# Note that the current and capital accounts in the U.S. Balance of payments (BOP)

November 24, 2016

Misty Wheeler

Economics

Chapter 6 Assignment

1. Note that the current and capital accounts in the U.S. Balance of payments (BOP) are mostly private transactions while the official settlements balance involves transactions between governments. If trade with China causes more imports than exports in the balance of merchandise trade account and the current account. Then there must be more debits than credits in these two subsets of BOB accounts. Because we didn’t pay for our imports with sufficient exports, foreigners must loan us money to finance our over consumption. If the purchases of U.S. stocks and bonds by private sector foreigners results in a net capital inflow in the capital account that is less than our current account deficit, then what can the Chinese government do to make up for the difference in the official settlements balance?

2. Assume that the U.S. dollar and the Japanese yen are the only two currencies in the world.

2a A bilateral nominal exchange rate S is the spot (now) exchange value of one currency in terms of the other and S can be written as dollars per 1 yen or yen per 1 dollar. If S = yen/1 dollar = 76.92 then the inverse 1/S gives dollars per 1 yen where 1/S = 1/(yen/1 dollar) = 1/76.92 = .013. If the 1/S increases to .014, has the dollar appreciated (1 dollar is worth more yen) or depreciated (1 dollar is worth less yen)? Explain.

2b. Changes in demand and supply in the foreign exchange (FX) market determine the value of floating exchange rates S. If S is expresses as S = yen/1 dollar, then we have the FX market in terms of the demand and supply of dollars. (If S = dollars/1 yen, then we get the FX market in terms of the demand and supply of yen. Note also that no matter which currency the FX market is expressed, it is still a FX market where dollars are exchanged for yen. This means that an upward sloping supply of dollars curve is exactly the same as a demand for yen curve and a downward sloping demand for dollars curve is exactly the same as a supply of yen curve). Using S = yen/1 dollar and the FX market in terms of the demand and supply of dollars, an increase in S (dollar appreciation) leads to an increase in the quantity of dollars supplied (increase in the quantity of yen demanded). For dollar demand (or the supply of yen), and increase in S (dollar appreciation) leads to a decrease in the quantity of dollars demanded (or an increase in the quantity of yen supplied). The dollar demand curve shifts to the right if more yen are offered for dollars at any exchange rate S. An increase in dollar demand is caused mostly by private sector transactions in the current and capital accounts. Either an increase in demand for U.S. goods (merchandise trade in the current account) or an increase in demand for U.S. stocks and bonds (capital account inflows) will shift the dollar demand curve to the right. If private transactions in the current and capital accounts also cause shifts in the dollar supply curve, what are the corresponding factors that would lead to an increase in dollars supplied (yen demanded) at any exchange rate S?

3. Because it acts like a price, U.S. export demand is inversely related to the U.S. real exchange rate. U.S. import demand is inversely related to the real exchange rate of foreign trading partners, which would just be the inverse of the U. S. real exchange rate for those two countries. A nominal variable like nominal GDP is converted to real GDP by dividing by the CPI (average price level (P) in the U.S.). Nominal bilateral exchange rates are converted to real exchange rates in the same way. Because one currency can be expressed in terms of another, dividing by the price level that corresponds to that currency involves cross-multiplication by the inverse of the price levels between the two trading countries. For example, if S = yen/1 dollar, then S x (the U.S. price level / price level in Japan) = the real exchange rate of yen per dollar.

3a. What is the real exchange rate equation for S = dollars per yen?

3b. If the percentage change is computed as the (change in a value/original value) x 100 = [(value now – value previous)/(value previous) x100] and the real exchange rate between the yen and the dollar is 105 today, but was only 100 last month, what is the percentage change in the real exchange rate?

4. A forward premium for a given currency (say the nominal bilateral exchange rate value of the dollar where S = 80 yen/1 dollar = 80) occurs when the value of the currency as given by the forward spot rate appreciates such as S = 85 yen/1 dollar = 85. If a currency such as the dollar has a lower forward spot rate where S = 75, it depreciates and is at a forward discount. If Fn = 85 is the forward spot rate for yen/1 dollar n months from now and S = 80 is the current spot rate of yen/1 dollar, then the dollar is at a forward premium while the yen is at a forward discount. The percentage change is the same formula but it can be converted to an annualized percentage change by using the formula (Fn – S)/S x (12/n) x 100. If Fn = 81 yen/dollar = 81, S = 79, and n = 3 months, what is the annualized percentage forward premium for the dollar? The annualized percentage forward discount for the yen?

5. Cross-rates allow you to calculate a third exchange rate from two that are known and that have a common currency. The method requires that you set up the cross-rate multiplication so that the common currency is canceled out. For example, if a U.S. dollar is worth 80 yen or 1.4 Canadian dollars, then how many yen is 1 Canadian dollar worth? This can be determined by setting up a cross-multiplication that cancels out the common currency, in this case the U.S. dollar. You can’t just go (80 yen/1 dollar) x (1.4 Canadian dollars/1 dollar) because the dollar doesn’t cancel. Thus you must invert one side or the other such as obtaining .013 dollars/1 yen. Now you can just do (.013 dollars/yen) x (1.4 Canadian dollars/1 dollar) = .013 x 1.4 and you will have the number of Canadian dollars per yen. If you want it as yen per Canadian dollars, just invert it. If the Danish Crone is 7.5 Kr/dollar and the British pound is worth \$1.58, then what is the exchange rate in Kr per British pound?

6. Forward premiums and discounts imply that there is risk in foreign exchange transactions.

6a. Explain the three types of FX risk?

6b. How can foreign exchange rate risk be fully covered or hedged?

6c. Foreign exchange risk also allows for speculation through financial instruments known as foreign exchange derivatives. What are three common types of foreign exchange derivatives and how do they work?

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