Download Chapter 20

Chapter Twenty
Options, Corporate Securities
and Futures
Copyright  2007 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan
20-1
Chapter Organisation
20.1 Options: The Basics
20.2 Fundamentals of Option Valuation
20.3 Valuing a Call Option
20.4 Black–Scholes Option Pricing Model
20.5 Equity as a Call Option on the Firm’s Assets
20.6 Types of Equity Option Contracts
20.7 Futures Contracts
20.8 Term Structure of Interest Rates
Summary and Conclusions
Copyright  2007 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan
20-2
Chapter Objectives
• Understand the key terminology associated with
options.
• Outline the five factors that determine option
values.
• Price call options using the Black–Scholes option
pricing model.
• Discuss the types of equity option contracts offered.
• Outline the types of warrants available to investors.
• Discuss the characteristics of future contracts.
• Understand the term structure of interest rates.
Copyright  2007 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan
20-3
Option Terminology
• Call option
– Right to buy a specified asset at a specified price on or
before a specified date.
• Put option
– Right to sell a specified asset at a specified price on or
before a specified date.
• European option
– An option that can only be exercised on a particular date
(on expiry).
• American option
– An option that can be exercised at any time up to its
expiry date.
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20-4
Option Terminology (cont’d)
• Striking price or exercise price
– The contracted price at which the underlying asset can be
bought (call) or sold (put).
• Expiration date
–
The date at which an option expires.
• Option premium
– The price paid by the buyer for the right to buy (call) or
sell (put) an asset
– The price received by the seller for the obligation to sell
(call) or buy (put) an asset.
Copyright  2007 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan
20-5
Option Terminology (cont’d)
• Exercising the option
– The act of buying or selling the underlying asset via the
option contract.
• Option writer
– The writer of an option is the seller of the option. The writer
is obligated to perform according to the terms of the option if
and when an exercise is enforced.
• Option buyer
– The buyer of an option is the taker or holder of the option.
The option buyer obtains the right conveyed by the option
and only the option buyer has a right to exercise an option.
Copyright  2007 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan
20-6
Australian Options Market
Contract Characteristics
• Expiration month
– The month in which the option expires.
• Option type
– All options are American options so that they can be
exercised at any time prior to expiration.
• Contract size
– The standard contract size is 1000 shares.
– When a share on which there exists a traded option
undergoes a capital issue (bonus issue, share split, etc.) an
adjustment is made to one or more of the:
 Exercise price
 The number of options outstanding
 The number of shares to which each option contract relates.
Copyright  2007 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan
20-7
Australian Options Market
Contract Characteristics (cont’d)
• Expiry
– The maturity date for an option series is the last Friday of the
expiration month, or if not a business day, the next business day.
• Exercise price
– A new series is generally opened for trading approximately nine
months prior to the expiration month.
– Exercise prices are set ‘reasonably close’ to the prevailing market
price of the underlying share.
– Additional exercise prices are added by the Exchange on an ad hoc
basis depending upon price movements of the underlying share.
Copyright  2007 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan
20-8
A Sample Newspaper Listing of
Call Options
Asxcode/
Series
Ex price Fair value Last sale Vol 000's Open int
Woolworths Ltd last sale price $18.85
Aug-06
18.5
0.61
0.79
4
125
Aug-06
19
―
0.28
57
314
Aug-06
19.5
―
0.11
14
707
Aug-06
20
0.04
0.06
6
484
Sep-06
16
2.99
2.9
8
105
Sep-06
18
1.09
1.23
3
61
Sep-06
18.5
0.73
0.78
19
190
Sep-06
19
0.59
0.39
44
331
Sep-06
20
