George Johnson is considering a $100 million floating rate bank loan tied to LIBOR. He is concerned about LIBOR rising and wants to hedge this risk using December Eurodollar futures contracts. The contracts expire on December 20, 1999, have a $1 million contract size and 7.3% discount yield. Johnson will ignore cash flow implications of marking to market, initial margins, and timing differences between futures and interest payments.
Determinants of exchange rates - International Business - Manu Melwin Joymanumelwin
International parity conditions: Relative purchasing power parity, interest rate parity, Domestic Fisher effect, International Fisher effect. Though to some extent the above theories provide logical explanation for the fluctuations in exchange rates, yet these theories falter as they are based on challengeable assumptions [e.g., free flow of goods, services and capital] which seldom hold true in the real world.
There are many of similarities between forex trading and Futures. First, they both use the same platforms, charts and pricing methods, authorize traders to guess the price movements of commodities, indices and currencies all from one account.
Determinants of exchange rates - International Business - Manu Melwin Joymanumelwin
International parity conditions: Relative purchasing power parity, interest rate parity, Domestic Fisher effect, International Fisher effect. Though to some extent the above theories provide logical explanation for the fluctuations in exchange rates, yet these theories falter as they are based on challengeable assumptions [e.g., free flow of goods, services and capital] which seldom hold true in the real world.
There are many of similarities between forex trading and Futures. First, they both use the same platforms, charts and pricing methods, authorize traders to guess the price movements of commodities, indices and currencies all from one account.
Options Pricing The Black-Scholes ModelMore or .docxhallettfaustina
*
Options Pricing: The Black-Scholes ModelMore or less, the Black-Scholes (B-S) Model is really just a fancy extension of the Binomial Model.
(Fancy enough, however, to win a Nobel Prize…).
*
How B-S extends the Binomial Model1. Instead of assuming two possible states for future exchange rates, and thus returns (i.e., “up” and “down”), B-S assumes a continuous distribution of returns, R, so that returns can take on a whole range of values.
Binomial B-S
*
How B-S extends the Binomial ModelIn fact, exchange rate returns are approximately normally distributed, so this is a “reasonable” assumption:
*
How B-S extends the Binomial Model2. Instead of just one time period, B-S assumes multiple time periods and that the time between periods is instantaneous (i.e., continuous).
(See lecture)
Also, the time between periods t=0, t=1, t=2, etc. shrinks to zero, so that spot rate is changing at every instant.
*
How B-S extends the Binomial ModelThis is more realistic, since actual currency trades take place on a second-to-second, nearly continuous basis.
*
How B-S extends the Binomial ModelIt turns out that these two extensions are enough to make the math very hard. Thus, deriving the B-S model is no easy task.
The most important thing to recognize is that despite the above complications, the basic underlying approach of the B-S model remains the same…
*
How B-S extends the Binomial Model3. Create a replicating portfolio and price the option using a no-arbitrage argument.Calculate NS and NB: Now, since these are constantly changing over time, this process is called “dynamic hedging”.Replicating portfolio:It turns out that it is possible to use a combination of foreign currency and USD, and now in addition, options themselves, to form a riskless portfolio (i.e., return is known for sure).No-arbitrage: Riskless portfolios must have the same price as risk-free securities, otherwise arbitrage is possible. Use this fact to figure out c.
*
The Black-Scholes Options Pricing FormulaPutting the above all together, we get the Black-Scholes formula for pricing a European call option on foreign currency:
where
and S, X, T as before
r = domestic risk-free rate, r* = foreign risk-free rate
s = volatility of the foreign currency (sd of returns).
*
The Black-Scholes Options Pricing Formula
Also, N(x) = Prob that a random variable will be less than x under the standard normal distribution (i.e., cumulative distribution function).Calculate in EXCEL using “=NORMSDIST(x)”.
represents discounting when interest rates are continuously compounded, so basically it corresponds to:
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what is the future of Pi Network currency.DOT TECH
The future of the Pi cryptocurrency is uncertain, and its success will depend on several factors. Pi is a relatively new cryptocurrency that aims to be user-friendly and accessible to a wide audience. Here are a few key considerations for its future:
Message: @Pi_vendor_247 on telegram if u want to sell PI COINS.
