Module 4
Derivatives Assignment
a. The Basics: Defining Derivatives
To understand what derivatives are, let’s begin with the basics. A derivative is
a financial instrument whose value depends on—is derived from—the value of some
other financial instrument, called the underlying asset. Some common examples of
underlying assets are stocks, bonds, wheat, snowfall, and orange juice. A simple
example of a derivative is a contractual agreement between two investors that
obligates one to make a payment to the other, depending on the movement in interest
rates over the next year. This type of derivative is called an interest rate futures
contract. Such an arrangement is quite different from the outright purchase of a bond
for two reasons. First, derivatives provide an easy way for investors to profit from
price declines. The purchase of a bond, in contrast, is a bet that its price will rise.1
Second, and more important, in a derivatives transaction, one person’s loss is always
another person’s gain.
The relationship between a buyer and a seller in a financial transaction can be
likened to a poker game, where both parties are engaged in a strategic contest with
potential gains and losses. In this analogy, how much each player—the buyer or the
seller—wins or loses is determined by the dynamics of the market and the specific
terms of the transaction. However, it's important to note that the total value on the
table remains constant, reflecting a zero-sum game where one party's gain is the other
party's loss.
To expand on this analogy, let's consider the scenario of buying and selling
bonds. In the bond market, the buyer and seller each have their own perspectives and
motivations. The buyer is looking to invest in a bond with the expectation of earning a
return through interest payments and potential capital gains. The seller, on the other
hand, might be seeking to liquidate their bond holdings to realize a profit, reallocate
their portfolio, or meet liquidity needs.
The "poker game" aspect comes into play as each party negotiates the bond's
price. The seller aims to sell the bond at the highest possible price to maximize their
proceeds, while the buyer aims to purchase the bond at the lowest possible price to
enhance their return. The agreed-upon price reflects a balance of these competing
interests, just as the outcome of a poker hand results from the strategies and decisions
of both players.
If the buyer successfully negotiates a lower purchase price, they effectively
"win" by securing the bond at a cost that may offer a higher yield or potential capital
gains. Conversely, the seller might perceive a "loss" if they had to accept a lower price
than desired. However, this loss is relative to their initial expectations and market
conditions.
On the flip side, if the seller manages to sell the bond at a higher price, they
"win" by obtaining a greater return on their investment, while the buyer faces a
relative "loss" by paying a premium. Yet, the buyer's loss is mitigated by their
assessment of the bond's future performance, which they expect to justify the higher
price through interest income and price appreciation.
In a broader context, this zero-sum nature extends beyond individual
transactions to the entire bond market. The total value of all bonds remains
unchanged; it is the distribution of gains and losses among market participants that
fluctuates. This dynamic interplay underscores the strategic considerations each
participant must weigh, akin to poker players calculating odds and making tactical
decisions.
Furthermore, the poker game analogy can be applied to other financial
markets, such as stocks, real estate, and commodities. In each market, buyers and
sellers engage in a complex dance of negotiations, leveraging their knowledge,
expectations, and market conditions to achieve favorable outcomes. The total value in
the market remains static, but the distribution of that value shifts with each
transaction.
Additionally, factors such as market sentiment, economic indicators, and
geopolitical events can influence the "game" by affecting the perceived value of assets
and the behavior of market participants. Savvy buyers and sellers stay informed and
adapt their strategies to navigate these influences, much like skilled poker players
adjusting their play based on the changing dynamics of the game.
In conclusion, the buyer-seller relationship in financial markets is analogous to
a poker game, where each party's gains and losses depend on their strategic
interactions and market conditions. The total value on the table doesn't change; rather,
it is the distribution of that value among participants that varies. Understanding this
dynamic helps investors and traders make informed decisions, manage risks, and
optimize their outcomes in the competitive landscape of financial markets.
While derivatives can be used to speculate, or gamble on future price
movements, the fact that they allow investors to manage and reduce risk makes them
indispensable to a modern economy. Bombardier used a derivative to hedge the risk of
having to pay rebates in the event of low snowfall. As we will see, farmers use
derivatives regularly, to insure themselves against fluctuations in the market prices of
their crops. Risk can be bought and sold using derivatives. Thus, the purpose of
derivatives is to transfer risk from one person or firm to another.
When people have the ability to transfer risks, they will do things that they
wouldn’t do otherwise. Think of a wheat farmer and a bread baker. If he or she cannot
insure against a decline in the price of wheat, the farmer will plant fewer acres of
wheat. And without a guarantee that the price of flour will not rise, the baker will
build a smaller bakery. Those are prudent responses to the risks created by price
fluctuations. Now introduce a mechanism through which the farmer and the baker can
guarantee the price of wheat. As a result the farmer will plant more and the baker will
build a bigger bakery. Insurance is what allows them to do it! Derivatives provide that
insurance.
Derivatives play a crucial role in modern financial markets by providing
mechanisms for managing and transferring risk. By allowing risk to be shifted to
those who are both willing and able to bear it, derivatives enhance the overall risk-
carrying capacity of the economy. This process not only improves the allocation of
resources but also contributes to increasing the overall level of economic output and
stability.
To understand the full impact of derivatives, it's essential to delve into their
functions and benefits. Derivatives are financial instruments whose value is derived
from the performance of underlying assets, such as stocks, bonds, commodities,
interest rates, or currencies. Common types of derivatives include options, futures,
forwards, and swaps. These instruments are used by various market participants,
including corporations, financial institutions, investors, and speculators, for purposes
such as hedging, speculation, and arbitrage.
One of the primary benefits of derivatives is their ability to facilitate risk
management. For instance, a corporation concerned about fluctuating commodity
prices can use futures contracts to lock in prices for raw materials, thereby stabilizing
production costs and protecting profit margins. Similarly, an investor with a portfolio
of international assets can use currency swaps to hedge against adverse exchange rate
movements. By transferring these risks to parties willing to take them on, derivatives
enable companies and investors to focus more effectively on their core activities,
enhancing operational efficiency and financial performance.
Moreover, derivatives markets are characterized by high liquidity and
flexibility, which further contribute to their risk-shifting capabilities. The presence of
liquid derivative markets allows participants to enter and exit positions with relative
ease, adjusting their risk exposures in response to changing market conditions. This
liquidity ensures that risks are efficiently priced and distributed across the market,
minimizing the concentration of risk in any single entity or sector.
