FINA 2322 - Derivatives
1. Introduction to Derivatives
Jiaheng Yu
HKU Business School
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Today’s outline
1. This course
2. General concepts: cash flow, payoff, profit and value of a position
3. Buying and short-selling financial assets
4. What is a derivative?
5. Uses of derivatives
6. Overview and the role of the financial markets* (asterisks in this course
mean “optional content”)
Required readings: Section 1.1, 1.2. 1.3, 1.4 and 1.5.
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Why study derivatives?
Critical knowledge for some career paths, highly useful for others.
▶ Hedge funds and asset management
▶ Sales and trading
▶ Insurance, investment banking, commercial banking
▶ Corporate finance (CFO’s office)
▶ Central banks and regulatory agencies
Ideas and models that are elegant, powerful and practical.
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About me
Jiaheng Yu (yujh@hku.hk)
Joined HKU in 2023.
Ph.D. Massachusetts Institute of Technology
Research Interest: corporate finance, financial markets.
Office hours: Thursdays 4:30-5:30pm at KK1017, or by appointment.
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Teaching assistants
Wonderful and experienced TAs
Hermione
Jason
Check their office hours and tutorial schedules on Moodle.
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This course
Very similar contents as in the other subclasses. There should be no
surprise and no arbitrage opportunity.
Now, I need your help to know your knowledge backgrounds better.
Occasionally after class, I invite you to write an anonymous short note on
what you like and dislike about the class.
Announcements, assignments, supplemental materials, etc. will be posted
on Moodle.
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Textbook
The required textbook is McDonald, Robert L., 2013, Derivatives Markets,
3rd Edition.
1. Go to HKU library and sign in.
https://julac.hosted.exlibrisgroup.com/primo-explore/search?vid=HKU
2. Search “Derivatives Markets” in Books+.
3. Click “See all versions”.
4. Click “Online access”.
Errata for the book https:
//derivatives.kellogg.northwestern.edu/errata/errata3e.html
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Grading and requirements
Class participation = 5%.
▶ Sign-ups in lectures + tutorials.
▶ Cheating in the sign-ups may lead to 0% in class participation.
Problem sets = 30%.
▶ 5 problem sets in total. Each is graded on a scale of 100, and counts 6% .
▶ You can work either in groups or by yourself.
▶ Late submissions with permissible excuses will receive partial credits.
Midterm = 30%, October 24 (Thursday), 7pm - 8:30pm.
End-of-term test = 35%, December 6 (Friday), 2pm-4pm.
Contents on slides with a * in the title will not be tested. Contents on all
the other slides, in all problem sets and tutorials, may be tested. Contents
on the textbook but not mentioned in slides/problem sets/tutorials will
not be tested.
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General concepts: cash flow, payoff, profit and value
of a position
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What is a position?
A position is associated with a cash flow or a series of cash flows in the
future.
Suppose you own a stock, then you are in a stock position: you can sell
the stock 10 days later and receive a positive cash flow.
Suppose you borrowed some money, then you are in a debt position: you
need to repay the lender in the future, and experience a negative cash
flow.
Payoff in this course is equivalent to the cash flow.
Profit = payoff - (future value of) the cost of entering into the position.
More on this in later lectures.
The value of a position = how much you can sell the position to others.
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What is a long vs. short position?
In general, we say that someone has a long position in X if his payoff is
positively affected by the price of X.
And, .... a short position in X if ..... negatively affected .....
We can also simply say someone is long or short X.
Question: does an airline company has an inherent long or short position
in oil?
The exact definition of a long/short position in a derivatives contract may
depend on the contract itself. We’ll see this in later lectures.
We will talk about how to enter into a short position soon.
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Buying and short-selling assets
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Transaction costs and the bid-ask spread
Things to consider when you buy an asset...
Suppose you want to buy shares of HSBC stock. To buy the stock, you
contact a broker.
First, you need to pay a commission, that is a transaction fee you pay to
your broker.
Second, the price at which you can buy is usually different from the price
at which you can sell.
