# Chapter 18

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```					Chapter 18 - Option Markets and Strategies

CHAPTER 18- OPTION MARKETS AND STRATEGIES

SELF-TEST PROBLEMS & SOLUTIONS

ST18.1 Use a spreadsheet to compute the Black-Scholes option price of a call and put
option. The underlying stock has a price is \$50, volatility of 35%, and pays a 1%
dividend yield. The call option has an exercise price is \$55 and will mature in 6
months. The risk free rate is 6%. What is the price of the call and put options? Use
the spreadsheet to investigate how the call option price changes when the inputs vary.

ST18.1 SOLUTION
The following spreadsheet shows the Black-Scholes Options Pricing Model
equations.

Note that the call option is out-of-the-money, but still has a high option premium of
\$3.58 per share. The put option is in-the-money by \$5 and the put price is \$6.95. If
the stock price rises by \$1, to \$51 per share, the call price rises by \$0.46 to \$4.04.
With this \$1 stock price increase, the put option price falls by \$0.54. Stock price
changes and option price changes are not the same, and investors seeking to hedge
their positions using options need to be aware of this dynamic. When the volatility of
the underlying stock decreases from 35% to 25%, the call price falls to \$2.20. Option
prices are very sensitive to volatility. As volatility rises both call and put option
prices increase; a decline in volatility lowers option prices. Long term options are
worth more because they give buyers a greater chance for the stock price to trade in-
the-money. If the call option in ST18.1 were a 9 month option instead of a 6 month
option, the price would increase \$1.39 to \$4.97. Option prices are not very sensitive
to dividend yield. An increase in yield to 3% results in a call price of \$3.569, a
decrease of only \$0.008 results when when the yield is tripled. Put and call options
react differently to changes in interest rates. When the risk free rate is changed to
5%, the call price declines \$0.092 to \$3.485 and the put option increases \$0.175 to
\$7.127.

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ST18.2      What is the Options Clearing Corporation (OCC)? How does the OCC reduce the
risk of options trading (www.optionsclearing.com)?

ST18.2 SOLUTION
The Options Clearing Corporation (OCC), founded in 1973, is the world's largest
equity derivatives clearing organization. They are dedicated to promoting stability
and financial integrity in the marketplaces that we serve by focusing on sound risk
management principles. By acting as guarantor, OCC ensures that the obligations of
the contracts they clear are fulfilled. As the marketplace evolves, so do OCC clearing
capabilities. Although OCC began as a clearinghouse for listed equity options, it has
grown into a globally recognized entity that clears a multitude of diverse and
sophisticated products. OCC operates under the jurisdiction of both the Securities and
Exchange Commission (SEC) and the Commodities Futures Trading Commission
(CFTC). Under its SEC jurisdiction, OCC clears transactions for put and call options
on common stocks and other equity issues, stock indexes, foreign currencies, interest
rate composites and single-stock futures. As a registered Derivatives Clearing
Organization (DCO) under CFTC jurisdiction, OCC offers clearing and settlement
services for transactions in futures and options on futures. Overseeing OCC is a
clearing member dominated board of directors. OCC operates as an industry utility
and receives most of its revenue from clearing fees charged to its members. OCC
offers volume discounts on fees and, as applicable, refund excess fees to our clearing
members.

QUESTIONS & ANSWERS

Q18.1       Identify and describe the two main components of option value.

Q18.1 ANSWER
Option value is comprised of two components. Time value refers to the value of an
option arising from the probability that the underlying common stock's price will
exceed the exercise price at the point of expiration. The minimum expiration value of
an option is the simple difference between the current market price and exercise price
of the underlying common stock.

Q18.2       When are call options and put options in-the-money versus out-of-the-money?

Q18.2 ANSWER
A call option is in-the-money if the strike price is less than the market price of the
underlying security. A put option is in-the-money if the strike price is greater than
the market price of the underlying security. A call option is out-of-the-money if the
strike price is greater than the market price of the underlying security. A put option is
out-of-the money if the strike price is less than the market price of the underlying
security.

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Q18.3       Do specialists buy and sell options on the Chicago Board Options Exchange (CBOE)
(www.cboe.com)?

Q18.3 ANSWER
No. Most option classes listed at the CBOE are traded in an open outcry system
where certain members of the Exchange may trade as market-makers. Market-makers
provide liquidity in option trading by risking their own capital for personal trading,
and are the backbone of the CBOE's trading system. They take the opposite side of
public orders by competing in an open outcry auction market. This differs from the
trading environment on many other exchanges where "specialists" are allowed to
accept orders from the public, to manage the public order book and to deal for their
own accounts in the same securities.