0.14
0.13
58
652
Sep-06
20.5
0.07
0.08
38
311
Oct-06
20
0.22
0.2
70
1
Dec-06
19
0.84
0.86
5
547
Dec-06
20
0.44
0.45
13
536
Mar-07
16
3.36
3.3
8
―
Source: Adapted from Australian Financial Review, 3 March 2006.
Implied
volatility Delta
19.83
15.54
15.96
18.25
20.2
14.44
15.39
20.51
16.26
16.18
15.07
14.78
15.16
―
Copyright  2007 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan
0.69
0.46
0.23
0.11
0.99
0.85
0.69
0.52
0.22
0.12
0.27
0.58
0.37
0.88
Annual %
return
21.46
21.04
8
3.79
4.84
8.42
13.62
21.33
5.02
2.33
5.07
11.28
5.81
4.12
20-9
Clearing and Margining
• Premium payable in full by buyer (taker) and credited
to account of seller (writer) at time of trade.
• At the same time, seller must lodge a deposit with the
Clearing House to ensure performance in the event
of price movement adverse to the position of seller.
• Deposit levels vary depending on value of underlying
shares and extent to which share price changes.
• The margin is comprised of two components:
– Premium margin
– Risk margin.
– Premium reflects the value of the contract and risk margin
reflects amount by which the value could change in a day.
Copyright  2007 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan
20-10
Option Valuation
• S1 = share price at expiration
• S0 = share price today
• C1 = value of call option on expiration
• C0 = value of call option today
• E = exercise price on the option
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20-11
Value of Call Option at Expiration
C1  0 if S1  E   0
Option is out of the money.
C1  S1  E if S1  E   0
Option is in the money.
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20-12
Value of Call Option at Expiration
Call option value
at expiration (C1)
S1  E
45 °
Exercise price (E)
S1 > E
Share price
at expiration (S1)
Copyright  2007 McGraw-Hill Australia Pty Ltd
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20-13
Call Option Boundaries
• Upper bound—a call option will never be worth more
than the share itself:
C0  S0
• Lower bound—share price cannot fall below 0 and
to prevent arbitrage, the call value must be (S0 – E):
The larger of 0 or (S0 – E)
Copyright  2007 McGraw-Hill Australia Pty Ltd
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20-14
Call Option Boundaries (cont’d)
• Opportunities for riskless profits are called arbitrages.
In a well organised market, significant arbitrages are
rare.
• Option price = Intrinsic value + Time value.
• Intrinsic value: what the option would be worth if it
were about to expire = lower bound
• Time value: the amount investors will pay for the
possibility of making a profit.
• For example, XYZ shares are $5.00, exercise price is
$4.75, and option price is $0.59 ($0.25 intrinsic value
+ $0.34 time value).
Copyright  2007 McGraw-Hill Australia Pty Ltd
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20-15
Value of a Call Option Before
Expiration
Call price
Upper bound
Lower bound
(C0)
C0  S0
C0  S0 – E
C0  0
45 °
Share price (S0)
Exercise price (E)
Copyright  2007 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan
20-16
Factors Determining Option
Values
Call option value  Share price  PV of exerciseprice
C0  S0  E/1  R f t
• The value of a call option depends on four factors:
–
–
–
–
Share price
Exercise price
Time to expiration
Risk-free rate.
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20-17
Another Factor to Consider?
• The above four factors are relevant if the option is to
finish in the money.
• If the option can finish out of the money, another
factor to consider is volatility.
• The greater the volatility in the underlying share
price, the greater the chance the option has of
expiring in the money.
Copyright  2007 McGraw-Hill Australia Pty Ltd
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20-18
The Factors that Determine
Option Value
Factor
Calls
Puts
Current value of the underlying asset
(+)
()
Exercise price on the option
()
(+)
Time to expiration on the option
(+)
(+)
Risk-free rate
(+)
()
Variance of return on underlying asset (+)
(+)
Copyright  2007 McGraw-Hill Australia Pty Ltd
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20-19
Black–Scholes Option Pricing
Model
C0  S0  N d1   E
 
