Chapter 15 – Options Markets
CHAPTER 15
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’
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. Price at expiration: $71
Cost Payoff Profit
Call option, X = 70 2.02 1.00 -1.02
Put option, X = 70 0.24 0.00 -0.24
Call option, X = 72 0.67 0.00 -0.67
Put option, X = 72 0.90 1.00 0.10
Call option, X = 74 0.13 0.00 -0.13
Put option, X = 74 2.37 3.00 0.63
5. If the stock price drops to zero, you will make $80 – $5.72 per stock, or $74.28. Given
7. a. Maximum loss happens when the stock price is the same to the strike price upon
expiration. Both the call and the put expire worthless, and the investor’s outlay
Chapter 15 – Options Markets
for the purchase of both options is lost: $7.00 + $8.50 = $15.50
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
10. The initial outlay of this position is $38, the purchase price of the stock, and the payoff
of such position will be between two boundaries, $35 and $40.
a. The maximum profit will thus be: $40 – $38 = $2, and the maximum loss will
be: $35 – $38 = –$3.
b.
Chapter 15 – Options Markets
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(Final value – Original investment) # of shares
= ($45 – $1) 5,000 = $220,000
Net proceeds without using collar = ST # of shares
= $50 5,000 = $250,000
d. 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 proceeds will be between $170,000 and $220,000 when the
position is closed. If we simply continued to hold the shares without using the
collar, the upside potential is not limited but the downside is not protected.
12. In terms of dollar returns:
Chapter 15 – Options Markets
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
b. All options (1,000 shares)
0
0
10,000
20,000
c. Bills + 100 options
9,360
9,360
10,360
11,360
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%
b. All options (1,000 shares)
–100%
–100%
0%
100%
c. Bills + 100 options
–6.4%
-6.4%
3.6%
13.6%
13.
a. Purchase a straddle, i.e., both a put and a call on the stock. The total cost of the
14.
a. Sell a straddle, i.e., sell a call and a put to realize premium income of:
$4 + $7 = $11
-150%
-100%
-50%
0%
50%
100%
150%
050 100 150
a. All stocks (100 shares)
b. All options (1,000 shares)
c. Bills + 100 options
Rate of Return
Stock Price ($)
–6.4%
Chapter 15 – Options Markets
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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,
you will have to pay off on either the call or the put.
c. The stock price can move by $11 (your initial revenue from writing the two at–
the-money options) in either direction before your profits become negative.
d. 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
Short put
–P = –4
–(50 – ST)
0
Lending
50/(1 + r)(1/4)
50
50
Total
7 – 4 + [50/(1 + r)(1/4)]
ST
ST
e. The initial outlay equals: (the present value of $50) + $3
In either scenario, you end up with the same payoff as you would if you bought
the stock itself.
15. 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:
$450,000 + $30,000 = $480,000
Stock Price
PortfolioValue
Less than $45
(10,000 times stock price) + $30,000
Greater than $45
$450,000 + $30,000 = $480,000
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.
That minimum value is: ($35 10,000) – $30,000 = $320,000
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:
Chapter 15 – Options Markets
Stock Price
Portfolio Value
Less than $35
$350,000 – $30,000 = $320,000
Greater than $35
(10,000 times stock price) – $30,000
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
Between $35 and $45
10,000 times stock price
Greater than $45
$450,000
If the stock price is less than or equal to $35, then the collar preserves the
$350,000 in principal. If the price exceeds $45, then Jones gains up to a cap of
$450,000. In between $35 and $45, his proceeds equal 10,000 times the stock
price.
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
16.
a. Butterfly Spread
Position
ST < X1
X1 < ST < X2
X2 < ST < X3
X3 < ST
Long call (X1)
0
ST –X1
ST –X1
ST –X1
Short 2 calls (X2)
0
0
–2(ST –X2)
–2(ST –X2)
Long call (X3)
0
0
0
ST –X3
Total
0
ST –X1
2 X2 –X1 –ST
(X2–X1 ) – (X3–X2) = 0
Chapter 15 – Options Markets
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b. Vertical combination
Position
ST < X1
X1 < ST < X2
ST > X2
Long call (X2)
0
0
ST –X2
Long put (X1)
X1 –ST
0
0
Total
X1 –ST
0
ST –X2
17. Bearish spread
Position
ST < X1
X1 < ST < X2
ST > X2
Long call (X2)
0
0
ST –X2
Short call (X1)
0
–(ST –X1)
–(ST –X1)
Total
0
X1 –ST
X1 –X2
Payoff
X2–X1
0
X1X2X3
ST
Chapter 15 – Options Markets
18. a. Strategy one: Protective put
Protective Put
ST < 1,040
ST > 1,040
Stock
ST
ST
Put
1,040 – ST
0
Total
1,040
ST
Strategy two: Bills plus calls
Bills and Call
ST < 1,120
ST > 1,120
Bills
1,120
1,120
Call
0
ST – 1,120
Total
1,120
ST
Payoff
0
X1–X2
X1
X2ST
Chapter 15 – Options Markets
Payoff
S
T
1,680
1,560
1,560
1,680
Bills plus calls
(Dashed line)
Protective put strategy
(Solid line)
0
b. The bills plus call strategy has a greater payoff for some values of ST and never
Chapter 15 – Options Markets
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consent of McGraw-Hill Education.
