Question

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.

Answer 1

Ans:

As per the covered interest rate parity theorem, the following formula must hold true, otherise there would be an arbitrage oppurtunity,

(1+i) = (S/F) × (1+if)

Here,

i _d = interest rate in the domestic currency

i_f =  interest rate in the foreign currency

S = Current spot foreign exchange rate

F = Forward foreign exchange rate

so (1+0.06) = (1.25/1.20) × (1+.02)

1.06 = 1.04166667 x 1.02

1.06 = 1.0625

So, here an arbitrage oppertunity is present.

That means a currency that offers lower interest rates tends to trade at a forward foreign exchange rate premium in relation to another currency is offering higher rates.

Calculation:

Particulars Amt.

Amt. Borrow in Euro   =  800000

Interest earned in Euro = (800000*6/100)= 48000

Total amtount repaid after one year in Euro=(800000+48000) = 848000

convert in $ at spot rate = (800000 × 1.25)= 1000000

Interest 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