Q18.4       What is the option premium?

Q18.4 ANSWER
The option premium is also the price at which the contract trades. The premium is
the amount paid by the buyer to the writer, or seller, of the option. For this amount,
the writer of the call option is obligated to deliver the underlying security if the call is
exercised. Alternatively, the writer of a put option is required to buy the underlying
security if the put is exercised. Writers keep the premium whether or not the option is
exercised. It is simply a non-refundable payment in full from the option holder to the
option writer for the rights conveyed by the option. Premium amounts are subject to
continuous change in response to the economic forces of supply and demand.
Premiums are affected by the current value of the underlying asset, exercise price,
values of related assets, expected volatility, and so on.

Q18.5       Give at least three ways in which the role played by a CBOE market maker is
different from that played by a floor broker or an exchange specialist
(www.cboe.com).

Q18.5 ANSWER
(1) On the CBOE, market makers provide liquidity in option trading by risking their
own capital for personal trading. They are the backbone of the CBOE's trading
system. They take the opposite side of public orders by competing in an open outcry
auction market. (2) Floor brokers, on the other hand, act as agents, executing orders
for public or firm accounts. Most option classes listed at the CBOE are traded in an
open outcry system where certain members of the Exchange may trade as
market-makers. (3) This differs from the trading environment on many other
exchanges where exchange specialists are allowed to accept orders from the public, to
manage the public order book and to deal for their own accounts in the same
securities.

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Q18.6       Describe the essential difference between a hedged position and a speculative
position.

Q18.6 ANSWER
A hedged position is created when an option contract is purchased or sold to offset
the risk inherent in some other investment. Hedgers use options to limit risk. A
speculative position is created when an option contract is purchased or sold to profit
from the inherent risk of some underlying asset. Speculators assume risk by taking
unhedged positions to profit from anticipated price changes. Options have
speculative appeal because they often exhibit significant leverage. This leverage
stems from the fact that options can often be purchased for a small fraction of the cost
of the underlying asset. Of course, leverage not only magnifies the potential benefits
from a favorable change in the price of the underlying asset, it also magnifies the loss
potential following an unfavorable change in price.

Q18.7       A stock option contract can be characterized as a zero-sum game between the buyer
and the seller about the short-term price action in a stock. Explain.

Q18.7 ANSWER
Before commissions and other transaction costs, option contracts represent a zero-
sum game between the buyer and the seller. Before commissions and other
transactions costs, when the price of the underlying asset rises unexpectedly, the
amount earned by the buyer of a call option is exactly equal to the amount lost by the
seller. When the price of the underlying asset falls unexpectedly, the amount lost by
the buyer of a call option is exactly equal to the amount earned by the seller. The
same holds true for put options. Gains and losses for put buyers and sellers are equal
in magnitude. A stock option contract is like a side bet between the buyer and the
seller about the short-term price action in a stock. No money is earned or lost by the
company itself. Only options market participants are affected.

Q18.8       What is the difference between an American-style option, a European-style option,
and a capped option?

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Q18.8 ANSWER
Option style refers to the time frame during which an option is exercisable. At the
present time, there are three different styles of options that are actively traded on
exchanges around the world. (1) An American-style option is an option contract that
can be exercised at any time between the date of purchase and the expiration date.
All stock options traded in the US are American-style options. Most exchange-traded
index options are American-style options. (2) European-style options are options
contracts that can only be exercised on the expiration date. The expiration date is the
last day of an American-style option, or the single exercise date of a European-style
option. (3) A capped option is an option that will be automatically exercised prior to
expiration if the options market on which it is trading determines that the value of the
underlying asset hits a specified cap price. Capped options may also be exercised,
like European-style options, during a designated period before expiration.
European-style or capped options having an expiration period that is longer or shorter
than their expiration date may be introduced in the future.

Q18.9       In general, is a physical delivery option more risky than a cash-settled option?
Explain.

Q18.9 ANSWER
No. In general, the manner of settlement has nothing to do with the risk of the option.
When it comes to the point of expiration, there are two different settlement
alternatives. Some options require physical delivery. Others have cash settlement
provisions. A physical delivery option gives its owner the right to receive physical
delivery of an asset if it is a call, or to make physical delivery of an asset if it is a put,
when the option is exercised. In the case of stock options, physical delivery takes the
form of stock certificates representing ownership if a specified number of shares. A
cash-settled option gives the holder the right to receive a cash payment based on the
difference between a determined value of the underlying interest at the time the
option is exercised and the fixed exercise price of the option. A cash-settled call
conveys the right to receive a cash payment if the settlement value exceeds the
exercise price. A cash-settled put grants the right to receive a cash payment if the
settlement value is less than the exercise price.

