(a) An investor enters into a short forward contract on 100 million yen. The for
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Question
(a) An investor enters into a short forward contract on 100 million yen. The forward exchange rate for US$ 1 is set at US$0.012 per yen. How much does the investor lose or gain if the exchange rate at the end of the contract is (i) US$0.011 per yen, and (ii) US$0.013 per yen.
(b) Suppose that the six-month interest rates in the United States and Japan are 5% and 1% per year, respectively. The spot exchange rate is 100yen/US$. Find the six-month forward exchange rate.
(c) Suppose that an I-bank is offering the exact same forward as (b) but with a rate strictly lower than the rate that you found in (b). Find an arbitrage implementation to capitalize on the arbitrage opportunity for a long position of the forward.
Explanation / Answer
As per the rule, I have to do first question only.
Value of forward contract = 100,000,000 yens
Exchange rate = USD 0.012 per yen
Dollar equivalent of the value of forward contract = 100,000,000 x 0.012
= 1,2 00,000
Value of contract at the time of expiry = = 100,000,000 x 0.011
= 1,1 00,000
Since we have shorted, if the value of contract reduces, we will gain. Here it is reducing.
Gain = USD 1,2 00,000 -1,1 00,000
= USD 100,000
Value of contract at the time of expiry = = 100,000,000 x 0.013
= 1,300,000
Gain = USD 1,200,000 -1,300,000
= -USD 100,000
So there is a loss of USD 100,000
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