In addition to risk management, derivatives also play a vital role in price
discovery and market efficiency. The prices of derivative contracts reflect market
expectations about the future movements of underlying assets, providing valuable
information to market participants. For example, the prices of interest rate futures can
signal expectations about future monetary policy actions, while options prices can
indicate the market’s assessment of volatility. This information contributes to more
informed decision-making and more efficient allocation of resources across the
economy.
Furthermore, by enabling the transfer of risk, derivatives encourage
investment and innovation. Entrepreneurs and businesses are more likely to undertake
new ventures and invest in growth opportunities when they can mitigate potential
risks through derivative instruments. This risk mitigation fosters an environment
conducive to economic expansion and technological advancement, ultimately leading
to higher levels of output and productivity.
Derivatives also enhance financial stability by providing tools for managing
systemic risk. For instance, credit default swaps (CDS) allow financial institutions to
insure against the risk of default on debt instruments, spreading credit risk more
broadly across the market. This dispersion of risk can prevent the failure of a single
institution from triggering a broader financial crisis, thereby contributing to the
overall stability of the financial system.
However, it is important to recognize that the use of derivatives also involves
risks, particularly if they are not properly managed or understood. The complexity and
leverage associated with some derivative products can lead to significant losses, as
seen in the financial crises of the past. Therefore, effective regulation, transparent
reporting, and robust risk management practices are essential to ensure that the
benefits of derivatives are realized while minimizing potential downsides.
In summary, by shifting risk to those willing and able to bear it, derivatives
increase the risk-carrying capacity of the economy, improving the allocation of
resources and enhancing economic output. These financial instruments facilitate risk
management, price discovery, and investment, contributing to a more dynamic and
resilient economy. While derivatives offer substantial benefits, their use must be
accompanied by careful oversight and prudent risk management to safeguard the
stability and integrity of financial markets.
While derivatives allow individuals and firms to manage risk, they also allow
them to conceal the true nature of certain financial transactions. In the same way that
stripping a coupon bond separates the coupons from the principal payment, buying
and selling derivatives can unbundle virtually any group of future payments and risks.
A company that hesitates to issue a coupon bond for fear analysts will frown on the
extra debt can instead issue the coupon payments and the principal payment as
individual zero-coupon bonds, using derivative transactions to label them something
other than borrowing. Thus, if stock market analysts penalize companies for obtaining
funding in certain ways, derivatives (as we will see) allow the companies to get
exactly the same resources at the same risk but under a different name.
Derivatives are complex financial instruments that play a vital role in modern
financial markets by allowing participants to manage risk, speculate on price
movements, and achieve other financial objectives. Derivatives can be broadly
categorized into three major types: forwards and futures, options, and swaps. Each
category has its unique characteristics and uses. Let's explore each of these categories
in greater detail.
Forwards are customized contracts traded over-the-counter (OTC), meaning
they are negotiated directly between two parties without being listed on an exchange.
This flexibility allows the terms of the contract—such as the asset type, quantity,
price, and delivery date—to be tailored to meet the specific needs of the parties
involved. Because forwards are OTC instruments, they carry counterparty risk, which
is the risk that one party may default on its contractual obligations.
Forwards are often used by businesses and investors to hedge against potential
price fluctuations in assets they plan to buy or sell in the future. For example, an
agricultural producer might enter into a forward contract to sell a crop at a fixed price
to hedge against the risk of falling prices.
Futures contracts, on the other hand, are standardized agreements traded on
organized exchanges, such as the Chicago Mercantile Exchange (CME) or the
Intercontinental Exchange (ICE). The standardization involves specific terms for the
contract size, expiration date, and settlement procedures, which makes futures
contracts highly liquid and easily tradable. The exchange acts as an intermediary and
guarantees the performance of the contracts, thereby mitigating counterparty risk.
Futures contracts require daily settlement of gains and losses through a
process called marking to market, where the value of the contract is adjusted to reflect
current market prices. This ensures that any profits or losses are realized on a daily
basis, reducing the risk of large, accumulated losses at the contract's expiration.
Futures are commonly used by speculators looking to profit from price
movements and by hedgers seeking to protect against adverse price changes. For
example, an airline company might use futures contracts to lock in fuel prices, thereby
hedging against the risk of rising fuel costs.
A call option gives the holder the right to buy an underlying asset at a
specified price, known as the strike price, before or on the expiration date. Investors
purchase call options when they anticipate that the price of the underlying asset will
rise above the strike price, allowing them to buy the asset at a lower price and
potentially sell it at a higher market price.
For example, if an investor buys a call option for a stock with a strike price of
$50, and the stock's price rises to $60, the investor can exercise the option to buy the
stock at $50, realizing a profit. A put option gives the holder the right to sell an
underlying asset at the strike price before or on the expiration date. Investors purchase
put options when they expect the price of the underlying asset to fall below the strike
price. This allows them to sell the asset at a higher strike price than the market price,
potentially profiting from the decline.
For instance, if an investor buys a put option for a stock with a strike price of
$50, and the stock's price drops to $40, the investor can exercise the option to sell the
stock at $50, realizing a profit. Options are used for a variety of purposes, including
speculation, hedging, and income generation. For example, a portfolio manager might
use put options to protect against potential declines in the value of a stock portfolio,
while an investor might sell call options to generate additional income from stocks
they already own.
Swaps are derivative contracts in which two parties agree to exchange cash
flows or other financial instruments over a specified period. Swaps are typically
customized OTC contracts, allowing them to be tailored to the specific needs of the
parties involved. There are several types of swaps, including interest rate swaps,
currency swaps, and commodity swaps.
Interest rate swaps involve the exchange of cash flows based on different
interest rate payment structures. The most common type is the fixed-for-floating
swap, where one party agrees to pay a fixed interest rate in exchange for receiving a
floating interest rate, typically based on a benchmark such as LIBOR (London
Interbank Offered Rate). This type of swap is often used by companies to manage
exposure to interest rate fluctuations. For example, a company with a floating-rate
loan might enter into an interest rate swap to convert its floating-rate payments to
fixed-rate payments, thereby locking in a stable interest expense.
