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of options.

Binary Options
Binary options (also called “bet” options) have fixed payoffs that depend on whether a con-
dition is satisfied by the price of the underlying asset. For example, a binary call option
might pay off a fixed amount of $100 if the stock price at maturity exceeds the exercise
price.




SUMMARY • A call option is the right to buy an asset at an agreed-upon exercise price. A put option is
the right to sell an asset at a given exercise price.
• American options allow exercise on or before the exercise date. European options allow
exercise only on the expiration date. Most traded options are American in nature.
• Options are traded on stocks, stock indexes, foreign currencies, fixed-income securities,
and several futures contracts.
• Options can be used either to lever up an investor™s exposure to an asset price or to
provide insurance against volatility of asset prices. Popular option strategies include
covered calls, protective puts, straddles, and spreads.
• Many commonly traded securities embody option characteristics. Examples of these
securities are callable bonds, convertible bonds, and warrants. Other arrangements, such as
collateralized loans and limited-liability borrowing, can be analyzed as conveying implicit
options to one or more parties.

KEY American option, 495 exercise price, 492 risk management, 506
TERMS at the money, 493 in the money, 493 spread, 508
call option, 492 out of the money, 493 straddle, 508
collar, 511 preminum, 492 strike price, 492
covered call, 506 protective put, 504 warrant, 516
European option, 495 put option, 493
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PROBLEM 1. Which one of the following statements about the value of a call option at expiration is
SETS false?
a. A short position in a call option will result in a loss if the stock price exceeds the
exercise price.
b. The value of a long position equals zero or the stock price minus the exercise price,
whichever is higher.
c. The value of a long position equals zero or the exercise price minus the stock price,
whichever is higher.
d. A short position in a call option has a zero value for all stock prices equal to or less
than the exercise price.
Bodie’Kane’Marcus: V. Derivative Markets 14. Options Markets © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition




521
14 Options Markets


2. The following diagram shows the value of a put option at expiration:


Long put
4
Exercise price
of both options
Option
0
value

Short put
4
76 80
Stock price ($)


Ignoring transaction costs, which of the following statements about the value of the put
option at expiration is true?
a. The value of the short position in the put is $4 if the stock price is $76.
b. The value of the long position in the put is $4 if the stock price is $76.
c. The long put has value when the stock price is below the $80 exercise price.
d. The value of the short position in the put is zero for stock prices equaling or
exceeding $76.
3. The following price quotations are for exchange-listed options on Primo Corporation
common stock.

Company Strike Expiration Call Put
Primo 61.12 55 Feb 7.25 .48


Ignoring transaction costs, how much would a buyer have to pay for one call option
contract?
4. Turn back to Figure 14.1, which lists the prices of various Microsoft options. Use the
data in the figure to calculate the payoff and the profits for investments in each of the
following January maturity options, assuming that the stock price on the maturity date
is $70.
a. Call option, X 65
b. Put option, X 65
c. Call option, X 70
d. Put option, X 70
e. Call option, X 75
f. Put option, X 75
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5. Suppose you think Wal-Mart stock is going to appreciate substantially in value in the
next six months. Say the stock™s current price, S0, is $100, and the call option expiring
in six months has an exercise price, X, of $100 and is selling at a price, C, of $10. With
$10,000 to invest, you are considering three alternatives:
a. Invest all $10,000 in the stock, buying 100 shares.
b. Invest all $10,000 in 1,000 options (10 contracts).
c. Buy 100 options (one contract) for $1,000 and invest the remaining $9,000 in a
money market fund paying 4% interest over six months.
What is your rate of return for each alternative for four stock prices six months from
now? Summarize your results in the table and diagram below.
Bodie’Kane’Marcus: V. Derivative Markets 14. Options Markets © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition




522 Part FIVE Derivative Markets


RATE OF RETURN ON INVESTMENT
Price of Stock Six Months from Now

$80 $100 $110 $120
a. All stocks (100 shares)
b. All options (1,000 shares)
c. Bills 100 options




