Question

1. Althea the arbitrageur wants to make a riskless profit by attempting covered interest arbitrage. She has $1,000,000 and sees the following spot and forward rate quotes offered: Spot = $1.40/Euro Forward180 day = $1.42/Euro Alana can earn 5% interest per annum on a 1-year US government bond and 3% interest per annum on the equivalent French bond. Assuming Alana can sell either bond after six months for the same price she paid, excluding trading costs does Alana have an arbitrage opportunity and if so, approximately how much profit can she make I NEED STEP BY STEP!!! I am VERY confused!

Answer 1

Given interest rates are per annum we have to convert them to half year (i.e., 180days)

so US interest rate = 5 / 2 = 2.5%

Euro interest rate = 3 / 2 = 1.5%

As per interest rate parity theory forward rate should be = spotrate*[(1 + IR1) / (1 + IR2)

where IR1 = US rate

IR2 = Euro rate

so forward rate should be = 1.40*[(1 + 2.5%) / (1 +1.5%) ]

= 1.41379

but actual forward rate given ONE EURO = $1.42

so arbitrage exists.

calculation of profit.

Step - 1:

convert $1,000,000 to euros using spot rate of 1.40

number of euros she gets = 1000000 / 1.40 = 714,285.71 Euros

Step - 2:

invest in Euro bonds and Earn 1.5%

amount after 180 - days = 714285.71*(1+1.5%) = 725,000 Euros

Step - 3:

convert them to dollars using forward rate of 1.42

amount of dollars = 725000 *1.42 = $1,029,500

Profit = 1029500 - 1000000 = $29,500

(Note: above amount of 29500 is normal profit.to calculate arbitrage profit it should be assumed that instead of all above procedure if she invests simply in US bonds she gets 2.5%. so amount after 180 days = 1000000*(1+2.5%) = 1,025,000.net profit would be = 1029500 - 1025000 = $4500)