Currency swaps involve the exchange of principal and interest payments in
different currencies. These swaps are used by multinational corporations and financial
institutions to manage exposure to exchange rate fluctuations and to obtain more
favorable borrowing terms. For example, a U.S. company needing euros for a
European investment might enter into a currency swap with a European company
needing dollars. Each company borrows in its domestic currency and then swaps the
principal and interest payments with the other company, effectively obtaining the
desired foreign currency.
Commodity swaps involve the exchange of cash flows based on the price of a
commodity, such as oil, natural gas, or agricultural products. These swaps are used by
producers and consumers of commodities to hedge against price volatility. For
example, an airline company concerned about rising jet fuel prices might enter into a
commodity swap to lock in fuel costs, stabilizing its operating expenses.
In conclusion, forwards and futures, options, and swaps are three major
categories of derivatives, each serving distinct purposes and offering unique benefits.
By enabling the transfer and management of risk, these derivatives contribute to the
efficiency and stability of financial markets, supporting economic growth and
development. Understanding the intricacies of these instruments is essential for
investors, businesses, and policymakers to effectively navigate the complexities of the
financial landscape.
b. Forwards and Futures
Of all derivative financial instruments, forwards and futures are the simplest to
understand and the easiest to use. A forward, or forward contract, is an agreement
between a buyer and a seller to exchange a commodity or financial instrument for a
specified amount of cash on a prearranged future date. Forward contracts are private
agreements between two parties. Because they are customized, forward contracts are
very difficult to resell to someone else. To see why forward contracts are difficult to
resell, consider the example of a yearlong apartment lease, in which the renter agrees
to make a series of monthly payments to the landlord in exchange for the right to live
in the apartment. Such a lease is a sequence of 12 forward contracts. Rent is paid in
predetermined amounts on prearranged future dates in exchange for housing. While
there is some standardization of leases, a contract between a specific renter and a
specific landlord is unlike any other rental contract. Thus, there is no market for the
resale or reassignment of apartment rental contracts.
In contrast, a future, or futures contract, is a forward contract that has been
standardized and sold through an organized exchange. A futures contract specifies that
the seller—who has the short position—will deliver some quantity of a commodity or
financial instrument to the buyer—who has the long position—on a specific date,
called the settlement or delivery date, for a predetermined price. No payments are
made initially when the contract is agreed to. The seller/short position benefits from
declines in the price of the underlying asset, while the buyer/long position benefits
from increases.2 Take the U.S. Treasury bond futures contract that trades on the
Chicago Board of Trade (CBOT, which is a part of the CME Group). The contract
specifies the delivery of $100,000 face value worth of 10-year, 6 percent coupon U.S.
Treasury bonds at any time during a given month, called the delivery month. The fact
that the contract is so specific means there is no need for negotiation. And the
existence of the exchange creates a natural place for people who are interested in a
particular futures contract to meet and trade. Historically, exchanges have been
physical locations, but with the Internet came online trading of futures. In recent
years, firms have created virtual futures markets for a wide variety of products,
including energy, bandwidth, and plastics.
One more thing is needed before anyone will actually buy or sell futures
contracts: assurance that the buyer and seller will meet their obligations. In the case of
the U.S. Treasury futures contract, the buyer must be sure that the seller will deliver
the bond, and the seller must believe that the buyer will pay for it. Market participants
have found an ingenious solution to this problem. Instead of making a bilateral
arrangement, the two parties to a futures contract each make an agreement with a
clearing corporation. The clearing corporation, which operates like a large insurance
company, is the counterparty to both sides of a transaction, guaranteeing that they will
meet their obligations. This arrangement reduces the risk buyers and sellers face. The
clearing corporation has the ability to monitor traders and the incentive to limit their
risk taking (see Lessons from the Crisis: Central Counterparties and Systemic Risk).
To reduce the risk it faces, the clearing corporation requires both parties to a
futures contract to place a deposit with the corporation itself. This practice is called
posting margin in a margin account. The margin deposits guarantee that when the
contract comes due, the parties will be able to meet their obligations. But the clearing
corporation does more than collect the initial margin when a contract is signed. It also
posts daily gains and losses on the contract to the margin accounts of the parties
involved.4 This process is called marking to market, and it is done daily. Marking to
market is analogous to what happens during a poker game. At the end of each hand,
the amount wagered is transferred from the losers to the winner. In financial parlance,
the account of each player is marked to market. Alternative methods of accounting are
too complicated, making it difficult to identify players who should be excused from
the game because they have run out of resources. For similar reasons, the clearing
corporation marks futures accounts to market every day. Doing so ensures that sellers
always have the resources to make delivery and that buyers always can pay. As in
poker, if someone’s margin account falls below the minimum, the clearing corporation
will sell the contracts, ending the person’s participation in the market.
An example will help you understand how marking to market works. Take the
case of a futures contract for the purchase of 1,000 ounces of silver at $20 per ounce.
The contract specifies that the buyer of the contract, the long position, will pay
$20,000 in exchange for 1,000 ounces of silver. The seller of the contract, the short
position, receives the $20,000 and delivers the 1,000 ounces of silver. We can think
about this contract as guaranteeing the long position the ability to buy 1,000 ounces of
silver for $20,000 and guaranteeing the short position the ability to sell 1,000 ounces
of silver for $20,000. Now consider what happens when the price of silver changes. If
the price rises to $21 per ounce, the seller needs to give the buyer $1,000 so that the
buyer pays only $20,000 for the 1,000 ounces of silver. By contrast, if the price falls
to $19 an ounce, the buyer of the futures contract needs to pay $1,000 to the seller to
make sure that the seller receives $20,000 for selling the 1,000 ounces of silver.
Marking to market is the transfer of funds at the end of each day that ensures the
buyers and sellers get what the contract promises.
Futures contracts allow the transfer of risk between buyer and seller. This
transfer can be accomplished through hedging or speculation. Let’s look at hedging
first. Say a government securities dealer wishes to insure against declines in the value
of an inventory of bonds. That is exactly what happens with the sale of a U.S.
Treasury bond futures contract: the seller/ short position benefits from price declines.
