual default is irrelevant, though the potential for default drives the equilibrium and limits borrowing.This result is valid with arbitrary preferences and endowments, arbitrary promises, many assets and consumption goods, production, and multiple periods.We also show that the no-default equilibrium would be selected if there were the slightest cost of using collateral or handling default.Second, our Binomial Leverage Theorem shows that equilibrium LT V for non-contingent debt contracts is the ratio of the worst-case return of the asset to the riskless rate of interest.Finally, our Binomial Leverage-Volatility theorem provides a precise link between leverage and volatility.

We provide a pricing theory for emerging asset classes, like emerging markets, that are not yet mature enough to be attractive to the general public. We show how leverage cycles can cause contagion, flight to collateral, and issuance rationing in a frequently recurring phase we call the anxious economy. Our model provides an explanation for the volatile access of emerging economies to international financial markets, and for three stylized facts we identify in emerging markets and high yield data since the late 1990s. Our analytical framework is a general equilibrium model with heterogeneous agents, incomplete markets, and endogenous collateral, plus an extension encompassing adverse selection.

This paper explores the general-equilibrium impact of social security portfolio diversification into private securities, either through the trust fund or private accounts. The analysis depends critically on heterogeneities in saving, production, assets, and taxes. Limited diversification weakly increases interest rates, reduces the expected return on short-term investment (and the equity premium), decreases safe investment, increases risky investment, and increases a suitably weighted social welfare function. However, the effects on aggregate investment, long-term capital values, and the utility of young savers hinges on assumptions about technology. Aggregate investment and long-term asset values can move in opposite directions.

Savings and Portfolio Choice in a Two-Period Two-Asset Model by Saku Aura, Peter Diamond and John Geanakoplos. Published in volume 92, issue 4, pages 1185-1191 of American Economic Review, September 2002

We extend the standard model of general equilibrium with incomplete markets to allow for default and punishment by thinking of assets as pools. The equilibrating variables include expected delivery rates, along with the usual prices of assets and commodities. By reinterpreting the variables, our model encompasses a broad range of adverse selection and signalling phenomena in a perfectly competitive, general equilibrium framework. Perfect competition eliminates the need for lenders to compute how the size of their loan or the price they quote might affect default rates. It also makes for a simple equilibrium refinement, which we propose in order to rule out irrational pessimism about deliveries of untraded assets. We show that refined equilibrium always exists in our model, and that default, in conjunction with refinement, opens the door to a theory of endogenous assets. The market chooses the promises, default penalties, and quantity constraints of actively traded assets.

We provide a theorem giving a set of conditions under which public observation of an aggregate of individual expectations leads to consensus. The key concept unkerlying the result is that of common knowledge, as formalized by Aumann (1976)

A firm’s actions in one market can change competitors’ strategies in a second market by affecting its own marginal costs in that other mar-ket. Whether the action provides costs or benefits in the second market depends on (a) whether it increases or decreases marginal costs in the second market and (b) whether competitors’ products are strategic substitutes or strategic complements. The latter distinction is determined by whether more “aggressive” play (e.g., lower price or higher quantity) by one firm in a market lowers or raises compet-ing firms’ marginal profitabilities in that market. Many recent results in oligopoly theory can be most easily understood in terms of strategic substitutes and complements.

We use a simple agent based model of value investors in financial markets to test three credit regulation policies. The first is the unregulated case, which only imposes limits on maximum leverage. The second is Basle II and the third is a hypothetical alternative in which banks perfectly hedge all of their leverage-induced risk with options. When compared to the unregulated case both Basle II and the perfect hedge policy reduce the risk of default when leverage is low but increase it when leverage is high. This is because both regulation policies increase the amount of synchronized buying and selling needed to achieve deleveraging, which can destabilize the market. None of these policies are optimal for everyone: risk neutral investors prefer the unregulated case with low maximum leverage, banks prefer the perfect hedge policy, and fund managers prefer the unregulated case with high maximum leverage. No one prefers Basle II.

Systemic risk must include the housing market, though economists have not generally focused on it. We begin construction of an agent-based model of the housing market with individual data from Washington, DC. Twenty years of success with agent-based models of mortgage prepayments give us hope that such a model could be useful. Preliminary analysis suggests that the housing boom and bust of 1997-2007 was due in large part to changes in leverage rather than interest rates.