Bid price: the price at which you can sell. That is the price at which the
broker bids to buy.
Offer price or ask price: the price at which you can buy. That is the price
at which the broker offers to sell.
▶ To understand these terms, better to think from the broker’s perspective.
The difference between the bid price and the offer/ask price is called the
bid-ask spread.
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Transaction costs and the bid-ask spread
Where does the stock you just bought come from?
Most likely, it comes from a market-maker who holds an inventory of
stocks. When you want to buy, he sells you, and when you want to sell,
he buys from you.
He makes the market for you, by meeting your needs of trading.
The bid-ask spread compensates for the market-maker’s service.
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Orders that trigger a transaction
A market order is an instruction to trade a specific quantity of the asset
immediately, at the best price that is currently available.
A limit order is an instruction to trade a specific quantity of the asset at a
price that is not worse than a specified price.
▶ A limit order to buy 100 shares at $47.50 can be filled at $47.50 or below.
A stop-loss order: if you already own some shares of a stock, you enter a
stop-loss order at $45, then your order becomes a market order to sell
once the price falls to $45.
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Short selling
Short-sale can be generally interpreted as the opposite of buy (or long).
Example: short-selling wine
You believe a wine is overpriced and expect the price to fall. In order to
short-sell it, you must first obtain wine. You borrow a case from a collector
and promise to return it 1 week later. Having reached agreement, you borrow
the wine and then sell it at the market price. After 1 week, you acquire a
replacement case on the market, then return it to the collector from whom
you originally borrowed the wine. This final step is called closing or covering
the short position.
Day 0 Day 7
cash flows from buying wine:
−S0
+S7
cash flows from short-selling wine +S0
−S7
Comment: Short-selling can be thought as borrowing money at an unknown
interest rate.
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Things that can make short-sale costly*
This example is obviously simplified. We have assumed several points.
It is easy to find a lender of wine. scarcity
It is easy to buy, at a fair price, satisfactory wine to return to the lender:
The wine you buy after 1 week is a perfect substitute for the wine you
borrowed. scarcity
The collector from whom you borrowed is not concerned that you will fail
to return the borrowed wine. credit risk
Complexities arise if these assumptions are not warranted.
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What is a derivative?
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What is a derivative?
A derivative is a financial instrument whose value is determined by
(derived from) the price of some other “underlying” assets.
▶ ... or, whose future payoffs are tied to some underlying variable.
The underlying variable is usually the price of a traded asset
equities
currencies
interest rates commodities
▶ interest rates are the largest derivatives asset class, followed by currencies
but can also be a property of asset prices
volatility max or min
or corporate decisions
default events
or other things
amount of rains
level of dividends
number of votes
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What is a derivative?
All of these variables have two essential features
they are objective and observable
their outcomes have economic importance
Some derivatives are tied to two or more underlying variables.
The basic types of derivatives are
forwards futures
swaps
options
exotics
The term exoctics is an umbrella label for a broad range of derivatives that do
not fit into the standard categories. Many exotics are widely traded, but some
are used only rarely.
In most cases exotics are variations of standard contracts, but sometimes they
are unique instruments created for a special purpose.
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Example
A contract that gives the investor the right, but not the obligation, to buy
100 shares of HSBC’s stock at $70 per share in 360 days. → This is a call
option.
A contract that requires another investor to buy 100 EUR at 10
HKD/EUR in 20 days. → This is a currency forward or currency futures.
A contract that pays the investor $1 if the Democratic party wins the
2020 presidential election, $0 otherwise. → This is an exotic option.
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Significant notional values and the quick growth
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How are derivatives traded?
The trading of a financial asset involves at least four discrete steps.
▶ Deal: a buyer and a seller must locate each other and agree on a price.
▶ Clearing: the trade must be cleared, i.e., the obligations of each party are
specified.
▶ Settling: the trade must be settled, i.e., the buyer and the seller must deliver
the cash or securities necessary to satisfy their obligations in the required
period of time.
