APPENDIX 4A: CONTINUOUS COMPOUNDING
5.7 SUMMARY
This is identical to Equation 5.10 except that Futtd/f2 is replaced by std/f2. Spot rate changes std/f2 can be substituted for futtd/f2 because futures prices converge to spot prices at maturity, and the maturity of the futures contract is the same as that of the underlying transaction exposure in the spot market.
If futures are not available in the currency that you wish to hedge, a cross hedge using a futures contract on a currency that is closely related to the desired currency can at least partially hedge against currency risk. As an example, a U.K.-based corporation can hedge a Canadian dollar (C$) obligation with a long U.S. dollar futures contract because the pound values of the U.S. dollar and the Canadian dollar are highly correlated. For a U.S. dollar hedge of a Canadian dollar obligation, the spot exposure is in Canadian dollars and the futures exposure is in U.S. dollars as in the following regression:
A cross hedge has a currency mismatch.
st£/C$=α+βfutt£/$+et (5.12) The quality of this cross-rate futures hedge is only as good as the correlation between the pound sterling values of the U.S. and Canadian dollars.
When both the maturity and the currency match that of the underlying obliga- tion, Equation 5.10 reduces to
std/f=α+βstd/f+et (5.13) Since the correlation of std/f with itself is+1, this is a perfect hedge (r-square=1) and the optimal hedge ratio is NFut∗= −β= −1. In this circumstance, the futures hedge is equivalent to a forward market hedge. There is no basis risk and currency risk can be completely eliminated.
MARKET UPDATE Competition between International Exchanges
Competition between derivatives exchanges has spawned a number of mergers, acquisitions, and alliances in the industry. One of the most active futures exchanges is the Eurex (www.eurexchange.com), which trades futures and options on indices and individual stocks, bonds, and currencies. Eurex was created in 1998 through a merger of Frankfurt’s DTB (Deutsche Terminb ¨orse) and Zurich’s SOFFEX (Swiss Options and Financial Futures Exchange). Eurex subsequently formed alliances with derivatives exchanges in Vienna (Austria), Dublin (Ireland), and the CBOT (United States).
The other large European futures exchange, Euronext (www.euronext.com), was created in 2001 through a merger of the Amsterdam, Brussels, and Paris exchanges. Euronext trades stocks, bonds, commodities, and derivatives.
Euronext acquired London’s LIFFE (London International Financial Futures Exchange) in 2001 for 907 million, a 100 percent premium to LIFFE’s pre-acquisition share price. Euronext subsequently signed deals with exchanges in Helsinki (Finland), Lisbon (Portugal), Warsaw (Poland), and Luxembourg.
Euronext LIFFE then merged with the New York Stock Exchange in 2007 to form NYSE Euronext.
Exchanges also are forming alliances in the battle for market share.
For example, the CME’s Globex trading system links derivatives trading from the CME, Euronext, Singapore (SGX), Spain (MEFF), Montreal, and Brazilian (BM&F) exchanges. Globex provides a 24-hour electronic trading platform for a variety of global derivatives contracts. Nearly 75 percent of the CME’s trading volume is conducted through Globex, with the remainder via open outcry on the exchange floor. The CME purchased the CBOT in 2006 for $8 billion in stock with the intention of further extending its Globex platform.
against transaction exposure, futures hedges are imperfect when there is a mismatch between the size, maturity, or currency of the underlying exposure and of the futures contract used to hedge the exposure. The choice between a forward or futures contract depends on the cost of each contract and on how close the underlying risk profile is to that of a standardized futures contract.
A delta hedge is used when the timing of the transaction exposed to currency risk is not the same as the maturity of available futures contracts. Although a delta hedge can eliminate currency risk, it typically cannot eliminate basis risk; that is, the risk that the relation of futures prices to spot prices will change. This is because spot and futures prices do not move in unison when there are changes in the basis — the difference in nominal interest rates between the foreign and domestic currencies.
The hedge ratio of a delta hedge can be estimated from
std/f=α+βfuttd/f+et (5.7)
where std/fand Futtd/fare percentage changes in spot and futures prices, respectively.
The hedge ratio
NFut∗=Amount in futures contracts/Amount exposed (5.9)
= −β
minimizes the risk of the hedged position.
