Question

1. Spot rate USD/AUD 1.56. Assume annual interest rate is 3% in USA and 5% in Australi What should be the one-year forward rate USD/AUD per interest rate parity condition? Show that there is no arbitrage opportunity based on the forward rate that you computed. Compute arbitrage profit if one-year forward rate is USD/AUD 1.60. Pick any initial borrowing amount of your choice.

Answer 1

IRR theory
IRR theory=F/S=(1+rh)/(1+ri)
F= forward rate
S=spot rate
rh=interest rate USA
ri=Interest rate AUD
IRR=1.60/1.56=(1+rh)/(1+0.05)
IRR=1.0256=(1+rh)/(1+0.05)
IRR=1.0769=(1+rh)
rh=1.0769-1
rh=0.0769
rh=7.79% (Theorotical rh)
Actual Rh=3%
since Actual Rh is less than theorotical Rh we have to borrow USD
there is scope for arbitrage
If Therotical Rh is less than actual Rh tjhen we have to invest
in this case we have to borrow 100000USD
Assuming 100000USD(given in question to assume some amount)
Convert 100000USd to AUD
so 100000USD/1.56=64102.564AUD
Invest 64102.564 for I year at 5% in AUD
Interest=64102.564*5%=3205.128AUD
So interest on investing is 3205.128AUD
so total 64102.564+3205.128=67307.692AUD
reconvert to USD after I year
67307.692AUD*1.60=107692.3072
so borrowings in USD has to be repaid at 3%
100000*3%=3000interest
so total repayment is 100000+3000=103000USD
So surplus from this 107692.3072-103000=4692.3072
surplus is 4692.3072