Question

FIM Bank is an Australian bank. The bank has been borrowing in the Australian markets and lending abroad, thus incurring foreign exchange risk. In a recent transaction, it borrowed $AUD 5 million via a one-year security at 4.5 per cent per annum nominal and funded a loan in Swiss Francs (CHF) at 5.0 per cent. The spot rate at the time of this transaction was 1.5152 AUD = 1 CHF (AUD/CHF = 1.5152).

(a)     Information received immediately after the transaction closing indicated that the Swiss Franc would depreciate to AU$1.5102/CHF 1 by year end (i.e. 1.5102 AUD = 1 CHF). If the information is correct, what will be the realised spread on the loan? Assume adjustments in principal values are included in the spread. [4 marks]

(b)     Suppose the bank had an opportunity to sell one-year forward Swiss Francs at AU$1.5121/CHF 1 (i.e. 1.5121 AUD = 1 CHF). What would have been the spread on the loan if the bank had hedged forward its foreign exchange exposure? [3 marks]

(c)    Explain how forward and spot rates would both change in response to the spread calculated in part (b)? In your answer, explain what the final value of the spread would be after the adjustment in forward and spot rates. [3 marks]

Answer 1

Amount in $AUD to be repaid after a year = 5*1045 = $AUD 5.225 million

Amount of loan funded in CHF = 5/1.5152 =CHF 3.299894 million

Amount to be realised in CHF after a year = 3.299894 *1.05 = CHF 3.464899 million

a) If the Swiss Franc would depreciate to AU$1.5102/CHF 1 by year end

Amount realised in $AUD = 3.464899 *1.5102 =$AUD 5.232676 million

So, net interest realised = $AUD 0.232676 million on $AUD 5 million

So, Interest rate realised = 0.232676/5 =0.046535 or 4.6535%

So, the Realised spread on the loan = 4.6535% -4.5% = 0.1535%

b) If the bank had sold one-year forward Swiss Francs at AU$1.5121/CHF 1

Amount realised in $AUD = 3.464899 *1.5121 =$AUD 5.239259 million

So, net interest realised = $AUD 0.239259 million on $AUD 5 million

So, Interest rate realised = 0.239259/5 =0.047852 or 4.7852%

So, the Realised spread on the loan = 4.7852% -4.5% = 0.2852%

c) As the spread indicates arbitrage, the forward rates and spot rates would move in a way to cancel the arbitrage. The spot rates would go up (CHF to appreciate) and forward rates to go down (CHF to depreciate) so that the equilibrium is reached when the arbitrage is gone.

After final adjustments in the rates the spread will become zero.