Chapter 15 – Options Markets
CHAPTER 15
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whole or part.
Chapter 15 – Options Markets
OPTIONS MARKETS
1. Options provide numerous opportunities to modify the risk profile of a portfolio. The
simplest example of an option strategy that increases risk is investing in an ‘all options’
portfolio of at-the-money options (as illustrated in the text). The leverage provided by
2. Options at the money have the highest time premium and thus the highest potential for
gain. Since the highest potential gain is at the money, the logical conclusion is that they
3. Each contract is for 100 shares: $7.25 100 = $725
4.
5. If the stock price drops to zero, you will make $160 – $2.62 per stock, or $157.38.
6. The price has to be at least as much as the sum of the exercise price and the premium of
7.
a. Maximum loss happens when the stock price is the same to the strike price upon
b. Loss: Final value – Original investment
c. There are two break even prices:
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distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in
whole or part.
Chapter 15 – Options Markets
8. Option c is the only correct statement.
a. The value of the short position in the put is –$4 if the stock price is $76.
9.
a. i. A long straddle produces gains if prices move up or down and limited losses if
prices do not move. A short straddle produces significant losses if prices move
b. i. Long put positions gain when stock prices fall and produce very limited losses
if prices instead rise. Short calls also gain when stock prices fall but create
10. The initial outlay of this position is $38, the purchase price of the stock, and the payoff
11. The collar involves purchasing a put for $3 and selling a call for $2. The initial outlay is
$1.
a. ST = $30
Value at expiration = Value of call + Value of put + Value of stock
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whole or part.
Chapter 15 – Options Markets
b. ST = $40
Value at expiration = Value of call + Value of put + Value of stock
= 0 + 0 + $40 = $40
c. ST = $50
Value at expiration = Value of call + Value of put + Value of stock
= ($45 – $50) + 0 + $50 =$45
With the initial outlay of $1, the collar locks the net proceeds per share in between the
lower bound of $34 and the upper bound of $44. Given 5,000 shares, the total net
12. In terms of dollar returns:
Price of Stock Six Months from Now
Stock price:
$80
$100
$110
$120
a. All stocks (100 shares)
8,000
10,000
11,000
12,000
In terms of rate of return, based on a $10,000 investment:
Price of Stock Six Months from Now
Stock price:
$80
$100
$110
$120
a. All stocks (100 shares)
–20%
0%
10%
20%
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distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in
whole or part.
Chapter 15 – Options Markets
0 20 40 60 80 100 120 140
-150%
-100%
-50%
0%
50%
100%
150%
a. All stocks (100 shares) b. All options (1,000 shares) c. Bills + 100 options
13.
a. Purchase a straddle, i.e., both a put and a call on the stock. The total cost of the
b. Since the straddle costs $17, this is the amount by which the stock would have
14.
a. Sell a straddle, i.e., sell a call and a put to realize premium income of:
b. If the stock ends up at $50, both of the options will be worthless and the profit
will be $11. This is the maximum possible profit since, at any other stock price,
c. Buy the call, sell (write) the put, lend the present value of $50. The payoff is as
follows:
Final Payoff
Position Initial Outlay ST < X ST > X
Long call
C = 7
0
ST – 50
15.
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distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in
whole or part.
Chapter 15 – Options Markets
a. By writing covered call options, Jones receives premium income of $30,000. If,
in January, the price of the stock is less than or equal to $45, he will keep the
stock plus the premium income. Since the stock will be called away from him if
its price exceeds $45 per share, the most he can have is:
(We are ignoring interest earned on the premium income from writing the option
over this short time period.) The payoff structure is:
Stock Price PortfolioValue
Less than $45 (10,000 times stock price) + $30,000
Greater than $45 $450,000 + $30,000 = $480,000
This strategy offers some premium income but leaves the investor with
b. By buying put options with a $35 strike price, Jones will be paying $30,000 in
premiums in order to insure a minimum level for the final value of his position.
This strategy allows for upside gain, but exposes Jones to the possibility of a
moderate loss equal to the cost of the puts. The payoff structure is:
Stock Price Portfolio Value
c. The net cost of the collar is zero. The value of the portfolio will be as follows:
Stock Price Portfolio Value
Less than $35 $350,000
The best strategy in this case is (c) since it satisfies the two requirements of
preserving the $350,000 in principal while offering a chance of getting $450,000.
Strategy (a) should be ruled out because it leaves Jones exposed to the risk of
substantial loss of principal.
Our ranking is: (1) c (2) b (3) a
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distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in
whole or part.
Chapter 15 – Options Markets
16.
a. Butterfly Spread
Position ST < X1X1 < ST < X2X2 < ST < X3X3 < ST
Long call (X1) 0 ST –X1ST –X1ST –X1
Payof
b. Vertical combination
Position ST < X1X1 < ST < X2ST > X2
Long call (X2) 0 0 ST –X2
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whole or part.
Chapter 15 – Options Markets
Payof
17. Bearish spread
Position ST < X1X1 < ST < X2ST > X2
Long call (X2) 0 0 ST –X2
Payof
In the bullish spread, the payoff either increases or is unaffected by stock price
increases. In the bearish spread, the payoff either increases or is unaffected by stock
price decreases.
18.
a. Strategy one: Protective put
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distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in
whole or part.
Chapter 15 – Options Markets
Put 1,040 – ST0
Total 1,040 ST
Strategy two: Bills plus calls
b. The bills plus call strategy has a greater payoff for some values of ST and never
a lower payoff. Since its payoffs are always at least as attractive and sometimes
greater, it must be more costly to purchase.
c. The initial cost of the stock plus put position is $1,208 and the cost of the bills plus
call position is $1,240.
Strategy one: Protective put
Position ST = 0 ST = 1,040 ST = 1,120 ST = 1,200 ST = 1,280
Stock 0 1,040 1,120 1,200 1,280
*Profit = Payoff – Initial Outlay = Payoff – $1,208
Strategy two: Bills plus calls
Position ST = 0 ST = 1,040 ST = 1,120 ST = 1,200 ST = 1,280
Bill 1,120 1,120 1,120 1,120 1,120
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Chapter 15 – Options Markets
+ Call 0 0 0 80 160
Payoff 1,120 1,120 1,120 1,200 1,280
d. The stock and put strategy is riskier. It does worse when the market is down,
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distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in
whole or part.