江财 国际财务管理复习

第二章

简答：

6.How large are the bid –ask spreads in the interbank spot market? What is their purpose?

Answer: The purpose of the bid-ask spread is to allow traders to profit by buying a currency at a low bid price and selling that currency at a higher ask price. Bid –ask spreads in the spot foreign exchange market are quite small, often only two or three basis points. For example, a yen –dollar trader might quote a bid price of yen per dollar at which she is willing to buy dollars in exchange for yen of, say, ￥83.74/$. The trader would then quote a higher ask price at which she is willing to sell dollars for yen, say, at an exchange rate of ￥83.76/$. This percentage bid-ask spread is

()′83.76/$ - ′83.74/$1000.02%′83.76/$ + ′83.74/$/2

?=

计算题：

1. Mississippi Mud Pies, Inc. needs to buy 1,000,000 Swiss francs (CHF) to pay its Swiss chocolate supplier. Its banker quotes bid –ask rates of CHF1.3990–1.4000/USD. What will be the dollar cost of the CHF1,000,000?

Answer: The bank’s bid rate is CHF1.3990/$. That is the price at which the bank is willing to buy $1 in return for CHF1.3990. The bank sells dollars at its ask price CHF1.4000/$. Mississippi Mud Pies must sell dollars to the bank to buy CHF. Therefore Mississippi Mud Pies will receive the bank’s bid rate of CHF1.3990/$. The dollar cost of CHF1,000,000 is consequently

CHF 1,000,000 / CHF1.399/$ = $714,796

2. If the Japanese yen –U.S. dollar exchange rate is ￥104.30/$, and it takes 25.15 Thai bahts to purchase 1 dollar, what is the yen price of the baht?

Answer: To prevent triangular arbitrage, the direct quote of the yen price of the baht (￥/THB) must equal the yen price of the dollar times the dollar price of the baht (which is the reciprocal of the baht price of the dollar):

￥104.30/$ ? 1/(THB25.15/$) = ￥104.30/$ ? $0.03976/THB = ￥ 4.1471/THB

3. As a foreign exchange trader, you see the following quotes for Canadian dollars (CAD), U.S. dollars (USD), and Mexican pesos (MXN):

USD0.7047/CAD MXN6.4390/CAD MXN8.7535/USD

Is there an arbitrage opportunity, and if so, how would you exploit it?

Answer: The direct quote for the cross-rate of MXN6.4390/CAD should equal the implied cross-rate using the dollar as an intermediary currency; otherwise there exists a triangular arbitrage opportunity. The indirect cross rate is

MXN8.7535/USD ?USD0.7047/CAD = MXN6.1686/CAD This indirect cross rate is less than the direct quote so there is an arbitrage opportunity to exploit between the three currencies. In this situation, buying the CAD with MXN by first buying USD with MXN and then buying the CAD with the USD and finally selling that amount of CAD directly for MXN would make a profit because we would be buying the CAD at a low MXN price and selling the CAD at a high MXN price.

4.The Mexican peso has weakened considerably relative to the dollar, and you are

trying to decide whether this is a good time to invest in Mexico. Suppose the current exchange rate of the Mexican peso relative to the U.S. dollar is MXN9.5/USD. Your investment advisor at Goldman Sachs argues that the peso will lose 15% of its value relative to the dollar over the next year. What is Goldman Sachs’s forecast of the exchange rate in 1 year?

Answer: One way to think of this is to say that the investment advisor is referring to the fact that the Mexican peso price of the dollar will be 15% higher next year. In this case, the forecast of the MXN/USD exchange rate in year 1

MXN9.5/USD ? 1.15 = MXN 10.925/USD

A 15% loss of value of the Mexican peso versus the U.S. dollar technically means that

dollar price of the peso is 15% lower. We know that the current USD price of the peso is

1 / (MXN9.5/USD) = USD0.105263/MXN

If this exchange rate falls by 15%, the new exchange rate will be

0.85 ?USD0.105263/MXN = USD0.089474/MNX

In this case the forecast for the future exchange rate measured in pesos per dollar is

1 / (USD0.089474/MXN) = MXN11.1765/USD

The difference arises because the simple percentage change in the exchange rate depends on how the exchange rate is quoted.

5.Deutsche Bank quotes bid–ask rates of $1.3005/€ - $1.3007/€and ￥104.30 - 104.40/$.

What would be Deutsche Bank’s direct asking price of yen per euro?

Answer: The direct asking price of yen per euro (￥/€) is the amount of yen that the bank charges someone who is buying euros with yen. The bank would want this to be the same as the price at which it sells dollars for yen (the bank’s ask price) times the price at which it sells euros for dollars (also the bank’s ask price). Thus, the asking price of yen per eu ro should be

(￥104.40/$) ?($1.3007/€)= ￥135.79/€

6.Alumina Limited of Australia has called Mitsubishi UFJ Financial Group to get its

opinion about the Japanese yen–Australian dollar exchange rate. The current rate is ￥67.72/A$, and Mitsubishi thinks the Australian dollar will weaken by 5% over the next year. What is Mits ubishi UFJ’s forecast of the future exchange rate?

