Practice Problems on Exchange Rates 1- Define nominal exchange rate and real exchange rate. How are changes in the real exchange rate and the nominal exchange rate related?

The nominal exchange rate is the rate at which two currencies can be exchanged for each other in the market. The real exchange rate is the price of domestic goods relative to foreign goods. Changes in the real exchange rate are related to changes in the nominal exchange rate depending on changes in the price levels of two countries:

∆e/e = ∆enom / enom + ∆P/P - ∆PFor / PFor

.

2- What are the two main types of exchange rate systems? Currently, which type of system determines the values of the major currencies, such as the dollar, yen, and mark?

The two major types of exchange-rate systems are fixed exchange rates and flexible exchange rates. In a fixed-exchange-rate system, exchange rates are set at officially determined levels. In a flexible-exchange-rate system, exchange rate are determined by conditions of demand and supply in the foreign exchange market.

Currently, the major currencies of the world are on a flexible-exchange-rate system.

3- Define purchasing power parity, or PPP. Does PPP work well empirically? Explain.

Purchasing power parity, PPP, is the idea that similar foreign and domestic goods, or baskets of goods, should have the same price when priced in terms of the same currency. Purchasing power parity does seem to explain exchange rates in the long run, but over shorter periods it doesn’t work well because countries produce very different sets of goods, because some goods aren’t traded internationally, and because there are transportation costs and legal barriers.

4- What is the fundamental value of a currency? What does saying that a currency is overvalued mean? Why is an overvalued currency a problem? What can a country do about an overvalued currency?

The fundamental value of a currency is the value of the exchange rate that would be determined by free-market forces of demand and supply without government intervention. When the official exchange rate is higher than its fundamental value, it is said to be overvalued. This is a problem, because to maintain the official exchange rate, the central bank will have to buy the currency with official reserve assets. To prevent having an overvalued currency, the country can change the official exchange rate, restrict international transactions, or use contractionary monetary policy.

5- Discuss the relative advantages and disadvantages of flexible exchange rates, fixed exchange rates, and a currency union.

Flexible exchange rates have the advantage of allowing a country to use expansionary monetary policy to combat recessions, but currency values fluctuate substantially, introducing uncertainty into international transactions. Fixed exchange rates avoid this problem, but a country may have to give up the independent use of monetary policy. This latter factor is a disadvantage when it comes to combating recessions, but might be an advantage in helping keep inflation low. As long as countries can coordinate on overall monetary policy, the fixed exchange rate system can be maintained. A currency union is very similar to a system of fixed exchange rates, but has further advantages. Costs of trading goods and assets across countries are even lower than under fixed exchange rates and speculative attacks on the currency cannot occur. But a currency union requires an even greater coordination of political and financial institutions than a fixed exchange rate system does.

6- Insurance against exchange rate risk On January 1, 2000 Xerox Corporation signs a contract with Japanese government to supply office machinery. The contract stipulates that Xerox will receive 500,000 Yen on January 1, 2001. Xerox wishes to insure itself against exchange rate risk. The yield on a one year US Treasury bill on January 1, 2000 is 5.73% and the yield on a one year Japanese Treasury bond is 1.17%. The spot exchange rate on the same date is 110 Yen per US dollar.

a. Suppose that Xerox uses the forward market to insure itself against exchange rate risk. Compute the amount of dollars that Xerox will receive for sure.

Using Covered Interest rate parity, the implied forward exchange rate is

F = [(1+0.0117)/(1+0.0573)]* 110 = 105.26,

(Yen per dollar) hence the amount of dollars that Xerox will receive is $500,000/105.26 = 4750.14.

b. Suppose that there were no forward markets and that Xerox does not want any exposure to exchange rate risk. The company can still eliminate all exchange rate risk by borrowing in Yen and investing in US Treasury bonds.

b1. Compute the magnitude of Yen borrowing that Xerox will have to conduct to insure against exchange rate risk.