▶ Record: ownership records are updated.
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Where are derivatives traded?
In two forums, exchanges and the over-the-counter (OTC) market.
Exchanges are where securities have been traded for centuries. They
provide a central location, either physical or electronic, where people
come together to buy or sell.
The over-the-counter market refers to the collection of large financial
firms offering derivatives and the customers of these firms.
For most derivatives, both forums are recent
exchanges - began in early 1970s
over-the-counter market - grew rapidly in 1980s
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Exchange
Exchanges used to be physical. Old CME trading floor:
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Exchange
Nowadays, exchanges are mostly electronic networks where trading happens.
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Exchange vs. OTC Market
Exchange activities are public and highly regulated. After a trade has
taken place, a clearinghouse keeps track of the buyer’s and the seller’s
obligations and payments.
OTC trading is not easy to observe or measure, and is generally less
regulated. All negotiations are bilateral. You do not see the prices of other
dealers at a given time, while on exchange you always see the best price.
Many categories of financial claims are traded more often in OTC markets
than on exchanges.
On exchanges, you can trade
▶ stock, commodity, futures, options.
In OTC markets, you can trade
▶ everything in exchange, and bond, forward, swap, etc.
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Summary of Exchange vs. OTC Market*
Features
Exchanges
Market Size
very large
Availability
global
Min. Trade Size
small
Clientele
large and small
Secondary market yes
Terms
standardized;
limited choices
Transactions
anonymous
(buyer doesn’t know seller)
Price info
public
Collateral
standardized;rigorous
Credit Risk
minimal
Large Trades
market impact uncertain
OTC
very large
global
large
large only
no
flexible;
unlimited choices
bilateral
private
flexible
varies
market impact
included in price
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800
Market size
400
Best data source for
derivatives summary
statistics is BIS.
https://www.bis.
org/statistics/
about_derivatives_
stats.htm
0
200
size of market ($trillion)
600
OTC
Exchange
2000
2005
2010
2015
2020
Source: Bank for International Settlements. Figure shows the
total notional amounts for OTC market and value of underlying
assets for exchange market.
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The origin of derivatives*
Derivatives markets have existed at least since the Middle Ages.
▶ In the 12th century, merchants at European trade fairs negotiated forward
contracts for the future delivery of their goods.
▶ During Amsterdam’s tulip mania in the 1630s, these financial instruments
helped protect some merchants from price swings.
▶ In the 17th century, Japan developed a forward market in rice.
The origin of modern futures markets is the Chicago Board of Trade
(CBOT) in 1848.
▶ Farmers faced uncertain price of grains because of supply and timing.
▶ A “to-arrive” contract was created that fixed the price of grains on the basis
of delivery in Chicago.
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The origin of derivatives*
Chicago Mercantile Exchange (CME) was created in 1919 (from Egg &
Butter Board started in 1989)
CME and CBOT have merged to form CME Group.
Chicago Board Options Exchange (CBOE) started trading standardized call
options on 16 stocks in 1973.
Put options contracts started trading on CBOE in 1977.
Nowadays CBOE trades options on thousands of stocks and many stock
indices.
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The uses of derivatives
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Why are derivatives useful?
Risk Management
▶ Derivatives are a tool for companies and other users to reduce risks.
▶ Used by > 94% of Fortune 500 companies for risk management.
Speculation
▶ Derivatives can serve as investment vehicles.
Reduce Transaction Costs
▶ Sometimes derivatives provide a lower-cost way to achieve a particular
financial position.
Regulatory Arbitrage
▶ It is sometimes possible to circumvent regulatory restrictions, taxes, and
accounting rules by trading derivatives.
Managerial Compensation
▶ Derivatives can provide incentives to managers to work harder.
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Derivatives as a risk management tool
Risk management is often about reducing risk, but it can also be about
increasing attractive risks. All of the derivative strategies that can be used
to reduce risk can be reversed to increase risk.
The ability of derivatives to greatly increase risk can be dangerous if not
properly understood and properly monitored. Rogue employees making
unauthorized derivatives trades have caused major losses for some firms.
