Chapter 8 international equity markets suggested answers and solutions to end-of-chapter




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CHAPTER 8 INTERNATIONAL EQUITY MARKETS

SUGGESTED ANSWERS AND SOLUTIONS TO END-OF-CHAPTER

QUESTIONS AND PROBLEMS


QUESTIONS


1. Get a current copy of The Wall Street Journal and find the Dow Jones Global Indexes listing in Section C of the newspaper. Examine the 12-month changes in U.S. dollars for the various national and regional indices. How do the changes from your table compare with the 12-month changes from the sample provided in the textbook as Exhibit 8.8? Are they all of similar size? Are the same national indexes positive and negative in both listings? Discuss your findings.


Answer: This question is designed to provide an intuitive understanding of the benefits from international diversification of equity portfolios. It is very unlikely that the student will find many, if any, national market indexes that have 12- month returns that are even close to the same level as in Exhibit 8.8. Over different time periods, different market forces will affect each national market in unique ways and the exchange rates will be different. Some markets that previously yielded a positive return will now show a negative return, and vice versa. Similarly, some markets that had yielded a large positive (negative) return may now show only a small positive (negative) return.


3. Compare and contrast the various types of secondary market trading structures.


Answer: There are two basic types of secondary market trading structures: dealer and agency. In a dealer market, the dealer serves as market maker for the security, holding an inventory of the security. The dealer buys at his bid price and sells at his asked price from this inventory. All public trades go through the dealer. In an agency market, public trades go through the agent who matches it with another public trade. Both dealer and agency markets can be continuous trade markets, but non-continuous markets tend to be only agency markets. Over-the-counter trading, specialist markets, and automated markets are types of continuous market trading systems. Call markets and crowd trading are each types of non-continuous trading market systems. Continuous trading systems are desirable for actively traded issues, whereas call markets and crowd trading offer advantages for smaller markets with many thinly traded issues because they mitigate the possibility of sparse order flow over short time periods.

5. Why might it be easier for an investor desiring to diversify his portfolio internationally to buy depository receipts rather than the actual shares of the company?


Answer: A depository receipt can be purchased on the investor’s domestic exchange. It represents a package of the underlying foreign security that is priced in the investor’s local currency and in a trading range that is typical for the investor’s marketplace. The investor can purchase a depository receipt directly from his domestic broker, rather than having to deal with an overseas broker and the necessity of obtaining foreign funds to make the foreign stock purchase. Additionally, dividends are received in the local currency rather than in foreign funds that would need to be converted into the local currency.


6. Why do you think the empirical studies about factors affecting equity returns basically showed that domestic factors were more important than international factors, and, secondly, that industrial membership of a firm was of little importance in forecasting the international correlation structure of a set of international stocks?


Answer: While national security markets have become more integrated in recent years, there is still a tremendous amount of segmentation that brings about the benefit to be derived from international diversification of financial assets. Monetary and fiscal policies differ among countries because of different economic circumstances. The economic policies of a country directly affect the securities traded in the country, and they will behave differently than securities traded in another country with other economic policies being implemented. Hence, it is not surprising that domestic factors are found to be more important than international factors in affecting security returns. Similarly, industrial activity within a country is also affected by the economic policies of the country; thus firms in the same industry group, but from different countries, will not necessarily behave the same in all countries, nor should we expect the securities issued by these firms to behave alike.


PROBLEMS


1. On the Milan bourse, Fiat stock closed at EUR31.90 per share on Friday, September 10, 1999. Fiat trades as and ADR on the NYSE. One underlying Fiat share equals one ADR. On September 10, the $/EUR spot exchange rate was $1.0367/EUR1.00. At this exchange rate, what is the no-arbitrage U.S. dollar price of one ADR?


Solution: The no-arbitrage ADR U.S. dollar price is: EUR31.90 x $1.0367 = $33.07.


2. If Fiat ADRs were trading at $35 when the underlying shares were trading in Milan at EUR31.90, what could you do to earn a trading profit? Use the information in problem 1, above, to help you and assume that transaction costs are negligible.


Solution: As the solution to problem 1 shows, the no-arbitrage ADR U.S. dollar price is $33.07. If Fiat ADRs were trading at $35, a wise investor would sell short the relatively overvalued ADRs and use the proceeds to buy the relatively undervalued Fiat shares on the Milan exchange. The profit would be $35 - $33.07 = $1.93 per ADR.