Similarly, futures do not provide a perfect hedge when there is a currency mismatch. A futures hedge with a maturity match and using a currency that is closely related to the exposed currency is called a cross hedge. For an underlying exposure in currency f1 and a futures hedge using currency f2, the hedge ratio is estimated from the regression
std/f1 =α+βstd/f2+et (5.11) where d is the hedger’s currency of reference.
A futures hedge for which there are both currency and maturity mismatches is called a delta-cross hedge. This is the most general form of futures hedge. The hedge ratio is estimated from
std/f1 =α+βfuttd/f2+et (5.10) If the underlying exposure and the futures contract are in the same currency, then f1 =f2=f and the hedge is a delta hedge. If there is a maturity match but a currency mismatch, then futtd/f2 =std/f2 and the hedge is a cross hedge. If there is a match on both maturity and currency, then a futures hedge is equivalent to a forward market hedge and can completely eliminate currency risk so long as the underlying transaction exposure is an even increment of the futures contract size.
KEY TERMS
basis basis risk cross hedge
currency futures contract delta-cross hedge
delta hedge hedge quality
hedge ratio
margin requirement marking-to-market perfect hedge
risk profile (or payoff profile)
r-square (coefficient of determination or r2)
CONCEPTUAL QUESTIONS
5.1 How do currency forward and futures contracts differ with respect to maturity, settlement, and the size and timing of cash flows?
5.2 What is the primary role of the exchange clearinghouse?
5.3 Draw and explain the payoff profile associated with a currency futures contract.
5.4 What is a delta hedge? A cross hedge? A delta-cross hedge?
5.5 What is the basis? What is basis risk?
5.6 How do you measure the quality of a futures hedge?
PROBLEMS
5.1 Suppose that at time zero the spot rate equals the 90-day forward rate at S0$/S$=F90$/S$=$0.65/S$. Assume that the spot rate increases by $0.0002/S$
each day over the ensuing 90 days. You buy Singapore dollars in both the forward and futures markets. Draw a time line for each contract showing the cash inflows/outflows arising from the daily change in the spot rate.
5.2 On September 11, a U.S.-based MNC with a customer in Singapore expects to receive S$3 million. The current spot exchange rate is $0.5950/S$. The transfer will occur on December 10. The current S$ futures price for December delivery is $0.6075/S$. The size of the CME futures contract is S$125,000. How many futures contracts should the U.S. multinational buy or sell in order to minimize the variance of the hedged position? What is the MNC’s net profit (or loss) on December 10 if the spot rate on that date is $0.5900/S$?
5.3 Snow White Manufacturing makes snowmobiles, some of which it sells to Japan for recreation in the wilderness of the northern islands. Snow White is expecting a payment of ¥9 million in six months.
a. Draw a time line illustrating the transaction.
b. Draw a payoff profile with dollars-per-yen on the axes.
c. Suppose Snow White takes out a forward contract to hedge this transaction.
Describe this contract.
d. Describe the advantages/disadvantages to Snow White if Snow White takes out a futures contract instead of a forward contract.
5.4 Suppose Cotton Bolls, Inc. does business with companies in Israel and Singa- pore. Cotton Bolls expects to pay 500,000 Israeli shekels and receive 125,000 Singapore dollars on the Friday before the third Wednesday of April. Forward rates for that date are FT$/shekel=$0.1625/shekel and FT$/S$=$0.65/S$.
a. Show time lines illustrating each transaction.
b. How would Cotton Bolls hedge these transactions with $/shekel and $/S$
futures contracts?
c. Suppose the forward rate is S$0.2500/shekel. Describe a cross hedge that would accomplish the same objective as the two hedges in part b.