Put differently, the seller of a futures contract—the securities dealer, in this case—can
guarantee the price at which the bonds are sold. The other party to this transaction
might be a pension fund manager who is planning to purchase bonds in the future and
wishes to insure against possible price increases.5 Buying a futures contract fixes the
price that the fund will need to pay. In this example, both sides use the futures
contract as a hedge. They are both hedgers.
Producers and users of commodities employ futures markets to hedge their
risks as well. Farmers, mining companies, oil drillers, and the like are sellers of
futures, taking short positions. After all, they own the commodities outright, so they
want to stabilize the revenue they receive when they sell. In contrast, millers,
jewelers, and oil distributors want to buy futures to take long positions. They require
the commodity to do business, so they buy the futures contract to reduce risk arising
from fluctuations in the cost of essential inputs. What about speculators? Their
objective is simple: They are trying to make a profit. To do so, they bet on price
movements. Sellers of futures are betting that prices will fall, while buyers are betting
that prices will rise. Futures contracts are popular tools for speculation because they
are cheap. An investor needs only a relatively small amount of investment—the
margin—to purchase a futures contract that is worth a great deal. Margin requirements
of 10 percent or less are common. In the case of a futures contract for the delivery of
$100,000 face value worth of 10-year, 6 percent coupon U.S. Treasury bonds, the
Chicago Board of Trade (the clearing corporation that guarantees the contract)
requires maintaining margin of $1,050 per contract.
In financial markets, leveraging plays a crucial role in amplifying potential
returns from investments, often allowing investors to achieve exposure to larger
positions than their initial capital outlay. The concept you've described pertains to the
use of futures contracts, where a relatively small initial investment—such as $1,050—
can provide exposure equivalent to a much larger investment in bonds, say $100,000.
This ability to magnify exposure without the need for immediate large capital outlays
is a hallmark of financial leverage.
Leverage in the context of futures contracts is achieved through margin
requirements. When an investor purchases a futures contract, they are required to
deposit a fraction of the contract's value known as initial margin. This initial margin
serves as collateral for the contract and ensures that the investor can meet potential
losses. The remaining value of the contract, in this case, the notional amount of
$100,000 worth of bonds, is effectively borrowed capital.
The use of leverage in futures trading allows investors to amplify both
potential gains and losses. In the scenario you've described, where an investor invests
$1,050 to gain exposure equivalent to $100,000 in bonds, the leverage ratio is
substantial—nearly 95 times the initial investment. This amplification of exposure
enables investors to potentially benefit from small movements in bond prices relative
to their initial investment.
The attractiveness of leverage lies in its potential to enhance returns on
invested capital. By deploying a fraction of the total contract value as initial margin,
investors can participate in larger market positions than would be feasible with cash
alone. This strategy is particularly advantageous in markets where price fluctuations
are anticipated or where investors seek to capitalize on short-term trading
opportunities.
However, it's important to note that leverage also introduces heightened risk.
While gains can be amplified, so too can losses. If the market moves against the
investor, the losses can exceed the initial margin deposit, leading to margin calls or
even liquidation of positions. Therefore, prudent risk management and understanding
of market dynamics are essential for investors utilizing leverage in futures trading.
In summary, leveraging through futures contracts allows investors to achieve
exposure to larger positions in bonds or other assets with a fraction of the capital
required for outright purchase. This financial mechanism facilitates broader market
participation, enhances liquidity, and can potentially optimize portfolio returns, albeit
with associated risks that must be carefully managed.
To see the impact of this kind of leverage on the return to the buyer and seller
of a futures contract, recall from footnote 4 that a rise of 22/32nds in the price of the
Treasury bond futures contract meant that the long position/buyer gained $687.50,
while the short position/seller lost $687.50. With a minimum initial investment of
$1,050 for each contract, this represents a 65.5 percent gain to the futures contract
buyer and a 65.5 percent loss to the futures contract seller. In contrast, the owner of
the bond itself would have gained $687.50 on an approximately $100,000 investment,
which is a gain of just 0.688 percent! Speculators, then, can use futures to obtain very
large amounts of leverage at a very low cost.
To understand how the price of a futures contract is determined, let’s start at
the settlement date and work backward. On the settlement or delivery date, we know
that the price of the futures contract must equal the price of the underlying asset the
seller is obligated to deliver. The reason is simple: If, at expiration, the futures price
were to deviate from the asset’s price, then it would be possible to make a risk-free
profit by engaging in offsetting cash and futures transactions. If the current market
price of a bond were below the futures contract price, someone could buy a bond at
the low price and simultaneously sell a futures contract (take a short position and
promise to deliver the bond on a future date). Immediate exercise of the futures
contract and delivery of the bond would yield a profit equal to the difference between
the market price and the futures price.
The concept of arbitrage in financial markets, as exemplified by bond basis
trading or convergence trading, revolves around exploiting price differentials between
related assets or instruments to generate profit. One of the intriguing aspects of
arbitrage is its potential to yield profits without the traditional risks associated with
market investments, such as directional price movements or economic uncertainties.
Let's delve deeper into why arbitrage can be perceived as a risk-free opportunity and
its broader implications.
Arbitrage opportunities arise when there are temporary price discrepancies
between assets or instruments that are fundamentally related and should theoretically
trade at the same price. In the context of bond basis trading, the arbitrageur identifies
and capitalizes on these discrepancies between bond prices in the cash market and
their equivalent futures prices. This strategy involves simultaneous buying and selling
to exploit the price differential until it narrows or disappears.
One of the key reasons why arbitrage can be seen as risk-free is the absence of
market risk in the traditional sense. Market risk typically refers to the potential for
losses due to adverse price movements in the underlying assets. However, in arbitrage
scenarios where an investor buys an underpriced asset and sells an overpriced
equivalent, the net exposure to market fluctuations is minimal or nonexistent.
For instance, in the example where an arbitrageur buys a bond in the cash
market and sells the corresponding futures contract, the positions effectively offset
each other. If the bond price increases, the futures price tends to decrease, and vice
versa. As a result, the arbitrageur locks in a profit based on the initial price differential
rather than relying on the directional movement of prices in either market.
