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position can be created in a portfolio by using put and call options on Treasury bonds.”
a. Identify the options market exposure or exposures that create a “futures-like
position” similar to being long Treasury bond futures. Explain why the position you
created is similar to being long Treasury bond futures.
b. Explain in which direction and why the exposure(s) you identified in part (a) would
affect portfolio duration.
c. Assume that a pension plan™s investment policy requires the fixed-income manager
to hold portfolio duration within a narrow range. Identify and briefly explain
circumstances or transactions in which the use of Treasury bond futures would be
helpful in managing a fixed-income portfolio when duration is constrained.
17. Consider the following portfolio. You write a put option with exercise price $90 and buy
a put with the same maturity date with exercise price $95.
a. Plot the value of the portfolio at the maturity date of the options.
b. On the same graph, plot the profit of the portfolio. Which option must cost more?
18. A Ford put option with strike price $60 trading on the Acme options exchange sells for
$2. To your amazement, a Ford put with the same maturity selling on the Apex options
exchange but with strike price $62 also sells for $2. If you plan to hold the options
position to maturity, devise a zero-net-investment arbitrage strategy to exploit the
pricing anomaly. Draw the profit diagram at maturity for your position.
19. You buy a share of stock, write a one-year call option with X $10, and buy a one-year
put option with X $10. Your net outlay to establish the entire portfolio is $9.50. What
must be the risk-free interest rate? The stock pays no dividends.
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20. Joe Finance has just purchased a stock index fund, currently selling at $1,200 per share.
To protect against losses, Joe also purchased an at-the-money European put option on
the fund for $60, with exercise price $1,200, and three-month time to expiration. Sally
Calm, Joe™s financial adviser, points out that Joe is spending a lot of money on the put.
She notes that three-month puts with strike prices of $1,170 cost only $45, and suggests
that Joe use the cheaper put.
a. Analyze Joe™s and Sally™s strategies by drawing the profit diagrams for the stock-
plus-put positions for various values of the stock fund in three months.
Bodie’Kane’Marcus: V. Derivative Markets 14. Options Markets © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition




525
14 Options Markets


b. When does Sally™s strategy do better? When does it do worse?
c. Which strategy entails greater systematic risk?
21. You write a call option with X $50 and buy a call with X $60. The options are on
the same stock and have the same maturity date. One of the calls sells for $3; the other
sells for $9.
a. Draw the payoff graph for this strategy at the option maturity date.
b. Draw the profit graph for this strategy.
c. What is the break-even point for this strategy? Is the investor bullish or bearish on
the stock?
22. Devise a portfolio using only call options and shares of stock with the following value
(payoff) at the option maturity date. If the stock price is currently $53, what kind of bet
is the investor making?

Payoff

50




50 60 110 ST




WEBMA STER
Options and Straddles
Go to http://www.nasdaq.com and enter EMC in the quote section to obtain an infor-
mation quote. Once you have the information quote, request the information on op-
tions. You will be able to access the prices and market characteristics for all put and call
options for EMC. Select the two expiration months that follow the closest expiration
month and obtain the prices for the calls and puts that are closest to being at the
money. (For example, if you are in February, you would select the April and July expi-
rations. If the price of EMC was $56.40, you would choose the options with the 55
strike or exercise price. Then, answer the following questions:
1. What are the prices for the put and call with the nearest expiration date?
2. What would be the cost of a straddle using the above options?
3. At expiration, what would be the break-even stock prices for the above
straddle?
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4. What would be the percentage increase or decrease in the stock price required
to break even?
5. What are the prices for the put and call with a later expiration date?
6. What would be the cost of a straddle using the later expiration date? At
expiration, what would be the break-even stock prices for the above straddle?
7. What would be the percentage increase or decrease in the stock price required
to break even?
Bodie’Kane’Marcus: V. Derivative Markets 14. Options Markets © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition




526 Part FIVE Derivative Markets


SOLUTIONS TO 1. a. Proceeds ST X ST $70 if this value is positive; otherwise, the call expires worthless.

>
Profit Proceeds Price of call option Proceeds $4.60.
Concept
CHECKS ST $60 ST $80
Proceeds $0 $10
Profits 4.60 5.40


b. Proceeds X ST $70 ST if this value is positive; otherwise, the put expires worthless.
Profit Proceeds Price of put option Proceeds $5.40.

ST $60 ST $80
Proceeds $10 $0
Profits 4.60 5.40

2. a.


Buy call Write put

Profit
Payoff

ST ST
Payoff
Profit



Write call Buy put


Profit
Payoff
ST ST

Profit
Payoff




b. The payoffs and profits to both buying calls and writing puts generally are higher when the
stock price is higher. In this sense, both positions are bullish. Both involve potentially taking
delivery of the stock. However, the call holder will choose to take delivery when the stock price
is high, while the put writer is obligated to take delivery when the stock price is low.
c. The payoffs and profits to both writing calls and buying puts generally are higher when the
stock price is lower. In this sense, both positions are bearish. Both involve potentially making
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delivery of the stock. However, the put holder will choose to make delivery when the stock
price is low, while the call writer is obligated to make delivery when the stock price is high.
3.

PAYOFF TO A STRIP
ST X ST X
ST)
2 Puts 2(X 0
ST X
1 Call 0
Bodie’Kane’Marcus: V. Derivative Markets 14. Options Markets © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition




527
14 Options Markets


Payoff and
profit of strip
2X
Slope = “2
Payoff
Slope = 1

2X“(2P C)

Profit

ST
X




“(2P+C )



PAYOFF TO A STRAP
ST X ST X
X ST
1 Put 0
X)
2 Calls 0 2(ST



Payoff
Payoff and
profit of strap Slope 2
Profit

X

Slope = 1

X (P 2C)


ST
X



(P 2C)



4. The payoff table on a per-share basis is as follows:
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ST 60 60 ST 80 ST 80
ST
Buy put (X 60) 60 0 0
ST ST ST
Share
Write call (X 80) 0 0 (ST 80)
ST
Total 60 80
Bodie’Kane’Marcus: V. Derivative Markets 14. Options Markets © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition




528 Part FIVE Derivative Markets


The graph of the payoff follows. If you multiply the per-share values by 2,000, you will see that the
collar provides a minimum payoff of $120,000 (representing a maximum loss of $20,000) and a
maximum payoff of $160,000 (which is the cost of the house).


Terminal
value

$80


$60



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