Q18.10      In the options market, what is meant by Aquadruple witching hours@ and when do
they occur?

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Q18.10 ANSWER
Options market players playfully refer to the last hour of trading on the third Friday
of March, June, September and December as quadruple-witching hour because of the
tendency of investors to rush to unwind their positions in expiring stock options,
index options, stock index futures, and single stock futures. The other eight times per
year, when only equity options and equity index options expire, is playfully referred
to as double-witching hour. The expiration of options and futures coincide only four
times per year, and quadruple witching hours are sometimes associated with sharp
price swings as investors buy and sell these derivative instruments and the underlying
equity securities.

Q18.11      Explain the circumstances under which the holder of a call option is entitled to
ordinary cash dividends.

Q18.11 ANSWER
Adjustments to the value of an option may be made following a variety of material
events, including: a stock dividend, stock distribution, stock split, rights offering,
reorganization, recapitalization, or merger. As a general rule, no adjustment is made
for ordinary cash dividends or distributions. A cash dividend or distribution by most
issuers is generally considered ordinary unless it exceeds 10% of the aggregate
market value of the underlying security. Stock options are not adjusted for ordinary
cash dividends and distributions. However, a call holder becomes entitled to the
dividend if such an investor exercises the option prior to the ex-dividend date.
Because call holders often seek to capture an impending dividend by exercising call
privileges, a call writer's chances of being assigned may increase as the ex-date
approaches for a dividend on the underlying security.

Q18.12      Describe the Chicago Board of Trade’s (CBOT) “open outcry” trading method
(www.cbot.com).

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Q18.12 ANSWER
The Chicago Board of Trade (CBOT), established in 1848, is a leading futures and
futures-options exchange. More than 3,600 CBOT member/stockholders trade 50
different futures and options products at the CBOT by open auction and
electronically. Volume at the Exchange in 2006 surpassed 805 million contracts, the
highest yearly total recorded in its history. In its early history, the CBOT traded only
agricultural commodities such as corn, wheat, oats and soybeans. Futures contracts at
the Exchange evolved over the years to include non-storable agricultural commodities
and non-agricultural products. In October 2005, the CBOT marked the 30th
anniversary of the Exchange's first financial futures contract, based on Government
National Mortgage Association mortgage-backed certificates. Since that introduction,
futures trading has been initiated in many financial instruments, including U.S.
Treasury bonds and notes, 30-Day Federal Funds, stock indexes, and swaps, to name
but a few. Another market innovation, options on futures, was introduced in 1982.
The CBOT added a new category to its diverse product mix in 2001 with the launch
of 100 percent electronic Gold and Silver futures contracts. Additionally, South
American Soybean futures and Ethanol futures, the Exchange’s newest products,
were introduced in 2005 in response to shifting trends in the global agricultural
economy. For decades, the primary method of trading at the CBOT was open auction,
which involved traders meeting face-to-face in trading pits to buy and sell futures
contracts. But to better meet the needs of a growing global economy, the CBOT
successfully launched its first electronic trading system in 1994. During the last
decade, as the use of electronic trading has become more prevalent, the Exchange has
upgraded its electronic trading system several times. Most recently, on October 12,
2005, the CBOT successfully launched its newly enhanced electronic trading
platform, e-cbot, powered by LIFFE CONNECT®, by introducing a major API
upgrade. Whether trading futures and options on futures through an electronic
platform or open auction, the CBOT’s primary role is to provide transparent and
liquid contract markets for its member/stockholders and customers to use for price
discovery, risk management and investment purposes. These futures markets also
allow speculators throughout the world to interpret economic data, news and other
information and use that information to make decisions about price and enter the
futures markets as investors. Speculators bridge the gap between hedgers’ bids and
offers, thereby making the market more liquid and cost effective.

Q18.13      Describe the circumstances in which a covered call position will result in a loss, and
be outperformed by a naked short position.

