Solution and Answer Guide: Don Chance, Robert Brooks, An Introduction to Derivatives and Risk Management,
11e, ©2027, 9798214057071; Chapter 1: Introduction
Solution and Answer Guide
DON CHANCE, ROBERT BROOKS, AN INTRODUCTION TO DERIVATIVES AND RISK MANAGEMENT,
11E, ©2027, 9798214057071; CHAPTER 1: INTRODUCTION
TABLE OF CONTENTS
End-of-Chapter Questions And Problems...........................................................................1
END-OF-CHAPTER QUESTIONS AND PROBLEMS
1. (LO2 Presuppositions for Financial Markets) There are at least three
presuppositions for well-functioning financial markets: a clear rule of law, well
defined clean property rights, and a culture of trust.
2. (LO4 Market Efficiency and Theoretical Fair Value) An efficient market is one
in which prices reflect the true economic values of the assets traded. trading
therein. In efficient markets, no one can earn returns that exceed those are
more than commensurate with the level of risk. Efficient markets are
characterized by low transaction costs and by the rapid incorporation of rate
at which new information is incorporated into prices.
3. (LO4 Arbitrage and the Law of One Price) Arbitrage is a type of investment
transaction that seeks to profit when identical goods are priced differently.
Buying an item at one price and immediately selling it at another is a type of
arbitrage. Because of the combined activities of arbitrageurs, identical goods,
primarily financial assets, cannot sell for different prices for long. This is the
law of one price. Arbitrage helps make our markets efficient by assuring that
prices are in line with what they are supposed to be. In short, we cannot get
something for nothing. A situation involving two identical goods or portfolios
that are not priced equivalently would be exploited by arbitrageurs until their
prices were equal. The “one price” that an asset must be is called the
“theoretical fair value.”
4. (LO4 Arbitrage and the Law of One Price) The law of one price is violated if the
same good is selling at different prices. On the surface it may appear as if that
is the case; however, it is important to look beneath the surface to determine
if the goods are identical. Part of the cost of the good is convenience and
customer service. Some consumers might be willing to pay more because the
dealer is located in a more desirable section of town. Also, the higher priced
dealer may have a better reputation for service and customer satisfaction.
Buyers may be willing to pay more if they feel that the premium they pay helps
assure them that they are getting a fair deal. It is important to note that many
© 2027 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 1
accessible website, in whole or in part.
, Solution and Answer Guide: Don Chance, Robert Brooks, An Introduction to Derivatives and Risk Management,
11e, ©2027, 9798214057071; Chapter 1: Introduction
goods are indeed identical and, if so, they should sell at the same price, but
the Law of One Price is not violated if the price differential accounts for some
economic value.
5. (LO4 The Storage Mechanism) Storage is simply holding the asset. Some
assets, such as commodities, require considerable storage space and incur
significant storage costs. Others, like stocks and bonds, do not consume much
space but, as we shall see later, do incur costs. Storage enables us to more
adequately meet our consumption needs and, thus, provides for a more
efficient alteration of our consumption patterns across time. For example, we
can store grains for the winter. In the case of stocks and bonds, we can store
them and sell them later. The proceeds from the sale of the securities can be
used to meet consumption needs at the later time. Likewise, storage enables
speculators to hold goods and securities in the hope of selling them later at a
profit. In addition, storage plays an important role in defining the relationship
between spot instruments and derivatives.
6. (LO4 Delivery and Settlement) In futures markets, physical delivery rarely
occurs. Since delivery is always possible, however, an expiring futures contract
will be priced like the spot instrument. The knowledge that futures prices will
eventually converge to spot prices is important to the pricing of futures
contracts.
7. (LO5 Role of Derivative Markets) Derivative markets allow investors to adjust
the risk of spot market investments to a more acceptable level and identifying
the consensus market beliefs. They make trading easier and less costly and
spot markets more efficient. These markets also provide a means of
speculating.