Answer: If the Australian dollar weakens by 5% over the next year, it will take 5% fewer Japanese yen to purchase the Australian dollar. Thus, the forecast is

￥67.72/A$ ?(1 – 0.05) = ￥64.334/A$

第三章

简答：

1.What is a forward exchange rate? When does delivery occur on a 90-day forward

contract?

Answer: The forward exchange rate is a price quoted today for the exchange of currencies at the maturity of the forward contract. To find the delivery date for a 90-day forward contract, one first finds the spot value date, which is typically two business days in the future relative to the day that the contract is made. Then, to find the forward value date, one goes to the calendar date in three months corresponding to the calendar date of the spot value date. If that calendar date in three months is a legitimate business day in both countries, that date is the forward value date. If the banks in one of the countries are closed on that date, because it is a weekend or holiday, the forward value date is the next available business day without going out of the month. If going forward in time would take you out of the month, you go backward in time. This rule is followed except when the spot value day is the last business day of the current month, in which case the forward value day is the last business day in both countries in three months (this is referred to as the end-end rule). 计算题：

1.If the spot exchange rate of the yen relative to the dollar is ￥105.75, and the 90-day

forward rate is ￥103.25/$, is the dollar at a forward premium or discount? Express the premium or discount as a percentage per annum for a 360-day year?

Answer: When the forward rate of yen per dollar is less than the spot rate of yen per dollar, the dollar is said to be at a discount in the forward market. The magnitude of the discount is expressed in percentage per annum by dividing the difference between the forward rate and the spot rate by the spot rate and multiplying by reciprocal of the fraction of the year corresponding to the maturity of the forward contract (360/N days) and by 100. Thus, the annualized forward discount is 9.46% because

′103.25/$ - ′105.75/$ 360

1009.46%

??=-

′105.75/$90

Notice that the word “discount” implies that the forward rate is less than the spot rate.

2.Suppose today is Tuesday, January 18, 2011. If you enter into a 30-day forward

contract to purchase euros, when will you pay your dollars and receive your euros?

(Hints: February 18, 2011, is a Friday, and the following Monday is a holiday.)

Answer: To determine the value date of the forward contract, which is the day on which the exchange of currencies happens, one must first find the spot value date. For dollar-euro contracts, the spot value date is two business days in the future. Thus, for a spot contract on Tuesday, January 18, 2011, the exchange of currencies would take place on Thursday, January 20, 2011. The 30-day forward contract settles on the calendar day in the next month corresponding to the date of spot settlement if that is a legitimate business day. The forward contract would therefore settle on February, 20, 2011 if that is a legitimate business day, but that date is a Sunday. Furthermore, Monday, February 21, 2011, is a holiday, so the settlement of the forward contract would be on Tuesday, February 22, 2011.

3.As a foreign exchange trader for JPMorgan Chase, you have just called a trader at

UBS to get quotes for the British pound for the spot, 30-day, 60-day, and 90-day forward rates. Your UBS counterpart stated, “We trade sterling at $1.7745-50, 47/44, 88/81, 125/115.” What cash flows would you pay and receive if you do a forward foreign exchange swap in which you swap into ￡5,000,000 at the 30-day rate and out of ￡5,000,000 at the 90-day rate? What must be the relationship between dollar interest rates and pound sterling interest rates?

Answer: The fact that you are swapping into ￡5,000,000 at the 30-day rate forward rate means that you are paying dollars and buying pounds. You would do this transaction at the bank’s 30-day forward ask rate. To find the forward ask rate, you must realize that the 30-day forward points of 47/44 indicate the amounts that must be subtracted from the spot bid and ask quotes to get the forward rates. We know to subtract the points because the first forward point is greater than the second. Hence, the first part of the swap would be done at $1.7750/￡ - $0.0044/￡ = $1.7706/￡. Therefore, to buy ￡5,000,000 you would pay

$1.7706/￡?￡5,000,000 = $8,853,000

In the second leg of the swap, you would sell ￡5,000,000 for dollars in the 90-day forward market. Because you are selling pound for dollars, you transact at the 90-day forward bid rate of $1.7745/￡ - $0.0125/￡ = $1.7620/￡. Therefore, you would receive

$1.7620/￡?￡5,000,000 = $8,810,000

Notice that you get back fewer dollars than you paid, but you had use of ￡5,000,000 for 60 days. Thus, the pound must be the higher interest rate currency.

4.Consider the following spot and forward rates for the yen–euro exchange rates:

Is the euro at a forward premium or discount? What are the magnitudes of the forward premiums or discounts when quoted in percentage per annum for a 360-day year?

Answer: The forward rates of yen per euro are lower than the spot rates. Therefore, the euro is at a discount in the forward market. The annualized forward premium or discount for the N day forward contract is

F - S S n

360

N days

= 100

If the value of this calculation is negative, say -2%, we say there is a 2% discount.

