Question

Alicia Strong is a foreign exchange dealer for a bank in Australia. She wishes to consider whether International Parity Condition (IPC) holds between the British pound and the Australian dollar. Alicia also wonders whether she should invest in AUD or in British pounds (£) to make a covered interest arbitrage (CIA) profit. Depending on the CIA opportunity, she can borrow either A$1,000,000 or £1,000,000 to invest for the next 12 months.

Consider Australia as home market and the UK as foreign market. She faces the following interest rates, exchange rates and inflation rates:

                Nominal interest rate is 5% in Australia (r_h)

                Nominal interest rate is 2% in the UK (r_f).

                Current spot rate, e₀ is A$1.50/£ and

                1-month forward rate, f₁ is A$1.65/£

                Inflation rate in Australia 3.5%

                Inflation rate in the UK 1.5%

               

Using this information:

1. Given the current spot rate and relative inflation rates for the UK and Australia, what does PPP suggest the future expected spot rate will be?

2. Does interest parity hold? If not, where do you recommend that Alicia borrow and invest and why?

3. Assuming no transaction costs, what would Alicia’s covered interest arbitrage profit be on the borrowed amount of A$1,000,000 or £1,000,000 (use 2 decimal points)?

Answer 1

(i) What will be the future expected spot rate as per PPP:

Given,

Spot rate (A$/£) = 1.50

Inflation rate in Australia = 3.5%

Inflation rate in UK = 1.5%

Future expected spot rate as per PPP:

F = S×(1+rA$)÷(1+r£)

Where F = Future Expected rate

S = Spot rate

rA$ = Inflation rate in Australia

r£ = Inflation rate in UK

F = 1.50×(1+0.035)÷(1+0.015)

F = 1.53

Therefore Future Expected spot rate as per PPP = A$1.53/£

(ii) Does Interest Parity hold?

As per Interest rate parity theory, Difference between forward rate and spot rate shall be equal to the difference between Interest rates.

Currency with lower interest rate shall be at forward premium @ interest rate differentials i.e., 3% which means £ shall be at forward premium of 3%

Given, Spot rate (A$/£) = 1.50

Assuming given interest rates are for 1 Month

Interest rate in Australia = 5%

Interest rate in UK = 2%

F = S×(1+iA$)÷(1+i£)

Where, F= Forward rate

S= Spot rate

iA$ = Interest rate in Australia

i£ = Interest rate in UK

F = 1.50×(1+0.05)÷(1+0.02)

F = 1.54

But Actual forward rate = 1.65 i.e., £ is at forward premium of 10% [1.65 - 1.50]÷1.50 which is overpriced [Formula for Calculation of Forward premium = [(F - S)÷S]×100, where F = Forward rate, S = Spot rate]

So, Interest Parity doesn't hold good

If not, where do you recommend Alicia borrow and invest? Why?:

As £ is overstated, it is recommended to invest in UK @ 2% and borrow in Australia @5%

Because as said above Interest rate parity doesn't hold good and £ is overstated, hence it is better to Invest in UK

(iii) What would be the covered interest arbitrage profit on borrowed amount of A$10,00,000:

Borrow A$ 10,00,000 in Australia @ 5% for 1 month

Amount payable after 1 month = 10,00,000×1.05 = A$10,50,000

Convert borrowed amount of A$10,00,000 into £ in spot market @1.50

£inflow = 10,00,000÷1.50 = £6,66,667

Invest £6,66,667 in UK @2% for 1 month

Amount receivable after 1 month = 6,66,667×1.02 = £6,80,000

Convert £6,80,000 at 1 month forward rate of 1.65

A$ inflow = 6,80,000×1.65 = A$11,22,000

Therefore Net Arbitrage profit after 1 month = 11,22,000 - 10,50,000 = A$72,000

Note: In the question, Forward rate is given for 1 month and hence point (iii) calculated for 1 month i.e., Borrowings and investments have been made for 1 month.

Points to be Remembered:

(1) If Interest rate parity doesn't hold good, and if Actual Currency is at forward premium other than which it has to be as per IRP, Invest in that country where Currency is at forward premium

(2) If Actual Currency is at forward discount, then Borrow in that country where Currency is at forward discount.