Chapter 11
AN INTRODUCTION TO
DERIVATIVE SECURITIES
Chapter 11 Questions
What are the basic features of forward
contracts, futures contracts, and options
contracts?
Why do derivative securities exist? How do
they help meet investor needs and increase
market efficiency?
What are the similarities and differences
between forward contracts and futures
contracts?
Chapter 11 Questions
What terminology do we use to describe
option contracts?
What does a payoff diagram show?
What are the risks and potential returns from
option positions such as buying and writing
calls; buying and writing puts; owning long
and short positions in spreads, straddles,
strangles, or butterfly spreads?
Chapter 11 Questions
What are the relationships among the
prices of puts, calls, and futures?
What are some uses of derivatives in
investment analysis and portfolio
management?
Derivative Instruments
Value is determined by, or derived from, the
value of another instrument vehicle, called
the underlying asset or security
Forward contracts are agreements between
two parties - the buyer agrees to purchase an
asset, the seller agrees to sell the asset, at a
specific date at a price agreed upon now
Futures contracts are similar, but are
standardized and traded on an organized
exchange
Derivative Instruments
Options offer the buyer the right, but not the
obligation, to buy or sell and underlying asset
at a fixed price up to or on a specific date
Buyer is long in the contract
Seller or “writer” is short the contract
The price at which the transaction would we
made is the exercise or strike price
The profit or loss on an option position
depends on the market price
Why Do Derivatives
Exist?
Assets are traded in the cash or spot
market
Sometimes have one’s fortunes
dependent on spot price movements
leads to considerable risk

Various derivatives markets have evolved
that allow some investors to manage these
risks, while also creating opportunities for
speculators to invest in the same contracts
Potential Benefits of
Derivatives
Risk shifting

Especially shifting the risk of asset price changes
or interest rate changes to another party willing to
bear that risk
Price formation

Speculation opportunities when some investors
may feel assets are mis-priced
Investment cost reduction

To hedge portfolio risks more efficiently and less
costly than would otherwise be possible
Forward Contracts
An agreement between two parties to
exchange an asset at a specified price on a
specified date
Buyer is long, seller is short; symmetric gains
and losses as price changes, zero sum game
Contracts are OTC, have negotiable terms,
and are not liquid
Subject to credit risk or default risk
Value realized only at expiration
Popular in currency exchange markets
Futures Contracts
Like forward contracts…


Buyer is long and is obligated to buy
Seller is short and is obligated to sell
Unlike forward contracts…




Standardized – traded on exchange
More liquidity - can “reverse” a position and offset
the future obligation, other party is the exchange
Less credit risk - initial margin required
Additional margin needs are determined through a
daily “marking to market” based on price changes
Futures Contracts
Chicago Board of Trade (CBOT)

Grains, Treasury bond futures
Chicago Mercantile Exchange (CME)

Foreign currencies, Stock Index futures, livestock
futures, Eurodollar futures
New York Mercantile Exchange (NYMEX)

Crude oil, gasoline, heating oil futures
Development of new contracts

Futures exchanges look to develop new contracts
that will generate significant trading volume
Futures Contracts
Futures Quotations

One contract is for a fixed amount of the
underlying asset



Prices are given in terms of the underlying asset




5,000 bushels of corn (of a certain grade)
$250 x Index for S&P 500 Index Futures (of a certain
maturity)
Cents per bushel (grains)
Value of the index
Value of one contract is price x contract amount
Settle is the closing price from the previous day
Futures Contracts
Example: Suppose you bought (go long) the
most recent (Sept.) S&P 500 contract at the
settle price (see Exhibit 11.5).
What was the original contract value?
Value = $250 x 1180.80 = $295,200
What is your profit if you close your position
(sell a contract) for 1250.00?
Value = $250 x 1250.00 = $312,500
Profit = $312,500 - $295,200 = $17,300
Options
Option Terminology
Option to buy is a call option
Option to sell is a put option
Option premium – price paid for the
option
Exercise price or strike price – the price
at which the asset can be bought or
sold under the contract
Options
Option Terminology
Expiration date


European: can be exercised only at expiration
American: exercised any time before expiration
In-the-money: the option has intrinsic value,
and would be exercised if it were expiring
Out-of-the-money: the option has no intrinsic
value, would not be exercised if expiring

If not expiring, could still have value since it could
later become in-the-money
Options
Example: Suppose you own a call option with
an exercise (strike) price of $30.
If the stock price is $40 (in-the-money):


Your option has an intrinsic value of $10
You have the right to buy at $30, and you can
exercise and then sell for $40.
If the stock price is $20 (out-of-the-money):


Your option has no intrinsic value
You would not exercise your right to buy
something for $30 that you can buy for $20!
Options
Example: Suppose you own a put option with
an exercise (strike) price of $30.
If the stock price is $20 (in-the-money):


Your option has an intrinsic value of $10
You have the right to sell at $30, so you can buy
the stock at $20 and then exercise and sell for $30
If the stock price is $40 (out-of-the-money):


Your option has no intrinsic value
You would not exercise your right to sell
something for $30 that you can sell for $40!
Options
Chicago Board Options Exchange (CBOE)





Centralized facility for trading standardized option
contracts
Clearing Corporation is the opposite party to all
trades, allowing buyers and sellers to terminate
positions prior to expiration with offsetting trades
Standardized expiration dates, exercise prices,
and contract sizes
Secondary market with standardized contracts
Offer options on almost 1,400 stocks and also
index options
Options
Stock Option Quotations


