In: Finance
David Jensen is a foreign exchange trader with Citibank who has access to $2,000,000 US or the UK pound (GBP) equivalent. He notices the following US dollar (USD) and UK pound (GBP) foreign exchange and interest rate quotes:
Spot exchange rate | USD 1.2490 /GBP |
Six months forward exchange rate | USD 1.2535 /GBP |
Expected spot exchange rate in six months | USD 1.2610 /GBP |
Six months $ interest rate | 2.2% per year |
Six months GBP interest rate | 1.4% per year |
Required:
Current spot exchange rate: USD1.2490/GBP
Six month $ interest=(2.2/2)=1.1%=0.011
Six month GBP interest=(1.4/2)=0.7%=0.007
Future Value of USD 1.2490=1.2490*(1+0.011)=$1.262739
Future Value of 1GBP=1*(1+0.007)=1.007 GBP
As per interest rate parity,
Forward rate:
$1.262739/1.007GBP
$(1.262739/1.007)/GBP
$1.2540/GBP
Arbitrage will be possible if the forward exchange rate is different from $1.2540/GBP
Uncovered interest rate arbitrage:
Borrow in USA and invest in GBP
Borrow 2 million in USA at 2.2% interest
Convert the USD to ($2million/1.2490)= 1.601281 million GBP,at current spot rate
Invest 1.601281millionGBP at 1.4% interest
Future Value at end of 6 months=1.601281million*(1+0.007)=1.61249 million GBP
Expected exchange rate after 6 months:USD1.2610/GBP
Conversion of GBP after 6 months will amount to (1.61249*1.2610)million USD=2.0335Million USD
Amount to be paid back with interest =2*(1+0.011) million USD=2.022 million USD
PROFIT=(2.0335-2.022)Million USD=0.01135 million USD=$11,349.88
covered interest arbitrage strategy :
Under this strategy , The future rate risk is covered by entering into a forward contract .