1. Mainnet Launch: As of my last knowledge update in January 2022, Pi was still in the testnet phase. Its success will depend on a successful transition to a mainnet, where actual transactions can take place.
2. User Adoption: Pi's success will be closely tied to user adoption. The more users who join the network and actively participate, the stronger the ecosystem can become.
3. Utility and Use Cases: For a cryptocurrency to thrive, it must offer utility and practical use cases. The Pi team has talked about various applications, including peer-to-peer transactions, smart contracts, and more. The development and implementation of these features will be essential.
4. Regulatory Environment: The regulatory environment for cryptocurrencies is evolving globally. How Pi navigates and complies with regulations in various jurisdictions will significantly impact its future.
5. Technology Development: The Pi network must continue to develop and improve its technology, security, and scalability to compete with established cryptocurrencies.
6. Community Engagement: The Pi community plays a critical role in its future. Engaged users can help build trust and grow the network.
7. Monetization and Sustainability: The Pi team's monetization strategy, such as fees, partnerships, or other revenue sources, will affect its long-term sustainability.
It's essential to approach Pi or any new cryptocurrency with caution and conduct due diligence. Cryptocurrency investments involve risks, and potential rewards can be uncertain. The success and future of Pi will depend on the collective efforts of its team, community, and the broader cryptocurrency market dynamics. It's advisable to stay updated on Pi's development and follow any updates from the official Pi Network website or announcements from the team.
US Economic Outlook - Being Decided - M Capital Group August 2021.pdfpchutichetpong
The U.S. economy is continuing its impressive recovery from the COVID-19 pandemic and not slowing down despite re-occurring bumps. The U.S. savings rate reached its highest ever recorded level at 34% in April 2020 and Americans seem ready to spend. The sectors that had been hurt the most by the pandemic specifically reduced consumer spending, like retail, leisure, hospitality, and travel, are now experiencing massive growth in revenue and job openings.
Could this growth lead to a “Roaring Twenties”? As quickly as the U.S. economy contracted, experiencing a 9.1% drop in economic output relative to the business cycle in Q2 2020, the largest in recorded history, it has rebounded beyond expectations. This surprising growth seems to be fueled by the U.S. government’s aggressive fiscal and monetary policies, and an increase in consumer spending as mobility restrictions are lifted. Unemployment rates between June 2020 and June 2021 decreased by 5.2%, while the demand for labor is increasing, coupled with increasing wages to incentivize Americans to rejoin the labor force. Schools and businesses are expected to fully reopen soon. In parallel, vaccination rates across the country and the world continue to rise, with full vaccination rates of 50% and 14.8% respectively.
However, it is not completely smooth sailing from here. According to M Capital Group, the main risks that threaten the continued growth of the U.S. economy are inflation, unsettled trade relations, and another wave of Covid-19 mutations that could shut down the world again. Have we learned from the past year of COVID-19 and adapted our economy accordingly?
“In order for the U.S. economy to continue growing, whether there is another wave or not, the U.S. needs to focus on diversifying supply chains, supporting business investment, and maintaining consumer spending,” says Grace Feeley, a research analyst at M Capital Group.
While the economic indicators are positive, the risks are coming closer to manifesting and threatening such growth. The new variants spreading throughout the world, Delta, Lambda, and Gamma, are vaccine-resistant and muddy the predictions made about the economy and health of the country. These variants bring back the feeling of uncertainty that has wreaked havoc not only on the stock market but the mindset of people around the world. MCG provides unique insight on how to mitigate these risks to possibly ensure a bright economic future.
Empowering the Unbanked: The Vital Role of NBFCs in Promoting Financial Inclu...Vighnesh Shashtri
In India, financial inclusion remains a critical challenge, with a significant portion of the population still unbanked. Non-Banking Financial Companies (NBFCs) have emerged as key players in bridging this gap by providing financial services to those often overlooked by traditional banking institutions. This article delves into how NBFCs are fostering financial inclusion and empowering the unbanked.
how to sell pi coins effectively (from 50 - 100k pi)DOT TECH
Anywhere in the world, including Africa, America, and Europe, you can sell Pi Network Coins online and receive cash through online payment options.
Pi has not yet been launched on any exchange because we are currently using the confined Mainnet. The planned launch date for Pi is June 28, 2026.
Reselling to investors who want to hold until the mainnet launch in 2026 is currently the sole way to sell.