8. (LO6 Criticisms of Derivatives Markets) At first glance, it may be difficult to
distinguish speculation from gambling. Both entail high risk with the
expectation of high gain. The major difference that makes speculation
somewhat more socially acceptable is that it offers benefits to society not
conveyed by gambling. For example, speculators are necessary to assume the
risk not wanted by others. In gambling, there is no risk being hedged. Gamblers
simply accept risk without there being a concomitant reduction in someone
else’s risk.
9. (LO6 Misuses of Derivatives) Derivatives can be misused by speculating when
one should be hedging, by not having acquired the requisite knowledge to use
them properly by acting irresponsibly when using derivatives such as by being
overly confident of one’s ability to forecast the direction of the market.
10. (LO5 Role of Derivative Markets) The presence of derivative markets in the
United States economy and indeed throughout most modern countries of the
world undoubtedly leads to a much higher degree of market efficiency.
Derivatives facilitate the activities of individual arbitrageurs so that unequal
© 2027 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 2
accessible website, in whole or in part.
, Solution and Answer Guide: Don Chance, Robert Brooks, An Introduction to Derivatives and Risk Management,
11e, ©2027, 9798214057071; Chapter 1: Introduction
prices of identical goods are arbitraged until they are equal. Because of the
large number of arbitrageurs, this is a quick and efficient process. Arbitrage on
this large a scale makes markets less capable of being manipulated, less
costly to trade in, and therefore more attractive to investors. (The opportunity
to hedge also makes the markets more attractive to investors in managing
risk.) This is not to say that an economy without derivative markets would be
inefficient, but it would not have the advantage of this arbitrage on a large
scale.
It is important to note that the derivative markets do not necessarily make the
U.S. or world economy any larger or wealthier. The basic wealth, expected
returns, and risks of the economy would be about the same without these
markets. Derivatives simply create lower cost opportunities for investors to
align their risks at more satisfactory levels. This may not necessarily make
them wealthier, but to the extent that it makes them more satisfied with their
positions, it serves a valuable purpose.
11. (LO2 Return and Risk) Return is the numerical measure of investment
performance. There are two main measures of return, dollar return and
percentage return. Dollar return measures investment performance as total
dollar profit or loss. For example, the dollar return for stocks is the dollar
profit from the change in stock price plus any cash dividends paid. It
represents the absolute performance. Percentage return measures investment
performance per dollar invested. It represents the percentage increase in the
investor’s wealth that results from making the investment. In the case of
stocks, the return is the percentage change in price plus the dividend yield.
The concept of return also applies to options, but, as we shall see later, the
definition of the return on a futures or forward contract is somewhat unclear.
12. (LO2 Repurchase Agreements) A repurchase agreement (known as repo) is a
legal contract between a seller and a buyer, the seller agrees to sell a
specified asset to the buyer currently as well as buy it back usually at a
specified time in the future at an agreed future price. The seller is effectively
borrowing money from the buyer at an implied interest rate. Typically, repos
involve low risk securities, such as U. S. Treasury bills. Repos are useful
because they provide a great deal of flexibility to both the borrower and
lender.
Derivatives traders often need to be able to borrow and lend money in the
most cost-effective manner possible. Repos are often a very low cost way of
borrowing money, particularly if the firm holds government securities. Repos
are a way to earn interest on short-term funds with minimal risk (for buyers)
and repos are a way to borrow for short-term needs at a relatively low cost
(for sellers).
© 2027 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 3
accessible website, in whole or in part.
, Solution and Answer Guide: Don Chance, Robert Brooks, An Introduction to Derivatives and Risk Management,
11e, ©2027, 9798214057071; Chapter 1: Introduction
13. (LO1 Derivative Markets and Instruments) An option is a contract between two
parties—a buyer and a seller—that gives the buyer the right, but not the
obligation, to purchase or sell something at a later date at a price agreed upon
today. The option buyer pays the seller a sum of money called the price or
premium. The option seller stands ready to sell or buy according to the
contract terms if and when the buyer so desires. An option to buy something
is referred to as a call; an option to sell something is called a put.