Therefore, the discounts are 4.51% for 30 days, 4.72% for 60 days, 4.24% for 90 days, 4.01% for 180 days, and 5.78% for 360 days.

5.As a currency trader, you see the following quotes on your computer screen:

a.What are the outright forward bid and ask quotes for the USD/EUR at the 3-month

maturity?

Answer: The spot bid and ask quotes for USD/EUR are 1.0435/45. These quotes mean that the bank buys euros with dollars spot at $1.0435/€, and the bank sells euros for dollars at $1.0445/€. Because the forward points at the 3-month maturity are 75/90, we know that we must add the points to get the outright forward bid and ask rates. Adding the points makes the bid-ask spread in the forward market larger than the bid-ask spread in the spot market.

Consequently, the forward bid rate is $1.0435/€ + $0.0075/€ = $1.0510/€, and the forward ask quote is $1.0445/€ + $0.0090/€ = $1.0535/€.

b.Suppose you want to swap out of $10,000,000 and into yen for 2 months. What are the

cash flows associated with the swap?

Answer : When you swap out of $10,000,000 into yen in the spot market, you are selling dollars to the bank. The bank buys dollars at its low bid rate of ￥98.75/$, so you get

￥98.75/$ $10,000,000 = ￥987,500,000

When you contract to buy the $10,000,000 back from the bank in the 2-month forward market, yo u must pay the bank’s ask rate of

￥98.85/$ - ￥00.16/$ = ￥98.69/$

You subtract the points because the 2-month forward quote is 20/16. Subtracting the points makes the bid-ask spread in the forward market larger than the bid-ask spread in the spot market. Hence, the amount of yen you pay is

￥98.69/$ $10,000,000 = ￥986,900,000

c. If one of your corporate customers calls you and wants to buy pounds with dollars in 6 months, what price would you quote?

Answer: If the customer wants to buy pounds with dollars, the customer must pay the bank’s 6-month ask rate. The spot quotes are 1.6623/33 which means the spot ask rate is $1.6633/￡. The 6-month forward points are 120/130. We add the points because the first one, 120, is less than the second, 130. Hence, the outright forward quote would be

$1.6633/￡ + $0.0130/￡ = $1.6763/￡

6. Intel is scheduled to receive a payment of ￥100,000,000 in 90 days from Sony

in connection with a shipment of computer chips that Sony is purchasing from Intel. Suppose that the current exchange rate is ￥103/$, that analysts are forecasting that the dollar will weaken by 1% over the next 90 days, and that the standard deviation of 90-day forecasts of the percentage rate of depreciation of the dollar relative to the yen is 4%.

a. Provide a qualita tive description of Intel’s transaction exchange risk.

Answer: Intel is a U.S. company, and it is scheduled to receive yen in the future. A weakening of the yen versus the dollar causes a given amount of yen to convert to fewer dollars in the future. This loss of value could be severe if the yen depreciates by a significant amount.

b. If Intel chooses not to hedge its transaction exchange risk, what is Intel’s expected dollar revenue?

Answer: If Intel chooses not to hedge, the expected dollar revenue is the expected dollar value of the ￥100,000,000. The expected spot rate

??

incorporates a 1% weakening of the dollar. This means that the expected yen price of the dollar is 1% less than the current spot rate of ￥103/$ or

Et[S(t+90,￥/$)] = 0.99 ￥103/$ = ￥101.97/$

Hence, Intel expects to receive ￥100,000,000 / ￥101.97/$ = $980,681

c. If Intel does not hedge, what is the range of possible dollar revenues that incorporates 95.45% of the possibilities?

Answer: We are told that the standard deviation of the rate of depreciation of the dollar is 4%. The standard deviation of the future spot rate is therefore 4% of the current spot rate or 0.04 ￥103/$ = ￥4.12/$. Thus, plus or minus 2 standard deviations around the conditional expected future spot rate is

￥101.97/$ + ￥8.24/$ = ￥110.21/$

￥101.97/$ - ￥8.24/$ = ￥93.73/$

The range that encompasses 95.45% of possible future values for Intel’s receivable

is therefore

￥100,000,000 / ￥110.21/$ = $907,359

￥100,000,000 / ￥93.73/$ = $1,066,894

第六章

简答：

6.What do economists mean by the external currency market?

Answer: The external currency market is an interbank market for deposits and loans that are denominated in currencies that are not the currency of the country in which the bank is operating. Its settlement procedures are identical to those of the foreign exchange market. The first currency for which these deposits and loans began to trade was the dollar, and the deposits were called Eurodollars because they were dollar-denominated deposits at European banks. The market for other currencies came to be called the Eurocurrency market, even though the trading might be done in Asia or the Americas. With the advent of the euro as a currency, the term external currency market seems less confusing.

7.What determines the bid –ask spread in the external currency market? Why is it usually so small?

