Ana Fostel Publications

We show how the timing of financial innovation might have contributed to the mortgage bubble and then to the crash of 2007-2009. We show why tranching and leverage first raised asset prices and why CDS lowered them afterwards. 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.

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.

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 procyclical leverage. The result also gives a rationale to the pattern of volatility smiles observed in the 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.

The literature on leverage until now shows how an increase in volatility reduces leverage. However, in order to explain pro-cyclical leverage it assumes that bad news increases volatility. 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 volatile in bad times. Together with the old literature this explains pro-cyclical leverage. The result also gives rationale to the pattern of volatility smiles observed in the 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.

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.

We provide a theory of pricing for emerging asset classes, like emerging markets, that are not yet mature enough to be attractive to the general public. Our model provides an explanation for the volatile access of emerging economies to international financial markets and for several stylized facts we identify in the data during the 1990’s. We present a general equilibrium model with incomplete markets and endogenous collateral and an extension encompassing adverse selection. We show that contagion, flight to liquidity and issuance rationing can occur in equilibrium during what we call global anxious times.

We show that very little is needed to create liquidity under-supply in equilibrium. Credit constraints on demand by themselves can cause an under-supply of liquidity, without the uncertainty, intermediation, asymmetric information or complicated international financial framework used in other models in the literature. We show that the under-supply is a non-monotone function of the demand distortion that causes it, a result that may have interesting implications for emerging markets economies. Finally, when we make the credit constraint endogenous, the inefficiency can be large due to the presence of a multiplier.

We define liquidity as the flexibility to move goods (money) from one project (investment) to another. We show that credit constraints on demand by themselves can cause an under-supply of liquidity, without the uncertainty, intermediation, asymmetric information or complicated international financial framework used in other models in the literature. In this respect liquidity is like a commodity: according to our offsetting distortions principle, a distortion in the demand for any good can often be understood as an inefficiency of supply.

We show that the liquidity under-supply is a non-monotone function of the credit constraint. This result is also a particular case of a more general principle applying to any commodity with supply alternatives: second best supply inefficiency is non-monotone in the demand distortion. Defining liquidity as flexibility ensures that there will be alternatives, and thus non monotonicity. If we interpret the credit constraints as the degree of financial development in the economy, our second proposition suggests that when financial markets are very undeveloped, as in some emerging markets, financial innovation may paradoxically make government intervention (taxation) more necessary.

Finally, we think about the magnitude of the under-supply in the context of a specific demand distortion. We model the credit constraint by assuming that borrowers will default unless their promises are covered by collateral. Further, we assume that only an exogenous proportion beta of a durable good can serve as collateral. This parameter will represent the degree of financial development of the economy. We show that when the price of the collateral is endogenous, the magnitude of the under supply can be much larger. Any policy intervention that affects the interest rate in equilibrium will have two effects on the borrowing constraint: a direct effect, also present in the case when the credit constraint is exogenous, and an indirect effect through the price of the collateral. We explore our findings by solving and simulating a particular case in which utilities for the consumption good and collateral are quadratic.

We show that very little is needed to create liquidity under-supply in equilibrium. Credit constraints on demand by themselves can cause an under-supply of liquidity, without the uncertainty, intermediation, asymmetric information or complicated international financial framework used in other models in the literature. We show that the under-supply is a non-monotone function of the demand distortion that causes it, a result that may have interesting implications for emerging markets economies. Finally, when we make the credit constraint endogenous, the inefficiency can be large due to the presence of a multiplier.

Keywords: Liquidity under-supply, Credit constraint, Non-monotonicity, Multiplier, Collateral equilibrium

JEL Classification: D51, E44, F30, G15

We define liquidity as the flexibility to move goods (money) from one project (investment) to another. We show that credit constraints on demand by themselves can cause an under-supply of liquidity, without the uncertainty, intermediation, asymmetric information or complicated international financial framework used in other models in the literature. In this respect liquidity is like a commodity: according to our offsetting distortions principle, a distortion in the demand for any good can often be understood as an inefficiency of supply.

We show that the liquidity under-supply is a non-monotone function of the credit constraint. This result is also a particular case of a more general principle applying to any commodity with supply alternatives: second best supply inefficiency is non-monotone in the demand distortion. Defining liquidity as flexibility ensures that there will be alternatives, and thus non monotonicity. If we interpret the credit constraints as the degree of financial development in the economy, our second proposition suggests that when financial markets are very undeveloped, as in some emerging markets, financial innovation may paradoxically make government intervention (taxation) more necessary.

Finally, we think about the magnitude of the under-supply in the context of a specific demand distortion. We model the credit constraint by assuming that borrowers will default unless their promises are covered by collateral. Further, we assume that only an exogenous proportion beta of a durable good can serve as collateral. This parameter will represent the degree of financial development of the economy. We show that when the price of the collateral is endogenous, the magnitude of the under supply can be much larger. Any policy intervention that affects the interest rate in equilibrium will have two effects on the borrowing constraint: a direct effect, also present in the case when the credit constraint is exogenous, and an indirect effect through the price of the collateral. We explore our findings by solving and simulating a particular case in which utilities for the consumption good and collateral are quadratic.

Keywords: Liquidity under-supply, Credit constraint, Non-monotonicity, Multiplier, Collateral equilibrium

JEL Classification: D51, E44, F30, G15

We provide two new, simple proofs of Afriat’s celebrated theorem stating that a finite set of price-quantity observations is consistent with utility maximization if, and only if, the observations satisfy a variation of the Strong Axiom of Revealed Preference known as the Generalized Axiom of Revealed Preference.