^ MINI CASE: SAN PICO’S NEW STOCK EXCHANGE


San Pico is a rapidly growing Latin American developing country. The country is blessed with miles of scenic beaches that have attracted tourists by the thousands to in recent years to new resort hotels financed by joint ventures of San Pico businessmen and moneymen from the Middle East, Japan, and the U.S. Additionally, San Pico has good natural harbors that are conducive for receiving imported merchandise and exporting merchandise produced in San Pico and other surrounding countries that lack access to the sea. Because of these advantages, many new businesses are being started in San Pico.

Presently, stock is traded in a cramped building in La Cobijio, the nation’s capital. Admittedly, the San Pico Stock Exchange system is rather archaic. Twice a day an official of the exchange will call out the name of each of the 43 companies whose stock trade on the exchange. Brokers wanting to buy or sell shares for their clients will then attempt to make a trade with one another. This crowd trading system has worked well for over one hundred years, but the government desires to replace it with a new modern system that will allow greater and more frequent opportunities for trading in each company, and will allow for trading the shares of the many new start-up companies that are expected to trade in the secondary market. Additionally, the government administration is rapidly privatizing many state-owned businesses in an attempt to foster their efficiency, obtain foreign exchange from the sale, and convert the country to a more capitalist economy. The government believes that it could conduct this privatization faster and perhaps at more attractive prices if it had a modern stock exchange facility where the shares of the newly privatized companies will eventually trade.

You are an expert in the operation of secondary stock markets and have been retained as a consultant to the San Pico Stock Exchange to offer your expertise in modernizing the stock market. What would you advise?


Suggested Solution to San Pico’s New Stock Exchange


Most new and renovated stock exchanges are being established these days as either a partially or fully automated trading system. A fully automated system is especially beneficial for a small to medium size country in which there is only moderate trading in most issues. Such a system that deserves special note is the continuous National Integrated Market system of New Zealand. This system is fully computerized and does not require a physical structure. Essentially, all buyers and sellers of a stock enter through their broker into the computer system the number of shares they desire to buy or sell and their required transaction price. The system is updated constantly as new purchase or sale orders are entered into the system. The computer constantly searches for a match between buyer and seller, and when one is found a transaction takes place. This type of system would likely serve San Pico’s needs very well. There is existing technology to implement, the bugs have been worked out in other countries, and it would satisfy all the demands of the San Pico government and easily accommodate growth in market activity.

^ CHAPTER 9 FUTURES AND OPTIONS ON FOREIGN EXCHANGE

SUGGESTED ANSWERS AND SOLUTIONS TO END-OF-CHAPTER

QUESTIONS AND PROBLEMS


QUESTIONS


1. Explain the basic differences between the operation of a currency forward market and a futures market.


Answer: The forward market is an OTC market where the forward contract for purchase or sale of foreign currency is tailor-made between the client and its international bank. No money changes hands until the maturity date of the contract when delivery and receipt are typically made. A futures contract is an exchange-traded instrument with standardized features specifying contract size and delivery date. Futures contracts are marked-to-market daily to reflect changes in the settlement price. Delivery is seldom made in a futures market. Rather a reversing trade is made to close out a long or short position.


2. In order for a derivatives market to function two types of economic agents are needed: hedgers and speculators. Explain.


Answer: Two types of market participants are necessary for the operation of a derivatives market: speculators and hedgers. A speculator attempts to profit from a change in the futures price. To do this, the speculator will take a long or short position in a futures contract depending upon his expectations of future price movement. A hedger, on-the-other-hand, desires to avoid price variation by locking in a purchase price of the underlying asset through a long position in a futures contract or a sales price through a short position. In effect, the hedger passes off the risk of price variation to the speculator who is better able, or at least more willing, to bear this risk.


3. Why are most futures positions closed out through a reversing trade rather than held to delivery?


Answer: In forward markets, approximately 90 percent of all contracts that are initially established result in the short making delivery to the long of the asset underlying the contract. This is natural because the terms of forward contracts are tailor made between the long and short. By contrast, only about one percent of currency futures contracts result in delivery. While futures contracts are useful for speculation and hedging, their standardized delivery dates make them unlikely to correspond to the actual future dates when foreign exchange transactions will occur. Thus, they are generally closed out in a reversing trade. In fact, the commission that buyers and sellers pay to transact in the futures market is a single amount that covers the round-trip transactions of initiating and closing out the position.