One contract is for 100 shares of stock
Quotations give:





Underlying stock and its current price
Strike price
Month of expiration
Premiums per share for puts and calls
Volume of contracts
Premiums are often small

A small investment can be “leveraged” into high
profits (or losses)
Options
Example: Suppose that you buy a
January $60 call option on Microsoft
(see Exhibit 11.10).
What is the cost of your contract?
Cost = $9 x 100 = $900
Is your contract in-the-money?
Yes. The current stock price is $63.20, so
the intrinsic value is $3.20 per share.
Options
Example (cont.):
What is your dollar profit (loss) if, at
expiration, Microsoft is selling for $50?
Out-of-the-money, so Profit = ($900)
Is your percentage profit with options?
Return = (0-9)/9 = (100%)
What if you had invested in the stock?
Return = (50-63.20)/63.20 = (20.89%)
Options
Example (cont.):
What is your dollar profit (loss) if, at
expiration, Microsoft is selling for $65?
Profit = 100(65-60) – 900 = ($400)
Is your percentage profit with options?
Return = (65-60-9)/9 = (44.44%)
What if you had invested in the stock?
Return = (65-63.20)/63.20 = 2.85%
Options
Example (cont.):
What is your dollar profit (loss) if, at
expiration, Microsoft is selling for $85?
Profit = 100(85-60) – 900 = $1,600
Is your percentage profit with options?
Return = (85-60-9)/9 = 177.78%
What if you had invested in the stock?
Return = (85-63.20)/63.20 = 34.49%
Options
Payoff diagrams


Show payoffs at expiration for different stock
prices (V) for a particular option contract with a
strike price of X
For calls:




if the V<X, the payoff is zero
If V>X, the payoff is V-X
Payoff = Max [0, V-X]
For puts:



if the V>X, the payoff is zero
If V<X, the payoff is X-V
Payoff = Max [0, X-V]
Option Trading
Strategies
There are a number of different option
strategies:
Buying call options
Selling call options
Buying put options
Selling put options
Option spreads
Buying Call Options
Position taken in the expectation that the
price will increase (long position)
Profit for a purchasing a Call Option:
Per Share Profit =Max [0, V-X] – Call Premium
Note that profits on an option strategy include
option payoffs and the premium paid for the
option
The following diagram shows different total
dollar profits for buying a call option with a
strike price of $70 and a premium of $6.13
Buying Call Options
3,000
Profit from Strategy
2,500
Exercise Price = $70
2,000
Option Price
= $6.13
1,500
1,000
500
0
(500)
(1,000)
40
Stock Price at
Expiration
50
60
70
80
90
100
Selling Call Options
Bet that the price will not increase greatly –
collect premium income with no payoff
Can be a far riskier strategy than buying the
same options
The payoff for the buyer is the amount owed
by the writer (no upper bound on V-X)
Uncovered calls: writer does not own the
stock (riskier position)
Covered calls: writer owns the stock
Selling Call Options
1,000
500
Profit from Uncovered Call
Strategy
Exercise Price = $70
Option Price
= $6.13
0
(500)
(1,000)
(1,500)
(2,000)
(2,500)
(3,000)
40
Stock Price at
Expiration
50
60
70
80
90
100
Buying Put Options
Position taken in the expectation that the
price will decrease (short position)
Profit for purchasing a Put Option:
Per Share Profit = Max [0, X-V] – Put Premium
Protective put: Buying a put while owning the
stock (if the price declines, option gains offset
portfolio losses)
The following diagram shows different total
dollar profits for buying a put option with a
strike price of $70 and a premium of $2.25
Buying Put Options
3,000
Profit from Strategy
2,500
2,000
Exercise Price = $70
1,500
Option Price
= $2.25
1,000
500
0
Stock Price at
Expiration
(500)
(1,000)
40
50
60
70
80
90
100
Selling Put Options
Bet that the price will not decline greatly
– collect premium income with no payoff
The payoff for the buyer is the amount
owed by the writer (payoff loss limited to
the strike price since the stock’s value
cannot fall below zero)
Selling Put Options
1,000
Profit from Strategy
500
0
Exercise Price = $70
(500)
Option Price
(1,000)
= $2.25
(1,500)
(2,000)
(2,500)
(3,000)
40
Stock Price at
Expiration
50
60
70
80
90
100
Option Spreads
Many other option strategies can be crafted
using combinations of option positions
Price spread (vertical spread)

Buying and selling options on the same stock with
the same expiration, but with different strike prices
Time spread (horizontal or calendar spread)

Buying and selling options on the same stock with
the same strike price, but with different expirations
Option Spreads
Bullish spreads

Buy a higher priced option and sell a lower priced
option on the same stock
Bearish spreads

Sell a higher priced option and buy a lower priced
option on the same stock
Straddle


Combination of a purchasing (long) or selling
(short) a put and a call on the same expiration
Betting on a large price movement (long straddle)
or little price movement (short straddle)
Option Spreads
Strangle


Combination of a call and put with the same
expiration but different exercise prices (long or
short)
Similar to straddle strategies
Butterfly spread

Combination strategy with 4 options, similar to
straddles and strangles, but with less risk of large
losses
The number of different strategies is
potentially limitless
Put/Call Parity
Premiums for puts and calls are not
completely independent otherwise arbitrage
opportunities would exist
Two investments with equally risky payoffs
should have similar costs
Parity relationships exist between options,
also between options and futures, options
and spot prices, and futures and spot prices