A forward contract is a contract between two parties—a buyer and a seller—to
purchase or sell something at a later date at a price agreed upon today. A
forward contract sounds a lot like an option, but an option carries the right,
not the obligation, to go through with the transaction. If the price of the
underlying good changes, the option holder may decide to forgo buying or
selling at the fixed price. On the other hand, the two parties in a forward
contract incur the obligation to ultimately buy and sell the good.
14. (LO4 The Underlying Asset) Because all derivatives are based on the random
performance of something, the word “derivative” is appropriate. The derivative
derives its value from the performance of something else. That “something
else” is often referred to as the underlying asset. The term underlying asset,
however, is somewhat confusing and misleading. For instance, the underlying
asset might be a stock, bond, currency, or commodity, all of which are assets.
However, the underlying “asset” might also be some other random element
such as the weather, which is not an asset. It might even be another
derivative, such as a futures contract or an option.
15. (LO1 Swaps) A swap would allow the two parties to exchange cash flows. A
firm may be receiving cash from one investment but would prefer another type
of investment in which the cash flows are different. The party contacts a swap
dealer who takes the opposite side of the transaction. Thus, the firm and the
dealer, in effect, swap cash flow streams.
16. (LO2 Risk Preference) The expected outcome of this opportunity is ($10 + $0 -
$1) / 3 = $3. As a risk neutral individual (one who is indifferent to the risk
inherent in the opportunity), you would be willing to pay $3 to take the risk of
playing the game. If you were instead risk averse, you would be willing only to
pay some amount less than $3. If you were risk seeking, you would be willing
to pay some amount more than $3.
17. (LO2 Short Selling) If an individual anticipates the price of a stock falling, he
can attempt to capture a profit by selling short. He would first borrow the
stock from a broker and sell that stock in the marketplace. If the price of the
stock then indeed fell, he would buy back the stock at a lower price. This
would allow him to capture a profit and repay the shares to the broker. Short
selling creates a liability in that the short seller is obligated to someday buy
back the stock and return it to the broker; however, the short seller does not
know how much he will have to pay to buy back the shares.
© 2027 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 4
accessible website, in whole or in part.
11e, ©2027, 9798214057071; Chapter 1: Introduction
Solution and Answer Guide
DON CHANCE, ROBERT BROOKS, AN INTRODUCTION TO DERIVATIVES AND RISK MANAGEMENT,
11E, ©2027, 9798214057071; CHAPTER 1: INTRODUCTION
TABLE OF CONTENTS
End-of-Chapter Questions And Problems...........................................................................1
END-OF-CHAPTER QUESTIONS AND PROBLEMS
1. (LO2 Presuppositions for Financial Markets) There are at least three
presuppositions for well-functioning financial markets: a clear rule of law, well
defined clean property rights, and a culture of trust.
2. (LO4 Market Efficiency and Theoretical Fair Value) An efficient market is one
in which prices reflect the true economic values of the assets traded. trading
therein. In efficient markets, no one can earn returns that exceed those are
more than commensurate with the level of risk. Efficient markets are
characterized by low transaction costs and by the rapid incorporation of rate
at which new information is incorporated into prices.
3. (LO4 Arbitrage and the Law of One Price) Arbitrage is a type of investment
transaction that seeks to profit when identical goods are priced differently.
Buying an item at one price and immediately selling it at another is a type of
arbitrage. Because of the combined activities of arbitrageurs, identical goods,
primarily financial assets, cannot sell for different prices for long. This is the
law of one price. Arbitrage helps make our markets efficient by assuring that
prices are in line with what they are supposed to be. In short, we cannot get
something for nothing. A situation involving two identical goods or portfolios
that are not priced equivalently would be exploited by arbitrageurs until their
prices were equal. The “one price” that an asset must be is called the
“theoretical fair value.”
4. (LO4 Arbitrage and the Law of One Price) The law of one price is violated if the
same good is selling at different prices. On the surface it may appear as if that
is the case; however, it is important to look beneath the surface to determine
if the goods are identical. Part of the cost of the good is convenience and
customer service. Some consumers might be willing to pay more because the
dealer is located in a more desirable section of town. Also, the higher priced
dealer may have a better reputation for service and customer satisfaction.