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Q18.13 ANSWER
A covered call is the simultaneous purchase of a stock and the sale of a call option on
that same security. Because the covered call writer owns the underlying stock, the
investor=s option position is hedged against upside volatility in the stock price.
Unlike a naked short seller, the covered call writer faces limited loss potential from
the short call option. A covered call strategy appeals to investors that are neutral to
moderately bullish on a stock, or bullish about a given company but wary about the
overall market. Naked short selling is a bearish strategy. Because a covered call
position requires ownership of the underlying common stock, it will result in a loss of
capital following a sharp downward move in the stock price. Under such
circumstances, the naked short seller would earn a profit. Thus, a covered call
position will result in a greater loss of capital than a naked short position in the case
of a rapidly declining stock price.

Q18.14      The Chicago Board Options Exchange (CBOE) has an outstanding Web Site
(www.cboe.com). Go to the CBOE site and find the definition for LEAPs. For what
type of investor do LEAPs hold the greatest appeal?

Q18.14 ANSWER
Long-term Equity AnticiPation Securities (LEAPS) are long-term option contracts
that allow investors to establish positions that can be maintained for a period of up to
three years. CBOE lists LEAPS on Equity and Index products. Please visit the CBOE
Symbol Directory for a listing of all CBOE Equity LEAPS and Index LEAPS. The
development and introduction of LEAPS by CBOE in 1990 added a whole new range
of options possibilities, many suited for conservative stock investors. Current options
investors are using LEAPS, as are stock investors, because of the similarities between
LEAPS and shares of stock, and the more conservative nature afforded to LEAPS by
their long-term expirations. Equity LEAPS calls can provide long-term stock market
investors an opportunity to benefit from the growth of large capitalization companies
without having to make outright stock purchases. Index LEAPS let you trade, hedge
or invest in the "entire" stock market or select industry sectors for a time that can be
measured in years.

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Chapter 18 - Option Markets and Strategies

PROBLEMS & SOLUTIONS

P18.1       The Federal Home Loan Mortgage Corporation, commonly referred to as Freddie
Mac (FRE), is a U.S. government-sponsored enterprise and a stockholder-owned
corporation authorized to make loans and loan guarantees. The table below shows
option quotes for Freddie Mac Jul08 calls four days prior to expiration on July 19,
2008. At a stock price of 6.54, indicate which among these calls are in-the-money
versus out-of-the money. When are call options at-the-money?

Calls
Strike                   Open                         Net
Price     Symbol        Interest     Volume          Change     Last    Bid     Ask
3.00   FREGF                  1           80           1.00    5.10    3.60    3.80
4.00   FREGN                 10          180           0.30    2.90    2.80    2.90
5.00   FREGA             10,152        1,966          -1.15    2.15    2.00    2.15
7.00   FREGR                  0           33           1.55    1.55    1.55    2.00
7.50   FREGU             19,751      11,810           -1.15    0.75    0.65    0.70
9.00   FREGL              5,020        9,439          -0.95    0.30    0.30    0.35
10.00   FREGB             14,274        6,408          -0.65    0.15    0.15    0.25

P18.1 SOLUTION
Call options are in-the-money when the stock price exceeds the strike price; call
options are out-of-the-money when the stock price is less than the strike price. Call
and put options are at-the-money when the market price of the stock equals the option
exercise or strike price. At a stock price of 6.54,

Strike Price         Calls
3.00        In-the-money
4.00        In-the-money
5.00        In-the-money
7.00       Out-of-the-money
7.50       Out-of-the-money
9.00       Out-of-the-money
10.00       Out-of-the-money

P18.2       Calculate the bid-ask spread in dollar terms and as a percentage of the bid price for
each of the Freddie Mac call option quotes given in Problem 18.1. Use this
information to help you explain why it is so expensive to trade options successfully.

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P18.2 SOLUTION
Successful options traders must be correct on their selection of the underlying
security, the near-term direction in price, and their estimation of volatility (magnitude
of the anticipated price move). Given the very large bid-ask spreads common for
short-term options, it is extremely difficult to trade such options successfully. In fact,
studies show many options traders actually lose money.

Calls
Strike                                      Bid-ask
Price     Symbol        Bid        Ask      Spread      % of Bid
3.00   FREGF           3.60       3.80        0.20      5.56%
4.00   FREGN           2.80       2.90        0.10      3.57%
5.00   FREGA           2.00       2.15        0.15      7.50%
7.00   FREGR           1.55       2.00        0.45     29.03%
7.50   FREGU           0.65       0.70        0.05      7.69%
9.00   FREGL           0.30       0.35        0.05     16.67%
10.00   FREGB           0.15       0.25        0.10     66.67%

P18.3       At a stock price of 6.54, calculate the intrinsic (or expiration) value and the time (or
speculative) value in dollar terms for each of the Freddie Mac call option quotes
given in Problem 18.1 using the mean of the bid and ask prices.