Consequently, right now. All you need to do is select the right pi network provider.
Who is a pi merchant?
An individual who buys coins from miners on the pi network and resells them to investors hoping to hang onto them until the mainnet is launched is known as a pi merchant.
debuts.
I'll provide you the Telegram username
@Pi_vendor_247
USDA Loans in California: A Comprehensive Overview.pptxmarketing367770
USDA Loans in California: A Comprehensive Overview
If you're dreaming of owning a home in California's rural or suburban areas, a USDA loan might be the perfect solution. The U.S. Department of Agriculture (USDA) offers these loans to help low-to-moderate-income individuals and families achieve homeownership.
Key Features of USDA Loans:
Zero Down Payment: USDA loans require no down payment, making homeownership more accessible.
Competitive Interest Rates: These loans often come with lower interest rates compared to conventional loans.
Flexible Credit Requirements: USDA loans have more lenient credit score requirements, helping those with less-than-perfect credit.
Guaranteed Loan Program: The USDA guarantees a portion of the loan, reducing risk for lenders and expanding borrowing options.
Eligibility Criteria:
Location: The property must be located in a USDA-designated rural or suburban area. Many areas in California qualify.
Income Limits: Applicants must meet income guidelines, which vary by region and household size.
Primary Residence: The home must be used as the borrower's primary residence.
Application Process:
Find a USDA-Approved Lender: Not all lenders offer USDA loans, so it's essential to choose one approved by the USDA.
Pre-Qualification: Determine your eligibility and the amount you can borrow.
Property Search: Look for properties in eligible rural or suburban areas.
Loan Application: Submit your application, including financial and personal information.
Processing and Approval: The lender and USDA will review your application. If approved, you can proceed to closing.
USDA loans are an excellent option for those looking to buy a home in California's rural and suburban areas. With no down payment and flexible requirements, these loans make homeownership more attainable for many families. Explore your eligibility today and take the first step toward owning your dream home.
Resume
• Real GDP growth slowed down due to problems with access to electricity caused by the destruction of manoeuvrable electricity generation by Russian drones and missiles.
• Exports and imports continued growing due to better logistics through the Ukrainian sea corridor and road. Polish farmers and drivers stopped blocking borders at the end of April.
• In April, both the Tax and Customs Services over-executed the revenue plan. Moreover, the NBU transferred twice the planned profit to the budget.
• The European side approved the Ukraine Plan, which the government adopted to determine indicators for the Ukraine Facility. That approval will allow Ukraine to receive a EUR 1.9 bn loan from the EU in May. At the same time, the EU provided Ukraine with a EUR 1.5 bn loan in April, as the government fulfilled five indicators under the Ukraine Plan.
• The USA has finally approved an aid package for Ukraine, which includes USD 7.8 bn of budget support; however, the conditions and timing of the assistance are still unknown.
• As in March, annual consumer inflation amounted to 3.2% yoy in April.
• At the April monetary policy meeting, the NBU again reduced the key policy rate from 14.5% to 13.5% per annum.
• Over the past four weeks, the hryvnia exchange rate has stabilized in the UAH 39-40 per USD range.
how can I sell my pi coins for cash in a pi APPDOT TECH
You can't sell your pi coins in the pi network app. because it is not listed yet on any exchange.
The only way you can sell is by trading your pi coins with an investor (a person looking forward to hold massive amounts of pi coins before mainnet launch) .
You don't need to meet the investor directly all the trades are done with a pi vendor/merchant (a person that buys the pi coins from miners and resell it to investors)
I Will leave The telegram contact of my personal pi vendor, if you are finding a legitimate one.
@Pi_vendor_247
#pi network
#pi coins
#money
Poonawalla Fincorp and IndusInd Bank Introduce New Co-Branded Credit Cardnickysharmasucks
The unveiling of the IndusInd Bank Poonawalla Fincorp eLITE RuPay Platinum Credit Card marks a notable milestone in the Indian financial landscape, showcasing a successful partnership between two leading institutions, Poonawalla Fincorp and IndusInd Bank. This co-branded credit card not only offers users a plethora of benefits but also reflects a commitment to innovation and adaptation. With a focus on providing value-driven and customer-centric solutions, this launch represents more than just a new product—it signifies a step towards redefining the banking experience for millions. Promising convenience, rewards, and a touch of luxury in everyday financial transactions, this collaboration aims to cater to the evolving needs of customers and set new standards in the industry.