While arbitrage can be perceived as low risk from a market perspective, it is
not entirely without risks. Execution risk and timing risk are critical considerations for
arbitrageurs. Execution risk refers to the potential for delays or difficulties in
executing trades at desired prices, especially in fast-moving markets or illiquid
securities. Timing risk involves the possibility that price differentials may change
before the arbitrageur completes their transactions, reducing or eliminating potential
profits.
To mitigate these risks, arbitrageurs often rely on advanced trading strategies,
technology-driven execution platforms, and real-time market data. They also monitor
market conditions closely to identify and capitalize on fleeting arbitrage opportunities
before they dissipate.
Arbitrage plays a crucial role in promoting market efficiency by aligning
prices across related markets. When arbitrageurs exploit price discrepancies, they
contribute to price convergence, ensuring that assets are valued correctly relative to
their intrinsic worth. Efficient pricing enhances liquidity, reduces volatility, and
encourages market participants to allocate capital more effectively.
Moreover, the presence of arbitrage opportunities incentivizes market
participants to engage in research and analysis, leading to more informed investment
decisions. This process enhances transparency and trust in financial markets,
benefiting investors and supporting economic growth.
While arbitrage can enhance market efficiency, regulators closely monitor
arbitrage activities to ensure fair and orderly markets. Regulatory frameworks aim to
prevent market manipulation, maintain market integrity, and protect investors from
abusive practices. Arbitrageurs must comply with applicable regulations, disclosure
requirements, and risk management guidelines to operate within legal and ethical
boundaries.
In conclusion, arbitrage offers the potential for risk-free profits by exploiting
temporary price discrepancies between related assets or instruments in financial
markets. By capitalizing on inefficiencies, arbitrageurs contribute to market efficiency
and price discovery, benefiting investors and the broader economy. However, while
arbitrage strategies may appear risk-free from a market perspective, they still entail
execution and timing risks that require careful management and expertise.
Understanding these dynamics is essential for investors and market participants
seeking to leverage arbitrage opportunities effectively while navigating regulatory and
operational considerations.
The practice of simultaneously buying and selling financial instruments in
order to benefit from temporary price differences is called arbitrage, and the people
who engage in it are called arbitrageurs. Arbitrage means that two financial
instruments with the same risk and promised future payments will sell for the same
price. If, for example, the price of a specific bond is higher in one market than in
another, an arbitrageur can buy at the low price and sell at the high price. The increase
in demand in the market where the price is low drives the price up there, while the
increase in supply in the market where the price is high drives the price down there,
and the process continues until prices are equal in the two markets.
Arbitrageurs play a crucial role in ensuring efficiency in financial markets,
particularly in the context of futures contracts for bonds. When a futures contract
approaches its settlement date, arbitrageurs closely monitor the relationship between
the futures price and the spot price of the underlying bond. The spot price, often
considered the current market price of the bond, represents its value for immediate
delivery and ownership.
Arbitrageurs capitalize on any discrepancies between the futures price and the
spot price. If the futures price is higher than the spot price, arbitrageurs may sell the
futures contract and buy the underlying bond in the spot market to lock in a risk-free
profit. Conversely, if the futures price is lower than the spot price, arbitrageurs may
buy the futures contract and sell the bond in the spot market.
This arbitrage activity tends to converge the futures price towards the spot
price as the settlement date approaches. The reason behind this convergence lies in the
economic incentive for arbitrageurs to exploit price differences and thereby eliminate
opportunities for riskless profit. As a result, on the settlement date of the futures
contract, the price of the bond futures contract typically equals the spot price of the
bond, reflecting the equilibrium reached through arbitrage activities.
Moreover, the relationship between futures and spot prices is also influenced
by factors such as interest rates, dividends (in the case of equity futures), storage costs
(for commodities), and other market dynamics. These factors can affect the arbitrage
opportunities and the pricing of futures contracts relative to their underlying assets.
In summary, arbitrageurs act as key participants in ensuring that futures prices
align closely with spot prices by capitalizing on pricing discrepancies. This process
contributes to the efficient pricing of futures contracts and enhances overall market
efficiency in financial and commodity markets alike.
So we know that on the settlement date, the price of a futures contract must
equal the spot price of the underlying asset. But what happens before the settlement
date? The principle of arbitrage still applies. The price of the futures contract depends
on the fact that someone can buy a bond and sell a futures contract simultaneously.
Here’s how it’s done. First, the arbitrageur borrows at the current market interest rate.
With the funds, the arbitrageur buys a bond and sells a bond futures contract. Now the
arbitrageur has a loan on which interest must be paid, a bond that pays interest, and a
promise to deliver the bond for a fixed price at the expiration of the futures contract.
Because the interest owed on the loan and received from the bond will cancel out, this
position costs nothing to initiate.
In financial markets, the relationship between futures prices and the market
prices of underlying assets, such as bonds, is crucial for understanding pricing
dynamics and arbitrage opportunities. When the market price of a bond is lower than
the futures contract price, arbitrageurs are incentivized to execute a strategy known as
cash and carry arbitrage. This strategy involves buying the bond in the spot market at
the lower market price and simultaneously selling the corresponding futures contract
at the higher futures price.
The profitability of cash and carry arbitrage relies on the principle that the
futures price must move in tandem with the market price of the bond. If the futures
price deviates significantly from the spot price, arbitrageurs can exploit this
discrepancy to earn riskless profits. By executing the cash and carry arbitrage strategy,
arbitrageurs effectively contribute to the alignment of futures prices with spot prices
over time.
The mechanism driving this convergence lies in arbitrageurs' actions. When
the futures price exceeds the spot price, arbitrageurs sell the futures contract and buy
the bond in the spot market, thereby increasing demand for the bond and decreasing
demand for the futures contract. This selling pressure on the futures contract drives its
price down towards the spot price of the bond. Conversely, if the futures price is
below the spot price, arbitrageurs buy the futures contract and sell the bond,
increasing demand for the futures contract and decreasing demand for the bond, thus
pushing the futures price up towards the spot price.
Market participants, including institutional investors, hedge funds, and
proprietary trading firms, actively engage in arbitrage activities to capitalize on price
differentials between futures and spot markets. These activities not only promote
efficient pricing but also enhance market liquidity and reduce transaction costs for all
participants.
