Question

Consider a financial institution which would like to invest 100 AUD today and receive USD in one year from now. The real rate is 5% in Australia and the inflation rate in Australia is 5%. The inflation rate in the US is 7.5%.

a) Assume that the real rate equivalence holds. Calculate the nominal interest rate in the US and Australia.

b) Assume the spot exchange rate is 0.80 USD per 1 AUD. Calculate the forward rate for one year from now.

c) Consider the following two strategies:
1. The financial institution invests 100 AUD in Australia for one year and transfers the repayment at the forward rate.

2. The financial institution transfers 100 AUD to USD at the spot exchange rate and invests in the US.

Calculate the investment result and interpret your finding.

Answer 1

Nominal interest rate =	((1+Real rate)*(1+Inflation))-1
Real rate	5%
Australia Inflation	5%
US Inflation	7.50%
a) Assume that the real rate equivalence holds. Calculate the nominal interest rate in the US and Australia.
Solution:
Nominal interest rate Australia =	10.25%	(1+5%)*(1+5%)-1
Nominal interest rate US =	12.88%	(1+5%)*(1+7.5%)-1
b) Assume the spot exchange rate is 0.80 USD per 1 AUD. Calculate the forward rate for one year from now.
Solution:
SPOT rate =	0.8	USD per 1 AUD
Nominal Interest rate of US is higher than Australia which means that AUD will appreciate and USD will depreciate in forward.
1-year forward =	Spot Rate*	(1+USD nominal interest rate)	=	0.8*	(1+12.88%)	=	0.82	USD per 1 AUD
		(1+AUD nominal interest rate)			(1+10.25%)
c) Consider the following two strategies:
1. The financial institution invests 100 AUD in Australia for one year and transfers the repayment at the forward rate.
Year 0	Invest 100 AUD @ 10.25% pa
AUD at Year 1	110.25	100*(1+10.25%)
Convert 110.25 AUD into USD at 1- year forward rate (assume the spot rate at year 1 is equal to 1-year forward rate)
USD at year 1 =	90.3	110.25*0.82
2. The financial institution transfers 100 AUD to USD at the spot exchange rate and invests in the US.
Year 0	Convert 100 AUD into USD with spot rate of 0.8 USD per 1 AUD
USD at Year 0	80	100*0.8
Invest 80 USD @ 12.88% pa
USD at Year 1	90.3	100*(1+12.88%)
Hence both the investment strategy will have the same result as the higher interest rate in US is offset by the decrease in currency value at year 1