Appendix to "Balance Sheets and Exchange Rate Policy"

Appendix to "Balance Sheets and Exchange Rate Policy"

| Luis F. Céspedes, Roberto Chang, and Andrés Velasco
This appendix provides a derivation of the risk premium in the model. The analysis considers a contracting problem between an entrepreneur and foreign lenders, where the entrepreneur is risk neutral and must choose investment, loan, and repayment schedules to maximize expected returns. The entrepreneur's investment yields a random return, which can only be observed by the entrepreneur, not by lenders, unless monitoring costs are incurred. The optimal contract is a standard debt contract with a fixed repayment, and monitoring occurs only if the return is low enough. The resulting problem is similar to that analyzed in BGG (1999), and the optimal contract is derived under the assumption that the future rental rate on capital is known at the time of contracting. The risk premium is derived as an increasing function of the value of aggregate investment relative to aggregate net worth. The derivation shows that the optimal cutoff for bankruptcy depends only on the external finance premium, and the investment-to-net-worth ratio is a function of this cutoff. The risk premium is then expressed as a function of the investment-to-net-worth ratio, showing that it increases with this ratio. The appendix also discusses the existence and uniqueness of a non-stochastic steady state, and provides a linear approximation to the equilibrium system. The analysis shows that the steady state values of key variables can be derived from the equilibrium conditions, and that the risk premium is a function of the investment-to-net-worth ratio. The linear approximation around the steady state leads to a system of equations that includes the interest parity condition and the risk premium equation. The analysis concludes with the derivation of the saddle-path coefficient, which determines the stability of the equilibrium. The results show that the risk premium is a function of the investment-to-net-worth ratio, and that the equilibrium is stable under certain conditions.This appendix provides a derivation of the risk premium in the model. The analysis considers a contracting problem between an entrepreneur and foreign lenders, where the entrepreneur is risk neutral and must choose investment, loan, and repayment schedules to maximize expected returns. The entrepreneur's investment yields a random return, which can only be observed by the entrepreneur, not by lenders, unless monitoring costs are incurred. The optimal contract is a standard debt contract with a fixed repayment, and monitoring occurs only if the return is low enough. The resulting problem is similar to that analyzed in BGG (1999), and the optimal contract is derived under the assumption that the future rental rate on capital is known at the time of contracting. The risk premium is derived as an increasing function of the value of aggregate investment relative to aggregate net worth. The derivation shows that the optimal cutoff for bankruptcy depends only on the external finance premium, and the investment-to-net-worth ratio is a function of this cutoff. The risk premium is then expressed as a function of the investment-to-net-worth ratio, showing that it increases with this ratio. The appendix also discusses the existence and uniqueness of a non-stochastic steady state, and provides a linear approximation to the equilibrium system. The analysis shows that the steady state values of key variables can be derived from the equilibrium conditions, and that the risk premium is a function of the investment-to-net-worth ratio. The linear approximation around the steady state leads to a system of equations that includes the interest parity condition and the risk premium equation. The analysis concludes with the derivation of the saddle-path coefficient, which determines the stability of the equilibrium. The results show that the risk premium is a function of the investment-to-net-worth ratio, and that the equilibrium is stable under certain conditions.
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Understanding Balance Sheets and Exchange Rate Policy