Question

An Italian currency dealer has good credit and can borrow €800,000 or $1,000,000 for one year. The one-year interest rate in the U.S. is i$ = 2% and in the euro zone the one-year interest rate is i€ = 5.5%. The spot exchange rate is $1.25 = €1.00 and the one-year forward exchange rate is $1.20 = €1.00

a) Show how to realize a certain profit via covered interest arbitrage.

b) Using given one-year forward rate answer what is the spot rate that should prevail if rates of inflation expected to prevail for the next year in the U.S. is 3 percent and 5 percent in the euro zone.

Answer 1

A) we can compute the justified $ interest rate to check whether there is any arbitrage opertunity available.

formula is.

justified forward rate = spot rate*(1+t*i$) / (1+t*i€)

where t=period= 1year

i€ = 5.5%

spot rate = $1.25/ €

i$ = ?

  

1.20 =$1.25 * (1+1*i$) / (1+1*0.055)

1.20 =1.25*(1+i$) /1.055

1.266 = 1.25*(1+i$)

i$ = 1.28%

since the justified $ interest rate(1.28%) is differ from the given rate there exist an arbitrage opertunity.we can borrow € at 5.5% and invest in $ at 2%.

step 1

outflow from borrowing € = 800,000*1.055 = € 8,44,000

step 2

$ inflow from selling € 800,000 at spot rate = 800,000*1.25 = $10,00,000

step 3

inflow from investing $ 10,00,000 at 2% = $10,20,000

step 4

buying the € at forward $1.20 = $10,20,000/1.20 = € 8,50,000

arbitrage profit = inflow-outflow = € 8,50,000 - € 8,44,000 = € 6000

B)  we can find the spot rate using the following formula

F / S = (1+rA / (1+rB)

Where = f = forward rate

s = spot rate

  rA= inflaton of $ = 0.03

  rB= inflationof € =0.05

1.20/S - (1+0.03/ (1+0.05)

spot rate = $1.177