Question 2 (a) Explain the meaning of interest rate parity. (b) Consider an open economy with...

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Question 2 (a) Explain the meaning of interest rate parity. (b) Consider an open economy with a domestic interest rate of it = 3%, a nominal exchange rate between the domestic and foreign economy of Et = 2, and where the foreign interest rate is it = 2%. In this case according to the "interest rate parity" what is the markets expectation of the future exchange rate Et+1? (c) Consider an open economy with a domestic interest rate of it = 5%,, a nominal exchange rate between the domestic and foreign economy of Et = 1, and where the foreign interest rate is it = 10%*. Calculate the expected appreciation or depreciation of the domestic currency according to the theory of "uncovered interest rate parity." (d) Suppose i = 4%, i* = 2%, and that the domestic currency is expected to depreciate by 3% during the coming year. Given this information, would you expect individuals to hold only domestic bonds or only foreign bonds? Explain. Hint: You will have to read the notes provided in Lesson 6 to do this question. Interest rate parity, Purchasing Power Parity Notes and Twin Deficits Notes Interest Rate Parity • The return on a financial asset (e.g. bond) is the interest rate on that asset plus the expected rate of appreciation over a given period. • When the rates of returns on two assets in different currencies are equal, interest rate parity prevails. Interest rate parity means equal interest rates when exchange rate changes are taken into account. Market forces achieve interest rate parity very quickly. To introduce the interest rate parity it is helpful to introduce the concept of arbitrage. What is arbitrage? • Arbitrage is the simultaneous purchase and sale of an asset to profit from price, interest rate or exchange rate differentials. • Arbitrage is a trade that profits by exploiting the price differences of identical or similar financial instruments on different markets or in different forms. • Arbitrage exists as a result of market inefficiencies and would therefore not exist if all markets were perfectly efficient. Deriving the Interest Rate Parity condition Suppose that you have 1 US dollar to invest in 1 year US bonds or Japanese bonds Let E denote the nominal exchange rate of the US dollar in terms of the Japanese Yen (in which case an increase in E means that the US dollar is appreciating and the Yen is depreciating). Let i denote the return on US bonds Let i* denote the returns on Japanese bonds Option 1: Invest in US bonds If you do you end up with (1+i) US dollars at the end of 1 year Option 2: Invest in Japanese bonds Step 1: Convert the 1 US dollar to Japanese Yen. At the exchange rate E as indicated above you get E Yen. Step 2: Use the E Yen to buy Japanese bonds which gives you E (1+i*) Yen at the end of 1 year. Step 3: Convert the E (1+i*) Yen back to US dollars using the expected future exchange rate E at the end of 1 year. If you do you end up with (E/ E°)(1+i*) dollars at the end of 1 year. To get the (E/E)(1+i*) dollars in Step 3 we note that if 1 dollar costs E Yen then 1 Yen costs (1/E) dollars. For example, if, hypothetically 1 dollar costs 2 Yen then 1 Yen would cost ½ dollar. Arbitrage suggests that the returns under Option 1 would be expected to be equal to the returns under Option 2. i.e. (1+i)= (E/E°)(1+i*) which is the interest rate parity formula. The above interest rate formula can be rewritten approximately as E = E(1+i*)/ (1+i) The above interest rate parity formulas can also be rewritten approximately as: i=i*+(E-E)/E i.e. US interest rates (i) = Japanese interest rates (i*) +expected rate of depreciation (relative to the Yen) of US dollars or, equivalently, i.e. US interest rates = Japanese interest rates +expected rate of appreciation (relative to the dollar) of Japanese Yen What the interest rate parity condition tells us: 1. If the US interest rate is higher than Japanese interest rate the US dollar is expected to depreciate against the Japanese Yen 2. If the US interest rate is lower than Japanese interest rate the US dollar is expected to appreciate against the Japanese Yen Purchasing Power Parity (PPP) • As mentioned in class, international comparisons of GDP as a measure of well-being necessitate adjusting for Purchasing Power Parity (PPP). PPP is deemed to prevail when two quantities of money can buy the same quantity of goods and services. • PPP means equal value of money. Twin deficits • Twin deficits relates to the link between trade deficits (trade balance or net exports) and the budget deficit (i.e. tax revenues minus government spending). The twin deficits formula is given by: NX = (T-G) + (S-1) • • The government sector surplus or deficit is equal to net taxes, T, minus government expenditure on goods and services G [i.e. T-G]. • The private sector surplus or deficit is saving, S, minus investment, I [i.e. S-I] Deriving the twin deficits formula: We start with the GDP formula Y=C+I+G+X-M Using the fact that disposable income YD=Y-T=C+S it means that Y=C+S+T Hence i.e. C+S+T=C+I+G+X-M S+T=I+G+X-M On reorganizing we get (X-M)=(T-G)+(S-I) NX-X-M (trade balance i.e. trade deficit/surplus) (T-G)= [public sector balance i.e. public sector deficit/surplus] (S-1)=[private sector balance i.e. private sector deficit/surplus] Thus the twin deficit formula (X-M)=(T-G)+(S-I) tells us that Trade balance (X-M) EQUALS public sector balance (T-G) PLUS private sector balance (I-S) Implications of the twin deficit formula: For the United States in 2016, Net exports were - $521 billion [this is the trade balance] Government sector balance was - $865 billion Private sector balance was $244 billion Net exports equals the sum of the government sector balance and the private sector balance. Question 2 (a) Explain the meaning of interest rate parity. (b) Consider an open economy with a domestic interest rate of it = 3%, a nominal exchange rate between the domestic and foreign economy of Et = 2, and where the foreign interest rate is it = 2%. In this case according to the "interest rate parity" what is the markets expectation of the future exchange rate Et+1? (c) Consider an open economy with a domestic interest rate of it = 5%,, a nominal exchange rate between the domestic and foreign economy of Et = 1, and where the foreign interest rate is it = 10%*. Calculate the expected appreciation or depreciation of the domestic currency according to the theory of "uncovered interest rate parity." (d) Suppose i = 4%, i* = 2%, and that the domestic currency is expected to depreciate by 3% during the coming year. Given this information, would you expect individuals to hold only domestic bonds or only foreign bonds? Explain. Hint: You will have to read the notes provided in Lesson 6 to do this question. Interest rate parity, Purchasing Power Parity Notes and Twin Deficits Notes Interest Rate Parity • The return on a financial asset (e.g. bond) is the interest rate on that asset plus the expected rate of appreciation over a given period. • When the rates of returns on two assets in different currencies are equal, interest rate parity prevails. Interest rate parity means equal interest rates when exchange rate changes are taken into account. Market forces achieve interest rate parity very quickly. To introduce the interest rate parity it is helpful to introduce the concept of arbitrage. What is arbitrage? • Arbitrage is the simultaneous purchase and sale of an asset to profit from price, interest rate or exchange rate differentials. • Arbitrage is a trade that profits by exploiting the price differences of identical or similar financial instruments on different markets or in different forms. • Arbitrage exists as a result of market inefficiencies and would therefore not exist if all markets were perfectly efficient. Deriving the Interest Rate Parity condition Suppose that you have 1 US dollar to invest in 1 year US bonds or Japanese bonds Let E denote the nominal exchange rate of the US dollar in terms of the Japanese Yen (in which case an increase in E means that the US dollar is appreciating and the Yen is depreciating). Let i denote the return on US bonds Let i* denote the returns on Japanese bonds Option 1: Invest in US bonds If you do you end up with (1+i) US dollars at the end of 1 year Option 2: Invest in Japanese bonds Step 1: Convert the 1 US dollar to Japanese Yen. At the exchange rate E as indicated above you get E Yen. Step 2: Use the E Yen to buy Japanese bonds which gives you E (1+i*) Yen at the end of 1 year. Step 3: Convert the E (1+i*) Yen back to US dollars using the expected future exchange rate E at the end of 1 year. If you do you end up with (E/ E°)(1+i*) dollars at the end of 1 year. To get the (E/E)(1+i*) dollars in Step 3 we note that if 1 dollar costs E Yen then 1 Yen costs (1/E) dollars. For example, if, hypothetically 1 dollar costs 2 Yen then 1 Yen would cost ½ dollar. Arbitrage suggests that the returns under Option 1 would be expected to be equal to the returns under Option 2. i.e. (1+i)= (E/E°)(1+i*) which is the interest rate parity formula. The above interest rate formula can be rewritten approximately as E = E(1+i*)/ (1+i) The above interest rate parity formulas can also be rewritten approximately as: i=i*+(E-E)/E i.e. US interest rates (i) = Japanese interest rates (i*) +expected rate of depreciation (relative to the Yen) of US dollars or, equivalently, i.e. US interest rates = Japanese interest rates +expected rate of appreciation (relative to the dollar) of Japanese Yen What the interest rate parity condition tells us: 1. If the US interest rate is higher than Japanese interest rate the US dollar is expected to depreciate against the Japanese Yen 2. If the US interest rate is lower than Japanese interest rate the US dollar is expected to appreciate against the Japanese Yen Purchasing Power Parity (PPP) • As mentioned in class, international comparisons of GDP as a measure of well-being necessitate adjusting for Purchasing Power Parity (PPP). PPP is deemed to prevail when two quantities of money can buy the same quantity of goods and services. • PPP means equal value of money. Twin deficits • Twin deficits relates to the link between trade deficits (trade balance or net exports) and the budget deficit (i.e. tax revenues minus government spending). The twin deficits formula is given by: NX = (T-G) + (S-1) • • The government sector surplus or deficit is equal to net taxes, T, minus government expenditure on goods and services G [i.e. T-G]. • The private sector surplus or deficit is saving, S, minus investment, I [i.e. S-I] Deriving the twin deficits formula: We start with the GDP formula Y=C+I+G+X-M Using the fact that disposable income YD=Y-T=C+S it means that Y=C+S+T Hence i.e. C+S+T=C+I+G+X-M S+T=I+G+X-M On reorganizing we get (X-M)=(T-G)+(S-I) NX-X-M (trade balance i.e. trade deficit/surplus) (T-G)= [public sector balance i.e. public sector deficit/surplus] (S-1)=[private sector balance i.e. private sector deficit/surplus] Thus the twin deficit formula (X-M)=(T-G)+(S-I) tells us that Trade balance (X-M) EQUALS public sector balance (T-G) PLUS private sector balance (I-S) Implications of the twin deficit formula: For the United States in 2016, Net exports were - $521 billion [this is the trade balance] Government sector balance was - $865 billion Private sector balance was $244 billion Net exports equals the sum of the government sector balance and the private sector balance.

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a Interest rate parity states that the rates of return on comparable assets in two different countri... View the full answer