Profit
Bills plus calls
Protective put
-180
-252
1,560
1,680
S
T
0
d. The stock and put strategy is riskier. It does worse when the market is down,
and better when the market is up. Therefore, its beta is higher.
19. The Excel spreadsheet for both parts (a) and (b) is shown on the next page, and the
profit diagrams are on the following page.
Chapter 15 – Options Markets
a. & b.
Stock Prices
Beginning Market Price 116.5
Ending Market Price 130 X 130 Straddle
Ending Profit
Buying Options: Stock Price –37.20
Call Options Strike Price Payoff Profit Return % 50 42.8
110 22.80 20.00 –2.80 -12.28% 60 32.8
120 16.80 10.00 –6.80 -40.48% 70 22.8
130 13.60 0.00 –13.60 –100.00% 80 12.8
140 10.30 0.00 –10.30 –100.00% 90 2.8
100 –7.2
Put Options Strike Price Payoff Profit Return % 110 –17.2
110 12.60 0.00 –12.60 –100.00% 120 –27.2
120 17.20 0.00 –17.20 –100.00% 130 –37.2
130 23.60 0.00 –23.60 –100.00% 140 –27.2
140 30.50 10.00 –20.50 -67.21% 150 –17.2
160 –7.2
Straddle Price Payoff Profit Return % 170 2.8
110 35.40 20.00 –15.40 -43.50% 180 12.8
120 34.00 10.00 –24.00 -70.59% 190 22.8
130 37.20 0.00 –37.20 –100.00% 200 32.8
140 40.80 10.00 –30.80 -75.49% 210 42.8
Selling Options: Bullish
Call Options Strike Price Payoff Profit Return % Ending Spread
110 22.80 -20 2.80 12.28% Stock Price 6.80
120 16.80 -10 6.80 40.48% 50 -3.2
130 13.60 0 13.60 100.00% 60 –3.2
140 10.30 0 10.30 100.00% 70 –3.2
80 -3.2
120 17.20 0 17.20 100.00% 110 -3.2
130 23.60 0 23.60 100.00% 120 -3.2
140 30.50 10 40.50 132.79% 130 6.80
140 6.80
Money Spread Price Payoff Profit 150 6.80
Sell 130 Call 13.60 0 13.60 180 6.80
Combined Profit 10.00 6.80 190 6.80
200 6.80
210 6.80
Chapter 15 – Options Markets
20. The bondholders have, in effect, made a loan which requires repayment of B dollars,
where B is the face value of bonds. If, however, the value of the firm (V) is less than B,
22. a.
Position
ST < 75
75 < ST < 80
ST > 80
Short call
0
0
– (ST – 80)
Short put
– (75 – ST)
0
0
Total
ST – 75
0
80 – ST
S
T
75
80
Payoff
Write call
Write put
-50.0
-40.0
-30.0
-20.0
-10.0
0.0
10.0
20.0
30.0
40.0
50.0
050 100 150 200 250
Bullish Spread
130 Straddle
Spreads & Straddles
Chapter 15 – Options Markets
b. Proceeds from writing options (from Figure 15.1):
Call = $2.64
c. You will break even when either the short position in the put or the short
position in the call results in a cash outflow of $6.61. For the put, this requires
that:
23. a.
S
T
0
5
Payoff
Profit
Net outlay
95
90
Value
24. Buy the X = 62 put (which should cost more than it does) and write the X = 60 put.
Since the options have the same price, the net outlay is zero. The proceeds at maturity
will be between 0 and 2 and will never be negative.
Position
ST < 60
60 < ST < 62
ST > 62
Long put (X = 62)
62 – ST
62 –ST
0
Short put (X = 60)
– (60 – ST)
0
0
Total
2
62 – ST
0
Chapter 15 – Options Markets
S
T
0
2
62
60
Payoff = Profit, because net outlay is 0.
