Chapter 20
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Subject
Finance
Date
Jan 9, 2024
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48
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1.
Award:
10.00
points
Problems?
Adjust credit
for all students.
Use
Figure 20.1
, which lists 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 December 17 expiration options, assuming that the stock
price on the expiration date is $300.
Note: Do not round intermediate calculations. Round your answers to 2 decimal places. Leave no cells blank - be certain to enter "0" wherever required. Negative amounts should be indicated by a minus sign.
$
$
$
$
$
$
$
$
$
$
$
$
Payoff
Profit or Loss
a. Call option,
X
= $290
10.00
(7.25)
b. Put option,
X
= $290
0.00
(11.72)
c. Call option,
X
= $300
0.00
(11.75)
d. Put option,
X
= $300
0.00
(16.25)
e. Call option,
X
= $310
0.00
(7.62)
f. Put option,
X
= $310
10.00
(12.05)
Explanation:
Cost
Payoff
Profit
a. Call option,
X
= $290
$ 17.25
$ 10.00
$ −7.25
b. Put option,
X
= $290
11.72
0.00
−11.72
c. Call option,
X
= $300
11.75
0.00
−11.75
d. Put option,
X
= $300
16.25
0.00
−16.25
e. Call option,
X
= $310
7.62
0.00
−7.62
f. Put option,
X
= $310
22.05
10.00
−12.05
Worksheet
Difficulty: 2 Intermediate
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 20: Options Markets: Introduction > Chapter 20 Problems - Algorithmic & Static
References
2.
Award:
10.00
points
Problems?
Adjust credit
for all students.
Suppose you think AppX stock is going to appreciate substantially in value in the next year. Say the stock’s current price,
S
0
, is $100, and a call option expiring in one year has an exercise price,
X
, of $100 and is selling at a
price,
C
0
, 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% annual interest.
What is your rate of return for each alternative for the following four stock prices in one year?
In terms of dollar returns
In terms of rate of return
Complete this question by entering your answers in the tabs below.
What is your rate of return for each alternative for the following four stock prices in one year?
The total value of your portfolio in one year for each of the following stock prices is:
Note: Leave no cells blank - be certain to enter "0" wherever required. Negative amounts should be indicated by a minus sign.
Round the "Percentage return of your portfolio (Bills + 100 options)" answers to 2 decimal places.
In terms of
dollar returns
In terms of
rate of return
Show less
$
$
$
$
Price of Stock one year from Now
Stock Price
80
100
110
120
a. All stocks (100 shares)
8,000
10,000
11,000
12,000
b. All options (1,000 options)
0
0
10,000
20,000
c. Bills + 100 options
9,360
9,360
10,360
11,360
Explanation:
No further explanation details are available for this problem.
Worksheet
Difficulty: 2 Intermediate
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 20: Options Markets: Introduction > Chapter 20 Problems - Algorithmic & Static
References
2.
Award:
10.00
points
Problems?
Adjust credit
for all students.
Suppose you think AppX stock is going to appreciate substantially in value in the next year. Say the stock’s current price,
S
0
, is $100, and a call option expiring in one year has an exercise price,
X
, of $100 and is selling at a
price,
C
0
, 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% annual interest.
What is your rate of return for each alternative for the following four stock prices in one year?
In terms of dollar returns
In terms of rate of return
Complete this question by entering your answers in the tabs below.
What is your rate of return for each alternative for the following four stock prices in one year?
The percentage return of your portfolio in one year for each of the following stock prices is:
Note: Leave no cells blank - be certain to enter "0" wherever required. Negative amounts should be indicated by a minus sign.
Round the "Percentage return of your portfolio (Bills + 100 options)" answers to 2 decimal places.
In terms of
dollar returns
In terms of
rate of return
Show less
$
$
$
$
Price of Stock one year from Now
Stock Price
80
100
110
120
a. All stocks (100 shares)
(20)
%
0
%
10
%
20
%
b. All options (1,000 options)
(100)
%
(100)
%
0 %
100
%
c. Bills + 100 options
(6.40)
%
(6.40)
%
3.60
%
13.60
%
Explanation:
No further explanation details are available for this problem.
Worksheet
Difficulty: 2 Intermediate
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 20: Options Markets: Introduction > Chapter 20 Problems - Algorithmic & Static
References
3.
Award:
10.00
points
Problems?
Adjust credit
for all students.
The common stock of the P.U.T.T. Corporation has been trading in a narrow price range for the past month, but you are convinced it is going to break far out of that range in the next six months. You do not know whether it will go
up or down, however. The current price of the stock is $100 per share, and the price of a six-month call option at an exercise price of $100 is $10.
