Equilibrium Exchange Rate Hedging

27 Pages Posted: 22 Apr 2004 Last revised: 23 Jul 2022

See all articles by Fischer Black

Fischer Black

Sloan School of Management, MIT (Deceased)

Date Written: April 1989


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.

Suggested Citation

Black, Fischer, Equilibrium Exchange Rate Hedging (April 1989). NBER Working Paper No. w2947, Available at SSRN: https://ssrn.com/abstract=227205

Fischer Black (Contact Author)

Sloan School of Management, MIT (Deceased)


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