P18.3 SOLUTION

Calls
Intrinsic or      Time or
Strike                    Mean         Expiration       Speculative
Price     Bid     Ask    Bid/Ask          Value           Value
3.00    3.60    3.80      3.700           3.54            0.160
4.00    2.80    2.90      2.850           2.54            0.310
5.00    2.00    2.15      2.075           1.54            0.535
7.00    1.55    2.00      1.775             -             1.775
7.50    0.65    0.70      0.675             -             0.675
9.00    0.30    0.35      0.325             -             0.325
10.00    0.15    0.25      0.200             -             0.200

P18.4       The table below shows option quotes for Freddie Mac Jul08 puts four days prior to
expiration on July 19, 2008. At a stock price of 6.54, indicate which among these puts
are described as in-the-money versus out-of-the money. When are put options at-the-
money?

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Puts
Strike                   Open                             Net
Price     Symbol        Interest      Volume             Change       Last    Bid     Ask
3.00   FRESF              3,324           648              0.10      0.10    0.10    0.15
4.00   FRESN                390           857             -0.30      0.25    0.20    0.30
5.00   FRESA             22,413         8,329             -0.10      0.55    0.45    0.50
7.00   FRESR                   0            6              0.75      0.75    0.85    1.05
7.50   FRESU             13,781         7,226             -0.05      1.65    1.55    1.65
9.00   FRESL                932         1,503              0.20      2.70    2.65    2.80
10.00   FRESB             22,429         1,191              0.29      3.69    3.50    3.70

P18.4 SOLUTION
Put options are in-the-money when the stock price is less than the strike price; put
options are out-of-the-money when the stock price exceeds the strike price. Call and
put options are at-the-money when the market price of the stock equals the option
exercise or strike price. At a stock price of 6.54,

Strike Price            Puts
3.00          Out-of-the-money
4.00          Out-of-the-money
5.00          Out-of-the-money
7.00           In-the-money
7.50           In-the-money
9.00           In-the-money
10.00           In-the-money

P18.5       Calculate the bid-ask spread as a percentage of the bid price for each of the Freddie
Mac put option quotes given in Problem 18.4. Are these bid-ask spreads higher for in-
the-money versus out-of-the-money options?

P18.5 SOLUTION
Bid-ask spreads tend to be lower for in-the-money versus out-of-the-money options,
and that is the case in this Freddie Mac example.

Puts
Strike                                         Bid-ask
Price     Symbol         Bid        Ask        Spread      % of Bid
3.00   FRESF            0.10       0.15          0.05     50.00%
4.00   FRESN            0.20       0.30          0.10     50.00%
5.00   FRESA            0.45       0.50          0.05     11.11%
7.00   FRESR            0.85       1.05          0.20     23.53%
7.50   FRESU            1.55       1.65          0.10      6.45%
9.00   FRESL            2.65       2.80          0.15      5.66%
10.00   FRESB            3.50       3.70          0.20      5.71%

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P18.6       At a stock price of 6.54, calculate the intrinsic (or expiration) value and the time (or
speculative) value in dollar terms for each of the Freddie Mac put option quotes given
in Problem 18.4 using the mean of the bid and ask prices.

P18.6 SOLUTION

Puts
Intrinsic or   Time or
Strike                   Mean       Expiration     Speculative
Price     Bid     Ask    Bid/Ask    Value          Value
3.00    0.10    0.15      0.125           -            0.13
4.00    0.20    0.30      0.250           -            0.25
5.00    0.45    0.50      0.475           -            0.48
7.00    0.85    1.05      0.950         0.46           0.49
7.50    1.55    1.65      1.600         0.96           0.64
9.00    2.65    2.80      2.725         2.46           0.27
10.00    3.50    3.70      3.600         3.46           0.14

P18.7       Holding all else equal, indicate how each of the following unexpected events will
increase, decrease, or have no effect on the time value and/or minimum expiration
value of a given outstanding option: (a) rise in interest rates, (b) decrease in the
underlying common stock's dividend, (c) decrease in the underlying common stock's
volatility, (d) decline in the underlying common stock's price.

