Ana Fostel Publications

Cross-border financial flows arise when (otherwise identical) countries differ in their abilities to use assets as collateral to back financial contracts. Financially integrated countries have access to the same set of financial instruments, and yet there is no price convergence of assets with identical payoffs, due to a gap in collateral values. Home (financially advanced) runs a current account deficit. Financial flows amplify asset price volatility in both countries, and gross flows driven by collateral differences collapse following bad news about fundamentals. Our results can explain financial flows among rich, similarly-developed countries, and why these flows increase volatility. 

We show that cross-border financial flows arise when countries differ in their abilities to use assets as collateral. Financial integration is a way of sharing scarce collateral. The ability of one country to leverage and tranche assets provides attractive financial contracts to investors in the other country, and general equilibrium effects on prices create opportunities for investors in the financially advanced country to invest abroad. Foreign demand for collateral and for collateral-backed financial promises increases the collateral value of domestic assets, and cheap foreign assets provide attractive returns to investors who do not demand collateral to issue promises. Gross global flows respond dynamically to fundamentals, exporting and amplifying financial volatility.

We review the theory of leverage developed in collateral equilibrium models with incomplete markets. We explain how leverage tends to boost asset prices, and create bubbles. We show how leverage can be endogenously determined in equilibrium, and how it depends on volatility. We describe the dynamic feedback properties of leverage, volatility, and asset prices, in what we call the Leverage Cycle. We also describe some cross-sectional implications of multiple leverage cycles, including contagion, flight to collateral, and swings in the issuance volume of the highest quality debt. We explain the differences between the leverage cycle and the credit cycle literature. Finally, we describe an agent based model of the leverage cycle in which asset prices display clustered volatility and fat tails even though all the shocks are essentially Gaussian.

We show that financial innovations that change the collateral capacity of assets in the economy can affect investment even in the absence of any shift in utilities, productivity, or asset payoffs. First we show that the ability to leverage an asset by selling non-contingent promises can generate over-investment compared to the Arrow-Debreu level. Second, we show that the introduction of naked CDS can generate under-investment with respect to the Arrow-Debreu level. Finally, we show that the introduction of naked CDS can robustly destroy competitive equilibrium.

Financial innovations that change how promises are collateralized can affect investment, even in the absence of any change in fundamentals. In C-models, the ability to leverage an asset always generates over-investment compared to Arrow Debreu. The introduction of CDS always leads to under-investment with respect to Arrow Debreu, and in some cases even robustly destroys competitive equilibrium. The need for collateral would seem to cause under-investment. Our analysis illustrates a countervailing force: goods that serve as collateral yield additional services and are therefore over-valued and over-produced. In models without cash flow problems there is never marginal under-investment on collateral.

Our paper provides a complete characterization of leverage and default in binomial economies with financial assets serving as collateral. 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, contingent or non-contingent promises, many assets and consumption goods, production, and multiple periods. We also show that no-default equilibria would be selected if there were the slightest cost of using collateral or handling default. Our Binomial Leverage Theorem shows that equilibrium Loan to Value (LTV) for non-contingent debt contracts is the ratio of the worst-case return of the asset to the riskless gross rate of interest. In binomial economies leverage is determined by down risk and not by volatility.

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 LTV 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 show that binomial economies with financial assets are an informative and tractable model to study endogenous leverage and collateral equilibrium: endogenous leverage can be highly volatile, but it is always easy to compute. The possibility of default can have a dramatic effect on equilibrium, if collateral is scarce, yet we prove the No-Default Theorem asserting that, without loss of generality, there is no default in equilibrium. Thus potential default has a dramatic effect on equilibrium, but actual default does not. This result is valid with arbitrary preferences, contingent promises, many assets and consumption goods, production, and multiple periods. On the other hand, we show that the theorem fails in trinomial models. For example, in a CAPM model, we find that default is robust. In a model with heterogeneous beliefs, we find that different agents might borrow on the same asset with different LTVs.

Our paper provides a complete characterization of leverage and default in binomial economies with financial assets serving as collateral. 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, contingent or non-contingent promises, many assets and consumption goods, production, and multiple periods. We also show that no-default equilibria would be selected if there were the slightest cost of using collateral or handling default. Our Binomial Leverage Theorem shows that equilibrium Loan to Value (LTV) for non-contingent debt contracts is the ratio of the worst-case return of the asset to the riskless gross rate of interest. In binomial economies leverage is determined by down risk and not by volatility.

We show how the timing of financial innovation might have contributed to the mortgage boom and then to the bust of 2007-2009. We study the effect of leverage, tranching, securitization and CDS on asset prices in a general equilibrium model with collateral. We show why tranching and leverage tend to raise asset prices and why CDS tend to lower them. This may seem puzzling, since it implies that creating a derivative tranche in the securitization whose payoffs are identical to the CDS will raise the underlying asset price while the CDS outside the securitization lowers it. The resolution of the puzzle is that the CDS lowers the value of the underlying asset since it is equivalent to tranching cash.