5.5 You work for Texas Instruments in the United States and are considering ways to hedge a 10 billion Danish kroner (DKK) obligation due in six months. Your currency of reference is the U.S. dollar. The current value of the kroner is S0$/DKK=$0.80/DKK in dollars and S0 /DKK= 0.75/DKK in euros.
a. A futures exchange in Copenhagen trades futures contracts on the U.S. dollar that expire in seven months with a contract size of $50,000. You estimate β=1.025 based on the regression st$/DKK=α+βfutt$/DKK+et. The r-square of the regression is 0.98. How many futures contracts should you buy to minimize the risk of your hedged position?
b. A commercial bank in Chicago is willing to sell a customized euro ( ) futures contract in any amount and maturing on the date that your obligation is due in six months. Based on the regression st$/DKK=α+βst$/ +et, you estimate β=1.04. The r-square of the regression is 0.89. How large a position in this euro futures contract should you take to minimize the risk of your hedged position?
c. Euronext in Frankfurt trades /$ futures contracts that expire in seven months and have a contract size of $50,000. Based on the regression st$/DKK= α+βfutt$/ +et, you estimate β=1.05. The r-square of this regression is 0.86. How many futures contracts should you buy to minimize the risk of your hedged position?
d. Which of these futures market hedges provides the best quality?
5.6 Refer to Figure 5.6. It is now March 13 and the current spot exchange rate between U.S. dollars ($) and Singapore dollars (S$) is $0.6010/S$. You have a S$10 million obligation due on October 26. The nearest S$ futures contract expires on December 16. Interest rates are 6.24 percent in the United States and 4.04 percent in Singapore.
a. Suppose the spot exchange rate on October 26 is $0.6089/S$. Fill in the three scenarios in Figure 5.6 assuming (1) i$=6.24% and iS$=4.04%, (2) i$=6.24% and iS$=4.54%, and (3) i$=6.74% and iS$=4.04%.
b. Suppose interest rates do not change (so that i$=6.24% and iS$=4.04%) but that the spot exchange rate does change. Fill in the three scenarios in Figure 5.6 assuming (1) St$/S$=$0.6089/S$, (2) St$/S$=$0.6255/S$, and (3) St$/S$=$0.5774/S$.
SUGGESTED READINGS
A comparison of futures and forward contracts appears in
Kenneth R. French, ‘‘A Comparison of Futures and Forward Prices,’’Journal of Financial Economics12, No. 3 (November 1983), 311 – 342.
The properties of the delta hedge ratio are developed in
Louis Ederington, ‘‘The Hedging Performance of the New Futures Markets,’’ Journal of Finance34, No. 1 (1979), 157 – 170.
Appropriate and inappropriate hedging strategies surrounding Metallgesellschaft’s crude oil futures hedges appear in
Christopher L. Culp and Merton H. Miller, ‘‘Metallgesellschaft and the Economics of Synthetic Storage,’’Journal of Applied Corporate Finance7 (Winter 1994), 62 – 76.
And in the following articles from the Journal of Applied Corporate Finance 8 (Spring 1995):
Franklin R. Edwards and Michael S. Canter, ‘‘The Collapse of Metallgesellschaft: Unhedgeable Risks, Poor Hedging Strategy, or Just Bad Luck?’’Journal of Applied Corporate Finance 8 (Spring 1995), 86 – 105.
Antonio S. Mello and John E. Parsons, ‘‘Maturity Structure of a Hedge Matters: Lessons from the Metallgesellschaft Debacle,’’Journal of Applied Corporate Finance8 (Spring 1995), 106 – 121.
Christopher L. Culp and Merton H. Miller, ‘‘Hedging in the Theory of Corporate Finance: A Reply to Our Critics,’’Journal of Applied Corporate Finance8 (Spring 1995), 121 – 128.
6
Currency Options and Options Markets
There are two times in a man’s life when he should not speculate: when he can’t afford it and when he can.
— Mark Twain
G
overnance of the multinational corporation involves creating and managing a wide variety of options. Options are embedded in the firm’s real assets, including options to expand, contract, suspend, or abandon the firm’s investments.Human resource management employs options as rewards in executive compensation contracts and in employment termination clauses. Options are attached to corporate securities in the form of call and convertibility options and interest rate caps and floors. Options insure the firm against property and casualty risks. Understanding how these options affect the firm is both a challenge and an opportunity for the financial manager.
Currency options are a useful tool for managing the multinational corporation’s exposures to currency risk. Currency options are derivative securities, in that their value is derived from the value of an underlying exchange rate. As exchange rates change, so do the values of options written on the exchange rate. This chapter employs simple graphs to develop the intuition behind option valuation and their use in hedging currency risks. The technical details of option valuation are presented in the appendix to the chapter.