Buyers may be willing to pay more if they feel that the premium they pay helps
assure them that they are getting a fair deal. It is important to note that many
© 2027 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 1
accessible website, in whole or in part.
, Solution and Answer Guide: Don Chance, Robert Brooks, An Introduction to Derivatives and Risk Management,
11e, ©2027, 9798214057071; Chapter 1: Introduction
goods are indeed identical and, if so, they should sell at the same price, but
the Law of One Price is not violated if the price differential accounts for some
economic value.
5. (LO4 The Storage Mechanism) Storage is simply holding the asset. Some
assets, such as commodities, require considerable storage space and incur
significant storage costs. Others, like stocks and bonds, do not consume much
space but, as we shall see later, do incur costs. Storage enables us to more
adequately meet our consumption needs and, thus, provides for a more
efficient alteration of our consumption patterns across time. For example, we
can store grains for the winter. In the case of stocks and bonds, we can store
them and sell them later. The proceeds from the sale of the securities can be
used to meet consumption needs at the later time. Likewise, storage enables
speculators to hold goods and securities in the hope of selling them later at a
profit. In addition, storage plays an important role in defining the relationship
between spot instruments and derivatives.
6. (LO4 Delivery and Settlement) In futures markets, physical delivery rarely
occurs. Since delivery is always possible, however, an expiring futures contract
will be priced like the spot instrument. The knowledge that futures prices will
eventually converge to spot prices is important to the pricing of futures
contracts.
7. (LO5 Role of Derivative Markets) Derivative markets allow investors to adjust
the risk of spot market investments to a more acceptable level and identifying
the consensus market beliefs. They make trading easier and less costly and
spot markets more efficient. These markets also provide a means of
speculating.
8. (LO6 Criticisms of Derivatives Markets) At first glance, it may be difficult to
distinguish speculation from gambling. Both entail high risk with the
expectation of high gain. The major difference that makes speculation
somewhat more socially acceptable is that it offers benefits to society not
conveyed by gambling. For example, speculators are necessary to assume the
risk not wanted by others. In gambling, there is no risk being hedged. Gamblers
simply accept risk without there being a concomitant reduction in someone
else’s risk.
9. (LO6 Misuses of Derivatives) Derivatives can be misused by speculating when
one should be hedging, by not having acquired the requisite knowledge to use
them properly by acting irresponsibly when using derivatives such as by being
overly confident of one’s ability to forecast the direction of the market.
10. (LO5 Role of Derivative Markets) The presence of derivative markets in the
United States economy and indeed throughout most modern countries of the
world undoubtedly leads to a much higher degree of market efficiency.
Derivatives facilitate the activities of individual arbitrageurs so that unequal
© 2027 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 2
accessible website, in whole or in part.
, Solution and Answer Guide: Don Chance, Robert Brooks, An Introduction to Derivatives and Risk Management,
11e, ©2027, 9798214057071; Chapter 1: Introduction
prices of identical goods are arbitraged until they are equal. Because of the
large number of arbitrageurs, this is a quick and efficient process. Arbitrage on
this large a scale makes markets less capable of being manipulated, less
costly to trade in, and therefore more attractive to investors. (The opportunity
to hedge also makes the markets more attractive to investors in managing
risk.) This is not to say that an economy without derivative markets would be
inefficient, but it would not have the advantage of this arbitrage on a large
scale.
It is important to note that the derivative markets do not necessarily make the
U.S. or world economy any larger or wealthier. The basic wealth, expected
returns, and risks of the economy would be about the same without these
markets. Derivatives simply create lower cost opportunities for investors to
align their risks at more satisfactory levels. This may not necessarily make
them wealthier, but to the extent that it makes them more satisfied with their
positions, it serves a valuable purpose.
