Ana Fostel

Why Does Bad News Increase Volatility and Decrease Leverage

A recent literature shows how an increase in volatility reduces leverage. However, in order to explain pro-cyclical leverage it assumes that bad news increases volatility, that is, it assumes an inverse relationship between first and second moments of asset returns. This paper suggests a reason why bad news is more often than not associated with higher future volatility. We show that, in a model with endogenous leverage and heterogeneous beliefs, agents have the incentive to invest mostly in technologies that become more volatile in bad times. Agents choose these technologies because they can be leveraged more during normal times. Together with the existing literature this explains pro-cyclical leverage. The result also gives a rationale to the pattern of volatility smiles observed in stock options since 1987. Finally, the paper presents for the first time a dynamic model in which an asset is endogenously traded simultaneously at different margin requirements in equilibrium.

Leverage and Default in Binomial Economies: A Complete Characterization

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.

Financial Innovation, Collateral and Investment

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.

Reviewing the Leverage Cycle

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.

Endogenous Leverage: VaR and Beyond

We study endogenous leverage in a general equilibrium model with incomplete markets. We prove that in any binary tree leverage emerges in equilibrium at the maximum level such that VaR = 0, so there is no default in equilibrium, provided that agents get no utility from holding the collateral. When the collateral does affect utility (as with housing) or when agents have sufficiently heterogenous beliefs over three or more states, VaR = 0 fails to hold in equilibrium. We study commonly used examples: an economy in which investors have heterogenous beliefs and a CAPM economy consisting of investors with different risk aversion. We find two main departures from VaR = 0. First, both examples show that with enough heterogeneity among the investors, equilibrium default is normal. Second, we find that more than one contract is actively traded in equilibrium on the same collateral, that is, the same asset is bought at different margin requirements by different agents. Finally, we study the relationship between leverage and asset prices. We provide an example that shows that as the regulatory authority gradually relaxes leverage restrictions from low levels and permits leverage to rise, asset prices start to rise, but eventually increased leverage paradoxically tends to reduce asset prices because the risky bonds become substitutes for the asset used as collateral.

Fiscal Discoveries and Yield Decouplings

The recent Eurozone debt crisis has witnessed sharp decouplings in cross-country bond yields without commensurate shifts in relative fundamentals. We rationalize this phenomenon in a model wherein countries with different fundamentals are on different equilibrium paths all along, but which become discernible only during bad times. Key ingredients are cross-country differences in the volatility and persistence of fiscal revenue shocks combined with their unobservability by investors. Differences in the cyclicality of fiscal revenues affect the option value of borrowing and resulting default risk; unobservability of fiscal shocks makes bond pricing responsive to market actions. When tax revenues are hit by common positive shocks, no country increases net debt and interest spreads stay put. When a common negative revenue shock hits and is persistent, low volatility countries with higher default costs adjust spending, while others resort to borrowing. This difference signals a relative deterioration of fiscal outlooks, interest spreads jump and decoupling takes place.

Endogenous Leverage in a Binomial Economy: The Irrelevance of Actual Default

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.

Global Collateral: How Financial Innovation Drives Capital Flows and Increases Financial Instability

We show that cross-border financial flows arise when levels of financial innovation differ across countries. 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 sophisticated 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.

Leverage and Asset Prices: An Experiment

This is the first paper to test the asset pricing implication of leverage in a laboratory. We show that as theory predicts, leverage increases asset prices: when an asset can be used as collateral (i.e., when the asset can be bought on margin), its price goes up. This increase is significant, and quantitatively close to what theory predicts. However, important deviations from the theory arise in the laboratory. First, the demand for the asset shifts when it can be used as a collateral, even though agents do not exhaust their purchasing power when collateralized borrowing is not allowed. Second, the spread between collateralizable and non-collateralizable assets does not increase during crises in contrast to what theory predicts.