Download Futures, Forwards, Options and Swaps FOCUS OF THE CHAPTER

PART 5: RISK MANAGEMENT
CHAPTER 15:
Hedging Instruments:
Futures, Forwards, Options and Swaps
FOCUS OF THE CHAPTER
This chapter explores some derivative products traded in derivative markets. These
include hedging instruments such as futures, forwards, options, and swaps. The
chapter begins with important definitions for the study of these instruments and ends with
a discussion of the importance of hedging in the financial system.
Learning Objectives:
 Identify how derivatives are created 
 Describe the roles that uncertainty and the desire to reduce risk play in derivative
products
 Explain the crucial difference between a hedger and a speculator
 Determine how investors can buy or sell a financial asset in the future at a price
negotiated today
 Identify the differences between futures and forward contracts
 Describe how the values of options are determined and their role in financial markets
 Explain how swaps function 
SECTION SUMMARIES
Definitions
Hedging is the process of protecting oneself against future price changes by assuming
two (or more) complementary positions in assets whose returns are to some degree
negatively correlated or ideally, perfectly negatively correlated. For example, a farmer
who is growing wheat is long in wheat. He or she would profit from a rise in the price of
wheat but would lose as a result of a fall in the price. If the farmer took a short position in
say, a wheat futures contract, wherein he or she agrees to sell wheat at a predetermined
price, the wheat futures contract would rise in value if wheat prices fell (and fall in value
if they rose) and the gains on the futures contract would offset some or all of the losses on
the wheat crop. The farmer would, however, forfeit the possibility of a gain on rising
wheat prices. The farmer is, however, presumably interested from profiting from growing
wheat, not in speculating on wheat prices.
Hedger is the one who wants to shift risk away from himself or herself by assuming two
or more offsetting positions.
Speculator is the one who accepts a greater risk, with a view to profit from the change in
the asset’s price. The speculator only holds either a long position to profit from a
potential rise in price or a short position to profit from a fall in price.
Hedge funds represent a pooling of funds from wealthy investors and large institutional
investors that use spot and derivative market instruments to reduce investment risk (by
combining leverage and short-selling).
Margin is the amount of cash (deposit) put up by the investor as a security against the
purchase of an asset or used to ensure that a particular contract is fulfilled. The margin is
a fraction of the value of the asset. In the case of futures contracts, the margin is simply a
performance bond.
Financial Futures and Forwards
Future contracts are agreements to accept (buy) or make delivery of (sell) an asset on a
particular future date at a price struck today. In a spot market (cash market), the asset is
delivered at the same time as the determination of price. Future contracts are made both
in financial and commodity markets.
Financial futures are an innovation of recent decades. Following the post-war
system of fixed exchange rates, many countries moved towards deregulation of financial
systems in response to the problem of exchange rate variability. This resulted in increased
volatility in the prices of all financial assets, leading to the emergence of financial
futures.
Forward Markets: Forward contracts are made in forward markets. In a forward contract,
the seller undertakes to provide the buyer with an amount of an asset at some future date
at a price agreed to in advance.
Forward and Futures Markets Compared: Forward and futures markets are alike in many ways:
both deal in durable storable products; both can be used for hedging; both require estimates of the
future from participants. They are different in that: a) the buyer in a forward contract generally
intends to take future delivery of the asset, whereas futures market participants typically intend to
make offset transactions; b) forward contract participants are directly responsible for ensuring
that the terms of agreement are fulfilled, while in a futures contract, an intermediary ensures that
the payment and delivery are made; c) forward contracts are concluded over the phone, while
futures markets operate in an auction setting (see Table 15.1 in the text); and d) futures contracts
are standardized as to the size of the contract and the delivery dates.
The Forward Market in Operation: A Canadian importer expects to receive US$2,000,000 worth
of widgets in three months. At the current exchange rate (US$1 = C$1.50), the Canadian dollar
cost would be C$3,000,000. The importer believes that the exchange rate will change to US$1 =
C$1.60 (i.e., the Canadian dollar will depreciate), and that the cost of imports in Canadian dollars
will rise, in three months. If this were to happen the cost would be C$3,200,000. To avoid this
foreign exchange risk, the importer can arrange with a bank to deliver US$2,000,000 in three
months at today’s prevailing forward exchange rate, say US$1 = C$1.55. With this forward
contract the cost of imports is fixed at
C$3,100,000, which is less than the otherwise anticipated cost of C$3,200,000. This is a simple
example which ignores several considerations.