25. This riskless strategy will yield a payoff of $10 for either position.. Therefore, the risk-
free rate is: ($10/$9.50) – 1 = .0526 = 5.26%
Position
ST < 10
ST > 10
Buy stock
ST
ST
Short call
0
– (ST – 10)
Long put
10 – ST
0
Total
10
10
26. a. Joe’s strategy
Position
Cost
Payoff
S T 2,400
S T > 2,400
Stock index
2,400
S T
S T
Put option, X = $2,400
120
2,400 – S T
0
Total
-2,520
2,400
S T
Profit = payoff – $2,520
–120
S T – 2,520
Sally’s strategy
Position
Cost
Payoff
S T 2,340
S T > 2,340
Stock index
2,400
S T
S T
Put option, X = $2,340
90
2,340 – S T
0
Total
2,490
2,340
S T
Profit = Payoff – $2,490
–150
S T – 2,490
b. Sally does better when the stock price is high, but worse when the stock price is
low.
Chapter 15 – Options Markets
27. The initial proceeds are: $9 – $3 = $6
a. The payoff is either negative or zero:
Position
ST < 50
50 < ST < 60
ST > 60
Long call (X = 60)
0
0
ST – 60
Short call (X = 50)
0
– (ST – 50)
– (ST – 50)
Total
0
– (ST – 50)
–10
b.
S
T
0
6
Payoff
Profit
－4
60
50
Value
－10
c. Breakeven occurs when the payoff offsets the initial proceeds of $6, which occurs
28. Buy a share of stock, write a call with X = 50, write a call with X = 60, and buy a call with
X = 110.
Position
ST < 50
50 < ST < 60
60 < ST < 110
ST > 110
Buy stock
ST
ST
ST
ST
Short call (X = 50)
0
– (ST – 50)
– (ST – 50)
– (ST – 50)
Short call (X = 60)
0
0
– (ST – 60)
– (ST – 60)
Long call (X = 110)
0
0
0
ST – 110
Total
ST
50
110 –ST
0
The investor is making a volatility bet. Profits will be highest when volatility is
low, such that if the stock price ends up in the interval between $50 and $60.
29. a. The farmer has the option to sell the crop to the government, for a guaranteed
minimum price, if the market price is too low.
Chapter 15 – Options Markets
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c. If the supported price is denoted PS and the market price PM, then we can say
that the farmer has a put option to sell the crop (the asset) at an exercise price of
PS even if the market price of the underlying asset (PM) is less than PS.
CFA 1
Answer:
CFA 2
Answer:
a. Donie should choose the long strangle strategy. A long strangle option strategy
consists of buying a put and a call with the same expiration date and the same
underlying asset, but different exercise prices. In a strangle strategy, the call has
an exercise price above the stock price and the put has an exercise price below
b. i. The maximum possible loss per share is $9.00, which is the total cost of the
two options ($5.00 + $4.00).
CFA 3
Answer:
a. If an investor buys a call option and writes a put option on a T-bond, then, at
maturity, the total payoff to the position is (ST – X), where ST is the price of the
b. Such a position would increase the portfolio duration, just as adding a T-bond
Chapter 15 – Options Markets
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established.
c. Futures can be bought and sold very cheaply and quickly. They give the manager
flexibility to pursue strategies or particular bonds that seem attractively priced
without worrying about the impact of these actions on portfolio duration. The
futures can be used to make adjustments to duration necessitated by other portfolio
actions.
CFA 4
Answer:
d. Conversion value of a convertible bond is the value of the security if it is
converted immediately. That is:
e. Market conversion price is the price that an investor effectively pays for the
common stock if the convertible bond is purchased:
CFA 5
Answer:
a. i. The current market conversion price is computed as follows:
ii. The expected one-year return for the Ytel convertible bond is:
iii. The expected one-year return for the Ytel common equity is:
b. The two components of a convertible bond’s value are:
• The straight bond value, which is the convertible bond’s value as a bond, and;
• The option value, which is the value associated with the potential conversion
into equity.
i. In response to the increase in Ytel’s common equity price, the straight bond value
should stay the same and the option value should increase.
Chapter 15 – Options Markets
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consent of McGraw-Hill Education.
The increase in equity price does not affect the straight bond value component of
the Ytel convertible. The increase in equity price increases the option value
component significantly, because the call option becomes deep “in the money”
when the $51 per share equity price is compared to the convertible’s conversion
price of: $1,000/25 = $40 per share.
ii. In response to the increase in interest rates, the straight bond value should
decrease and the option value should increase.
The increase in interest rates decreases the straight bond value component (bond
values decline as interest rates increase) of the convertible bond and increases the
value of the equity call option component (call option values increase as interest
rates increase). This increase may be small or even unnoticeable when compared to
the change in the option value resulting from the increase in the equity price.