Turin Startup Ecosystem 2024 - Ricerca sulle Startup e il Sistema dell'Innov...Quotidiano Piemontese
Turin Startup Ecosystem 2024
Una ricerca de il Club degli Investitori, in collaborazione con ToTeM Torino Tech Map e con il supporto della ESCP Business School e di Growth Capital
how can I sell pi coins after successfully completing KYCDOT TECH
Pi coins is not launched yet in any exchange 💱 this means it's not swappable, the current pi displaying on coin market cap is the iou version of pi. And you can learn all about that on my previous post.
RIGHT NOW THE ONLY WAY you can sell pi coins is through verified pi merchants. A pi merchant is someone who buys pi coins and resell them to exchanges and crypto whales. Looking forward to hold massive quantities of pi coins before the mainnet launch.
This is because pi network is not doing any pre-sale or ico offerings, the only way to get my coins is from buying from miners. So a merchant facilitates the transactions between the miners and these exchanges holding pi.
I and my friends has sold more than 6000 pi coins successfully with this method. I will be happy to share the contact of my personal pi merchant. The one i trade with, if you have your own merchant you can trade with them. For those who are new.
Message: @Pi_vendor_247 on telegram.
I wouldn't advise you selling all percentage of the pi coins. Leave at least a before so its a win win during open mainnet. Have a nice day pioneers ♥️
#kyc #mainnet #picoins #pi #sellpi #piwallet
#pinetwork
how to swap pi coins to foreign currency withdrawable.DOT TECH
As of my last update, Pi is still in the testing phase and is not tradable on any exchanges.
However, Pi Network has announced plans to launch its Testnet and Mainnet in the future, which may include listing Pi on exchanges.
The current method for selling pi coins involves exchanging them with a pi vendor who purchases pi coins for investment reasons.
If you want to sell your pi coins, reach out to a pi vendor and sell them to anyone looking to sell pi coins from any country around the globe.
Below is the contact information for my personal pi vendor.
Telegram: @Pi_vendor_247
Even tho Pi network is not listed on any exchange yet.
Buying/Selling or investing in pi network coins is highly possible through the help of vendors. You can buy from vendors[ buy directly from the pi network miners and resell it]. I will leave the telegram contact of my personal vendor.
@Pi_vendor_247
how can i use my minded pi coins I need some funds.DOT TECH
If you are interested in selling your pi coins, i have a verified pi merchant, who buys pi coins and resell them to exchanges looking forward to hold till mainnet launch.
Because the core team has announced that pi network will not be doing any pre-sale. The only way exchanges like huobi, bitmart and hotbit can get pi is by buying from miners.
Now a merchant stands in between these exchanges and the miners. As a link to make transactions smooth. Because right now in the enclosed mainnet you can't sell pi coins your self. You need the help of a merchant,
i will leave the telegram contact of my personal pi merchant below. 👇 I and my friends has traded more than 3000pi coins with him successfully.
@Pi_vendor_247
how can i use my minded pi coins I need some funds.
Chapter7 International Finance Management
1. CHAPTER 7 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 most efficiently, two types of economic agents are
needed: hedgers and speculators. Explain.
Answer: Two types of market participants are necessary for the efficient 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
2. 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.
5. What is the major difference in the obligation of one with a long position in a futures (or forward)
contract in comparison to an options contract?
Answer: A futures (or forward) contract is a vehicle for buying or selling a stated amount of foreign
exchange at a stated price per unit at a specified time in the future. If the long holds the contract to the
delivery date, he pays the effective contractual futures (or forward) price, regardless of whether it is an
advantageous price in comparison to the spot price at the delivery date. By contrast, an option is a
contract giving the long the right to buy or sell a given quantity of an asset at a specified price at some
time in the future, but not enforcing any obligation on him if the spot price is more favorable than the
exercise price. Because the option owner does not have to exercise the option if it is to his disadvantage,
the option has a price, or premium, whereas no price is paid at inception to enter into a futures (or
forward) contract.
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.
3. 7. List the arguments (variables) of which an 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, r$, 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 r$,
5. the larger (smaller) r$ is relative to ri, and
6. the greater is .
