International Finance: Putting Theory Into Practice

4.4. THE MARKET VALUE OF AN OUTSTANDING FORWARD CONTRACT 143

• You bought forward, at timet 0 , onenokatclp/nok115. At expiry,T, the
  nokspot rate turns out to beclp/nok123, so you pay 115 for something
  you can immediately re-sell at 123. The net value is, therefore, 123-115=8.


• Idem, except thatST turns out to beclp/nok110. You have to pay 115
  for something worth only 110. The net value is, therefore, 110-115=–5: you
  would be willing topay5 to get out of this contract.
  The value of a unit forward sale contract is, of course, just the negative of the
  value of the forward purchase: forward deals are zero-sum games. The seller wins if
  the spot value turns out to be below the contracted forward price, and loses if the
  spot value turns out to be above. Figure 4.5 pictures the formulas, with smileys and
  frownies indicating the positive and negative parts.

Equation [4.17] can be used to formally show how hedging works. Suppose that
you have to pay one unit of foreign currency at some future timeT. The foreign
currency debt is risky because the cash flow at timeT, in home currency, will
be equal to minus the future spot rate—and, at time t, this future spot rate is
uncertain, a characteristic we stress by adding a tilde (∼) over the variable. By
adding a forward purchase, the combined cash flow becomes risk free, as the bit of
arcane math shows, below:

Cash flow from amortizing the debt at expiration: −S ̃T

Value of the forward purchase at expiration: S ̃T−Ft 0 ,T

Combined cash flow: −Ft 0 ,T.

(4.18)

Putting this into words, we say that hedging the foreign-currency debt with a for-
ward purchase transforms the risky debt into a risk-free debt, with a known outflow

Figure 4.5:The Value of a Forward Purchase or Sales Contract at Expiry

V^6

T

• 
  

ST

Ft 0 ,T

ST−Ft 0 ,T

^o o

x x_

Buy forward

V^6

T

• 
  

ST

Ft 0 ,T

Ft 0 ,T−ST

^o o

x x_

Sell forward

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