Answer: The bid-ask spread in the external currency market is the difference between the bid rate, which is the interest rate that the bank pays on its deposits and the ask rate, which is the interest rate that the bank charges on its loans. The market is very competitive, and the bid-ask spreads are small. The reason is because the banks accepting the deposits and making the loans are subject only to the regulations of the government of the country in which the bank is operating, not the government of the country that issues the money in which the deposits and

??

loans are denominated. These regulations include how much banks must keep on reserve with their nation’s central bank. Because reserve requirements are often lower for foreign currency deposits than for domestic currency deposits, banks can lend out a larger part of these deposits. Thus, the foreign currency deposits are potentially more profitable.

计算题：

1. In the entry forms for its contests, Publisher’s Clearing House states, “You

may have already won $10,000,000.” If the Prize Patrol visits your house to inform you that you have won, it offers you $333,333.33 each and every year for 30 years. If the interest rate is 8% p.a., what is the actual present value of the $10,000,000 prize?

Answer: The present value of 30 annual payments of $333,333.33 when discounted at 8% is

30

1$333,333.33$3,752,594.411.08k k ==∑

This value can be found in Excel by using the function NPV(rate , cashflows ), where rate = 8% and cashflows refers to a sequence of 30 cells that all have the value $333,333.33.

2. Suppose the 5-year interest rate on a dollar-denominated pure discount bond

is 4.5% p.a., whereas in France, the euro interest rate is 7.5% p.a. on a similar pure discount bond denominated in euros. If the current spot rate is $1.08/€, what is the value of the forward exchange rate that prevents covered interest arbitrage?

Answer: We know that the 5-year forward rate must satisfy

()()5

5

551+i(t,5,$) 1.045F(t,5,$/ū) = S(t,$/ū)? = $1.08/ū ? = $0.9375/ū1.0751+i(t,5,ū)

3. Carla Heinz is a portfolio manager for Deutsche Bank. She is considering two

alternative investments of EUR10,000,000: 180-day euro deposits or 180-day Swiss francs (CHF) deposits. She has decided not to bear transaction foreign exchange risk. Suppose she has the following data: 180-day CHF interest rate, 8% p.a., 180-day EUR interest rate, 10% p.a., spot rate EUR1.1960/CHF, 180-day forward rate, EUR1.2024/CHF. Which of these deposits provides the

higher euro return in 180 days? If these were actually market prices, what would you expect to happen?

Answer: The euro return to investing directly in euros is 1805%10%360??

=? ???, so the euros available in 180 days is EUR10,000,000 ? 1.05 = EUR10,500,000. Alternatively, the EUR10,000,000 can be converted into Swiss francs at the spot rate of EUR1.1960/CHF. The Swiss francs purchased would equal EUR10,000,000 / EUR1.1960/CHF = CHF8,361,204. This amount of Swiss francs can be invested to provide a 1804%8%360??

=? ??? return over the next 180 days. Hence, interest plus principal on the Swiss francs is CHF8,361,204 ? 1.04 = CHF8,695,652. If we sell this amount of Swiss francs forward for euros at the 180-day forward rate of EUR1.2024/CHF, we get a euro return of CHF8,695,652 ? EUR1.2024/CHF = EUR10,455,652. This is less than the return from investing directly in euros.

If these were the actual market prices, you should expect investors to do covered interest arbitrages. Investors would borrow Swiss francs, which would tend to drive the CHF interest rate up; they would sell the Swiss francs for euros in the spot foreign exchange market, which would tend to lower the spot rate of EUR/CHF; they would deposit euros, which would tend to drive the EUR interest rate down; and they would contract to buy CHF with EUR in the 180-day forward market, which would put upward pressure on the forward rate of EUR/CHF. Each of these actions would help bring the market back to equilibrium.

4. If the 30-day yen interest rate is 3% p.a., and the 30-day euro interest rate is

5% p.a., is there a forward premium or discount on the euro in terms of the yen? What is the magnitude of the forward premium or discount?

Answer: We know that the high interest rate currency must sell at a forward discount when priced in the low interest rate currency to prevent a covered interest arbitrage. Therefore the euro is at a discount in the forward market. To determine the magnitude of the discount, recognize that interest rate parity requires equality of the return to investing in yen versus converting the yen principal into euros, investing the euros, and selling the euro principal plus interest in the forward market for yen:

()()11 + i(′) = ? 1 + i(ū) ? F(′/ū)S(′/ū)

Solving this expression for the forward premium, we find

()

F(′/ū) - S(′/ū)i(′) - i(ū) = S(′/ū) 1 + i(ū)

The de-annualized interest rates are 0.0025 = (3/100) ? (30/360) for the yen and 0.004167 = (5/100) ? (30/360) for the euro. The right-hand side of the above expression is therefore -0.00166. The annualized value is -0.00166 ? (100) ? (360/30) = -1.99%. We therefore say that the euro sells at an annualized discount of 1.99%.

5. Suppose the spot rate is CHF1.4706/$ in the spot market, and the 180-day

forward rate is CHF1.4295/$. If the 180-day dollar interest rate is 7% p.a., what is the annualized 180-day interest rate on Swiss francs that would prevent arbitrage?