The Workings of Futures Markets: In futures markets, an individual who expects that
some asset prices will rise (fall) is said to take a long position (short position). The long
position is the purchase of an asset that is to be held until it matures or must be sold. The
short position is the sale and delivery of an asset in the future, with the intent to buy it at
a lower price. Hedging requires one person to take a long position and another to take a
short position. It may involve taking one position in the spot market and an opposite
position in futures market.
The difference between the futures price [F(t)] and the spot price [S(t)] is known
as the basis:
F(t) - S(t) = basis
For commodity futures, basis represents the cost of carry for the time between the date of
the futures contract and the delivery or completion date, in effect, the remaining life of
the futures contract. The cost of carry is comprised of interest of financing cost, plus
insurance and storage costs for the underlying commodity. For commodity futures basis
will generally be positive and will diminish as the completion date is approached. For
financial futures, basis can be positive or negative depending on whether the cost of
financing the asset exceeds or falls short of the interest income from the underlying asset.
Futures contracts are mark-to-market or marked-to market, which means that gains
and losses are settled at the close of trading each day, not at the end of the contract. The
reporting of financial futures differs from that of spot markets. The prices listed are
points of 100 percent, not percentages of face value. Brisk trade in futures means that
their market price changes almost constantly. There are limits on how much the price of
an instrument can vary during any one day. Stock index futures are sold in multiples of
the prevailing index.
A Long Hedge: A long hedge involves an attempt to reduce the risk of rising financial
asset prices due to lower future interest rates. For example, suppose that interest rates are
high now and that an investor expects them to fall. The investor also expects to receive
$100,000 in three months. If the interest rates do fall, the yield on the asset the investor
purchases will be less than the yield the same asset would produce today. This implies a
loss of potential interest income. To reduce this risk (or loss), the investor can lock into
the current high interest rates by taking a long position in a financial futures contract
today. If interest rates do fall as the investor feared, the futures contract will gain value
and this gain will offset the loss resulting from the falling returns on his or her future
investment.
A Short Hedge: A short hedge involves an attempt to reduce the risk of falling financial
asset prices due to higher future interest rates. For example, suppose that an investor
owns a $100,000, 9% Government of Canada bond due today, and that the bond sells at
87.35 in the spot market. A futures contract is sold at a cash price of 95. The investor
expects a fall in bond prices to 86.8 in three months. The investor can reduce the potential
loss by selling the equivalent of a $100,000 bond in futures at a cash price of 95, and
buying a futures contract at a lower cash price in three months.
The Difficulty of Perfect Hedges: The sequence of future market transactions that would
produce a gain exactly equal to the loss is called a perfect hedge. A perfect hedge is
unlikely for several reasons: 1) it is not always possible to buy and sell the same asset in
the futures market; 2) spot and futures prices do not necessarily move in concert; and 3)
futures prices in both the spot and futures markets are uncertain. Therefore, hedging
cannot eliminate risk entirely.
Future Prices and Spot Prices: The futures price [F(t)] is the spot price [S(t)] plus the
cost of carry, which is the opportunity cost of carrying the contract until delivery.
F(t) = S(t) + [(RS- RL) (-t)/360)S(t)]
where RS is the yield on a short-term instrument, RL is the yield on a long-term
instrument,  is the date of the delivery, t is the today’s date. Note that as the delivery
date approaches, the cost of carry approaches zero and F(t) = S(t).
Financial Options and Swaps
An option is the right (but not the obligation) to buy or sell a given amount of a
particular security at a particular price in the cash or futures market before a specified
expiration date.
The set price of options is called the exercise or strike price. The right to buy a
financial asset is a call option. The call price includes the interest and hence is greater
than the face value. A put option is the right to sell a financial asset. A call option whose
strike price is below (above) the market price is said to be "in the money" ("out of the
money"). The buyer of a call option (put option) is protected against unexpected price
increases (decreases), while the buyer of a put option is protected against unanticipated
decreases in price.
The Mechanics of an Option: Two Illustrations: Suppose a Canadian exporter expects
future exports earnings in US dollars, and wants to protect the Canadian dollar value of
those export earnings from falling due to future exchange rate changes. The exporter can
purchase a put option at a certain strike price (say, C$1.45 per US$1), and thereby protect
against the exchange rate falling below the strike price. A call option can be used to
protect against the exchange rate rising above the strike price.
