A currency dealer has good credit and can borrow either $1,000,000 or €800,000 for one year. The one-year interest rate in the U. S. is i$ = 2% and in the euro zone the one-year interest rate is i€ = 6%. The spot exchange rate is $1.25 = €1.00 and the one-year forward exchange rate is $1.20 = €1.00. Show how to realize a certain profit via covered interest arbitrage.

Under the covered interest rate parity theoram, the following formula must hold true, otherise there would be an arbitrage oppurtunity (1+id) = (S/F) * (1+if)

where id - interest rate in the domestic currency

if - interest rate in the foreign currency

S - Current spot foreign exchange rate

F - Forward foreign exchange rate

so (1+.06) = (1.25/1.20)*(1+.02)

1.06 = 1.0625

that measn there is present an arbitrage position.

so a currency that offers lower interest rates tends to trade at a forward foeign exchange rate premium in relation to another currency offering higher rates.

in short which has higher int. rate borrow in that currency.

now as given

Particulars                                                                       Amt.

Amt. Borrow in Euro                                                             800000

Int. earned in Euro (800000*6/100)                                      48000

Total amt. repaid after one year in Euro (800000+48000)     848000

convert in $ at spot rate (800000*1.25)                             1000000

Int earned in $ (1000000*2/100)                                        20000

after one year total $ (1000000 + 20000)                    1020000

convert in Euro at forward rate (1020000/1.20)             850000

Arbitrage Gain in $ (850000 - 848000)                                2000

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