Question

# Suppose that the annual interest rate is 2.47 percent in the United States and 4.25 percent...

Suppose that the annual interest rate is 2.47 percent in the United States and 4.25 percent in Germany, and that the spot exchange rate is \$1.60/€ and the forward exchange rate, with one-year maturity, is \$1.58/€. Assume that an arbitrager can borrow up to \$2,750,000 or €1,718,750. If an astute trader finds an arbitrage, what is the net profit in one year?

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An Italian currency dealer has good credit and can borrow €937,500 for one year. The one-year interest rate in the U.S. is i\$ = 2.19% and in the euro zone the one-year interest rate is i€ = 6.089%. The spot exchange rate is \$1.25 = €1.00 and the one-year forward exchange rate is \$1.20 = €1.00. Show how to realize and calculate the certain euro-denominated profit via covered interest arbitrage:

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You are Microsoft's CFO and have an extra U.S. \$1B to invest for six months. You are considering the purchase of U.S. T-bills that yield 1.7975% (that's a six month rate, not an annual rate) and have a maturity of 26 weeks. The spot exchange rate is \$1.00 = ¥103.732, and the six month forward rate is \$1.00 = ¥111.879. What must the interest rate in Japan (on an investment of comparable risk) be before you are willing to consider investing there for six months?

Part A:

1. Consider the case where you borrow \$2,750,000 in the U.S.
2. Given the interest rate of 2.47%, you will be liable to pay back \$2,817,925 = \$2,750,000*(1+ 2.47%)
3. Post borrowing in the U.S, you can convert the amount to 1,718,750 Euros considering the spot exchange rate of \$1.6/Euro
4. Given the interest rate of 4.25% in Germany, you will receive 1,791,796.875 Euros. = 1,718,750 *(1+ 4.25%)
5. Convert this amount back to dollars, to pay back what is owed. So, converting 1,791,796.875 Euros to Dollars using the 1 year forward exchange rate of \$1.58/Euros, we get \$2,831,039.063.
6. Given that we have to pay back \$2,817,925, we can calculate our arbitrage profit as  \$2,831,039.063 - \$2,817,925 = \$13114.0625

Part B:

1. Consider the case where you borrow 937,500 Euros in Italy.
2. Given the interest rate of 6.089%, you will be liable to pay back 994,584.375 Euros = 937,500*(1+ 6.089%)
3. Post borrowing in Italy, you can convert the amount to \$1,171,875 considering the spot exchange rate of \$1.25/Euro
4. Given the interest rate of 2.19% in U.S, you will receive \$1,197,539.063 = 1,171,875 *(1+ 2.19%)
5. Convert this amount back to Euros, to pay back what is owed. So, converting \$1,197,539.063 to Euros using the 1 year forward exchange rate of \$1.2/Euros, we get 997,949.218 Euros.
6. Given that we have to pay back 994,584.375 Euros, we can calculate our arbitrage profit as  997,949.218 - 994,584.375 = 3364.84 Euros

Part C:

Interest Rate Parity provides us with the interest rate in a non arbitrage condition. IRP formula is given as follows:

(1+id) = S/F*(1+if)

where id is the domestic interest rate, S is the spot exchange rate, F is the forward exchange rate, if is the foreign exchange rate.

So, domestic interest rate is 1.7975%, S is 103.732 Yen/\$, F is 111.879 Yen/\$.

We can calculate the interest rate in Japan as:

(1+id)*F/S = (1+if)

if = ((1+1.7975%)*(111.879/103.732))-1 = 9.7926%

So, the interest rate in Japan must be atleast 9.7926% to consider investing there.

Please find the screenshots below for numbers keyed into excel:

Hope you find the screenhot & the solution helpful

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