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Andrew W. Lo & Thomas J. Brennan, Do Labyrinthine Legal Limits on Leverage Lessen the Likelihood of Losses? An Analytical Framework, 90 Tex. L. Rev. 1775 (2012).

Abstract: A common theme in the regulation of financial institutions and transactions is leverage constraints. Although such constraints are implemented in various ways—from minimum net capital rules to margin requirements to credit limits—the basic motivation is the same: to limit the potential losses of certain counterparties. However, the emergence of dynamic trading strategies, derivative securities, and other financial innovations poses new challenges to these constraints. We propose a simple analytical framework for specifying leverage constraints that addresses this challenge by explicitly linking the likelihood of financial loss to the behavior of the financial entity under supervision and prevailing market conditions. An immediate implication of this framework is that not all leverage is created equal, and any fixed numerical limit can lead to dramatically different loss probabilities over time and across assets and investment styles. This framework can also be used to investigate the macroprudential policy implications of microprudential regulations through the general-equilibrium impact of leverage constraints on market parameters such as volatility and tail probabilities.