Question

The current spot exchange rate between the US Dollar and the Yen is 113 (i.e., $1 buys 113 Yen). What is the “fair price” for a 12month forward contract (dollars for yen) if the US borrowing cost is 5% per annum and the investment return on a Yen denominated Certificate of Deposit is 1.0%?  Given the above information, would you purchase a forward contract offered at 105 Yen to the Dollar from your dealer or create a “synthetic forward contract” on your own? Why?

Answer 1

Let us say I borrow $1 now and buy 113 Yen with it.

At the end of 1 year Yen with me = 113 * 1.01 = 114.13

Amount of US Dollar to be returned to bank = 1* 1.05 = $1.05

So for fair price, $1.05 = 114.13 Yen

or $1 = 114.13/1.05 Yen = 108.70 Yen

If the offered forward contract is 105 Yen to the Dollar, it means at the end of 12 months, if I have a dollar, I can get 105 Yen.

However, if I borrow $1 today, change it into Yen and deposit it into Certificate of Deposit, I have 114.13 Yen.

Since I have to return $1.05, at the dealer's price, it is equal to 110.25 Yen. So I still profit by 4.13 Yen.

So it is better to make a synthetic forward contract than to buy the contract from the dealer.

Another way to look at it is I will have 108.70 Yen for $1 at the end of 1 year instead of 105 Yen for $1 if I buy from the dealer. So it is better to make the synthetic forward contract.

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