4. How can the FX futures market be used for price discovery?


Answer: To the extent that FX forward prices are an unbiased predictor of future spot exchange rates, the market anticipates whether one currency will appreciate or depreciate versus another. Because FX futures contracts trade in an expiration cycle, different contracts expire at different periodic dates into the future. The pattern of the prices of these contracts provides information as to the market’s current belief about the relative future value of one currency versus another at the scheduled expiration dates of the contracts. One will generally see a steadily appreciating or depreciating pattern; however, it may be mixed at times. Thus, the futures market is useful for price discovery, i.e., obtaining the market’s forecast of the spot exchange rate at different future dates.


6. What is meant by the terminology that an option is in-, at-, or out-of-the-money?


Answer: A call (put) option with St > E (E > St) is referred to as trading in-the-money. If St  E the option is trading at-the-money. If St < E (E < St) the call (put) option is trading out-of-the-money.


7. List the arguments (variables) of which a FX call or put option model price is a function. How does the call and put premium change with respect to a change in the arguments?


Answer: Both call and put options are functions of only six variables: St, E, ri, rus, T and . When all else remains the same, the price of a European FX call (put) option will increase:

1. the larger (smaller) is S,

2. the smaller (larger) is E,

3. the smaller (larger) is ri,

4. the larger (smaller) is rus,

5. the larger (smaller) rus is relative to ri, and

6. the greater is .

When rus and ri are not too much different in size, a European FX call and put will increase in price when the option term-to-maturity increases. However, when rus is very much larger than ri, a European FX call will increase in price, but the put premium will decrease, when the option term-to-maturity increases. The opposite is true when ri is very much greater than rus. For American FX options the analysis is less complicated. Since a longer term American option can be exercised on any date that a shorter term option can be exercised, or a some later date, it follows that the all else remaining the same, the longer term American option will sell at a price at least as large as the shorter term option.


PROBLEMS


1. Assume today’s settlement price on a CME DM futures contract is $0.6080/DM. You have a short position in one contract. Your margin account currently has a balance of $1,700. The next three days’ settlement prices are $0.6066, $0.6073, and $0.5989. Calculate the changes in the margin account from daily marking-to-market and the balance of the margin account after the third day.


Solution: $1,700 + [($0.6080 - $0.6066) + ($0.6066 - $0.6073)

+ ($0.6073 - $0.5989)] x DM125,000 = $2,837.50,

where DM125,000 is the contractual size of one DM contract.


2. Do problem 1 over again assuming you have a long position in the futures contract.


Solution: $1,700 + [($0.6066 - $0.6080) + ($0.6073 - $0.6066) + ($0.5989 - $0.6073)] x DM125,000 = $562.50,

where DM125,000 is the contractual size of one DM contract.

With only $562.50 in your margin account, you would experience a margin call requesting that additional cash be added to the margin account to bring it back up to the initial margin level.


3. Using the quotations in Exhibit 9.3, calculate the face value of the open interest in the December 1999 Swiss franc futures contract.


Solution: 172 contracts x SF125,000 = SF21,500,000.

where SF125,000 is the contractual size of one SF contract.


4. Using the quotation in Exhibit 9.3, note that the March 2000 Mexican peso futures contract has a price of $0.11695. You believe the spot price in March will be $0.09550. What speculative position would you enter into to attempt to profit from your beliefs? Calculate your anticipated profits assuming you take a position in three contracts. What is the size of your profit (loss) if the futures price is indeed an unbiased predictor of the future spot price and this price materializes?


Solution: If you expect the Mexican peso to rise from $0.09550 to $0.11000, you would take a long position in futures since the futures price of $0.09550 is less than your expected spot price.

Your anticipated profit from a long position in three contracts is: 3 x ($0.11000 - $0.09550) x MP500,000 = $21,750.00, where MP500,000 is the contractual size of one MP contract.

If the futures price is an unbiased predictor of the expected spot price, the expected spot price is the futures price of $0.09550/MP. If this spot price materializes, you will not have any profits or losses from your short position in three futures contracts: 3 x ($0.09550 - $0. 09550) x MP500,000 = 0.


