Question

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?

Answer #1

Part A:

- Consider the case where you borrow $2,750,000 in the U.S.
- Given the interest rate of 2.47%, you will be liable to pay back $2,817,925 = $2,750,000*(1+ 2.47%)
- 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
- Given the interest rate of 4.25% in Germany, you will receive 1,791,796.875 Euros. = 1,718,750 *(1+ 4.25%)
- 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.
- 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:

- Consider the case where you borrow 937,500 Euros in Italy.
- Given the interest rate of 6.089%, you will be liable to pay back 994,584.375 Euros = 937,500*(1+ 6.089%)
- Post borrowing in Italy, you can convert the amount to $1,171,875 considering the spot exchange rate of $1.25/Euro
- Given the interest rate of 2.19% in U.S, you will receive $1,197,539.063 = 1,171,875 *(1+ 2.19%)
- 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.
- 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+i_{d}) = S/F*(1+i_{f})

where i_{d} is the domestic interest rate, S is the spot
exchange rate, F is the forward exchange rate, i_{f} 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+i_{d})*F/S = (1+i_{f})

i_{f} = ((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*

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?

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 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, 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 $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 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 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 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
$2,250,000 for one year or its equivalent in Euro. The one-year
interest rate in the U.S. is i$ = 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.

1. You observe that one U.S. dollar is currently equal to 3.6
Brazilian reals in the spot market. The one year US
interest rate is 7% and the one year Brazilian interest rate is 4%.
One year later, you observe that one U.S. dollar is now equal to
3.2 Brazilian reals in the spot market. You would have made a
profit if you had:
Borrowed U.S. dollars and invested in U.S. dollars
Borrowed Brazilian reals and invested in Brazilian reals
Borrowed...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 1 minute ago

asked 13 minutes ago

asked 35 minutes ago

asked 38 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago