Question

which is an important relationship determining the movement of exchange rates. Let "today" be periodi and "next year" be period 7+ 1. Also assume that the interest rate of U.S. bond is given by US = 0.1, the interest rate of EU bond is U = 0.3, and today and next year's exchange rates are E = 1 (S/€) and E41 = 0.5 ($/€). Please answer the following questions. (a) Suppose you purchase $100 U.S. bonds today. What is your revenue from the bond (=principal + interest payment) next year? (b) In order to know the "dollar-denominated revenue" from the EU bond, follow the procedure below: i. First, using today's exchange rate E = 1 ($/€), compute the euro-value of $100. ii. Next compute the revenue from the EU bond if you invest all the euros you computed in i. iii. Finally, using the next year's exchange rate E+1 = 0.5 (S/€), compute the dollar-value of the revenue from the EU bond computed in ii, which is the "dollar-denominated revenue" from investing on the EU bond. iv. Comparing the revenues from the two bonds, which is the better asset to invest on? Do these two bonds satisfy no-arbitrage condition? (c) Now let us = 0.3 and Er+1=1 ($/€) (other parameters are unchanged). Com- pute the dollar-values of the revenues from U.S. and EU bonds, and show that no- arbitrage condition is satisfied. Remark 1. This no-arbitrage condition dollar-revenue from U.S. bond dollar-revenue from EU bond is called the interest parity condition for dollar and euro.

Answer 1

US Bond Value	$100
US Interest rate	10%
a. Revenue from US Bond in year 1	$110

b. Current Exchange rate ($/Euro)	1
i. Euro Bond Value	€ 100
Euro Interest Rate	30%
ii. Revenue from Euro Bond in year 1	€ 130
Exchange rate after 1 year ($/Euro)	0.5
iii. Dollar value of revenue from Euro Bond in year 1	$65

There is opportunity for arbitrage as person can borrow Euros and convert it into dollars at the beginning and invest it for a year and convert it back to Euro to get 220 Euros instead of getting 130 Euros if he had directly invested in the European bonds.

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c. US Bond Value	$100
US Interest rate	30%
Revenue from US Bond in year 1	$130
Current Exchange rate ($/Euro)	1
i. Euro Bond Value	€ 100
Euro Interest Rate	30%
ii. Revenue from Euro Bond in year 1	€ 130
Exchange rate after 1 year ($/Euro)	1
iii. Dollar value of revenue from Euro Bond in year 1	$130

There is no opportunity for arbitrage as the revenue in $ from both European and American bonds are the same. This is because the interest rates are the same for both the bonds and the exchange rate has remained during the period of investment.