Furthermore, the relationship between futures and spot prices is influenced by
various factors, such as interest rates, economic indicators, geopolitical events, and
supply and demand dynamics. These factors can affect the profitability and feasibility
of arbitrage strategies, shaping the overall pricing dynamics of futures contracts
relative to their underlying assets.
In conclusion, the synchronization of futures prices with spot prices of bonds
is driven by arbitrageurs' continuous efforts to exploit pricing inefficiencies. This
process ensures that futures prices accurately reflect market expectations and
contribute to the efficient functioning of financial markets globally.
To see how arbitrage works, consider an example in which the spot price of a
4Ipercent coupon 10-year bond is $100, the current interest rate on a 3-month loan is
also 4Ipercent (quoted at an annual rate), and the futures market price for delivery of a
4Ipercent, 10-year bond is $101. An investor could borrow $100, purchase the 10-year
bond, and sell a bond future for $101 promising delivery of the bond in three months.
The investor could use the interest payment from the bond to pay the interest on the
loan and deliver the bond to the buyer of the futures contract on the delivery date.
This transaction is completely riskless and nets the investor a profit of $1—without
even putting up any funds. A riskless profit is extremely tempting, so the investor will
continue to engage in the transactions needed to generate it.
In financial markets, particularly in the realm of bond trading, arbitrage
strategies play a significant role in ensuring price efficiency and market equilibrium.
One common arbitrage strategy involves taking advantage of price disparities between
bonds and related derivative instruments, such as futures contracts, to generate profit.
This process, known as bond basis trading or convergence trading, relies on the
principle of exploiting temporary price divergences until they normalize, thereby
eliminating further profit opportunities.
Arbitrage is the practice of simultaneously buying and selling similar assets or
instruments in different markets to profit from price discrepancies. In the context of
bond markets, arbitrageurs identify situations where bonds and their corresponding
futures contracts are mispriced relative to each other. This mispricing may occur due
to factors such as supply and demand imbalances, interest rate expectations, or market
sentiment.
Bond futures contracts are standardized derivative instruments that represent a
basket of deliverable bonds. These contracts typically have a specified maturity date
and contract size, making them highly liquid and tradable on organized exchanges.
The futures price reflects market expectations of the underlying bond prices at the
contract's expiration.
When bond prices in the cash market (actual bonds) diverge from the futures
prices, arbitrage opportunities arise. For example, if a bond's price in the cash market
is higher than its equivalent futures price, arbitrageurs may engage in a "buy bond,
sell futures" strategy. Conversely, if bond prices are lower in the cash market than in
futures, arbitrageurs may execute a "sell bond, buy futures" strategy.
Consider a scenario where a bond's cash market price is $1,020, while its
equivalent futures contract is priced at $1,010. An arbitrageur might buy the bond in
the cash market for $1,020 and simultaneously sell the futures contract at $1,010. This
initial trade locks in a profit of $10 per contract ($1,020 - $1,010).
As more arbitrageurs execute similar trades, buying bonds and selling futures,
the increased demand for bonds and selling pressure on futures contracts would drive
up the bond price and bring down the futures price. This process continues until the
price differential diminishes to a level where the arbitrage opportunity no longer
exists or is negligible.
Arbitrage activities, such as bond basis trading, contribute to market efficiency
by aligning prices across related markets. Efficient pricing ensures that investors
receive fair value for their investments and reduces opportunities for profit through
price discrepancies. Moreover, by stabilizing prices, arbitrage helps to maintain
liquidity and mitigate excessive volatility in financial markets.
While arbitrage strategies can be lucrative, they are not without risks.
Arbitrageurs must carefully manage factors such as execution timing, transaction
costs, and market liquidity. Additionally, unexpected changes in interest rates, market
sentiment, or regulatory developments can impact arbitrage opportunities and
profitability.
In conclusion, convergence trading through arbitrage plays a crucial role in
balancing prices between bonds and futures contracts in financial markets. By
exploiting temporary price disparities, arbitrageurs contribute to market efficiency and
facilitate price convergence, ultimately benefiting investors and promoting stability in
the broader economy. Understanding these dynamics is essential for participants in
financial markets to navigate and capitalize on arbitrage opportunities effectively.
c. Options
Everyone likes to have options. Having the option to go on vacation or buy a
new car is nice. The alternative to having options, having our decisions made for us, is
surely worse. Because options are valuable, people are willing to pay for them when
they can. Financial options are no different; because they are worth having, we can
put a price on them. Calculating the price of an option is incredibly complicated. In
fact, no one knew how before Fischer Black and Myron Scholes figured it out in
1973. Traders immediately programmed their famous Black-Scholes formula into the
computers available at the time, and the options markets took off. By June 2000, the
market value of outstanding options was in the neighborhood of $500 billion. Today,
hundreds of millions of options contracts are outstanding, and millions of them
change hands every day. Before we learn how to price options, we’ll need to master
the vocabulary used to describe them. Once we have the language, the next step is to
move on to how to use options and how to value them.
Like futures, options are agreements between two parties. There is a seller,
called an option writer, and a buyer, called an option holder. As we will see, option
writers incur obligations, while option holders obtain rights. There are two basic
options, puts and calls. A call option is the right to buy—“call away”—a given
quantity of an underlying asset at a predetermined price, called the strike price (or
exercise price), on or beforeIa specific date. For example, a July 2019 call option on
100 shares of Apple stock at a strike price of 100 gives the option holder the right to
buy 100 shares of Apple for $100Iapiece prior to the third Friday of July 2019. The
writer of the call option must sell the shares if and when the holder chooses to use the
call option. The holder of the call is not required to buy the shares; rather, the holder
has the option to buy and will do so only if buying is beneficial. When the price of
Apple stock exceeds the option strike price of 100, the option holder can either call
away the 100 shares from the option writer by exercising the option or sell the option
to someone else at a profit. If the market price rose to $105, for example, then
exercising the call would allow the holder to buy the stock from the option writer for
$100 and reap a $5 per share profit. Whenever the price of the stock is above the
strike price of the call option, exercising the option is profitable for the holder, and the
option is said to be in the money (as in “I’m in the money!”). If the price of the stock
exactly equals the strike price, the option is said to be at the money. If the strike price
exceeds the market price of the underlying asset, it is termed out of the money.