Answer: Interest rate parity requires equality of the return to investing in CHF versus converting the CHF principal into dollars, investing the dollars, and selling the dollar principal plus interest in the forward market for CHF:

()()11 + i(CHF) = ? 1 + i($) ? F(CHF/$)S(CHF/$)

If we de-annualize the dollar interest rate, we find that the 180 day interest rate is 0.035. Hence, the Swiss franc interest rate that prevents arbitrage is

1i(CHF) = ? 1.035 ? CHF1.4295/$ - 1 = 0.0061CHF1.4706/$

If we annualize this value, we find 0.0061 ? (100) ? (360/180) = 1.21%.

6. As a trader for Goldman Sachs you see the following prices from two

different banks:

The interest rates are quoted on a 360-day year . Can you do a covered interest arbitrage?

Answer: We need to check the two inequalities that characterize the absence of covered interest arbitrage. In the first, we will borrow euros at 6.125%, convert to ringgits in the spot market at MYR4.6602 / EUR, invest the ringgits at 10.5%, and sell the ringgit principal plus interest forward for euros at MYR4.9650 / EUR. We find that

MYR4.66021

1.06125 > ? 1.105 ? = 1.0372

EUR MYR4.9650/EUR

Thus, it is not profitable to try to arbitrage in this direction as the amount that we would owe is greater than the amount that we would gain.

Let’s try the other direction, arbitraging out of ringgits into euros and covering the foreign exchange risk. We will borrow ringgits at 10.625%, convert to euros in the spot market at MYR4.6622 / EUR, invest the euros at 6.0%, and sell the euro principal plus interest forward for ringgits at MYR4.9500 / EUR. We find that

1MYR4.9500

1.10625 < ? 1.06 ? = 1.1254

MYR4.6622/EUR EUR

Thus, there is a possible arbitrage opportunity because the amount that we owe from borrowing ringgits is less than the amount that we gain by converting from ringgits to euros, investing the euros, and covering the transaction exchange risk with a forward sale of euros for ringgits.

7.As an importer of grain into Japan from the United States, you have agreed

to pay $377,287 in 90 days after you receive your grain. You face the following exchange rates and interest rates: spot rate, ￥106.35/$, 90-day forward rate ￥106.02/$, 90-day USD interest rate, 3.25% p.a., 90-day JPY interest rate, 1.9375% p.a.

a.Describe the nature and extent of your transaction foreign exchange risk.

Answer: As a Japanese grain importer, you are contractually obligated to pay $377,287 in 90 days. Any weakening of the yen versus the dollar will increase the yen cost of your grain. The possible loss is unbounded.

b.Explain two ways to hedge the risk.

Answer: You could hedge your risk by buying dollars forward at ￥106.02/$.

Alternatively, you could determine the present value of the dollars that you owe and buy that amount of dollars today in the spot market. You could borrow that amount of yen to avoid having to pay today.

c.Which of the alternatives in part b is superior?

Answer: If you do the forward hedge, you will have to pay

￥106.02/$ ?$377,287 = ￥39,999,967.74

in 90 days. If you do the money market hedge, you first need to find the present value of $377,287 at 3.25%. The de-annualized interest rate is

(3.25/100) ?(90/360) = 0.008125. Thus, the present value is

$377,287 / 1.008125 = $374,246.25

Purchasing this amount of dollars in the spot market costs

￥106.35/$ ?$374,246.25 = ￥39,801,088.69

To compare this value to the forward hedge, we must take its future value at

1.9375% p.a. The de-annualized interest rate is (1.9375/100) ?(90/360) =

0.00484375, and the future value is

￥39,801,088.69 ?(1.00484375) = ￥39,993,875.21 The cost of the money market hedge is essentially the same as the cost of the forward hedge because interest rate parity is satisfied.

8.You are a sales manager for Motorola and export cellular phones from the

United States to other countries. You have just signed a deal to ship phones to

a British distributor. The deal is denominated in pounds, and you will receive

￡700,000 when the phones arrive in London in 180 days. Assume that you can borrow and lend at 7% p.a. in U.S. dollars and at 10% p.a. in British pounds.

Both interest rate quotes are for a 360-day year. The spot exchange rate is $1.4945/￡, and the 180-day forward exchange rate is $1.4802/￡.

a.Describe the nature and extent of your transaction foreign exchange risk.

Answer: As a U.S. exporter, you have a contract to receive ￡700,000 in 180 days. Any weakening of the pound versus the dollar will decrease the dollar value of your pound-denominated receivable. Large losses are possible as the dollar value could go to zero, although that is highly unlikely.

b.Describe two ways of eliminating the transaction foreign exchange risk.

Answer: You could hedge by selling pounds forward for dollars. Alternatively, you could do a money market hedge in which you borrow the present value of the pounds, and convert the loan principal to dollars in the spot market, and

then use the pound receivable to pay off the interest plus principal on the loan at maturity.

c.Which of the alternatives in part b is superior?