Example
an airline wants to hedge against changes in the price of jet fuel → use
commodity forward or commodity swap
an exporter wishes to protect against unfavorable exchange rate changes
but still benefit for favorable changes → use currency option
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Derivatives as a risk management tool
The introduction of derivatives to a market often coincides with an increase in
risks in that market.
Currencies were permitted to float in 1971 when gold standard was
abandoned. Currency futures started trading in 1972.
OPEC’s 1973 reduction in oil supply was followed by high and volatile oil
prices.
US interest rates became more volatile following inflation and recessions
in the 70s.
Deregulation of the natural gas market began since 1978, resulting in a
volatile market.
Deregulation of electricity market began in the 90s.
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1950
1970
1990
2010
(a)
Date
(a)
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.0
0.0
–0.4
–0.4
1950
1970
1990
Date
(b)
2010
–0.15
–0.10
–0.15
–0.20
–0.20
1970
1990
1970
1990
Date
Date
(c)
(c)
2010
2010
1970
1990
2010
2500
2500
2000
2000
1500
1500
1000
1000
500
500
0
1950
1950
1950
derivatives
trading
volume:
Date
1950
1970
1990
2010
Date (b)
1947-2011
(b)
0.8
–0.2
–0.2
–0.20
2010
–4
–0.05
0.00
(millions of contracts)
–0.10
–0.15
–4
0.00
0.05
–0.10
–0.05
Trading volume
(millions
of contracts)
Trading
volume
0.00
–0.05
–2
Date1990
oil prices:
1947-2011
1950
1970
2010
%Change
Changeinin
WTI
spot
price
%
WTI
spot
price
% Change in dollar-pound
exchange rate
0.10
0.05
0
–2
exchange ra
% Change in dollar-pou
rate
% exchange
Change in
dolla
Derivatives as a risk management tool
nth Treasury bill rate, 1947–2011. (b) The monthly percentage
e rate, 1947–2011. (c) The monthly percentage change in the
oil price, 1947–2011. (d) Millions of futures contracts traded
$/£ rate:
1947-2011
ade (CBT), Chicago Mercantile
Exchange
(CME), and the New
X), 1970–2011.
0
19801980
1990 1990
2000 2000
2010 2010
Date Date
(d) (d)
Sources:
(a)(a)
St. St.
Louis
Fed;Fed;
(b) DRI
and St.
Fed; (c)
St. (c)
Louis
(d)Fed;
CRB(d)
Yearbook.
Sources:
Louis
(b) DRI
andLouis
St. Louis
Fed;
St.Fed;
Louis
CRB Yearbook.
Trading volume
illions of contracts)
90
7 02
Change
in 3-month
Change
in 3-month
T-bill
1.2 An Overview of Financial Markets
2500
Sources: (a) St. Louis Fed; (b) DRI and St. Louis Fed; (c) St. Louis Fed; (d) CRB Yearbook
2000
1500
1000
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Using derivatives for speculation and investment
Derivatives can serve as investment vehicles.
They provide a way to make bets that are highly leveraged.
Financial engineering: a structured product that combines stocks, bonds,
and derivatives to achieve a certain risk-return profile.
Example
If you want to bet that S&P 500 stock index will be between 3500 and
3600 one year from now, you can use derivatives to make exactly that
bet.
“ The Big Short”: in 2006, if you believe the housing market is overheated,
you can short collateralized debt obligations and buy credit default swaps
to short the housing market.
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Using derivatives to reduce transaction costs
Sometimes derivatives provide a lower-cost way to achieve a financial
position.
Example
The manager of a mutual fund may wish to sell stocks and buy bonds.
Doing this entails paying transaction fees to brokers.
It is possible to trade derivatives to achieve the same position, yet pay
lower fees.
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Using derivatives to exploit regulatory arbitrage
It is sometimes possible to circumvent regulatory restrictions, taxes, and
accounting rules by trading derivatives.
