Question

Suppose that the $/€ spot exchange rate is 1.20 $/€ and the 1 forward rate is 1.24$/€. The yields on 1 U.S. and EU. Treasury Bills are U.S 10% and EU 7%. Use the exact form interest parity condition. Note that these numbers are hypothetically constructed to give arbitrage profits.

(1) Calculate the covered interest differentials using Covered IPC (extra profits from investing in EU).

(2) Suppose that U.S. investor is considering a covered investment in EU Treasury bills financed by borrowing from U.S. banks at 12% interest rate. Given the exchange rates above, would the investor can obtain profits from this investment? If so, how much?

(3) (continue from question 2) Suppose that this investor also faces transaction costs that further reduce the gains from investing abroad by 0.80%. How much proifit would this investor get from this?

Answer 1

Following information are given in the question:

$/€ spot exchange rate = 1.20 $/€

1 forward rate is 1.24$/€.

Yield on 1 U.S. Treasury Bills =10%

Yield on 1 EU Treasury Bills = 7%

(1) Calculate the covered interest differentials using Covered IPC (extra profits from investing in EU).

As per Covered Interest Parity Condition =

(1+rd) = F/S*(1+rf)) where

rd = Interest in domestic country = 10%

F = Forward Rate = to be found

S = Spot Rate = 1.20$/€.

rf = Interest in foriegn country = 7%

Changing the equation to find Forward Rate, F = (1+rd)/(1+rf)*S

F = ((1+10%)/(1+7%))*1.20 = 1.2336$/€

1 year forward rate = $1.24

Covered Interest Differential = $1.24/€-$1.2336/€ = $0.00636$/€

Arbitrage opportunity under this covered Interest Differential will be as follows:

Step 1: Borrow a sum of say $1 Million in US at a rate of 10% per annum

Step 2: Convert the $1 Million into € with the spot rate which will be $1 Million/1.2 = €833,333.33

Step 3: Buy a forward contract to sell € in one year at 1.24$/€

Step 4: Invest the €833,333.33 in Europe at interest rate of 7% for 1 year

Step 5: After 1 year, the investment of €833,333.33 at 7% interest rate will be €891,666.67 (€833,333.33*(1+7%))

Step 6: Convert this €891,666.67 at the forward contract rate of 1.24$/€ which will be $1,105,666.67 (€891,666.67*1.24)

Step 7: The $1 Million loan after 1 year will be $1,100,000 ($1,000,000*(1+10%))

Step 8: From the available $1,105,666.67 , $1,100,000 loan will be repaid resulting in profit of $5,666.67 ($1,105,666.67-$1,100,000).

2. U.S. investor is considering a covered investment in EU Treasury bills financed by borrowing from U.S. banks at 12% interest rate

Taking the same steps as above except that loan of $1 Million is taken at 12% (and not at 10%).

Step 1: Borrow a sum of say $1 Million in US at a rate of 12% per annum

Step 2: Convert the $1 Million into € with the spot rate which will be $1 Million/1.2 = €833,333.33

Step 3: Buy a forward contract to sell € in one year at 1.24$/€

Step 4: Invest the €833,333.33 in Europe at interest rate of 7% for 1 year

Step 5: After 1 year, the investment of €833,333.33 at 7% interest rate will be €891,666.67 (€833,333.33*(1+7%))

Step 6: Convert this €891,666.67 at the forward contract rate of 1.24$/€ which will be $1,105,666.67 (€891,666.67*1.24)

Step 7: The $1 Million loan after 1 year will be $1,120,000 ($1,000,000*(1+12%))

Step 8: $1,105,666.67 will only be available to repay the loan of $1,120,000 with shortfall of $14,333.33

Thus, if the U.S. investor is considering a covered investment in EU Treasury bills financed by borrowing from U.S. banks at 12% interest rate, the investor cannot obtain profit but will only make loss of $14,333.33.

This is mainly because the interest rate borrowed is higher than what is considered for IPC computation.

3. Suppose that this investor also faces transaction costs that further reduce the gains from investing abroad by 0.80%. How much proifit would this investor get from this?

Under 2 above, the investor already makes loss of $14,333.33 and further transaction loss of 0.80% will only increase the loss as below:

Transaction costs on $1 Million loan will be $1,000,000*0.80% = $8,000

Thus, the total loss will be $14,333.33 + $8,000 = $22,333.33