Question

In: Economics

You notice that the interest rate in euros is 5% and the U.S. interest rate is...

You notice that the interest rate in euros is 5% and the U.S. interest rate is 15%. The current exchange rate is 1.1 $ / €. The forward rate (one year) is 1.25 $ / €. Suppose you had $1,000.

How could you make money with covered interest arbitrage? Circle dollars or pounds, put numbers in blanks.

Borrow 1,000 (dollars or euros) at _______%

Turn the 1,000 (euros or dollars) into _________________ (dollars or euros).

Earn interest of ______% to have ________________ (dollars or euros) after a year.

Use the forward rate to turn proceeds into ___________________ (dollars or euros)

Pay back loan and earn _______________ (dollars or euros)

Expert Solution

Interest rate in euros = 5%

Interest rate in the US = 15%

Scenario 1: Borrow in euros and invest in dollars

Exchange rate is 1 euro = $1.1

Therefore, 1,000 euros = $1.1 * $1,000 = $1,100

Invest $11,00 in the US at an interest rate of 15%

Amount of dollars received after 1 year = (1+15%)*$1,100 = 1.15 * $1,100 = $1,265

Forward exchange rate is 1 euro = $1.25 => $1 = 1/1.25 euro

Converting $1,265 into euros: $1,265 * 1/1.25 euro/$ = 1,012 euros

Euro repayment = (1+5%) * 1,000 euros = 1.05 * 1,000 euros = 1,050 euros

The euro repayment value is higher than the interest received in the US $. Therefore, there is no arbitrage opportunity in this scenario

Scenario 2: Borrow in US $ and invest in euros

Exchange rate is 1 euro = $1.1

Therefore, $1,000 = $1,000 * 1 euro/$1.1 = 909.09 euros

Amount of euros received after 1 year = (1+5%) * 909.09 = 1.05 * 909.09 euros = 954.54 euros

Forward exchange rate is 1 euro = $1.25

Converting 954.54 euros into US $: 954.54 * $1.25/euro = $1,193.18

Dollar repayment = (1+15%) * $1,000 = 1.15 * $1,000 = $1,150

Dollar amount earned through arbitrage = $1,193.18 - $1,150 = $43.18

1. Borrow 1,000 dollars at 15%

2. Turn the 1,000 dollars into 909.09 euros

3. Earn interest of 5% to have 954.54 euros after a year

4. Use the forward rate to turn proceeds into $1,193.18 dollars

5. Pay back loan and earn 43.18 dollars

Rahul Sunny answered 2 years ago

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