An Australian company is planning to sell 1 000 US-based shares to a US company.

Question

An Australian company is planning to sell 1 000 US-based shares to a US company. The two companies enter into a forward contract to sell the shares for some US$ amount F in one month’s time. To ensure it can get a reasonable exchange rate for the payment in US$, the Australia company also enters into a short forward contract to sell the US$ currency F at some forward rate k. The current price of one share is S(0) = US$10 and the current exchange rate is X(0) = 1.25 (i.e., US$1 buys AU$1.25). The current Australian return is Rd = 1.030 over one month and the current US return is Rf = 1.035 over one month.

(a) Consider the forward contract with shares as the underlying asset. According to the one-step binomial model, what is a fair forward price F (in US$) for the 1 000 shares?

(b) Consider the forward contract with US$ as the underlying asset. According to the one-step binomial model, what is a fair value for the forward rate k?

(c) In AU$, what payoff will the Australian company receive after both forward contracts are completed?

Explanation / Answer

Current share price (P0) = 10 USD

Spot rate = 1.25 AUD / USD

a) Forward price = Current price * (1+Rate)^t

Since shares price in USD , We will use USD rate

So , 1+R = 1.035

t=1

Forward rate = 10 * 1.035 = $ 10.35

Total Forward Price = 1000 * 10.35 = $ 10350

b) Forward rate = Spot rate * (1+Rate(domestic)) / (1+Rate(foreign))

Domestic currency here is AUD and foreign currency is USD

So (1+Rate(domestic)) = 1.030

(1+Rate(foreign)) = 1.035

So Forward rate = 1.25 * 1.030 / 1.035 = 1.243

c) So in forward contract of shares company wants to sell, they will receive 10350 USD after 1 month when the contract expire.

Also since company has short forward contract of exchange rate, the rate at which company will exchange this USD amount will be 1.243 AUD / USD

So total amount = 10350 * 1.243 = 12865 AUD

If the company has sold 1000 shares initially @ 1.25

Total Amount = 1.25*1000*10 = 12500 AUD

If they have invested this money for a month:

Total amount after 1 month = 12500*1.030 = 12875 AUD

Payoff = 12875 - 12865 = -10 AUD

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