P18.7 SOLUTION
(a) An unexpected rise in interest rates will increase time value, but have no effect on
the expiration value of an option. Higher interest rates decrease the relative
attractiveness of holding the underlying common stock rather than the option.
(b) An unexpected fall in the underlying common stock's dividend will increase time
value, but have no effect on the expiration value of an option. When dividends
comprise relatively less of the expected total return on a stock, a higher
probability of capital gains and positive expiration value is present.
(c) An unexpected fall in the underlying common stock's volatility decreases the
probability of positive value at expiration. Thus, a decrease in time value, and no
effect on expiration value will be noted.
(d) An unexpected fall in the underlying common stock's price will decrease both the
time value and expiration value of an option. At lower prices, time value will fall
since there is a lower probability that the option will have any value at expiration.

P18.8       Assume an option trader bought 10 July 25 calls on General Electric Co. (GE) for
1.35. If the stock closed at 28 on expiration and the option position was liquidated,
calculate the dollar amount of profit or loss on the trade before commissions and
taxes.

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P18.8 SOLUTION
Cost =      \$1.35 × 10 × 100
=     \$1,350
Proceeds =      (\$28 -\$25) × 10 × 100
=     \$3,000
Profit =     Proceeds – Cost
=     \$3,000 - \$1,350
=     \$1,650

P18.9       Assume an investor established a covered call position in McDonalds Corp. (MCD)
by selling 25 November 60 calls at 3 and bought an offsetting position in the stock at
58. Calculate the investor’s profit on this covered call position if the stock is called
away at expiration. For simplicity, ignore taxes and commissions.

P18.9 SOLUTION
Stock cost =       \$58 × 2,500
=      \$145,000
Option proceeds =       \$3 × 25 × 100
=      \$7,500
Profit =      Stock Proceeds + Option proceeds – Stock cost
=      (\$60 × 2,500) + \$7,500 - \$145,000
=      \$12,500

P18.10      Assume an option trader bought 10 August 15 puts on Citigroup, Inc. (C) for 0.85. If
the position was held to expiration at which point the stock closed at 16, calculate the
dollar amount of profit or loss on the trade before commissions and taxes.

P18.10 SOLUTION

Cost =      \$0.85 × 10 × 100
=     \$850
Proceeds =      (\$0) × 10 × 100
=     \$0
Profit =     Proceeds – Cost
=     \$0 - \$850
=     -\$850 (a total loss)

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P18.11      Suppose the S&P 100 Index (OEX) is at 672.42 and an options speculator bought one
OEX September 670 put at 18.50 and sold one OEX September 660 put at 14.50. (1)
Characterize this position and calculate the amount of net debit or net credit to the
speculator’s account. (2) Calculate the amount of net profit or net loss if the OEX
remained unchanged. (3) Calculate the maximum amount of potential gain and the
conditions under which it would be achieved. (4) Calculate the maximum amount of
potential loss and the conditions under which it would be achieved. (5) Calculate the
speculator’s breakeven price for the OEX at expiration.

P18.11 SOLUTION
(1) This is a Bear Put Spread on the OEX, and the net debit to the speculator’s
account is 4, or \$400. (2) If the OEX remained unchanged a loss of \$400 would be
incurred. (3) The maximum gain is \$600 if OEX is less than or equal to 660 (- 1.85%)
at expiration. (4) The maximum loss is \$400 if OEX is greater than or equal to 670 (-
0.36%) at expiration. (5) At September expiration, the break-even point (before
commissions) for this Bear Put Spread on the OEX is 666.00 or a -0.95% change in
the underlying index value.

P18.12      Suppose the American Express Co. (AXP) stock is at 32.50 and an options speculator
sells one AXP Apr 30 call at 5.75 and buys one AXP Apr 35 call at 2.75. (1)
Characterize this position and calculate the amount of net debit or net credit to the
speculator’s account. (2) Calculate the amount of net profit or net loss if AXP
remained unchanged. (3) Calculate the maximum amount of potential gain and the
conditions under which it would be achieved. (4) Calculate the maximum amount of
potential loss and the conditions under which it would be achieved. (5) Calculate the
speculator’s breakeven price for AXP at expiration.

P18.12 SOLUTION
(1) This is a Bear Call Spread on AXP, and the net credit to the speculator’s account
is 3, or \$300(=\$575-\$275). (2) If AXP remained unchanged a gain of \$50 would be
incurred, equal to the net credit of \$300 minus the \$250 intrinsic value at expiration
of the Apr 30 call. (3) The maximum gain is \$300 if AXP is less than or equal to 30 at
expiration. (4) The maximum loss is \$200 if AXP is greater than or equal to 35 at
expiration, equal to the net credit of \$300 minus the \$500 intrinsic value at expiration
of the Apr 30/35 call spread. (5) At April expiration, the break-even point (before
commissions) for this Bear Call Spread on AXP is 33 in the underlying stock price.
At a stock price of 33, the Apr 30/35 call spread is worth 3 or \$300, the amount of net
credit to the speculator’s account.

