Question

# Given: US interest rate 5% German interest rate 3.5% One-year forward rate is \$1.16/Euro Spot rate...

Given:
US interest rate 5%
German interest rate 3.5%
One-year forward rate is \$1.16/Euro
Spot rate \$1.12/Euro

Arbitrager can borrow up to \$1,000,000 or Euro 892,857. Doing a Covered Interest Arbitrage (CIA) how much will the arbitrager make:

Hint: Start by borrowing \$1,000,000 and converting this to Euro, then convert back Euro to USD after one year.

As per IRPT forward rate = spot rate*[(1+IRH) / (1+IRF)]

where IRH = interest rate of home currency

IRF = interest rate of foreign currency

Forward rate should be = 1.12*[(1.05/1.035)] = 1.13

how ever given forward rate = \$1.16, so arbitrage possible

Step - 1:

borrow \$1,000,000 at 5%

Step - 2:

convert this to Euros using spot rate

Euros = 1,000,000 / 1.12 = 892,857.14

Step -3:

Deposit above amount in Germany and earn interest rate of 3.5%

amount after one year = 892,857.14*(1+3.5%) = 924,107.14 euros

Step - 4:

convert this to dollars using forward rate

amount in dollars = 924,107.14*1.16 = 1,071,964.29

use above amount to repay loan

Step - 5:

after one year repaying amount of loan = 1,000,000*(1+5%) = 1050000

Profit = 1071964.29 - 1050000 = \$21,964.29

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