Figure 15.1 shows how a put option places a minimum value on the US dollar
and how a call option places a maximum value on the US dollar. Figure 15.2 shows how
options narrow the distribution of asset returns and reduce interest rate risk.
The Value of Options: The value of a call at expiration (Call) is given by:
Call = MAX {0, S-E}
where S is spot price, E is exercise price, and MAX means maximum. The value of a put
option (Put) is given by:
Put = MAX{0, E-S}
where S is spot price, E is exercise price, and MAX means maximum.
The values determined by the above formulas are actually referred to as intrinsic values.
Options will always trade in the market at prices that are at least equal to their intrinsic
values. However, options also have a time value which, according to the Black-Scholes
options pricing model, includes at least three other factors, the anticipated volatility of an
underlying asset’s price, the interest on a riskless asset, and the time until the exercise
date. The value of the options is the sum of its intrinsic value and its time value.
A Numerical Example: This example shows how a British company which wants to
purchase C$2,000,000 in 90 days, and anticipates an appreciation of the Canadian dollar,
protects itself from a possible increase in the cost of purchasing Canadian dollars by
purchasing a call option.
Speculating with Options: Options are an attractive method of speculating. Purchasers of
call options can speculate on a rise in the price of a stock without buying the stock. They
are therefore, highly leveraged. This does, however, imply considerable risk. Puts are an
alternative to selling short.
Hedging with Options:
As discussed above, hedging involves the assumption of two positions in different
securities whose returns are negatively correlated. An investor who owns a particular
stock who is worried about a short term decline in market value (but doesn’t want to sell
the stock) can use a put to offset the losses from a possible decline in price. An investor
who has taken a short position in a stock can offset some of his or her risk by purchasing
a call option.
Swaps: Interest rate swaps and foreign exchange swaps are derivatives designed to
protect lenders and borrowers from unfavourable changes in interest rates and exchange
rates.
A swap is an agreement to exchange, for a pre-agreed period into the future, a series of
interest payments or foreign exchange at fixed rates for a series of available interest
payments or for foreign currency at a variable exchange rate. Note that, in the case of
swaps, the ownership of the underlying asset does not change.
The Importance of Hedging in the Financial System
The dollar value of futures and options is difficult to measure since they appear as offbalance sheet items in the financial statements of chartered banks. Banks, large
corporations, and small businesses all use derivatives to hedge against unfavourable
changes in interest rates and exchange rates. Globally, hedging instruments have spread
rapidly. Among the derivative products, swaps pose relatively less "systematic risk" in
the financial system than do other derivative products.
MULTIPLE-CHOICE QUESTIONS
1. The process of protecting oneself against future price changes by taking both a long
and a short position is called
a) speculation.
b) hedging.
c) portfolio diversification.
d) portfolio management.
2. A speculator is an individual
a) who holds only a long or a short position with respect to a particular asset.
b) who wants to shift risk away from him/herself.
c) who is a risk averter.
d) who is a money market dealer.
3. A deposit placed as security against the purchase of an asset is called
a) principal.
b) value of the option.
c) margin.
d) face value.
4. An agreement entered into by two parties to buy and sell an asset at a specified future
date at a price struck today
a) is a futures contract.
b) is a forward contract.
c) is neither a futures contract nor a forward contract.
d) is a spot market transaction.
5. Futures are similar to forward contracts except that
a) they are standardized as to contract size and delivery date.
b) they are exchange traded.
c) a clearing house assumes the opposite position to each trader.
d) all of the above.
6. A typical futures market participant
a) is likely to engage in offset transactions before the delivery date.
b) is unlikely to engage in offset transactions before the delivery date.
c) could be a speculator or hedger.
d) a) and c).
7. A speculator who takes a long position in a futures contract
a) hopes and expects the underlying asset price to rise in future.
b) hopes and expects the underlying asset price to fall in future.
c) expects the underlying asset price to rise in future but hopes that it falls.
d) expects the underlying asset price to fall in future but hopes that it rises.
8. A hedger who takes a long position in a futures contract
a) is worried that the underlying asset price will rise in future.
b) is worried that the underlying asset price will fall in future.
c) expects the underlying asset price to rise in future but hopes that it falls.
d) expects the underlying asset price to fall in future but hopes that it rises.