Answer: The forward hedge gives

$1.4802/￡?￡700,000 = $1,036,140

in 180 days. The money market hedge requires the present value of the ￡700,000. The interest rate is (10/100) ?(180/365) = 0.0493. Thus, the present value is

￡700,000 / 1.0493 = ￡667,111.41

The dollar value of this is

$1.4945/￡?￡667,111.41 = $996,998

To compare this to the forward hedge we must take its future value at 7% p.a.

The interest rate is (7/100) ?(180/360) = 0.035. Therefore the future value is

$996,998 ? 1.035 = $1,031,892.93

The forward hedge provides slightly more dollar revenue.

d.Assume that the dollar interest rate and the exchange rates are correct.

Determine what sterling interest rate would make your firm indifferent between the two alternative hedges.

Answer: We know that if interest rate parity is satisfied, the money market hedge and the forward hedge will provide the same revenue. The pound interest rate that satisfies interest rate parity is

()()1

1 + i(￡) = S($/￡) ? 1 + i($) ?

F($/￡)

The value of the right-hand side is $1.4945/￡? 1.035 / $1.4802/￡ = 1.0450.

Thus the annualized pound interest rate that would make the firm indifferent between the forward hedge and the money market hedge is 0.0450 ?100 ?(365/180) = 9.12%.

9.Suppose that there is a 0.5% probability that the government of Argentina

will nationalize its banking system and freeze all foreign deposits indefinitely during the next year. If the dollar deposit interest rate in the United States is

5%, what dollar interest would Argentine banks have to offer in order to attract deposits from foreign investors?

Answer: If the freezing of deposits is an idiosyncratic event, then the expected value of the return should equal the risk free return of 5%. If investors effectively get a return of zero with 0.5% probability, they must get a return of (1 + X%) with 99.5% probability, such that

[(1 + X%) ?0.995] + [0 ? 0.005] = 1.05

When we solve this equation for X%, we find X% = 5.53%. Of course, the more that you eventually recover in the event of a freeze of deposits, the smaller the interest rate can be.

10. Suppose the market price of a 20-year pure discount bond with a face value

of $1,000 is $214.55. What is the spot interest rate for the 20-year maturity expressed in percentage per annum?

Answer: We know that the relationship between the price of a pure discount bond and the spot interest rate at the 20 year maturity satisfies

()20$1,000

P(t) = 1 + i(t,20)

Substituting the price of $214.55 and solving for i(t,20), we find

1/20$1,000i(t,20) = - 1 = 0.08$214.55??????

Therefore, the spot interest rate for the 20-year maturity expressed in percentage per annum is 8%.

11. Consider a 2-year euro-denominated bond that has a current market price of

€970, a face value of €1,000, and an annual coupon of 5%. Suppose the 1-year euro-denominated spot interest rate is 5.5%. What is the 2-year euro-denominated spot interest rate?

Answer: The present value of a coupon paying bond is found by discounting each annual coupon and the final principal payment at the appropriate spot interest rates for those maturities. Thus, to find the 2-year euro-denominated spot interest rate we must solve for the two-period spot interest rate in the following equation:

()

2ū50ū1050ū970 = + 1.0551+i(t,2)

The answer is i(t,2) = 6.68%.

第八章

简答：

10.What is the real exchange rate, and how are fluctuations in the real exchange rate related to deviations from absolute PPP?

Answer: The real exchange rate, say, of the dollar relative to the euro, is denoted RS(t,$/€). It is defined to be the nominal exchange rate multiplied by the ratio of the price levels:

S(t,$/ū) P(t,ū)RS(t,$/ū) = P(t,$)

?

Notice that the real exchange rate would be 1 if absolute purchasing power parity held because the nominal exchange rate, S(t,$/€), would equal the ratio of the two price levels, P(t,$)/P(t,€). Similarly, if absolute PPP is violated, the real exchange rate is not equal to 1. Thus, fluctuations in the deviations from absolute PPP are fluctuations in the real exchange rate.

计算题：

1. If the consumer price index for the United States rises from 350 at the end of

a year to 365 at the end of the next year, how much inflation was there in the United States during that year?

Answer: Price indexes are ratios of the price level in a given year to the price level in a base year. Because the base year is the same in the two price indexes under consideration, we can take the ratio of the two price indexes and find the rate of inflation over that year. The ratio is 365/350 = 1.0429 or an inflation rate of

4.29%.

2. As a wheat futures trader, you observe the following futures prices for the

purchase and sale of wheat in 3 months: $3.00 per bushel in Chicago and ￥320 per bushel in Tokyo. Delivery on the contracts is in Chicago and Tokyo, respectively. If the 3-month forward exchange rate is ￥102/$, what is the magnitude of the transaction cost necessary to make this situation not represent an unexploited profit opportunity?