P18.13      Suppose DELL is trading at \$26 and you buy one July25 call for \$2.95 and sell one
July30 call for \$0.50. Calculate your maximum potential profit and loss at expiration.
Is this a bearish or bullish position?

18-14
Chapter 18 - Option Markets and Strategies

P18.13 SOLUTION
This is called a Bull Call Spread position where the investor is bullish (positive) on
the outlook for the stock. By selling the 30 call, you lower your exposure but also
lower your upside potential. The net premium paid is \$245 (= (\$2.95 - \$0.50) × 100).
If DELL rises to close above 30 at the time of expiration, the spread rises in value to
\$500 and the highest potential net profit on the trade is \$255 (= (\$30 -\$25) × 100 -
\$245). If the stock falls to close at 25 or below at the time of expiration, both calls
expire worthlessly and the most you could lose is the net premium paid or \$245. The
payoff to a Bull Call Spread is exactly the opposite to the other side of the trade, a
Bear Call Spread.

P18.14      Suppose DELL is trading at \$26 and you sell one July25 call for \$2.95 and buy one
July30 call for \$0.50. Calculate your maximum potential profit and loss at expiration.
Is this a bearish or bullish position?

P18.14 SOLUTION
This is called a Bear Call Spread position where the investor is bearish (negative) on
the outlook for the stock. By selling one July25 call for \$2.95 and buying a July30
call for \$0.50, net proceeds from the trade are \$245 (= (\$2.95 - \$0.50) × 100). This is
the maximum potential profit in the event that the spread expires worthlessly. If
DELL falls to close below 25 at the time of expiration, the spread falls in value to \$0
and the \$245 premium received represents the maximum potential profit. If the stock
rises above 30 at the time of expiration, your total exposure and the most you could
lose is \$255 (= (\$30 - \$25) × 100 - \$245). The payoff to a Bear Call Spread is exactly
the opposite to the other side of the trade, a Bull Call Spread.

P18.15      Suppose the Coca-Cola Co. (KO) is trading at \$54 and you sell one Aug55 put for
\$2.55 and buy one Aug50 put for \$0.85. Calculate your maximum potential profit and
loss. Is this a bearish or bullish position?

P18.15 SOLUTION
This is called a Bull Put Spread position where the investor is bullish (positive) on the
outlook for the stock. By buying the 50 put, you lower your exposure but also lower
your upside potential. If KO rises to close above 55 at the time of expiration, the
spread falls in value to \$0. The highest potential profit on the trade is the net premium
received \$170 (= (\$2.55 - \$0.85) × 100). If the stock falls to close at 50 or below at
the time of expiration, your total cost and the most you could lose is \$330 (= (\$55 -
\$50) × 100 - \$170). The payoff to a Bull Put Spread is exactly the opposite of the
other side of the trade, a Bear Put Spread.

P18.16      Suppose Coca-Cola Co. (KO) is trading at \$54 and you buy one Aug55 put for \$2.55
and sell one Aug50 put for \$0.85. Calculate your maximum potential profit and loss.
Is this a bearish or bullish position?

18-15
Chapter 18 - Option Markets and Strategies

P18.16 SOLUTION
This is called a Bear Put Spread position where the investor is bearish (negative) on
the outlook for the stock. By selling the 50 put, you lower your exposure but also
lower your upside potential. The net premium paid is \$170 (= (\$2.55 - \$0.85) × 100).
If KO falls to close at 50 or below at the time of expiration, the spread rises in value
to \$5 and the maximum profit of \$330 is achieved (= (\$55 - \$50) × 100 - \$170). If the
stock rises to close at 55 or above at the time of expiration, both puts expires
worthlessly, and the maximum loss of \$170 (the net premium paid) is realized. The
payoff to a Bear Put Spread is exactly the opposite of the other side of the trade, a
Bull Put Spread.

P18.17      Assume an investor establishes a straddle position on Chevron Corp. (CVX) by
buying a December 95 call priced at 1.50 and simultaneously selling a December 95
put priced at 3.50. Graph the profit picture of this straddle position.

