1. (No-Arbitrage Condition and Interest Parity Condition) Using the concept of no-arbitrage, we can compute a condition that a foreign exchange rate has to satisfy in the short run. Exchange rate is a ratio of the values of two currencies such as dollar and euro. Denote by E the exchange rate of euro in terms of dollar, that is, a dollar value of 1 euro. For example, if E = 1.1 ($/e), then $220 = e ( 220 E ) = e ( 220 1.1 ) = e200, or e100 = $(100×E) = $(100×1.1) = $110 that is, if you want to convert dollar-values to euro-values, you could divide the dollarvalue by the exchange rate, and if you want to convert euro-values to dollar-values, you could multiply the euro-values with the exchange rate. No-arbitrage condition between domestic bond and foreign bond gives a condition called “interest parity condition,” which is an important relationship determining the movement of exchange rates. Let “today” be period t and “next year” be period t + 1. Also assume that the interest rate of U.S. bond is given by i US = 0.1, the interest rate of EU bond is i EU = 0.3, and today and next year’s exchange rates are Et = 1 ($/e) and Et+1 = 0.5 ($/e). Please answer the following questions. (a) Suppose you purchase $100 U.S. bonds today. What is your revenue from the bond (=principal + interest payment) next year? 1 (b) In order to know the “dollar-denominated revenue” from the EU bond, follow the procedure below: i. First, using today’s exchange rate Et = 1 ($/e), compute the euro-value of $100. ii. Next compute the revenue from the EU bond if you invest all the euros you computed in i. iii. Finally, using the next year’s exchange rate Et+1 = 0.5 ($/e), 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 i US = 0.3 and Et+1 = 1 ($/e) (other parameters are unchanged). Compute the dollar-values of the revenues from U.S. and EU bonds, and show that noarbitrage 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
a) Revenue from the bond = $100 +.1*$100 = $110
b) Euro value of $100 = 1*100e = 100e
Revenue from bond (in Euro) = 100e +.3*100e = 130e
Converting Euro revenue into $ = 130e*$.5 = $65
No, these bonds don't satisfy no-arbitrage condition. Comparing (a) and (b), investment in $ denomination is more rewarding by $45 ($110-$65).
c) Revenue from the bond = $100 +.3*$100 = $130
Euro value of $100 = 1*100e = 100e
Revenue from bond (in Euro) = 100e +.3*100e = 130e
Converting Euro revenue into $ = 130e*$1 = $130
In this case, no-arbitrage condition is satisfied.
1. (No-Arbitrage Condition and Interest Parity Condition) Using the concept of no-arbitrage, we can compute a condition...
which is an important relationship determining the movement of exchange rates. Let "today" be periodi and "next year" be period 7+ 1. Also assume that the interest rate of U.S. bond is given by US = 0.1, the interest rate of EU bond is U = 0.3, and today and next year's exchange rates are E = 1 (S/€) and E41 = 0.5 ($/€). Please answer the following questions. (a) Suppose you purchase $100 U.S. bonds today. What is your...
Question 23 (0.8 points) According to the interest parity condition, if the U.S. interest rate is 2 percent and the Japanese interest rate is 4%, and the current exchange rate is 100 yens per dollar. Then the market expects the future exchange rate to be yens per dollar Question 24 (0.8 points) If the exchange rate at time tis E = €1/$. You invest $1 in an euro asset at t, which has an interest of 8%. If Et+1 =...
II. Consider two bonds, one issued in euros () in Germany, and one issued in dollars (S) in the United States. Assume that both government securities are one-year bonds-paying the face value of the bond one year from now. The exchange rate, E, stands at 0.75 euros per dollar. The face values and prices on the two bonds are given by Face Value $10,000 10,000 Pric S9,615.38 9,433.96 United States Germany a. Compute the nominal interest rate on each of...
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Please show work and choose A, B, C, or D. The 12-month interest rate on dollar-denominated assets (like bank deposits) is 2.00%. The 12- month interest rate on euro-denominated assets is 4.50%. The current spot exchange rate is $1.15 per euro. The current forward exchange rate is $1.05 per euro. You have an initial dollar fund of $100,000. Suppose that you decide to invest your dollar fund in euro-denominated assets while also using the forward exchange market to hedge against...
Consider two bonds, one issued in euros () in Germany, and one issued in dollars (S) in the United States. Assume that both government securities are one-year bonds-paying the face value of the bond one year from now The face values and prices on the two bonds are given by Face Value $10,000 10,000 Price $9,615.38 €3,345 79 United States Germany Compute the nominal interest rate on each of the bonds. bond-||% Nominal interest rate on the US (Enter your...
9) Suppose today that US nominal interest rate = 1% and German nominal interest rate = 6% and the current nominal exchange rate is E = €0.50/$. a. Use the uncovered interest party equation to compute the expected rate of appreciation of the US$ relative to the Euro. (Approximate form of the equation is fine.) b. Given your answer to a, what the expected future exchange rate? c. If you expect the US$ to depreciate relative to the Euro which...
Suppose you are a currency speculator trying to forecast what will happen to the value of the dollar over the next year. Suppose all of our usual theories hold (uncovered, covered and real interest rate parities, absolute and relative purchasing power parities, as well as the Fisher effect for nominal interest rates). For each of the separate cases below, use the information in that case to compute the expected depreciation of the dollar , or state if there is not...
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