11. (LO2 Return and Risk) Return is the numerical measure of investment
performance. There are two main measures of return, dollar return and
percentage return. Dollar return measures investment performance as total
dollar profit or loss. For example, the dollar return for stocks is the dollar
profit from the change in stock price plus any cash dividends paid. It
represents the absolute performance. Percentage return measures investment
performance per dollar invested. It represents the percentage increase in the
investor’s wealth that results from making the investment. In the case of
stocks, the return is the percentage change in price plus the dividend yield.
The concept of return also applies to options, but, as we shall see later, the
definition of the return on a futures or forward contract is somewhat unclear.
12. (LO2 Repurchase Agreements) A repurchase agreement (known as repo) is a
legal contract between a seller and a buyer, the seller agrees to sell a
specified asset to the buyer currently as well as buy it back usually at a
specified time in the future at an agreed future price. The seller is effectively
borrowing money from the buyer at an implied interest rate. Typically, repos
involve low risk securities, such as U. S. Treasury bills. Repos are useful
because they provide a great deal of flexibility to both the borrower and
lender.
Derivatives traders often need to be able to borrow and lend money in the
most cost-effective manner possible. Repos are often a very low cost way of
borrowing money, particularly if the firm holds government securities. Repos
are a way to earn interest on short-term funds with minimal risk (for buyers)
and repos are a way to borrow for short-term needs at a relatively low cost
(for sellers).
© 2027 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 3
accessible website, in whole or in part.
, Solution and Answer Guide: Don Chance, Robert Brooks, An Introduction to Derivatives and Risk Management,
11e, ©2027, 9798214057071; Chapter 1: Introduction
13. (LO1 Derivative Markets and Instruments) An option is a contract between two
parties—a buyer and a seller—that gives the buyer the right, but not the
obligation, to purchase or sell something at a later date at a price agreed upon
today. The option buyer pays the seller a sum of money called the price or
premium. The option seller stands ready to sell or buy according to the
contract terms if and when the buyer so desires. An option to buy something
is referred to as a call; an option to sell something is called a put.
A forward contract is a contract between two parties—a buyer and a seller—to
purchase or sell something at a later date at a price agreed upon today. A
forward contract sounds a lot like an option, but an option carries the right,
not the obligation, to go through with the transaction. If the price of the
underlying good changes, the option holder may decide to forgo buying or
selling at the fixed price. On the other hand, the two parties in a forward
contract incur the obligation to ultimately buy and sell the good.
14. (LO4 The Underlying Asset) Because all derivatives are based on the random
performance of something, the word “derivative” is appropriate. The derivative
derives its value from the performance of something else. That “something
else” is often referred to as the underlying asset. The term underlying asset,
however, is somewhat confusing and misleading. For instance, the underlying
asset might be a stock, bond, currency, or commodity, all of which are assets.
However, the underlying “asset” might also be some other random element
such as the weather, which is not an asset. It might even be another
derivative, such as a futures contract or an option.
15. (LO1 Swaps) A swap would allow the two parties to exchange cash flows. A
firm may be receiving cash from one investment but would prefer another type
of investment in which the cash flows are different. The party contacts a swap
dealer who takes the opposite side of the transaction. Thus, the firm and the
dealer, in effect, swap cash flow streams.
16. (LO2 Risk Preference) The expected outcome of this opportunity is ($10 + $0 -
$1) / 3 = $3. As a risk neutral individual (one who is indifferent to the risk
inherent in the opportunity), you would be willing to pay $3 to take the risk of
playing the game. If you were instead risk averse, you would be willing only to
pay some amount less than $3. If you were risk seeking, you would be willing
to pay some amount more than $3.
17. (LO2 Short Selling) If an individual anticipates the price of a stock falling, he
can attempt to capture a profit by selling short. He would first borrow the
stock from a broker and sell that stock in the marketplace. If the price of the
stock then indeed fell, he would buy back the stock at a lower price. This
would allow him to capture a profit and repay the shares to the broker. Short
selling creates a liability in that the short seller is obligated to someday buy
back the stock and return it to the broker; however, the short seller does not
know how much he will have to pay to buy back the shares.
© 2027 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 4
accessible website, in whole or in part.