When r$ 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 r$ 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 r$. 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.
4. PROBLEMS
1. Assume today’s settlement price on a CME EUR futures contract is $1.3140/EUR. You have a short
position in one contract. Your performance bond account currently has a balance of $1,700. The next
three days’ settlement prices are $1.3126, $1.3133, and $1.3049. Calculate the changes in the
performance bond account from daily marking-to-market and the balance of the performance bond
account after the third day.
Solution: $1,700 + [($1.3140 - $1.3126) + ($1.3126 - $1.3133)
+ ($1.3133 - $1.3049)] x EUR125,000 = $2,837.50,
where EUR125,000 is the contractual size of one EUR contract.
2. Do problem 1 again assuming you have a long position in the futures contract.
Solution: $1,700 + [($1.3126 - $1.3140) + ($1.3133 - $1.3126) + ($1.3049 - $1.3133)] x EUR125,000 =
$562.50,
where EUR125,000 is the contractual size of one EUR contract.
With only $562.50 in your performance bond account, you would experience a margin call
requesting that additional funds be added to your performance bond account to bring the balance back up
to the initial performance bond level.
3. Using the quotations in Exhibit 7.3, calculate the face value of the open interest in the March 2008
Swiss franc futures contract.
Solution: 66,265 contracts x SF125,000 = SF8,283,125,000.
where SF125,000 is the contractual size of one SF contract.
4. Using the quotations in Exhibit 7.3, note that the March 2008 Mexican peso futures contract has a
price of $0.90975 per 10MXN. You believe the spot price in March will be $0.97500 per 10MXN. 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?
5. Solution: If you expect the Mexican peso to rise from $0.90975 to $0.97500 per 10 MXN, you would
take a long position in futures since the futures price of $0.90975 is less than your expected spot price.
Your anticipated profit from a long position in three contracts is: 3 x ($0.097500 - $0.090975) x
MP500,000 = $9,787.50, where MXN500,000 is the contractual size of one MXN contract.
If the futures price is an unbiased predictor of the expected spot price, the expected spot price is the
futures price of $0.90975 per 10 MXN. If this spot price materializes, you will not have any profits or
losses from your short position in three futures contracts: 3 x ($0.090975 - $0.090975) x MP500,000 = 0.
5. Do problem 4 again assuming you believe the March 2008 spot price will be $0.77500 per 10 MXN.
Solution: If you expect the Mexican peso to depreciate from $0.90975 to $0.77500per 10 MXN, you
would take a short position in futures since the futures price of $0.90975 is greater than your expected
spot price.
Your anticipated profit from a short position in three contracts is: 3 x ($0.090975 - $0.077500) x
MP500,000 = $20,212.50.
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. George Johnson is considering a possible six-month $100 million LIBOR-based, floating-rate bank
loan to fund a project at terms shown in the table below. Johnson fears a possible rise in the LIBOR rate
by December and wants to use the December Eurodollar futures contract to hedge this risk. The contract
expires December 20, 1999, has a US$ 1 million contract size, and a discount yield of 7.3 percent.
Johnson will ignore the cash flow implications of marking to market, initial margin requirements, and any
timing mismatch between exchange-traded futures contract cash flows and the interest payments due in
March.
6. Loan Terms
September 20, 1999 December 20, 1999 March 20, 2000
Borrow $100 million at Pay interest for first three Pay back principal
September 20 LIBOR + 200 months plus interest
basis points (bps) Roll loan over at
September 20 LIBOR = 7% December 20 LIBOR +
200 bps
Loan First loan payment (9%) Second payment
initiated and futures contract expires and principal
9/20/99 12/20/99 3/20/00
a. Formulate Johnson’s September 20 floating-to-fixed-rate strategy using the Eurodollar future contracts
discussed in the text above. Show that this strategy would result in a fixed-rate loan, assuming an
increase in the LIBOR rate to 7.8 percent by December 20, which remains at 7.8 percent through March
20. Show all calculations.
Johnson is considering a 12-month loan as an alternative. This approach will result in two additional
uncertain cash flows, as follows:
Loan First Second Third Fourth payment
initiated payment (9%) payment payment and principal
9/20/99 12/20/99 3/20/00 6/20/00 9/20/00
b. Describe the strip hedge that Johnson could use and explain how it hedges the 12-month loan (specify
number of contracts). No calculations are needed.
