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?

--------------------------------------------------------------------

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:

------------------------------------------------------------------------

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?

Homework Answers

Answer #1

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

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Suppose that the annual interest rate is 3.25 percent in the United States and 4 percent...
Suppose that the annual interest rate is 3.25 percent in the United States and 4 percent in Germany and that the spot exchange rate is $1.50/€ and the forward exchange rate, with one-year maturity, is $1.55/€. Assume that an arbitrager can borrow up to $1,000,000 or its equivalent in Euro. If an astute trader finds an arbitrage, what is the net cash flow in one year in dollar and in Euro?
suppose that the anual intrest rate is 1.5 percent in the united states and 3 percent...
suppose that the anual intrest rate is 1.5 percent in the united states and 3 percent in germany, and that the spot exchange rate is 1.8 assume tht an arbitrager can borrow up to 1,000,000 or 625,000, if an astute trader finds an arbitrage, what is the arbitrage profit in one year
Currently, interest rate is 2 percent per annum in the U.S. and 6 percent per annum...
Currently, interest rate is 2 percent per annum in the U.S. and 6 percent per annum in the euro zone, respectively. The spot exchange rate is $1.25 = €1.00, and the one-year forward exchange rate is $1.20 = €1.00. As informed traders recognize the deviation from IRP and start carrying out covered interest arbitrage transactions to earn a certain profit, how will IRP be restored as a result? A. Interest rate in the euro zone will rise; interest rate in...
Suppose that the one-year interest rate is 2.45 percent in the United States; the spot exchange...
Suppose that the one-year interest rate is 2.45 percent in the United States; the spot exchange rate is $1.1527/€; and the one-year forward exchange rate is $1.1231/€. What must one-year interest rate be in the euro zone to avoid arbitrage?
Suppose that the annual interest rate is 2.5 percent in Korea and 4.2 percent in Germany,...
Suppose that the annual interest rate is 2.5 percent in Korea and 4.2 percent in Germany, and that the spot exchange rate is Won1933.2/€ and the forward exchange rate, with one-year maturity, is W1915.5/€. Assume that a trader can borrow up to €2,000,000 or Won3,866,400,000. Does the interest rate parity hold? Show your work. Is there an arbitrage opportunity? (covered interest arbitrage) If there is an arbitrage opportunity, what steps should we take in order to make an arbitrage profit?...
Given: US interest rate 5% German interest rate 3.5% One-year forward rate is $1.16/Euro Spot rate...
Given: US interest rate 5% German interest rate 3.5% One-year forward rate is $1.16/Euro Spot rate $1.12/Euro Arbitrager can borrow up to $1,000,000 or Euro 892,857. Doing a Covered Interest Arbitrage (CIA) how much will the arbitrager make: Hint: Start by borrowing $1,000,000 and converting this to Euro, then convert back Euro to USD after one year.
IRP arbitrage a. If the interest rate in the United Kingdom is 4 percent, the interest...
IRP arbitrage a. If the interest rate in the United Kingdom is 4 percent, the interest rate in the United States is 6 percent, the spot exchange rate is $1.4528/£1, and interest rate parity holds, what must be the one-year forward exchange rate? (Do not round intermediate calculations. Round your answer to 4 decimal places. (e.g., 32.1616))   One-year forward exchange rate $  per £   b. If the forward rate is actually $1.4822/£1, would you borrow in dollars or pounds to make...
IRP arbitrage2 a. If the interest rate in the United Kingdom is 5 percent, the interest...
IRP arbitrage2 a. If the interest rate in the United Kingdom is 5 percent, the interest rate in the United States is 4 percent, the spot exchange rate is $1.6789/£1, and interest rate parity holds, what must be the one-year forward exchange rate? (Do not round intermediate calculations. Round your answer to 4 decimal places. (e.g., 32.1616))   One-year forward exchange rate $  per £   b. If the forward rate is actually $1.6617/£1, would you borrow in dollars or pounds to make...
1. Suppose the annual interest rate is 3.5% in U.S. and 4.5% in U.K., and that...
1. Suppose the annual interest rate is 3.5% in U.S. and 4.5% in U.K., and that the spot exchange rate is S($/£) = 1.3918 and the forward exchange rate with 12-month maturity is F12($/£) = 1.3526. Assume you are a U.S. trader and can borrow up to $1,000,000 (or £1,000,000). Answer the following questions. a. Is there an arbitrage opportunity according to the Interest Rate Parity based on the above information? (show your work!) b. Show the strategy to capture...
A Euro based currency dealer has good credit and can borrow $2,250,000 for one year or...
A Euro based currency dealer has good credit and can borrow $2,250,000 for one year or its equivalent in Euro. The one-year interest rate in the U.S. is i$ = 2.15% and in the euro zone the one-year interest rate is i€ = 5.58%. The spot exchange rate is $1.35 = €1.00 and the one-year forward exchange rate is $1.29 = €1.00. Show how to realize a certain Euro profit via covered interest arbitrage. Convert it into dollars as well.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT