Question

Currently, the spot exchange rate is €_____/$ and the three-month forward exchange rate is €_____/$ (Please refer to the assigned figures in Table 3 below). The three-month interest rate is 2.8% per annum in the U.S. and 1.6% per annum in France. Assume that you can borrow as much as $1,000,000 or €__________(Please refer to the assigned figures in Table 1 below).

a. Determine whether the interest rate parity is currently holding.

2. If the IRP is not holding, how would you carry out covered interest arbitrage? Show all the steps and determine the arbitrage profit.

c. Explain how the IRP will be restored as a result of covered arbitrage activities.

TABLE1

SPORT RATE (EURO/USD)	3 MONTHS FORWARD RATE(EURO/USD)	INVESTMENT AMOUNT (EURO)
0.8900	0.9590	890,000

Answer 1

Part A:

According to Int Rate parity Theorm,
Fwd rate After 3 Months = Spot rate * [ ( 1 + Hi ) ^ n ] / [ ( 1 + Fi ) ^ n ]
= $ 1.1236 * [ ( 1 + 0.007) ^ 1 ] / [ ( 1 + 0.004 ) ^ 1 ]
= $ 1.1236 * [ ( 1.007) ^ 1 ] / [ ( 1.004 ) ^ 1 ]
= $ 1.1236 * [ 1.007 ] / [ 1.004 ]
= $ 1.1236 * [ 1.003 ]
= $ 1.127

Spot Rate USD / EUro = 1/ 0.8900

= 1.1236 USD

3 Month Fwd rate USD / Euro = 1 / 0.9590

=1.0428 USD

As Actual Fwd rate is not equal to IRPT Fwd rate, IRPT doesn't hold good. Covered Interest arbitrage exists.  

Part B:
  
Foreign Currency Premium or Discount:  
= [ [ Fwd rate - Spot Rate ] / Spot Rate ] * 100   
= [ [ $ 1.127 - $ 1.1236 ] / $ 1.1236 ] * 100   
= [ [ $ 0.0034 / $ 1.1236 ] * 100   
= [ 0.003 ] * 100   
= 0.3026 %  
  
Annualized % = Premium or Discounted / No. of Years  
= 0.3026 % / 1  
= 0.3026 %   
  
Effective Rate in Home Country   0.7000%
Effective Rate in Foreign Country   0.7026%
  
Effective Rate in Foreign currency = Int rate + Fwd Premium %  
= 0.4 % + 0.3026 %   
= 0.7026 %  
  
  
Step 1:
Amount Borrowed   $1,000,000.00
Step 2:  
Amount in Foreign Currency   889,996.44
Step 3:  
Invest in foreign currency for specified period   1 Years
Step 4:
Realize the Maturity Value in Foreign Currency  
Maturity Value = Amount Deposited * ( 1 +r ) ^ n   
r = Int Rate per anum  
n - Time period in Years  
= 889996.44 * ( 1 + 0.004 ) ^ 1  
= 889996.44 * ( 1.004 ) ^ 1  
= 889996.44 * ( 1.004 )   
= 893556.43  
  
Step 5:
Convert foreign currency proceedings into Home Currency using Actual Fwd Rate  
= 893556.43 * 1.127  
= 1007038.10
  
Step 6:  
Maturity of Loan in Home country  
= 1000000 * ( 1 + 0.007 ) ^ 1  
= 1000000 * ( 1.007 ) ^ 1  
= 1000000 * ( 1.007 )  
= 1007000  
  
Step 7
Profit = Amount realized from Inv - maturity Value of Loan  
= 1007038.09661 - 1000000  
= 7038.10  
  

Arbitrage profit is $ 7038.10

Part C:

As Home currency is cheap, Borrow funds in home currency, It leads to increase in Int Rates. Int rate in Home currency shall be equal to Foreign currency int Rate and Forex fluctuations. Then Actual Fwd rate and IRPT forward rate will be same and arbitrage will be eliminated.

Pls comment,if any further assistance is required.