t  N d2
1  R f 
C0  option value
S0  share price
Nd1   some probability theshare priceis relevant
E/1  R f t  PV exerciseprice
N d 2   some probability theexercisepriceis paid
Copyright  2007 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan
20-20
Black–Scholes Option Pricing
Model (continued)


1

2
1n S 0 /E    R f  2     t 

 

d1 
 t


d 2  d1    t
Note: The risk-free rate, the standard deviation and the time to
maturity must all be quoted using the same time units.
Copyright  2007 McGraw-Hill Australia Pty Ltd
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20-21
Example—Black–Scholes Option
Pricing Model
• S0 = $25
• E = $20
• Rf = 8%
•  = 30%
• t = 0.5 years
Copyright  2007 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan
20-22
Example—Black–Scholes Option
Pricing Model (continued)


1

2
1n 25 / 20    0.08  2  0.3   0.5



d1  
0.3  0.5
 0.223  0.0625/ 0.212 


 1.34

d 2  1.34  0.3  0.5

 1.34  0.212
 1.13
Copyright  2007 McGraw-Hill Australia Pty Ltd
PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan
20-23
Example—Black–Scholes Option
Pricing Model (continued)
• From the cumulative normal distribution table:
N(d1) = N(1.34) = 0.9099
N(d2) = N(1.13) = 0.8708
• Therefore, the value of the call option is:
C0  25 0.9099 
20
0 .080 .5 
e
 22.7475  16.7331
0.8708
 $6.01
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PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan
20-24
Equity as a Call Option on the
Firm’s Assets
• Equity can be viewed as a call option on the
company’s assets when the firm is leveraged.
• The exercise price is the value of the debt.
• If the assets are worth more than the debt when it
becomes due, the option will be exercised and the
shareholders retain ownership.
• If the assets are worth less than the debt, the
shareholders will let the option expire and the assets
will belong to the bondholders.
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20-25
Equity Option Contracts
• Types of equity option contracts offered in
Australia:
– Exchange traded put and call options on company shares
(called ‘share options’ or ‘stock options’)
– Exchange traded long dated contracts issued by a
financial institution to holders who can then trade them
(called ‘warrants’ in Australia)
– Over-the-counter options on company shares (called
‘company options’ in Australia, but ‘warrants’ on
international markets)
– Convertible notes issued by companies, comprising both
a debt and an equity component.
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20-26
Warrants
• Warrants are a financial instrument issued by banks
and other financial institutions and are traded on the
ASX.
• They are tradeable securities that give the holder the
right to purchase the underlying security at a fixed
price for a fixed period of time.
• Like options, there are both call and put warrants.
• Basically, warrants are long-term options.
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20-27
Warrants (continued)
• Types of warrants available:
–
–
–
–
–
–
–
–
–
Equity warrants
Fractional warrants
Basket warrants
Fully covered warrants
Index warrants
Instalment warrants
Low exercise price warrants
Endowment warrants
Currency warrants.
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20-28
Company Options
• A company option is a security that gives the holder
the right to purchase shares in a company at a
specified price over a given period of time.
• Usually offered as a ‘sweetener’ or ‘equity kicker’ to a
debt issue.
• These options are often detached and sold
separately.
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20-29
Company Options versus
Exchange Traded Options
• Company options have longer maturity periods and
are often European-type options.
• Company options are issued as part of a capitalraising program and are therefore limited in number.
• The clearing house has no role in the trading of
company options.
• Company options are issued by firms.
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Earnings Dilution
• Put and call options have no effect on the value of the
firm.
• Company options do affect the value of the firm.
• Company options cause the number of shares on
issue to increase when:
– the options are exercised
– the debts are converted.
• This increase does not lower the price per share but
EPS will fall.
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20-31
Forward Contracts
• A contract where two parties agree on the price of an
asset today to be delivered and paid for at some
future date. Legally binding on both parties.
• Can be tailored to meet the needs of both parties.
• Positions:
– Long—agrees to buy the asset at the future date
– Short—agrees to sell the asset at the future date.
• Can be used to reduce or eliminate uncertainty by