Derivatives are often used to achieve the economic sale of stock, i.e.,
receive cash and eliminate the risk of holding the stock, while still
maintaining physical possession of the stock.
This transaction may allow the owner to defer taxes on the sale of the
stock, or retain voting rights, without the risk of holding the stock.
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Using derivatives for managerial compensation
Sometimes derivatives provide a way to incentivize the manager.
Example
To provide incentives to the CEO who controls the firm, you want to
compensate the CEO with out-of-the-money call options on the firm’s
stock.
Assume the stock price is $ 100. The call option says the CEO can buy
the stock at $150 in 2 years. Then, he would work harder to push up the
stock price.
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Overview and the role of financial markets*
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Financial markets
Money Market
▶ treasury bills, certificate of deposits, commercial paper, bankers acceptance
Bond Market
▶ treasury bonds and notes, municipal bonds, corporate bonds,
mortgage-backed securities
Equity Markets
▶ common stocks, preferred stocks
Commodities Markets
▶ spot market of energy, food, metal, (bitcoins).
Currency Markets
Derivatives Markets
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Cash flows among different macro sectors
Funds
• Mutual funds,
hedge funds
• Pensions, insurance
companies
Suppliers of capital
• Households (savings)
• Firms (savings)
• Governments (surplus)
Markets
• Money market
• Bonds
• Equity
• Commodities
• Derivatives
Users of capital
• Firms (investment)
• Governments (spending)
• Households (purchases)
Bank
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The role of financial markets
Intertemporal smoothing: allocation of resources over time.
▶ Bonds, stocks, and many other instruments to use.
▶ Households, firms and governments want to borrow and lend.
Risk sharing: allocation of resources over different states of the world.
▶ Individual communities/families have traditionally helped each other share
risks.
▶ Markets make risk-sharing more efficient.
▶ Diversifiable risks vanish (portfolio optimization, health insurance).
▶ Non-diversifiable risks are reallocated to those most willing to hold it
▶ for example, risk lovers buy stocks while risk haters buy bonds.
▶ derivatives transfer non-diversifiable risks between the two parties.
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The role of financial markets
Example: The Averages working for XYZ Co.
The Averages invest their savings in mutual funds that own stocks and
bonds from companies around the world. They select mutual funds that
provide diversified investments. As a result, the Averages are not heavily
exposed to any one company.
The Averages live in an area susceptible to tornadoes and insure their
home. The local insurance company reinsures tornado risk in global
markets, effectively pooling the tornado risk with Japan earthquake risk
and Florida hurricane risk.
The Averages financed their home with a mortgage from a bank. The
bank in turn sold the mortgage to other investors, freeing itself from
interest rate and default risk associated with the mortgage.
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The Role of Financial Markets
Example: The Averages working for XYZ Co.
The Average’s employer, XYZ Co., can access global markets to raise
money. Investors in Asia, for example, may thereby finance an
improvement to the Anytown factory.
XYZ Co. uses global derivatives markets to protect itself against adverse
currency, interest rate, and commodity price changes. By being able to
manage these risks, XYZ is less likely to go into bankruptcy, and the
Averages are less likely to become unemployed.
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A final note
There is a lot of vocabulary and jargon associated with derivatives
▶ long, short
▶ hedge, arbitrage
▶ leverage
▶ counterparty, broker, dealer, market maker
▶ FX, OTC, CDS,...
If you don’t know the meaning of a term, please ask! Don’t let them
impede your study.
Learning these vocabulary is an important part of knowledge you will
acquire in this course.
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Summary
Short-sale can be understood as the opposite of buy (long).
Derivatives are financial instruments whose value is derived from other
underlying assets.
Derivatives are traded on exchange and in OTC markets. The markets are
huge.
Derivatives are widely used for risk management, speculation, and other
purposes.
Financial markets play important roles in allocating resources.
Please spend one minute to write down the parts of this lecture that you are
confused about (or that you enjoyed). The link:
https://forms.office.com/r/EzLkQ7qrSh
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