Xerox will borrow in yen the amount

500,000/(1+0.0117)=494217.65,

that is the present value of 500,000 yen. Then invest this amount, in dollars, in U.S. t-bills. The amount of USD invested is 500,000/((1+0.0117)*110), and the amount of dollars received at the end of the year is [500,000/((1+0.0117)*110)]*(1+0.0573).

b2. Compute the amount of dollars that Xerox will receive.

As shown above the amount of dollars Xerox will receive is

[500,000/((1+0.0117)*110)]*(1+0.0573)=$4750.33

7- Mexican Tequila crises Attached are graphs that show Mexican inflation and interest rates (CETES rate), the Peso/Dollar exchange rate, and the change in foreign reserves of the Mexican central bank. Answer the following questions (assume the real interest rate in Mexico is constant):

a. Relate the rise in the CETES interest rate to the Mexican government budget constraint and its ability to finance its expenditures.

The Government budget constraint was defined earlier. The rise in the CETES interest rate, given fixed real interest rates, is consistent with a rise in expected inflation. The expected inflation in Mexico went up sharply because the market believed that the Government will be able to meet its future expenditures only by monetization of its debt, i.e. by new money creation. This raises the expected inflation in Mexico and raises the nominal interest rates.

b. Provide an explanation relating the high CETES interest rate in Mexico to the movement of Mexico's foreign exchange reserves and the sharp devaluation of the peso vis-a-vis the dollar since December of 1994.

As discussed the high CETES interest rate was an outcome of high inflationary expectations. We also know that higher the expected inflation less is the demand for the Mexican Peso as the expected rate of return on the peso is i-pie, hence the return on the peso fell. This means that people want to sell the peso and instead buy dollars. The Mexican central bank can only sustain the fixed exchange rate of the peso to the dollar by draining their foreign exchange reserves, (i.e keep loosing Dollars and keep acquiring pesos), once it looses all its Dollar foreign exchange reserves it has to let the peso devalue as desired by the market forces.

8- Why might changes in Brazil affect the financial Markets in the U.S., as the article suggests, both the Dow and the Nasdaq share price indices reacted negatively to the decline in Brazil.

Recall that MPK(i) = r + rp(i). Apart of this risk-premia is due to movements that are common across all markets (for example the world CAPM will imply that rp(i) = beta(i) * lambda(t), where beta(i) is unique to Brazil and lambda(t) is common across all world markets). If investors in the U.S. learn (i.e., infer) that a drop in Brazil's markets is due to potentially a larger world wide risk-premia, then they demand a higher risk-premia in all markets. Therefore, all financial markets, including the ones in the U.S., will face higher discount rates, and all markets will consequently drop.

9- Below is information on short-term interest rates in the U.S., Germany, and Japan from 1993 to 1995. Also shown are the Mark/Dollar and Yen/Dollar exchange rates during this time period. Given the movement in short-term interest rates in these economies, provide an explanation for the movement of the two exchange rates.

We see the dollar depreciate against the mark and the Yen. At the same time we see U.S nominal interest rates increase vis-a-vis the German and Japanese short term nominal interest rates.

We know that nominal interest rates i, i= r + pie, where r is the real interest rates and pie is the expected inflation. We also know that if real interest rates increase the U.S the dollar will appreciate and if expected inflation increases the dollar will depreciate. Hence, the depreciation of the dollar and the rise in the U.S nominal interest rates is consistent with the inference that expected inflation in the U.S went up vis-a-vis Germany and Japan. This rise in expected inflation will raise U.S nominal interest rates and cause the dollar to depreciate.

