Question

A Japanese bank expects to lend €10 million to a Spanish firm. If negotiations are successful, the loan will be made one month from today. The terms of the loan have already been established: the Spanish firm is to pay a fixed rate of 5%; the term of the loan will be one year; interest and principal, in euros, will be repaid to the bank one year after the loan is made. The Japanese bank is interested in maximizing its yen-denominated wealth of its shareholders.

a. Clearly discuss the nature of the interest rate risk the Japanese bank faces.

b. Clearly state how the Japanese bank can use forward rate agreements to manage the interest rate risk it faces. Explain how the FRA will reduce the interest rate risk faced by the bank. Be as precise and thorough as you can, given the information provided.

c. Should the bank desire that the contract rate on the FRA be above or below 5%? Why?

For the next two questions, assume the bank enters an FRA to borrow in yen at a fixed rate:

d. Clearly discuss the nature of the foreign exchange rate risks the bank will face after the loan is actually made.

e. Given your response in part d, clearly state how the bank can use forward exchange contracts to manage the exchange rate risk it will face after the loan is actually made. Again, be as precise and thorough as you can, given the information provided. Explain how the forward exchange contract will reduce the exchange rate risk faced by the bank?

Answer 1

a. interest rate risk is a part of market risk for the transaction made here. For the Japanese bank, the loan is made out at a fixed rate of 5% in Euro.

There are 2 ways by which the bank can face interest rate risk. If the interest rate in Euro increases, the fixed rate paying side, which is the Spanish borrower here, will benefit from the fixed rate payment agreement. The Japanese bank will lose on opportunity cost as it could have lent the same money at a higher rate at now increased rate. Additionally, if the bank does not want to hold the loan till maturity and sell it in the market as a bond, the price of the bond will be lower and hence, the Japanese bank will face a loss. The risk will be present even if the rates in Euro decline but the bank will be in a profitable position in this case.

Alternatively, assume that the bank had borrowed the funds in the Japanese markets at floating rate and if the interest rates in Yen increase. Now the bank has a fixed inflow of funds at the end of one year from the Spanish borrower but has to pay more in interest in Yen. Hence, the bank is again in a loss. On the other hand, if the rates in the Japanese markets decline, the bank will have to pay out less in Yen and hence, will be in a profitable position.

If the borrowing and lending of the bank are both at a fixed rate and the bank aims to hold both the borrowing and lending till maturity, the interest rate risk is lower. The bank will still face currency exchange risk, credit risk, settlement risk among other risks but those are not the topic of discussion here.

b. as seen from above, the bank will face interest rate risk if the interest rates change in yen or Euro during the period of the loan. Hence, the bank can enter into a FRA. The FRA set up will be as follows-

Borrow in Yen at fixed rate, preferably lower than 5%. This way the Yen liability of the bank is fixed. The other side of the FRA is to receive variable interest rate. This could be a benchmark rate such as LIBOR.

Exchange the Yen to Euro at the spot rate.

Lend out in Euro at a fixed rate of 5%.

Receive principal + 5% interest after 1 year in Euro

Exchange the Euro to Yen after 1 year at then spot rate

Pay off the FRA liability which will be equal to the differential in the fixed rate and the floating rate of the FRA. Suppose the benchmark rate is lower than fixed rate, the bank will pay the differential amount. Since the floating rate is lower than the fixed rate, the bank will have benefitted from the increase in the price of the loan which will offset the FRA differential payment. On the other hand, if the floating rate is above the fixed rate, the bank will receive money. This will be a profit position for the bank.

There is an aspect of currency exchange risk between Yen and Euro for the bank (and the borrower). The bank can mitigate this risk by entering into a foreign exchange contract for a maturity of 1 year and notional value of (loan principal + 5% interest amount). this will further reduce the risk.

c. as seen from the above transaction, the bank is the fixed rate payer in the FRA. Hence, it will desire the fixed rate in FRA to be lower than 5%. This will provide the bank a net interest margin which is the difference between the 5% interest rate lent to the Spanish borrower and the fixed rate of the FRA. The changes in exchange rates between Yen and Euro will impact the actual amount exchanged one year from now but that will be covered by the forward exchange rate agreement and not by FRA.

d. the bank has entered into a FRA as a fixed rate payer. Assume the current exchange rate between Euro and Yen is 1 Euro = 100 Yen. As of the loan start date, the loan amount of Euro 10 Mn will be equal to Yen 1 Bn. Suppose after 1 year, the Euro depreciate and the exchange rate after 1 year, when the loan is maturing is 1 Euro = 90 Yen. The principal + interest @5% is Euro 10.5 Mn. This amount will be converted into Yen at the then spot rate of 1 Euro = 90 Yen. The Yen equivalent amount will be Yen 945 Mn (= 10.5 Mn * 90). The depreciation in Yen is 90-100/100= 10%. This is more than the gain from interest rate in Euro. Hence, the bank is at a net loss. The bank will have to repay the Yen 1 Bn borrowed at the beginning of the loan after 1 year. Suppose that interest rate is 2%. Hence, the total payable amount for the bank after 1 year will be Yen 1.02 Bn. However, it received only Yen 945 Mn from the loan. Hence, the loss for the bank will be Yen 57 Mn. This loss is arising from the exchange rate risk.

Alternatively, if the exchange rate in Euro and Yen had depreciated by less than the interest rate differential (approx. 5%-2%) or appreciated, then the bank would have been in overall profit.

e. as seen from the above explanation, the bank will face an exchange rate risk if the Euro-Yen rate depreciates more than the interest rate differential. To mitigate this risk, the bank can enter into a forward exchange contract, which is calculated as follows-

Risk free rate in Euro 5%

Risk free rate in Yen 2%

Current (spot) exchange rate 1 Euro = 100 Yen

By interest parity principal, the expected spot rate after 1 year will be-

1 Euro= (100* 1.02)/ (1* 1.5)= 97.14286 Yen

It is obvious that the since the interest rate in Euro is more than in Yen, Euro will depreciate as compared to the Yen. If the bank can enter into a forward exchange contract at the above exchange rate, it will have reduced to the foreign exchange risk for itself. In the bank could enter into a forward exchange contract at any rate higher than the above calculates rate, say, 1 Euro = 99 Yen after 1 year, it will benefit from the forward exchange contract.