Restricted Export Flexibility and Risk Management with Options and Futures

expected profits. As shown in Proposition 2, it is optimal for the firm to eliminate all
exchange rate risk if the two currency derivative markets are jointly unbiased, i.e. when full
hedging is costless in terms of expected profits. Proposition 5 compares two situations
with identical expected marginal revenue. In the first situation, characterized by the
absence of an unbiased currency options market, marginal revenue is risky. In the second,
with jointly unbiased currency futures and options markets, marginal revenue is riskless
at the optimum. It follows that a risk-averse firm produces more under riskless marginal
revenue than under risky marginal revenue.

5 Conclusions

Foreign exchange risk management and its interaction with real operations play a sig-
nificant role for an international firm’s success. This paper has examined the optimal
production and risk management decisions of an export flexible firm under exchange rate
uncertainty. The paper focuses on restrictions of export flexibility in that the firm is
assumed to serve both the domestic market and a foreign market with certain minimum
levels of domestic sales and exports. The separation theorem requires the existence of
currency call options only. Optimal production is unaffected by the tightness of the re-
strictions of the firm’s flexibility. The optimal hedge portfolio eliminates all exchange rate
risk if the currency derivatives markets are jointly unbiased. The hedge portfolio consists
of both currency futures and currency options. Hence, our simple model of a restricted
export flexible firm is sufficiently rich to provide a rationale for the joint use of currency
futures and options in exchange rate risk management. In contrast to the production
decision, the structure of the optimal hedge portfolio directly depends on how severe the
restrictions are.

In the absence of currency options, neither separation nor full hedging can be derived.
Since currency futures do not allow for complete elimination of the firm’s piecewise linear
exchange rate risk, the firm has to bear some exchange rate risk whatever its futures
position will be. In this case, it is clear that preferences and the assessment of the

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