Answer: The forward dollar price of wheat in Tokyo is the ratio of the futures price, ￥320 per bushel, to the forward exchange rate, ￥102/$. This ratio is ￥320 per bushel / (￥102/$) = $3.14 per bushel. Since we can buy wheat for delivery in Chicago at $3 per bushel, if transaction costs of shipping wheat from Chicago to Tokyo are smaller than $0.14 per bushel, we could make an arbitrage profit. Thus, the minimum magnitude of the transaction cost necessary to make this situation not represent an unexploited profit opportunity is $0.14 per bushel.

3.Suppose that the price level in Canada is CAD16,600, the price level in

France is EUR11,750, and the spot exchange rate is CAD1.35/EUR.

a.What is the internal purchasing power of the Canadian dollar?

Answer: It is probably best to calculate the purchasing power of CAD10,000.

If we divide this amount by the price level in Canada of CAD16,600, we find

CAD10,000

=0.6024 consumption bundles

CAD16,600 / consumption bundle

b.What is the internal purchasing power of the euro in France?

Answer: Performing a similar calculation to the one in part a., we find

EUR10,000

= 0.8511 consumption bundles EUR11,750 / consumption bundle

c.What is the implied exchange rate of CAD/EUR that satisfies absolute

PPP?

Answer: The implied PPP exchange rate equates the internal purchasing power of the CAD to its external purchasing power. This implies that the PPP exchange rate is the ratio of the Canadian price level in Canadian dollars to the French price level in euros:

() PPP CAD16,600CAD1.4128

S CAD/EUR = =

EUR11,750EUR

d.Is the euro overvalued or undervalued relative to the Canadian dollar?

Answer: Because the actual exchange rate of CAD1.35/EUR is less than the PPP exchange rate, the euro is undervalued on the foreign exchange market because it would have to strengthen to move from CAD1.35/EUR to CAD1.4128/EUR.

e. What amount of appreciation or depreciation of the euro would be

required to return the actual exchange rate to its PPP value?

Answer: The exchange rate moves from the actual value of CAD1.35/EUR to the PPP value of CAD1.4128/EUR for a percentage change of1.4128/1.35– 1 = 0.0466. This is a 4.66% appreciation of the euro versus the Canadian dollar.

4. Suppose that the rate of inflation in Japan is 2% in 2011. If the rate of

inflation in Germany is 5% during 2011, by how much would the yen strengthen relative to the euro if relative PPP is satisfied during 2011?

Answer: The approximately correct answer is that the yen should strengthen by the differential in the rates of inflation or 5% - 2% = 3%. The exact answer is found from equation (8.4) of the text, which incorporates a denominator correction, and we get ()()()?t+1,DC -?t+1,FC DC s t+1,=FC 1+?t+1,FC ?? ???

Since we are concerned about the strengthening of the yen, let the yen be the foreign currency (FC), and let the euro be the domestic currency (DC). Then, the relative PPP formula states that the rate of appreciation of the yen is 0.05 - 0.02 0.0294 or 2.94%1+0.02

=

5. One of your colleagues at Deutsche Bank thinks that the dollar is severely

undervalued relative to the yen. He has calculated that the PPP exchange rate is ￥140/$, whereas the current exchange rate is ￥105/$. Because interest rates are 3% p.a. lower in Japan than in the United States, he thinks that this is a good time to speculate by borrowing yen and lending dollars. What do you think?

Answer: Deviations from PPP are a weak reason to engage in speculation. While the data in the problem indicate that the dollar is 33.33% undervalued, because that is the amount of dollar appreciation that would be required to take the actual exchange rate from ￥105/$ to the PPP prediction of ￥140/$, we know that the return to PPP will not be an overnight event.

The empirical analysis of the issue indicates that the half-life of PPP deviations is around 5 years. Thus, you might expect that the dollar will appreciate by 16.67%

over the next 5 years. But, uncovered interest rate parity actually suggests that the yen will appreciate in the short run, because the yen interest rate is 3% less than the dollar interest rate. Notice, though, that the correction back toward PPP can take place with differential rates of inflation in the two countries. If Japanese rate of inflation falls below the U.S. rate of inflation, the PPP prediction will begin falling toward the actual exchange rate. Finally, although the dollar is 33.33% undervalued, there is no guarantee that the undervaluation will begin to be corrected now. It may, in fact, get worse. If the undervaluation of the dollar goes to 50% over the next 2 years, you would lose 16.67% in the foreign exchange market which would not be compensated by the approximate 6% that you would earn by borrowing yen and lending dollars. Finally, do not forget that your boss in proprietary trading at Deutsche Bank would not be happy with such a situation.

7.Suppose that you are trying to decide between two job offers. One consulting firm offers you $150,000 per year to work out of its New York office. A second consulting firm wants you to work out of its London office and offers you ￡100,000 per year. The current exchange rate is $1.65/￡. Which offer should you take, and why? Assume that the PPP exchange rate is $1.40/￡ and that you are indifferent between working in the two cities if the purchasing power of your salary is the same.

