Question

1. Suppose that S = $1.1045/€ and F=$1.1459/€ (one year). The annualized risk-free interest rates are 2.6% and 1.75% in the U.S and Germany, respectively. If feasible, find the profit earned by a U.S. investor conducting a covered interest arbitrage. Suppose that the U.S. investor is able to borrow $500,000. Do not write any symbol. Make sure to round your answers to the nearest 100th decimal points. For example, write 234.45 for $234.45.

2. Suppose that S = $1.1045/€. The annualized inflation rates are 2.6% and 1.75% in the U.S and Germany, respectively. Find the exact expected currency movement for the euro in 5 years. Do not write any symbol. Express your answers as a percentage. Make sure to round your answers to the nearest 100th decimal points. For example, write 2.45 for 2.45%.

3. Suppose that S = ¥180/$. The annualized risk-free rates are 4.6% and 2.75% in Japan and the U.S., respectively. Find the expected currency movement over the next 3 years. Do not write any symbol. Express your answers as a percentage. Make sure to round your answers to the nearest 100th decimal points.

4. Suppose that S = ¥180/$. The annualized risk-free rates are 4.6% and 2.75% in Japan and the U.S., respectively. The annualized inflation rate is 2% in Japan. Find the exact real interest rate in Japan and the U.S. according to the international Fisher relation. Do not write any symbol. Express your answers as a percentage. Make sure to round your answers to the nearest 100th decimal points.

Answer 1

1. Theoretical Forward rate as per Interest rate parity

F = Spot rate * (1+ interest rate in Dollars)/(1+interest rate in Euros)

=1.1045*1.026/1.0175

= $1.1137/Euro

As the theoretical forward rate is different than the actual rate, Arbitrage is possible as follows

a) Today, Borrow $500000 for one year at 2.6% from US

b) Today, Convert the amount to Euro at the spot rate to get 500000/1.1045 =Euro 452693.53

c) Today, Invest the Euro amount at 1.75% for one year in Germany. maturity amount = 452693.53*1.0175 =Euro 460615.66

d) Today, Sell Euro 460615.66 in forward contract at $1.1459/Euro

e) After one year, Get the Euro maturity amount and sell it using forward contract to get

$460615.66 *1.1459 = $527819.49

Pay the maturity amount of $ borrowing = $500000*1.026 =$513000

and take the remaining amount =$527819.49-$513000 =$14819.49 as arbitrage profit

Profit earned is $14819.49 at the end of the year