A put option gives the holder the right but not the obligation to sell the
underlying asset at a predetermined price on or before a fixed date. The holder can
“put” the asset in the hands of the option writer. Again, the writer of the option is
obliged to buy the shares should the holder choose to exercise the option. Returning to
the example of Apple stock, consider a put option with a strike price of 100. This is
the right to sell 100Ishares at $100 per share, which is valuable when the market price
of Apple stock falls below $100. If the price of a share of Apple stock were $90, then
exercising the put option would yield a profit of $10 per share. The same terminology
that is used to describe calls—in the money, at the money, and out of the money—
applies to puts as well, but the circumstances in which it is used are reversed. Because
the buyer of a put obtains the right to sell a stock, the put is in the money when the
option’s strike price is above the market price of the stock. It is out of the money
when the strike price is below the market price.
While it is possible to customize options in the same way as forward contracts,
many are standardized and traded on exchanges, just like futures contracts. The
mechanics of trading are the same. A clearing corporation guarantees the obligations
embodied in the option—those of the option writer. And the option writer is required
to post margin. Because option holders incur no obligation, they are not required to
post margin. There are two types of calls and puts: American and European. American
options can be exercised on any date from the time they are written until the day they
expire. As a result, prior to the expiration date, the holder of an American option has
three choices: (1) continue to hold the option, (2) sell the option to someone else, or
(3)Iexercise the option immediately. European options can be exercised only on the
day that they expire. Thus, the holder of a European option has two choices on a date
prior to expiration: hold or sell. The vast majority of options traded in the United
States are American.
Who buys and sells options, and why? To answer this question, we need to
understand how options are used. Options transfer risk from the buyer to the seller, so
they can be used for both hedging and speculation. Let’s take hedging first.
Remember that a hedger is buying insurance. For someone who wants to purchase an
asset such as a bond or a stock in the future, a call option ensures that the cost of
buying the asset will not rise. For someone who plans to sell the asset in the future, a
put option ensures that the price at which the asset can be sold will not go down. To
understand the close correspondence between options and insurance, think of the
arrangement that automobile owners have with their insurance company. The owner
pays an insurance premium and obtains the right to file a claim in the event of an
accident. If the terms of the policy are met, the insurance company is obligated to pay
the claim. If no accident occurs, then there is no claim and the insurance company
makes no payment; the insurance premium is lost. In effect, theIinsurance company
has sold an American call option to the car’s owner where the underlying asset is a
working car and the strike price is zero. This call option can be exercised if and only
if the car is damaged in an accident on any day before the policy expires.
Options can be used for speculation as well. Say that you believe that interest
rates are going to fall over the next few months. There are three ways to bet on this
possibility. The first is to purchase a bond outright, hoping that its price will rise as
interest rates fall. This is expensive, because you will need to come up with the
resources to buy the bond. A second strategy is to buy a futures contract, taking the
long position. If the market price of the bond rises, you will make a profit. As we saw
in the last section, this is an attractive approach, because it requires only a small
investment. But it is also very risky, because the investment is highly leveraged. Both
the bond purchase and the futures contract carry the risk that you will take a loss, and
if interest rates rise substantially, your loss will be large. The third strategy for betting
that interest rates will fall is to buy a call option on a U.S. Treasury bond. If you are
right and interest rates fall, the value of the call option will rise. But if you are wrong
and interest rates rise, the call will expire worthless and your losses will be limited to
the price you paid for it. This bet is both highly leveraged and limited in its potential
losses.
In the same way that purchasing a call option allows an investor to bet that the
price of the underlying asset will rise, purchasing a put option allows the investor to
bet that the price will fall. Again, if the investor is wrong, all that is lost is the price
paid for the option. In the meantime, the option provides a cheap way to bet on the
movement in the price of the underlying asset. The bet is highly leveraged, because a
small initial investment creates the opportunity for a large gain. But unlike a futures
contract, a put option has a limited potential loss. So far we have discussed only the
purchase of options. For every buyer there must be a seller. Who is it? After all, an
option writer can take a large loss. Nevertheless, for a fee, some people are willing to
take the risk and bet that prices will not move against them. These people are simply
speculators. A second group of people who are willing to write options are insured
against any losses that may arise. They are primarily dealers who engage in the
regular purchase and sale of the underlying asset. These people are called market
makers because they are always there to make the market. Because they are in the
business of buying and selling, market makers both own the underlying asset so that
they can deliver it and are willing to buy the underlying asset so that they have it
ready to sell to someone else. If you own the underlying asset, writing a call option
that obligates you to sell it at a fixed price is not that risky. These people write options
to obtain the fee paid by the buyer.
Writing options can also generate clear benefits. To see how, think about the
case of an electricity producer who has a plant that is worth operating only when
electricity prices exceed a relatively high minimum level. Such peak-load plants are
relatively common. They sit idle most of the time and are fired up only when demand
is so high that prices spike. The problem is that when they are not operating—which
is the normal state of affairs—the owner must pay maintenance charges. To cover
these charges, the producer might choose to write a call option on electricity. Here’s
how the strategy works. For a fee, the plant owner sells a call option with a strike
price that is higher than the price at which the plant will be brought online. The buyer
of the call might be someone who uses electricity and wants insurance against a spike
in prices. The option fee will cover the producer’s maintenance cost while the plant is
shut down. And, because the producer as option writer owns the underlying asset here
—electricity—he or she is hedged against the possibility that the call option will pay
off. As the price of electricity rises, the plant’s revenue goes up with it.
Options are very versatile and can be bought and sold in many combinations.
They allow investors to get rid of the risks they do not want and keep the ones they do
want. In fact, options can be used to construct synthetic instruments that mimic the
payoffs of virtually any other financial instrument. For example, the purchase of an
at-themoney call and simultaneous sale of an at-the-money put gives the exact same
payoff pattern as the purchase of a futures contract. If the price of the underlying asset
rises, the call’s value increases just as a futures contract does, while the put remains
worthless. If the price falls, the put seller loses, just as a futures contract does, while
the call is out of the money. Finally, options allow investors to bet that prices will be
volatile. Buy a put and a call at the same strike price, and you have a bet that pays off
only if the underlying asset price moves up or down significantly.
