Question

Suppose that the annual interest rate is 5.0 percent in the United States and 3.5 percent in Germany, and that the spot exchange rate is $1.12/€ and the forward exchange rate, with oneyear maturity, is $1.16/€. Assume that an arbitrager can borrow up to $1,000,000 or € 892,857.14

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

b) Using given spot rate answer what is the one-year forward rate that should prevail if rates of inflation expected to prevail for the next year in the U.S. is 2.5 percent and 4.5 percent in the euro zone.

Answer 1

(a)

For check of arbitrage possibility, We require to calculate forward rate using interest rate parity.

Forward rate = Spot rate x (1+ru) / (1 + rg)

Where:

ru = Interest rate in U.S.

rg = Interest rate in germany

Forward rate = $1.12 x (1+0.05) / (1+0.035) = $1.12 x 1.05/1.035 = $1.1362

As per interest rate parity forward rate should be $1.1362 and actual $$1.16 so arbitrage opportunity exist.

Arbitrager want to buy lower and sell higher so, Higher is actual forward rate so sell it means arbitrager received dollar in future so now require to borrow dollar and convert it into the euro and invest it for period of forward contract and convert that matured investment to dollar at rate of forward contract.

Calculation of Arbitrage profit.

Particular	Amount
In U.S.
Amount to be borrow	$               1,000,000.00
Convert to Euro
Exchange rate	$1.12 / €
Amount to be receive	€                  892,857.14
In Germany
Invest (in germany @5% for 1-year)	€                  892,857.14
Add : Interest on invest @3.5% for 1-year	€                     31,250.00
Total Matured Amount to be receive	€                  924,107.14
Now convert to dollar
Exchange rate at Forward rate agreement	$1.16 / €
Amount received after 1-Year	$               1,071,964.29
In U.S.
Full Payment on borrowing
Borrow Amount	$               1,000,000.00
Add : Interest paid on above @5% for 1-Year	$                     50,000.00
Total payment on borrowing	$               1,050,000.00
Arbitrage Profit
Amount received after 1-Year	$               1,071,964.29
Less: Payment on borrowing	$               1,050,000.00
Arbitrage Profit	$             21,964.29

Arbitrage profit is $21,964.29

(b)

Here inflation rate given so we use Purchasing Power Parity to calculate forward rate.

Forward rate = Spot Rate x (1+iu) / (1+ig)

Where:

iu = Inflation rate in U.S.

ig = Inflation rate in Germany.

Forward rate = $1.12 x (1+0.025) / (1+0.045) = $1.12 x 1.025/1.045 = $1.0986

So forward rate as per Purchasing Power Parity is $1.0986 / €.