Question

QUESTION 3

(a) Differentiate between Translation and Transaction Exposure

(b) Currently the exchange rate is USD1.5000/GBP and the three-month forward exchange rate is USD1.5200/GBP. The three-month interest rate is 8.0% per annum in the U.S. and 5.80% in the U.K. Assume you can borrow as much as USD1,500,000 or GBP1,000,000.

(i) Determine whether the interest rate parity (IRP) is currently holding.

(ii) If the IRP is not holding, show the procedures you carry out covered interest arbitrage. Calculate the arbitrage profit.

(iii) Explain how the IRP will be restored as a result of the covered arbitrage activities.

Answer 1

Question 3:

(a) Transaction exposure occurs when a Firm has a receivable or payable in foreign currency, the home currency equivalent of which is unknown. The amount is payable or receivable at a later date and the exchange rate prevailing at that time is unknown and hence this poses a potential threat to investors. For eg, an importer who has foreign currency payable is afraid that the exchange rate prevailing at the time of payment might increase than the rate prevailing when the transaction was entered.

Translation Exposure occurs when a Firm has foreign subsidaries and associates and as a regulatory norm, it has to prepare consolidated financial statements including those of the foreign subsidiaries. Thus, the FS assertions have to be converted using the stipulated exchange rates and then included in the Firm's consolidated financial statements. There exists a potential risk that the values of the assertions might change as compared to the rates prevailing at the time of entering the transactions. This might lead to decrease in value of assets or increase in liabilities for the Group as a whole.

(b) Interest Rate Parity- It states that there must exist a relationship between spot and future exchange rates and their relative interest rates, such that no covered interest arbitrage opportunities can exist.

This relationship is given by:

F1/S0 = (1+R fc)/(1+ R us)

where, F1= Forward exchamge rate; S0= current spot exchange rate

R fc= Interest rate of foreign country;    R us= Interest rate of USA

(i) As per the question, putting values in the above equation:

F1/S0= 1.52/ 1.50= 1.0133

(1+R fc)/(1+ R us)= (1+ 0.058)/ (1+0.08)= 0.97963

Since the two values are not the same, hence we can conclude that Interest rate parity does not exist. And thus, there exists an opportunity for covered interest arbitrage.

(ii) Since, IRP doesn't hold good, we should identify which currency to borrow and which one to invest so as to make arbitrage profit.

Step 1: Identification of currencies:

Strategy 1- Invest US$ 15,00,000 in US investment paying 8% p.a. Hence, $ value in 3 months= 15,00,000(1+ 0.08/4)= $ 15,30,000

Return= (15,30,000-15,00,000)/15,00,000= 2%

Strategy 2- Invest in risk free UK investments:

1. Convert $ 15,00,000 into GBP using spot rate and simultaneously execute a forward trade to convert back GBP into US dollars in 3 months.

Convert $ into GBP= 15,00,000/1.50 = GBP 10,00,000

forward contract to convert $ into GBP= forwrad rate is $ 1.52= 1 GBP

2. Invest in GBP at 5.8% p.a ; GBP value in 3 months= GBP 10,00,000* (1+0.058/4)= GBP 10,14,500

3. Convert GBP 10,14,500 at forward rate; hence, $ value in 1 year= GBP 10,14,500*1.52= $ 15,42,040

Return= (15,42,040-15,00,000)/15,00,000= 2.8%

Since the return is higher in 2nd strategy (2.8%), hence we should borrow at lower US rate and invest at the higher UK rate to exploit the arbitrage opportunity.

Arbitrage profit calculation:

1. Borrow $15,00,000 at 8%p.a, hence, payable $ after 3 months= 15,00,000(1+0.08/4)= $15,30,000

2. Convert $15,00,000 to GBP at $1.50/GBP and get 10,00,000 GBP.

3. Enter into a forward agreement at $ 1.52= 1 GBP

4. Invest GBP 10,00,000 at 5.8% p.a for 3 months, GBP value after 3 months= 10,00,000(1+ 0.058/4)= GBP 10,14,500.

5. Convert back 10,14,500 GBP using forward rate, getting= 10,14,500*1.52= $15,42,040.

6. therefore, arbitrage profit= $ (15,42,040- 15,30,000)= $12,040

iii) The IRP shall be restored as a result of the arbitrage activities in the following manner:

The US $ interest rate will rise; (since investors will keep borrowing to make profits)

the UK GBP interest rate will fall ((since investors will keep investing to make profits)

the spot exchange rate will rise

the forward rate will fall

All the above mentioned activities will continue till the IRP holds true.