CFA Guideline Answer
7. a. The basis point value (BPV) of a Eurodollar futures contract can be found by substituting the contract
specifications into the following money market relationship:
BPV FUT = Change in Value = (face value) x (days to maturity / 360) x (change in yield)
= ($1 million) x (90 / 360) x (.0001)
= $25
The number of contract, N, can be found by:
N = (BPV spot) / (BPV futures)
= ($2,500) / ($25)
= 100
OR
N = (value of spot position) / (face value of each futures contract)
= ($100 million) / ($1 million)
= 100
OR
N = (value of spot position) / (value of futures position)
= ($100,000,000) / ($981,750)
where value of futures position = $1,000,000 x [1 – (0.073 / 4)]
102 contracts
Therefore on September 20, Johnson would sell 100 (or 102) December Eurodollar futures contracts at
the 7.3 percent yield. The implied LIBOR rate in December is 7.3 percent as indicated by the December
Eurofutures discount yield of 7.3 percent. Thus a borrowing rate of 9.3 percent (7.3 percent + 200 basis
points) can be locked in if the hedge is correctly implemented.
A rise in the rate to 7.8 percent represents a 50 basis point (bp) increase over the implied LIBOR rate.
For a 50 basis point increase in LIBOR, the cash flow on the short futures position is:
= ($25 per basis point per contract) x 50 bp x 100 contracts
= $125,000.
However, the cash flow on the floating rate liability is:
= -0.098 x ($100,000,000 / 4)
= - $2,450,000.
Combining the cash flow from the hedge with the cash flow from the loan results in a net outflow of
$2,325,000, which translates into an annual rate of 9.3 percent:
8. = ($2,325,000 x 4) / $100,000,000 = 0.093
This is precisely the implied borrowing rate that Johnson locked in on September 20. Regardless of the
LIBOR rate on December 20, the net cash outflow will be $2,325,000, which translates into an annualized
rate of 9.3 percent. Consequently, the floating rate liability has been converted to a fixed rate liability in
the sense that the interest rate uncertainty associated with the March 20 payment (using the December 20
contract) has been removed as of September 20.
b. In a strip hedge, Johnson would sell 100 December futures (for the March payment), 100 March futures
(for the June payment), and 100 June futures (for the September payment). The objective is to hedge each
interest rate payment separately using the appropriate number of contracts. The problem is the same as in
Part A except here three cash flows are subject to rising rates and a strip of futures is used to hedge this
interest rate risk. This problem is simplified somewhat because the cash flow mismatch between the
futures and the loan payment is ignored. Therefore, in order to hedge each cash flow, Johnson simply
sells 100 contracts for each payment. The strip hedge transforms the floating rate loan into a strip of fixed
rate payments. As was done in Part A, the fixed rates are found by adding 200 basis points to the implied
forward LIBOR rate indicated by the discount yield of the three different Eurodollar futures contracts.
The fixed payments will be equal when the LIBOR term structure is flat for the first year.
7. Jacob Bower has a liability that:
has a principal balance of $100 million on June 30, 1998,
accrues interest quarterly starting on June 30, 1998,
pays interest quarterly,
has a one-year term to maturity, and
calculates interest due based on 90-day LIBOR (the London Interbank Offered
Rate).
Bower wishes to hedge his remaining interest payments against changes in interest rates.
Bower has correctly calculated that he needs to sell (short) 300 Eurodollar futures contracts to accomplish
the hedge. He is considering the alternative hedging strategies outlined in the following table.
9. Initial Position (6/30/98) in
90-Day LIBOR Eurodollar Contracts
Strategy A Strategy B
Contract Month (contracts) (contracts)
September 1998 300 100
December 1998 0 100
March 1999 0 100
a. Explain why strategy B is a more effective hedge than strategy A when the yield curve
undergoes an instantaneous nonparallel shift.
b. Discuss an interest rate scenario in which strategy A would be superior to strategy B.