10- Stock markets and exchange rates Given below are the behavior of the exchange rate for some East-Asian economies and the behavior of their stock market. Note that their currencies (quoted as local currency per U.S. dollar) and stock market fell in value over the last year. (See circled numbers).

a. Explain the reason for the fall in currency values of these economies (additional information: in these economies the local currency nominal interest rate has increased over the last year)

The rise in the local currency interest rates in these economies implies that expected inflation increased. A rise in expected inflation implies that agents will move out of local currency to hold other assets (such as dollars and dollar denominated assets), the effect of this is to lower the value of the East-Asian currencies. b. Explain the reason for the fall in the value of the stock market in these

economies.

Consider the result that E[Requity] = i + rp, where Requity is the return to equity, i is the local currency interest rate and rp is the risk premium. A rise in the nominal interest rate (discussed above) would imply that the expected return to equity must rise – this implies that the value of the stock market must drop to ensure that the equity offers the required rate of expected return of i+rp. Further, it is possible that the risk-premium for these economies also increased, leading to an even bigger drop in the stock market.

11- Budget deficits, expected inflation and exchange rates. Venezuela, a small open economy, has seen very high rates of inflation. Recall that the money demand function, as discussed in class, is given by

M / P = L(y,i) where y is real GDP and i is the nominal interest rate. In the context of Venezuela we assume the following simple money demand function (Venezuela's currency is Bolivar (Bs)).

Mt / Pt = 1/(1+it )

where Pt is the price level (CPI), it is the nominal interest rate, and Mt is the nominal money supply in Venezuela in period t. Let Mt be equal to 100 Bolivar. The real interest rate in Venezuela is R=1% and the annual growth rate of money supply is 20%. The growth rate of money is also expected to remain at 20%. For this problem assume that real GDP is constant. Assume that purchasing power parity determines the spot exchange rate. The current spot exchange rate is 672 Bolivar per US Dollar. In answering this question assume that all risk premia are zero, and that the price level (CPI) in the US is constant.

a) What is the nominal (Bolivar) interest rate in Venezuela? b) What is the current price level in Venezuela, that is Pt?

c) Suppose news arrives that the expected growth rate of money in Venezuela will

rise to 35%. What is the percentage change in the spot Bolivar per US Dollar exchange rate (relative to the current spot rate of 672) in response to this news?

Solution

a) The nominal interest rate in Venezuela is given by it =R+pit

e, with real GDP fixed we must have pit

e = 20 %, hence it =21%$. b) Given the money demand function, it follows, that

Pt = Mt *(1+it ) Given Mt =100 and it =21% it follows that Pt = 121. c) The new price level in Venezuela will be

Pt = Mt *(1+it )=100*(1.36)=136. The new it is 36%. The rise in prices implies that the Bolivar should fall in value. PPP implies that

e = Pvenz/ PUS , as the CPI in the U.S. is fixed it follows that the percentage change in the nominal exchange is

(Pvenzpost-news - Pvenz

pre-news)/ PUS) / (Pvenzpre-news / PUS).

This ratio is equal to [(136-121)/121]=0.1239. Hence the Bolivar falls in value by 12.39%.

12- Exchange rates - covered interest rate parity. Suppose the one-year interest rate in the US is 5.5% and in Germany is 6.0%. The dollar per D-mark exchange rate is 0.50. a) What is the current forward exchange rate on a 1-year contract? b) Suppose the current US interest rate happens to equal 8% and Germany's is 6%. Further, the spot exchange rate is 0.50. Compute the forward exchange rate. Solution

a) The covered interest rate parity requires (Note that E(t) here is the amount of German marks needed to receive a US dollar.

1+it = [Et * (1+it*) / Ft]

It follows

Ft = (Et *(1+it*) / (1+it) = (2 DM/$*(1+0.06) / (1+0.055) = 2.0095 DM/$

Consequently the forward exchange rate in dollars per d-mark is 0.4976 (=1/2.0095). b) Using the same formula as above it follows

Ft = (Et *(1+it*) / (1+it) = (2 DM/$ (1+0.06) / (1+0.08) = 1.962 DM/$

Consequently the forward exchange rate in dollars per d-mark is 0.509 (=1/1.962).