5. Do problem 4 over again assuming you believe the March 2000 spot price will be $0.08500.


Solution: If you expect the Mexican peso to depreciate from $0.09550 to $0.08500, you would take a short position in futures since the futures price of $0. 09550 is greater than your expected spot price.

Your anticipated profit from a short position in three contracts is: 3 x ($0.09550 - $0.08500) x MP500,000 = $15,750.00.

If the futures price is an unbiased predictor of the future spot price and this price materializes, you will not profit or lose from your long futures position.


6. Recall the forward rate agreement (FRA) example in Chapter 6. Show how the bank can alternatively use a position in Eurodollar futures contracts to hedge the interest rate risk created by the maturity mismatch it has with the $3,000,000 six-month Eurodollar deposit and rollover Eurocredit position indexed to three-month LIBOR. Assume the bank can take a position in Eurodollar futures contracts maturing in three months’ time that have a futures price of 94.00.


Solution: To hedge the interest rate risk created by the maturity mismatch, the bank would need to buy (go long) three Eurodollar futures contracts. If on the last day of trading, three-month LIBOR is 5 1/8%, the bank will earn a profit of $6,562.50 from its futures position. This is calculated as:

[94.875 - 94.00] x 100 bp x $25 x 3 contracts = $6,562.50.

Note that this sum differs slightly from the $6,550.59 profit that the bank will earn from the FRA for two reasons. First, the Eurodollar futures contract assumes an arbitrary 90 days in a three-month period, whereas the FRA recognizes that the actual number of days in the specific three-month period is 91 days. Second, the Eurodollar futures contract pays off in future value terms, or as of the end of the three-month period, whereas the FRA pays off in present value terms, or as of the beginning of the three-month period.


7. Use the quotations in Exhibit 9.6 to calculate the intrinsic value and the time value of the 80 ½ September Japanese yen American put options.


Solution: Premium - Intrinsic Value = Time Value

80 ½ Sep Put .60 - [80.5 – 82.64 = - 2.14] = 2.74 cents per 100 yen


8. Assume spot Swiss franc is $0.7000 and the six-month forward rate is $0.6950. What is the minimum price that a six-month American call option with a striking price of $0.6800 should sell for in a rational market? Assume the annualized six-month Eurodollar rate is 3 ½ percent.


Solution:

Note to Instructor: A complete solution to this problem relies on the boundary expressions presented in endnote 2 of the text of Chapter 9.

CaMax[(70 - 68), (69.50 - 68)/(1.0175), 0]

Max[ 2, 1.47, 0] = 2 cents


9. Do problem 8 over again assuming an American put option instead of a call option.


Solution: PaMax[(68 - 70), (68 - 69.50)/(1.0175), 0]

Max[ -2, -1.47, 0] = 0 cents


10. Use the European option pricing models developed in the chapter to value the call of problem 8 and the put of problem 9. Assume the annualized volatility of the Swiss franc is 14.2 percent. This problem can be solved using the FXOPM.xls spreadsheet.


Solution:

d1 = [ln(69.50/68) + .5(.142)2(.50)]/(.142).50 = .2675

d2 = d1 - .142.50 = .2765 - .1004 = .1671

N(d1) = .6055

N(d2) = .5664

N(-d1) = .3945

N(-d2) = .4336

Ce = [69.50(.6055) - 68(.5664)]e-(.035)(.50) = 3.51 cents

Pe = [68(.4336) - 69.50(.3945)]e-(.035)(.50) = 2.03 cents


11. Use the binomial option-pricing model developed in the chapter to value the call of problem 8. The volatility of the Swiss franc is 14.2 percent.


Solution: The spot rate at T will be either 77.39¢ = 70.00¢(1.1056) or 63.32¢ = 70.00¢(.9045), where u = e.142.50 = 1.1056 and d = 1/u = .9045. At the exercise price of E = 68, the option will only be exercised at time T if the Swiss franc appreciates; its exercise value would be CuT = 9.39¢ = 77.39¢ - 69. If the Swiss franc depreciates it would not be rational to exercise the option; its value would be CdT = 0.


The hedge ratio is h = (9.39 – 0)/(77.39 – 63.32) = .6674.


Thus, the call premium is:


C0 = Max{[69.50(.6674) – 68((70/68)(.6674 – 1) +1)]/(1.0175), 70 – 68}


= Max[1.64, 2] = 2 cents per SF.

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