CFA Guideline Answer
a. Strategy B’s Superiority
Strategy B is a strip hedge that is constructed by selling (shorting) 100 futures contracts maturing in each
of the next three quarters. With the strip hedge in place, each quarter of the coming year is hedged
against shifts in interest rates for that quarter. The reason Strategy B will be a more effective hedge than
Strategy A for Jacob Bower is that Strategy B is likely to work well whether a parallel shift or a
nonparallel shift occurs over the one-year term of Bower’s liability. That is, regardless of what happens
to the term structure, Strategy B structures the futures hedge so that the rates reflected by the Eurodollar
futures cash price match the applicable rates for the underlying liability-the 90day LIBOR-based rate on
Bower’s liability. The same is not true for Strategy A. Because Jacob Bower’s liability carries a floating
interest rate that resets quarterly, he needs a strategy that provides a series of three-month hedges.
Strategy A will need to be restructured when the three-month September contract expires. In particular, if
the yield curve twists upward (futures yields rise more for distant expirations than for near expirations),
Strategy A will produce inferior hedge results.
10. b. Scenario in Which Strategy A is Superior
Strategy A is a stack hedge strategy that initially involves selling (shorting) 300 September contracts.
Strategy A is rarely better than Strategy B as a hedging or risk-reduction strategy. Only from the
perspective of favorable cash flows is Strategy A better than Strategy B. Such cash flows occur only in
certain interest rate scenarios. For example Strategy A will work as well as Strategy B for Bower’s
liability if interest rates (instantaneously) change in parallel fashion. Another interest rate scenario where
Strategy A outperforms Strategy B is one in which the yield curve rises but with a twist so that futures
yields rise more for near expirations than for distant expirations. Upon expiration of the September
contract, Bower will have to roll out his hedge by selling 200 December contracts to hedge the remaining
interest payments. This action will have the effect that the cash flow from Strategy A will be larger than
the cash flow from Strategy B because the appreciation on the 300 short September futures contracts will
be larger than the cumulative appreciation in the 300 contracts shorted in Strategy B (i.e., 100 September,
100 December, and 100 March). Consequently, the cash flow from Strategy A will more than offset the
increase in the interest payment on the liability, whereas the cash flow from Strategy B will exactly offset
the increase in the interest payment on the liability.
8. Assume that the Japanese yen is trading at a spot price of 92.04 cents per 100 yen. Further assume that
the premium of an American call (put) option with a striking price of 93 is 2.10 (2.20) cents. Calculate
the intrinsic value and the time value of the call and put options.
Solution: Premium - Intrinsic Value = Time Value
Call: 2.10 - Max[92.04 – 93.00 = - .96, 0] = 2.10 cents per 100 yen
Put: 2.20 - Max[93.00 – 92.04 = .96, 0] = 1.24 cents per 100 yen
9. 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
footnote 3 of the text of Chapter 7.
11. Ca Max[(70 - 68), (69.50 - 68)/(1.0175), 0]
Max[ 2, 1.47, 0] = 2 cents
10. Do problem 9 again assuming an American put option instead of a call option.
Solution: Pa Max[(68 - 70), (68 - 69.50)/(1.0175), 0]
Max[ -2, -1.47, 0] = 0 cents
11. Use the European option-pricing models developed in the chapter to value the call of problem 9 and
the put of problem 10. 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
12. Use the binomial option-pricing model developed in the chapter to value the call of problem 9.
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¢ - 68. If the Swiss
franc depreciates it would not be rational to exercise the option; its value would be CdT = 0.
12. 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.
MINI CASE: THE OPTIONS SPECULATOR
A speculator is considering the purchase of five three-month Japanese yen call options with a
striking price of 96 cents per 100 yen. The premium is 1.35 cents per 100 yen. The spot price is 95.28
cents per 100 yen and the 90-day forward rate is 95.71 cents. The speculator believes the yen will
appreciate to $1.00 per 100 yen over the next three months. As the speculator’s assistant, you have been
asked to prepare the following:
1. Graph the call option cash flow schedule.
2. Determine the speculator’s profit if the yen appreciates to $1.00/100 yen.
3. Determine the speculator’s profit if the yen only appreciates to the forward rate.
4. Determine the future spot price at which the speculator will only break even.
Suggested Solution to the Options Speculator:
1. +
-
13. 2. (5 x ¥6,250,000) x [(100 - 96) - 1.35]/10000 = $8,281.25.
3. Since the option expires out-of-the-money, the speculator will let the option expire worthless. He will
only lose the option premium.
4. ST = E + C = 96 + 1.35 = 97.35 cents per 100 yen.