Question

1. Suppose that the annual interest rate is 3 percent in the United States and 4 percent in Germany, and that the S(EUR/USD) = $1.60 and the forward exchange rate, with one-year maturity, is F₁₂(EUR/USD ) = $1.57. Assume that an arbitrager can borrow up to $10,000,000 or €6,250,000. If an astute trader finds an arbitrage opportunity, what is the net cash flow in one year? (Show each step and the values)

Answer 1

As per interest parity

Forward rate

=

Spotrate*(1+domestic int rate)/(1+foreign interestrate)

Domestic int rate

=

3% or 0.03

Forgien int rate

=

4% or 0.04

Spot rate

=

$1.6/euro

Forward rate

=

1.6*(1+0.03)/(1+0.04)

=

1.6(1.03/1.04)

=

1.6*0.9904

=

$1.5846/Euro

Actual forward rate

=

$1.57/euro

Since actual forward rate ($1.57) is lower than theoritical forwardrate ($1.5846),there is arbitrage opputunity

here are the steps

Step1-Borrow Euro 6,250,000 @ 4% for one year.Amount to be repaid after 1 year = Euro 6,250,000*1.04= Euro 6,500,000

step2-Purchase for Forward contract to purchase Euro 6,500,000 @ $1.57/euro

Step 3-Convert the Euro 6,250,000 into dollars @ spot rate of 41.6 per Euro getting 1.6*6,250,000=$10,000,000

Step4-Invest $10,000,000 @3% in US getting 10,000,000*1.03=$10,300,000 at year end

Step5- Convert $10,205,000 (1.57*6,500,000) into Euro at forwardrate in step 1

Step6-Repay the amount calculated in step1 from the amount convetred in step 5

Net cashflow in dollars

=

Amount recived -amount paid

=

$10,300,000-$10,205,000

Net cashflow in dollars

=

$ 95,000.00

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