Required:
a.
If the semiannual risk-free interest rate is 3%, what must be the price of a six-month put option on P.U.T.T. stock at an exercise price of $100? (The stock pays no dividends.)
b.
What would be a simple options strategy to exploit your conviction about the stock price’s future movements? How far would it have to move in either direction for you to make a profit on your initial investment?
Required A
Required B
Complete this question by entering your answers in the tabs below.
If the semiannual risk-free interest rate is 3%, what must be the price of a six-month put option on P.U.T.T. stock at an
exercise price of $100? (The stock pays no dividends.)
Note: Do not round intermediate calculations. Round your answer to 2 decimal places.
Required A
Required B
$
Price of a six-month put option on P.U.T.T. stock
8.53
Explanation:
a.
From put-call parity:
b.
Purchase a straddle, i.e., both a put and a call on the stock. The total cost of the straddle is $10.00 + $8.53 = $18.53
Worksheet
Difficulty: 2 Intermediate
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 20: Options Markets: Introduction > Chapter 20 Problems - Algorithmic & Static
References
3.
Award:
10.00
points
Problems?
Adjust credit
for all students.
The common stock of the P.U.T.T. Corporation has been trading in a narrow price range for the past month, but you are convinced it is going to break far out of that range in the next six months. You do not know whether it will go
up or down, however. The current price of the stock is $100 per share, and the price of a six-month call option at an exercise price of $100 is $10.
Required:
a.
If the semiannual risk-free interest rate is 3%, what must be the price of a six-month put option on P.U.T.T. stock at an exercise price of $100? (The stock pays no dividends.)
b.
What would be a simple options strategy to exploit your conviction about the stock price’s future movements? How far would it have to move in either direction for you to make a profit on your initial investment?
Required A
Required B
Complete this question by entering your answers in the tabs below.
What would be a simple options strategy to exploit your conviction about the stock price’s future movements? How far would
it have to move in either direction for you to make a profit on your initial investment?
Note: Round your intermediate calculations and final answer to 2 decimal places.
Required A
Required B
$
Strategy
Straddle
Price change for profit
18.53
Explanation:
a.
From put-call parity:
b.
Purchase a straddle, i.e., both a put and a call on the stock. The total cost of the straddle is $10.00 + $8.53 = $18.53
Worksheet
Difficulty: 2 Intermediate
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 20: Options Markets: Introduction > Chapter 20 Problems - Algorithmic & Static
References
4.
Award:
10.00
points
Problems?
Adjust credit
for all students.
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 six months. The price of a 6-month put option with
an exercise price of $50 is $4.
Required:
a.
If the semiannual risk-free interest rate is 3%, what must be the price of a 6-month call option on C.A.L.L. stock at an exercise price of $50 if it is at the money? (The stock pays no dividends.)
b.
What would be a simple options strategy using a put and a call to exploit your conviction about the stock price’s future movement? 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? What is the net cost of establishing that position now?
Required A
Required B
Complete this question by entering your answers in the tabs below.
If the semiannual risk-free interest rate is 3%, what must be the price of a 6-month call option on C.A.L.L. stock at an
exercise price of $50 if it is at the money? (The stock pays no dividends.)
Note: Do not round intermediate calculations. Round your answer to 2 decimal places.
Required A
Required B
Required C
$
Price of a 6-month call option
4.73
Explanation:
a.
From put-call parity:
b.
Sell a straddle, i.e., sell a call and a put, to realize premium income of: $4.73 + $4 = $8.73
If the stock ends up at $50, both options will be worthless → profit will be $8.73. This is your maximum possible profit since, at any other stock price, you will have to pay off on either the call or the put. The stock price can
move by $8.73 in either direction before your profits become negative.
c.
Buy the call, sell (write) the put, lend
$50 ÷
(1.03)
1/2
The payoff is as follows:
Position
Immediate CF
CF in 6 months
S
T
<
X
S
T
>
X
Call (long)
C = 4.73
0
S
T
− 50
Put (short)
−P = −4.00
−(50 − S
T
)
0
Lending position
50 ÷ 1.03
0.5
= 49.27
50
50
Total
50
S
T
S
T
By the put-call parity theorem, the initial outlay equals the stock price:
S
0
= $50
In either scenario, you end up with the same payoff as you would if you bought the stock itself.
Worksheet
Difficulty: 2 Intermediate
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 20: Options Markets: Introduction > Chapter 20 Problems - Algorithmic & Static
References
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Find the annual simple interest rate of a loan, where $200 is borrowed and where $216 is repaid at the end of 9 months.
Annual simple interest rate =
%.
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