Rate of return




0
ST



6. The common stock of the P.U.T.T. Corporation has been trading in a narrow price range
for the past month, and you are convinced it is going to break far out of that range in the
next three months. You do not know whether it will go up or down, however. The current
price of the stock is $100 per share, the price of a three-month call option with an exercise
price of $100 is $10, and a put with the same expiration date and exercise price costs $7.
a. What would be a simple options strategy to exploit your conviction about the stock
price™s future movements?
b. How far would the price have to move in either direction for you to make a profit on
your initial investment?
7. The common stock of the C.A.L.L. Corporation has been trading in a narrow range
around $50 per share for months, and you believe it is going to stay in that range for the
next three months. The price of a three-month put option with an exercise price of $50
is $4, and a call with the same expiration date and exercise price sells for $7.
a. What would be a simple options strategy using a put and a call to exploit your
conviction about the stock price™s future movement?
b. What is the most money you can make on this position? How far can the stock price
move in either direction before you lose money?
c. How can you create a position involving a put, a call, and riskless lending that
would have the same payoff structure as the stock at expiration? The stock will pay
no dividends in the next three months. What is the net cost of establishing that
position now?
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8. Joseph Jones, a manager at Computer Science, Inc. (CSI), received 10,000 shares of
company stock as part of his compensation package. The stock currently sells at $40 a
share. Joseph would like to defer selling the stock until the next tax year. In January,
however, he will need to sell all his holdings to provide for a down payment on his new
house. Joseph is worried about the price risk involved in keeping his shares. At current
prices, he would receive $40,000 for the stock. If the value of his stock holdings falls
below $35,000, his ability to come up with the necessary down payment would be
jeopardized. On the other hand, if the stock value rises to $45,000, he would be able to
maintain a small cash reserve even after making the down payment. Joseph considers
three investment strategies:
Bodie’Kane’Marcus: V. Derivative Markets 14. Options Markets © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition




523
14 Options Markets


a. Strategy A is to write January call options on the CSI shares with strike price $45.
These calls are currently selling for $3 each.
b. Strategy B is to buy January put options on CSI with strike price $35. These options
also sell for $3 each.
c. Strategy C is to establish a zero-cost collar by writing the January calls and buying
the January puts.
Evaluate each of these strategies with respect to Joseph™s investment goals. What are the
advantages and disadvantages of each? Which would you recommend?
9. a. A butterfly spread is the purchase of one call at exercise price X1, the sale of two
calls at exercise price X2, and the purchase of one call at exercise price X3. X1 is less
than X2, and X2 is less than X3 by equal amounts, and all calls have the same
expiration date. Graph the payoff diagram to this strategy.
b. A vertical combination is the purchase of a call with exercise price X2 and a put with
exercise price X1, with X2 greater than X1. Graph the payoff to this strategy.
10. A bearish spread is the purchase of a call with exercise price X2 and the sale of a call
with exercise price X1, with X2 greater than X1. Graph the payoff to this strategy and
compare it to Figure 14.11.
11. You are attempting to formulate an investment strategy. On the one hand, you think
there is great upward potential in the stock market and would like to participate in the
upward move if it materializes. However, you are not able to afford substantial stock
market losses and so cannot run the risk of a stock market collapse, which you also
think is a possibility. Your investment adviser suggests a protective put position: Buy
shares in a market index stock fund and put options on those shares with three-month
maturity and exercise price of $1,040. The stock index is currently at $1,200. However,
your uncle suggests you instead buy a three-month call option on the index fund with
exercise price $1,120 and buy three-month T-bills with face value $1,120.
a. On the same graph, draw the payoffs to each of these strategies as a function of the
stock fund value in three months. (Hint: Think of the options as being on one “share”
of the stock index fund, with the current price of each share of the index equal to
$1,200.)
b. Which portfolio must require a greater initial outlay to establish? (Hint: Does either
portfolio provide a final payoff that is always at least as great as the payoff of the
other portfolio?)
c. Suppose the market prices of the securities are as follows.

Stock fund $1,200
T-bill (face value $1,120) 1,080
Call (exercise price $1,120) 160
Put (exercise price $1,040) 8
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Make a table of profits realized for each portfolio for the following values of the
stock price in three months: ST $0, $1,040, $1,120, $1,200, and $1,280. Graph the
profits to each portfolio as a function of ST on a single graph.
d. Which strategy is riskier? Which should have a higher beta?
12. The agricultural price support system guarantees farmers a minimum price for their
output. Describe the program provisions as an option. What is the asset? The exercise
price?
13. In what ways is owning a corporate bond similar to writing a put option? A call option?
Bodie’Kane’Marcus: V. Derivative Markets 14. Options Markets © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition




524 Part FIVE Derivative Markets


14. An executive compensation scheme might provide a manager a bonus of $1,000 for every
dollar by which the company™s stock price exceeds some cutoff level. In what way is this
arrangement equivalent to issuing the manager call options on the firm™s stock?
15. Consider the following options portfolio. You write a January maturity call option on
Microsoft with exercise price $75. You write a January maturity Microsoft put option
with exercise price $70.
a. Graph the payoff of this portfolio at option expiration as a function of Microsoft™s
stock price at that time.
b. What will be the profit/loss on this position if Microsoft is selling at $72 on the
option maturity date? What if Microsoft is selling at $80? Use The Wall Street
Journal listing from Figure 14.1 to answer this question.
c. At what two stock prices will you just break even on your investment?
d. What kind of “bet” is this investor making; that is, what must this investor believe
about Microsoft™s stock price in order to justify this position?
16. A member of an investment committee, interested in learning more about fixed-income
investment procedures, recalls that a fixed-income manager recently stated that
derivative instruments could be used to control portfolio duration, saying “a futures-like

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