setting a buying or selling price in advance.
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20-32
Futures Contracts
• An agreement between two parties to exchange a
specified asset at a specified price at a specified time
in the future.
• A futures contract is a special type of forward contract
that is standardised and traded on an organised
exchange.
• Do not need to own an asset to sell a future contract.
• Either buy before delivery or close out position with
an opposite market position.
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20-33
Futures Markets
• Enable buyers and sellers to avoid risk in
commodities (and other) markets with high price
variability → hedging.
• Deposit required by all traders to guarantee
performance.
• Adverse price movements must be covered daily by
further deposits called margins (‘marked to market’).
• Futures also available for short-term interest rates, to
protect against interest rate movements.
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20-34
Futures Quotes
• Commodity, exchange, size, quote units
– The contract size is important when determining the daily
gains and losses for marking-to-market.
• Delivery month
– Open price, daily high, daily low, settlement price, change
from previous settlement price, contract lifetime high and
low prices, open interest
– The change in settlement price multiplied by the contract
size determines the gain or loss for the day:
 Long—an increase in the settlement price leads to a gain
 Short—an increase in the settlement price leads to a loss.
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20-35
Example—Hedging with Wool
Futures
• It is August and Jill Farmer expects to have 5000 kgs
of wool to sell in December. Wool futures for
December delivery are currently trading at 945 cents
per kg. Jill would like to get a price close to that. One
standardised contract equals 2500kg
• To lock in that price, Jill will need to sell two
December futures delivery contracts now (August).
The value of her open position will be:
5000kg x 945 cents = $47 250
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20-36
Example—Hedging with Wool
Futures (continued)
• It is now December. The price of wool at auction is
910 cents/kg and December wool futures are also
selling for 910 cents/kg. What does Jill do?
• Jill will now need to close out her position by buying
two December wool futures:
5000kg x 910 cents = $45 500
This gives her a profit on futures of $1750.
• Jill will also sell her wool at auction:
5000kg x 910 cents = $45 500
• Her net proceeds are $1750 + $45 500 = $47 250, or
945 cents/kg, which is the price she wanted.
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20-37
Example—Hedging with Wool
Futures (continued)
• What if, in December, the price of wool at auction is
975 cents/kg and December wool futures are also
selling for 975 cents/kg. What does Jill do this time?
• Jill will still need to close out her position by buying
December wool futures:
5000kg x 975 cents = $48 750
This time she has a loss on futures of $1500.
• Jill will also sell her wool at auction for $48 750.
5000kg x 975 cents = $48 750
• Net proceeds are $48 750 – 1500 = $47 250, or 945
cents/kg, which again is the price she wanted.
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20-38
Term Structure of Interest Rates
• Yield curve shows the different interest rates
available for investments of different maturities, at a
point in time.
• The relationship between interest rates of different
maturities is called the term structure.
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20-39
Term Structure of Interest Rates
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20-40
Factors Determining the Term
Structure
• Risk preferences—borrowers prefer long-term credit
whereas lenders prefer short-term loans (explains
upward-sloping yield curve only).
• Supplydemand conditions—segmented capital
markets can cause supplydemand imbalances
(explains all yield curve shapes).
• Expectations about future interest rates (most
favoured explanation).
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20-41
Summary and Conclusions
• Options takers have the right, but not the obligation to sell
(puts) or buy (calls) ordinary shares at a given price during
a specified period.
• Option writers have an obligation to sell (calls) or buy
(puts) ordinary shares at a given price during a specified
period.
• The value of any option depends only on five factors:
–
–
–
–
–
The price of the underlying asset
The exercise price
The expiration date
The interest rate on risk-free debt
The volatility of the underlying asset’s value.
• A futures contract can be used to hedge prices.
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20-42