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Equilibrium Exchange Rate Hedging

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  • Fischer Black
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    Abstract

    In a one-period model where each investor consumes a single good, and where borrowing and lending are private and real, there is a universal constant that tells how much each investor hedges his foreign investments. The constant depends only on average risk tolerance across investors. The same constant applies to every real foreign investment held by every investor. Foreign investors are those with different consumption goods, not necessarily those who live in different countries. In equilibrium, the price of the world market portfolio will adjust so that the constant will be related to an average of world market risk premia, an average of world market volatilities, and an average of exchange rate volatilities, where we take the averages over all investors. The constant will not be related to exchange rate means or covariances. In the limiting case when exchange risk approaches zero, the constant will be equal to one minus the ratio of the variance of the world market return to its mean. Jensen's inequality, or "Siegel's paradox," makes investors want significant amounts of exchange rate risk in their portfolios. It also makes investors prefer a world with more exchange rate risk to a similar world with less exchange rate risk.

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    Bibliographic Info

    Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 2947.

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    Date of creation: Apr 1989
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    Publication status: published as Journal of Finance, Vol. 45, no. 3 (1990): 899-908.
    Handle: RePEc:nbr:nberwo:2947

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    1. Fischer Black, 1989. "Mean Reversion and Consumption Smoothing," NBER Working Papers 2946, National Bureau of Economic Research, Inc.
    2. Grauer, Frederick L. A. & Litzenberger, Robert H. & Stehle, Richard E., 1976. "Sharing rules and equilibrium in an international capital market under uncertainty," Journal of Financial Economics, Elsevier, Elsevier, vol. 3(3), pages 233-256, June.
    3. McCulloch, J Huston, 1975. "Operational Aspects of the Siegel Paradox: Comment," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 89(1), pages 170-72, February.
    4. Frankel, Jeffrey A., 1988. "Recent estimates of time-variation in the conditional variance and in the exchange risk premium," Journal of International Money and Finance, Elsevier, Elsevier, vol. 7(1), pages 115-125, March.
    5. Breeden, Douglas T., 1979. "An intertemporal asset pricing model with stochastic consumption and investment opportunities," Journal of Financial Economics, Elsevier, Elsevier, vol. 7(3), pages 265-296, September.
    6. Adler, Michael & Dumas, Bernard, 1983. " International Portfolio Choice and Corporation Finance: A Synthesis," Journal of Finance, American Finance Association, American Finance Association, vol. 38(3), pages 925-84, June.
    7. R. Mehra & E. Prescott, 2010. "The equity premium: a puzzle," Levine's Working Paper Archive 1401, David K. Levine.
    8. Jeffrey A. Frankel, 1985. "The Implications of Mean-Variance Optimization for Four Questions in International Macroeconomics," NBER Working Papers 1617, National Bureau of Economic Research, Inc.
    9. Taylor, Stephen J., 1987. "Forecasting the volatility of currency exchange rates," International Journal of Forecasting, Elsevier, Elsevier, vol. 3(1), pages 159-170.
    10. Eun, Cheol S & Resnick, Bruce G, 1988. " Exchange Rate Uncertainty, Forward Contracts, and International Portfolio Selection," Journal of Finance, American Finance Association, American Finance Association, vol. 43(1), pages 197-215, March.
    11. Stulz, ReneM., 1981. "A model of international asset pricing," Journal of Financial Economics, Elsevier, Elsevier, vol. 9(4), pages 383-406, December.
    12. Roll, Richard & Solnik, Bruno, 1977. "A pure foreign exchange asset pricing model," Journal of International Economics, Elsevier, Elsevier, vol. 7(2), pages 161-179, May.
    13. Paul R. Krugman, 1981. "Consumption Preferences, Asset Demands, and Distribution Effects in International Financial Markets," NBER Working Papers 0651, National Bureau of Economic Research, Inc.
    14. Sebastian Edwards, 1988. "Real Exchange Rate Behavior in Developing Countries: The Cross Country Evidence," UCLA Economics Working Papers, UCLA Department of Economics 510, UCLA Department of Economics.
    15. Solnik, Bruno H., 1974. "An equilibrium model of the international capital market," Journal of Economic Theory, Elsevier, Elsevier, vol. 8(4), pages 500-524, August.
    16. Frankel, Jeffrey A., 1988. "Recent Estimates of the Time-Variation in the Conditional Variance and in the Exchange Risk Premium," Department of Economics, Working Paper Series, Department of Economics, Institute for Business and Economic Research, UC Berkeley qt23c9q73d, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
    17. Friend, Irwin & Blume, Marshall E, 1975. "The Demand for Risky Assets," American Economic Review, American Economic Association, American Economic Association, vol. 65(5), pages 900-922, December.
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