Question

Problem 5: Interest Rate Parity The current US Dollar to Yen exchange rate is ?0 = 110. The CCIR US rate is 4% and the CCIR Japanese rate is 2%. Banco Santander is currently willing to offer a one-month forward contract (assuming either the short or long position). The bank’s problem is to set the forward exchange rate ?0, 1/ 12 .

1. If the bank invests $500 M over one month, what is the FV of such investment?

2. Now instead, suppose that the bank takes the $500 M and exchanges that amount into Yen and invest the Yen amount over one month. What is the FV of that investment? 3. If the bank has the option to exchange Yen to USD one month from now at an exchange rate of ?0,? of Yen for 1 USD, what is the value of ?0, 1 /12 that makes the bank indifferent between 1) and 2).

4. Instead of following the “no-arbitrage guidelines” to price an asset, the bank decides to set the forward price at ?0, 1 /12 = 108 (Yen per USD). Michael, once again, decides to trade with the bank and does the following:

i. Borrow an amount $100 over one month. Enter into a one-month contract to sell Yen.

ii. Exchange that amount into Yen at the current rate and the invest the proceeds over one month at the Yen rate. iii. Exchange the Yen into USD at the ?0, 1 /12 = 108 rate set by the bank.

iv. Repay the loan in USD. Compute the payoff from this strategy. Is it positive? Negative? Zero? Compute the reverse strategy:

v. Borrow an amount 100 Yen over one month. Enter into a one-month contract to buy Yen.

vi. Exchange that amount into USD at the current rate and the invest the proceeds over one month at the US rate.

vii. Exchange the USD into Yen at the ?0, 1 /12 = 108 rate set by the bank. i. Repay the loan in Yen.

Answer 1

1.

where

• F.V is equal to the future value of the investment
• P.V. is equal to the present value of the investment
• r is equal to the rate of interest at which the amount is invested
• n is number of years for which the amount is invested

So in this problem, the future value of investment is equal to the present value of investment after the bank investments $500 million for a month.

Since the amount is invested for a month, the formula would be

.

where m is the number of compounding periods.

Using the forumla,

So, if the bank invests $500 Million for a month compounding at 4% per month, it could expect a sum of $501.65 Million.

2. If we exchange $500 Million into Yen at the rate of 1 USD = 110, the amount would sum upto 55000 Million Yen. If the amount is invested by bank for a month, applying the same formula, we'll get,

So, if the bank invests 55000 Million Yen for a month at 2%, it would totalled upto 55091.85 Million Yen.

3. If the bank invests 55091.85 Million Yen at the rate of $1 = 110 Yen, the amount would equal to $500.835 Million.

There would be a difference of $0.815 Million ($501.65 M - $500.835 M). The bank would be indifferent between option (1) and option(2), if it receives the above mentioned amount of $0.815 Million on $500 Million investment.

4. In the first condition,

• Micheal borrows $100 for a month
• Exchanges the amount into Yen, which would be 11000 Yen (where $1 = 110 Yen)
• Invests the amount at 2% for a month,
• He would receive an amount of 11,018.37 Yen.
• Exchanges 11,018.37 Yen into Dollars at the exchange rate of $1 = 108 Yen, which totals the amount to $102.022 (approx)
• Repay $100

Therefore, the payoff strategy would earn Micheal a profit of $2.022 over every $100.

In the reverse strategy,

• Micheal borrows 100 Yen for a month
• Exchanges the amount into Dollars, which would be $0.910 (approx) (where $1 = 110 Yen)
• Invests the amount at 4% for a month,

He could expect an amount of $0.9130 approx

After a month, if he exchanges the amount ($0.9130) for Yen at the rate set by bank, it would receive 98.604 Yen.

In this case, the payoff would be negative to an amount of 1.396 Yen or $0.01269, when the exchange rate is $1 = 110 Yen.