Answer: We know from the extensive discussion in Question 8 that we should use the PPP exchange rate to compare the pound salary to the dollar salary. If we do so, we find $1.40/￡?￡100,000 = $140,000. This is less than the $150,000 that you are being offered in New York. The fact that the dollar is undervalued on the foreign exchange markets makes the perceived salary of $1.65/￡?￡100,000 = $165,000, calculated with the spot exchange rate, seem more attractive. But, the key point is that to achieve $165,000 of spending in the United States, you would have to work in London and consume in New York.

8. Suppose that in 2008, the Japanese rate of inflation is 2%, and the German rate of inflation is 5%. If the euro weakens relative to the yen by 10% during 2011, what would be the magnitude of the real depreciation of the euro relative to the yen?

Answer: The real exchange rate is

//S(t,) P(t,)

RS(t,) = P(t,)?′ūū′ū′

We also know that a real depreciation of the euro means that this real exchange rate decreases. The new real exchange rate will be the old real exchange rate with

each term multiplied by one plus the respective percentage rate of change. Thus, one plus the percentage rate of change of the real exchange rate is

[][][][][][]

// 1 + s(t,) 1 + (t,) 1 - 0.10 1 + 0.051 + rs(t,) = 0.92651 + (t,) 1 + 0.02ππ??==′ūū′ū′

So, we conclude that the real depreciation of the euro is 7.35%.

第十章

计算题：

1. Suppose the 1-year nominal interest rate in Zooropa is 9%, and Zooropa’s

expected inflation rate is 4%. What is the real interest rate in Zooropa?

Answer: The expected real interest rate is approximately 9% - 4% = 5%. The correct computation is: (1 + 0.09) / (1 + 0.04) – 1 = 0.0481 or 4.81%.

2. You were recently hired by the Doolittle Corporation corporate treasury to

help oversee its expansion into Europe. Blake Francis, the CFO, wants to hire a foreign exchange forecasting company. Blake has asked you to evaluate three different companies, and he has obtained information on their past performances. Out of a total of 50 forecasts for the $/€ rate, the companies reported the number of times they correctly forecast appreciations and depreciations:

There are a total of 35 dollar appreciations (down periods) and 15 dollar depreciations (up periods) in the sample. Blake wants to know two things:

a. Can anything be said about the companies’ forecasting ability with the

available data?

Answer: Yes, one can compute the number of correct “directional” forecasts. Morrissey has the highest correct proportion with 25 out of 50 correct, whereas the other firms have less than 50% correct. However, note that the dollar over this period was relatively strong and appreciations (down forecasts for the $/€ rate) dominate. Hence, forecasts in the down period may be more useful (see footnote 3

in the chapter). If we look at correct conditional forecasts, we see that Morrissey is correct 20/35 or 57.14% of the time when the dollar appreciates, but only 5/15 or

33.33% of the time when the dollar depreciates. According to the

Henriksson–Merton test, the sum of these two proportions should be over 1 for a firm to have market timing ability. However, the sum in this case is only 90.47%.

While Morrissey obviously dominates Pixie Land Exchange, it is not clear that it is better than FOREX Cures. The proportions of correct conditional forecasts of FOREX Cures are 12/35 (34.29%) and 12/15 (80%) for a sum of 114.29%.

Consequently, only FOREX Cures shows directional forecasting ability.

b.What additional information should Blake try to obtain in order to form

a better judgment?

Answer: Directional forecasting ability in the foreign exchange market is not particularly useful if the forecasts are to be used in speculative strategies. To this end, it would have been more useful to know whether the forecasting firms were on the correct side of the forward rate. Ideally, a full record of forecasts would be obtained. Then, accuracy statistics (like the RMSE) and profitability statistics (like the Sharpe ratio) could be computed.

3.Mini-Case: Currency Turmoil in Zooropa

Fad Gadget has never worked so hard in his entire life. It is near midnight, and he is still poring over statistics and tables. Fad recently joined Smashing Pumpkins, a relatively young but fast-growing British firm. Smashing Pumpkins produces and distributes an intricate device that turns fresh pumpkins into pumpkin pie in about 30 minutes. Recently, the firm has started exporting to Zooropa. Some of the largest and tastiest pumpkins are grown in Zooropa, and Zooropa’s population boasts the highest per cap ita pumpkin consumption in the world. A recent analysis of the pumpkin market in Zooropa has left the company’s senior managers very impressed with the profit potential.

Although Zooropa consists of 10 politically independent countries, their currencies are linked through a system called the Currency Rate Linkage System (CRLS) that works exactly like the former Exchange Rate Mechanism (ERM) of the EMS worked before the currency turmoil started in September 1992. The anchor currency is the banshee of Enigma, the leading country in Zooropa.

Initial contacts with importers in Zooropean countries indicated that they typically insist on payment in their own local currency. About a week ago, Cab Voltaire, the CEO of Smashing Pumpkins, expressed concerns about this development and asked Fad to lead a research team to further examine the present state of the currency system of Zooropa. Cab viewed the