Restricted Export Flexibility and Risk Management with Options and Futures

Proposition 4 Suppose that the restricted export flexible firm can trade unbiased cur-
rency futures only. Then, its optimal futures position, H*, satisfies Pf Qf < H* <

Pf (q: - Qd).

Figure 4: Hedged and unhedged profits with futures only

Proposition 4 can be illustrated using Figure 4. Without hedging, the firm’s profits
are piecewise linear and convex in the exchange rate. However, currency futures only
allow for hedging against a linear exposure. For S > Pd/Pf , the optimal export policy is
to export as much as possible which generates foreign currency revenue of Pf (Q - Q_d).
This is the steeper part of the unhedged profits line in the north-east of Figure 4. Setting
H = Pf(Q - Qd), the firm could eliminate exchange rate risk for high exchange rate
realizations, S > P_d/Pf . For lower realizations, S < P_d/Pf , export revenue only amounts
to PfQf . For these realizations, exchange rate risk can be eliminated by setting H =
PfQf . This shows that there is a conflict between hedging exchange rate risk for high
and for low realizations of the exchange rate. Proposition 4 states that the firm prefers a

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