9. An individual who takes a short position in a financial futures contract
a) expects interest rates and asset prices to rise in future.
b) expects interest rates and asset prices to fall in future.
c) expects interest rates to rise and asset prices to fall in future.
d) expects interest rates to fall and asset prices to rise in future.
10. In a futures contract, basis is
a) the sum of the spot price and the futures price of the asset.
b) the futures price divided by the spot price of the asset.
c) the futures price multiplied by the spot price of the asset.
d) the difference between the futures price and the spot price of the asset.
11. A perfect hedge produces
a) gains in excess of losses.
b) gains twice the losses.
c) only gains and not losses.
d) gains exactly equal to losses.
12. The intrinsic value of a put option is given by (where E is the exercise price and S is
the spot price)
a) Put = MAX{0, E-S}.
b) Put = MIN{0, E-S}.
c) Put = MAX{0, S-E}.
d) Put = MAX{0, E+S}.
13. Derivative products such as futures, options, and swaps
a) are risk-free assets in the financial system.
b) reduce the systematic risk in the financial system.
c) increase the systematic risk in the financial system.
d) do not increase or decrease the systematic risk in the financial system.
PROBLEMS
1. A Canadian asset holder can purchase a US security for $1200 and sell it for $1350 one
year later.
a) What is the yield on the US security?
b) If the spot exchange rate is $1.20 (i.e., C$1.20 = US$1.00) and $1.30 one year later,
what will be the effective yield to the Canadian investor?
c) If the spot exchange rate is $1.20 (i.e., C$1.20 = US$1.00) and $1.00 one year later,
what will be the effective yield to the Canadian investor?
2. Suppose that you need 500,000 US dollars in 90 days and expect the US dollar to
appreciate. The spot rate is C$1.20 and the exercise price on a call 90 days from today
is C$1.30. Each option is for the purchase of US$100,000. Suppose also that you have
to purchase the call option at a premium of C$0.02 per US$1. Would you exercise the
option if the spot rate 90 days from today increased to C$1.35?
3. Suppose that silver sold for $10/oz in the spot market. Futures can be bought for
$7.50/oz and sold for $10.90/oz. What would be the net cost of financing 5000 oz?
Explain.
4. Explain the difference between each of the following pairs.
a) hedger and speculator
b) forward market and futures market
c) call option and put option
ANSWER SECTION
Answers to multiple-choice questions:
1.
2.
3.
4.
5.
6.
b
a
c
b
d
d
(see page 290)
(see page 290)
(see page 290)
(see page 291)
(see pages 291-292)
(see pages 292-293)
7.
8.
9.
10.
11.
12.
13.
a
a
c
d
d
a
c
(see page 295)
(see page 295-296)
(see pages 296-297)
(see page 298)
(see page 297)
(see page 302)
(see pages 305)
Answers to problems:
1.
(a) (1350-1200)/1200 = 0.125 (or 12.5%).
(b) The yield in Canadian dollars can be calculated as follows:
[(1350 x 1.30) - (1200 x 1.20)]/(1200 x 1.20) = (1755-1440)/1440
= 0.21875 (or 21.875%)
(c) The yield in Canadian dollars can be calculated as follows:
[(1350 x 1.00) - (1200 x 1.20)]/(1200 x 1.20) = (1350-1440)/1440
= -0.0625 (or -6.25%)
2. Cost of exercising the option = C$1.30 x 500,000 + C$0.02 x 500,000
= C$650,000.00 + C$10,000.00
= C$660,000.00
Cost at the spot rate 90 days from today = C$1.35 x 500,000
= C$575,000.00
Therefore, exercising the option is relatively less costly.
3. If unhedged, the cost of the unhedged purchase would be $10 x 5000 = $50,000.
If hedged, the purchase cost would be $7.50 x 5000 = $37,500; sales revenue would be
$10.90 x 5000 = $54,500, and profit generated would be $(54,000-37,000) = $17,000.
The net cost, therefore, would be $(50,000-17,000) = $33,000.
4.a) A hedger is one who wants to shift risk away from him/herself. A speculator is one
who accepts a greater risk with a view to profit from the change in an asset’s price.
b) A futures contract is a contract to buy or sell an asset at a specified future date. A
forward contract is a contract according to which a seller agrees to sell an amount
of an asset to a buyer at a future date at a price agreed upon in advance.
c) A call option is the right, but not obligation, to buy an asset at a particular price
during a stipulated period. A put option is the right, but not obligation, to sell an
asset at a particular price during a stipulated period.