P18.17 SOLUTION

5
3.5                                                    write put
1.5

95
Straddl
e
write call

P18.18      Using the Black-Scholes option valuation formula, compute the price of a Marathon
Oil (MRO) call option with 4 months to expiration that has a strike price of 45.
Assume the current stock price is 48, the T-bill yield is 4.5%, and the volatility of
MRO is 30%.

18-16
Chapter 18 - Option Markets and Strategies

P18.18 SOLUTION
First, compute d1 and d2 using equations 18.3 and 18.4:

d1 
                     
ln 48 45   0.045  0.5  0.3 2  0.333

0.0645  0.03
 0.546
0.3 0.333                                 0.1731
d 2  0.546  0.3 0.333  0.373

Using Table 18.4, N(d1) = N(0.55) = 0.7089 and N(d2) = N(0.37) = 0.6443. Then
using equation 18.2, the call price is:
45
Call price  48[0.7089]  ( 0.045)(0.333) [0.6443]  \$5.46
e

P18.19      Using the information provided and solution to P18.18 and the put-call parity concept
to compute the value of a strike price 45 MRO put option of the same time to
expiration.

P18.19 SOLUTION
Using equation 18.5,
45
Put price         (0.045)(0.
333)
 48  5.46  \$1.79
e

P18.20      Assume a call option has a delta = 0.709, gamma = 0.038, 7 day theta = -0.103, vega
= 0.092, and rho = 0.095. Compute the option price change when these valuation
parameters change by one unit each.

P18.20 SOLUTION
A delta of 0.709 means that the option value will change 70.9% of the change in the
underlying stock. So a \$1 change in stock price will cause a change of \$0.709. The
gamma of 0.038 means that delta will increase by 0.038 if the stock price increases
\$1. A theta value of -0.103 describes the sensitivity to time. Theta suggests that the
value of the call option will decrease \$0.103 each week. If the volatility of the stock
changes, a vega of 0.092 tells us that the option price will increase by \$0.09 for every
1% increase in volatility. Lastly, a rho of 0.095 means that if interest rates change by
1%, the value of the option will change by \$0.095.

18-17
Chapter 18 - Option Markets and Strategies

CFA PROBLEMS & SOLUTIONS
CFA18.1The current price of an asset is 100. An out-of-the-money American put option with
an exercise price of 90 is purchased along with the asset. If the breakeven point for
this hedge is at an asset price of 114 at expiration, then the value of the American put
at the time of purchase must have been:

A. 0.
B. 4.
C. 10.
D. 14.

Answer: D

Joel Franklin is a portfolio manager responsible for derivatives. Franklin observes
European-style put options and call options on Abaco Ltd. common stock with the
same strike price and time to expiration. Selected information relevant to Abaco Ltd.
stock and options is shown in Exhibit 1.
Exhibit 1
Abaco Ltd. Securities Selected Data
Closing price of Abaco common stock                    \$43.00
Put and call option exercise price                     \$45.00
Time to expiration                                    One year
Price of the European-style put option                  \$4.00
Price of the European-style call option One-
year U.S. Treasury bill rate               5.50%

Samantha Crowe, a colleague of Franklin, believes that Abaco stock is overpriced and
she decides to sell short the stock. However, her broker informs her that an adequate
inventory of the stock may not be available to sell short.

CFA18.2Based on a put-call parity, the value of the European-style call option is closest to:

A. \$0.00.
B. \$2.00.
C. \$4.35.
D. \$4.41.

Answer: D

18-18
Chapter 18 - Option Markets and Strategies

CFA18.3If the volatility of Abaco’s stock price decreases, what is most likely to happen to the
values of the related call and put?

A. Both the call and the put will decrease in value.
B. Both the call and the put will increase in value.
C. The value of the call will increase while the value of the put will decrease.
D. The value of the call will decrease while the value of the put will increase.

Answer: A

CFA18.4The Chief Economist at Franklin’s firm is forecasting a substantial decline in interest
rates. To help gain from this forecast while assuming limited risk, Franklin should
take which of the following actions with regard to the European-style options in
Exhibit 1?

A. Buy the call option.
B. Buy the put option.
C. Sell the call option.
D. Sell the put option.

Answer: B

CFA18.5Franklin considers selling the European-style put option described in Exhibit 1.
Ignoring time value of money and given current prices, the maximum possible loss
from this strategy is:

A. \$39.00.
B. \$41.00.
C. \$45.00.
D. Unlimited.

Answer: B

18-19

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