In summary, options are extremely useful. Remember the example at the
beginning, in which the snowmobile manufacturer Bombardier purchased insurance
so it could offer its customers a rebate? What it bought were put options with a payoff
tied to the amount of snow that fell. The puts promised payments in the event of low
snowfall. This hedged the risk the company incurred when it offered rebates to the
purchasers of its snowmobiles. The providers of this insurance, the sellers of the
snowfall options, may have been betting that snowfall would not be low. That is, they
may have been speculating—but not necessarily. After all, there are many companies
whose sales and profits rise during warm weather and that are well positioned to take
such a risk. Insurance companies, for instance, have lower claims during warm
winters, because there are fewer accidents when there is less snow. If there is little
snow, the insurance company has the funds to make the payments, while if there is
lots of snow, they can use the price they were paid to write the put to help pay the cost
of the claims they face.
d. Swaps
Like other derivatives, swaps are contracts that allow traders to transfer risks.
Swaps come in numerous varieties. We will study two types: Interest rate swaps allow
one swap party—for a fee—to alter the stream of payments it makes or receives.
Interest rate swaps have been used widely for decades to synchronize receipts and
payments. Credit default swaps (CDS) are more recent. CDS are a form of insurance
that allow a buyer to own a bond or mortgage without bearing its default risk. We will
see that CDS played an important role in the financial crisis of 2007–2009 and were
also a factor in the euro-area crisis that began in 2010.
Government debt managers—the people at the U.S. Treasury who decide
when and how to issue U.S. Treasury bonds, notes, and bills—do their best to keep
public borrowing costs as low as possible. That means (a) selling bonds at the lowest
interest rates possible and (b) ensuring that government revenues will be available
when payments must be made. Because of the structure of financial markets, keeping
interest costs low usually is not a problem. Demand for long-term government bonds
is high. (They are used as collateral in many financial transactions.) Thus, government
debt managers can sell them at relatively high prices. Selling long-term debt also
limits rollover risk if future investors come to doubt the government’s willingness or
ability to repay.
Managing government revenues is more of a challenge. Revenues tend to rise
during economic booms and fall during recessions. Even if tax revenues fall, the
government must still make its bond payments. Short-term interest rates, like tax
revenues, tend to move with the business cycle, rising during booms and falling
during recessions. Ensuring that future interest expenses matchIfuture tax revenues
might be easier if government borrowers issued shortterm bonds. This difficulty
leaves the public debt manager in a quandary. Which is more important, keeping
interest costs and rollover risk down by issuing long-term debt or matching costs with
tax revenues by issuing short-term debt? Fortunately, derivatives allow government
debt managers to meet both these goals using a tool called an interest rate swap.
Interest rate swaps are agreements between two counterparties to exchange
periodic interest rate payments over some future period, based on an agreed-upon
amount of principal—what’s called the notional principal. The term notional is used
here because the principal of a swap is not borrowed, lent, or exchanged; it just serves
as the basis for calculation of the periodic cash flows between the counterparties to
the swap. In the simplest type of interest rate swap, one party agrees to make
payments based on a fixed interest rate, and in exchange the counterparty agrees to
make payments based on a floating interest rate. The effect of this agreement is to
transform fixed-rate payments into floating-rate payments and vice versa. For
example, as we write in 2019, the conventional five-year swap rate is the rate paid for
five years by the fixed-rate payer in return for receiving floating payments of three-
month LIBOR.
Pricing interest rate swaps means figuring out the fixed interest rate to be paid.
To do so, financial firms begin by noting the market interest rate on a U.S. Treasury
bond of the same maturity as the swap, called the benchmark. The rate to be paid by
the fixed-rate payer, called the swap rate, will be the benchmark rate plus a premium.
The difference between the benchmark rate and the swap rate, called the swap spread,
is a measure of risk: For example, the spread of the 10-year swap rate over the 10-
year Treasury bond yield averaged about ¼ percentage point during the 10 years
through 2015. In recent years, the swap spread has attracted substantial attention as a
measure of systematic risk, or overall risk in the economy. When it widens, it signals
that general economic conditions are deteriorating.
Interest rate swaps are just one example of the exchange of future payoffs.
Investors engage in a wide variety of swaps involving foreign exchange and equities,
though interest rate swaps are the most important. By one estimate, by mid-2018, the
notional value of interest rate swaps worldwide was $350 trillion––more than
13Itimes the total of foreign currency swaps at theItime.14 Who uses all these interest
rate swaps? Two groups have a comparative advantage in issuing bonds of a particular
maturity. The first group is government debt managers, who find long-term fixed-rate
bonds cheaper to issue but prefer short-term variable-rate obligations for matching
revenues with expenses. The second group uses interest rate swaps to reduce the risk
generated by commercial activities. The prime example is a bank that obtains funds
by offering interest-bearing checking accounts but makes mortgage loans at a fixed
rate. In essence, the bank is issuing short-term variable-rate bonds (the checking
accounts) and buying long-term fixedrate bonds (the mortgages) with the borrowed
funds. The problem is, changes in the slope of the yield curve create risk. That is, the
revenue from the mortgages may fall short of the payments due on the checking
accounts. Swaps insure the bank against such a shortfall.
On September 16, 2008, the Federal Reserve Bank of New York, part of the
U.S. central bank, made an extraordinary $85 billion loan to American International
Group (AIG). AIG, the largest insurance company in the world, was on the verge of
collapse because it had sold several hundred billion dollars’ worth of credit default
swaps (CDS). A CDS is a credit derivative that allows lenders to insure themselves
against the risk that a borrower will default. The buyer of a CDS makes payments—
like insurance premiums— to the seller, and the seller agrees to pay the buyer if an
underlying loan or security defaults. The CDS buyer pays a fee to transfer the risk of
default—the credit risk—to the CDS seller. Using CDS, a lender can make a loan
without facing the possibility of default. By combining a loan with a CDS to insure
against default, a lender who is good at identifying attractive loan opportunities and
collecting the loan payments can function efficiently, while letting someone else
worry about the default risk. This division of labor can improve resource allocation.
