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18-13. a. This problem illustrates a bear spread designed to profit from a decline in the price of
the stock. The investor purchases the option with the $20 strike price for $2 and sells the other
option for $5. The position generates a cash inflow ($3). The profit-loss profile is as follows:
Price Intrinsic value: Profit:
of the Call at Call Buying the Selling the Total
stock $20 at $15 $20 call $15 call profit
for $2 for $5
$14 $0 $0 ($2) $5 $3
b. If the investor had sold the stock short (another position designed to take advantage of a price
decline), the maximum possible profit is $18, but the maximum possible loss is unlimited. The
bear spread has less potential absolute profit but does not require a cash outflow, which would be
Price Intrinsic value: Profit:
of the Call at Call Selling the Buying the Total
stock $20 at $15 $20 call $15 call profit
for $2 for $5
$14 $0 $0 $2 ($5) ($3)
d. If the investor had bought the stock (another position designed to take advantage of a price
increase), the maximum possible loss is $18, but the maximum possible gain is unlimited. The
18-14. A straddle involves the use of two options at the same strike price. If the investor buys a
straddle, he or she purchases the options. If the investor writes a straddle, he or she sells the two
options. In this problem, the individual buys a put and a call.
a. Profit if the price of the stock is $60:
Intrinsic value of the call: $60 - 50 = $10
Intrinsic value of the put: $50 - 60 = nil
b. Profit if the price of the stock is $40:
Intrinsic value of the call: $40 - 50 = nil
Intrinsic value of the put: $50 - 40 = $10
c. If the price of the stock is $50, both options expire. The investor’s loss is ($5) + ($3.50) =
($8.50).18-15. a. This problem illustrates the ideal execution of a collar because there is no cash
outflow. Since the purpose of the collar is solely to lock in the price of the stock, the individual
wants the sale of the call to generate exactly the funds necessary to buy the put. That occurs in
b. The profit/loss profile:
Price of Profit on the Net
the stock Stock Call Put Profit
$60 $5.00 ($2.00) ($3.00) $0.00
c. The strategy works because any gain in the stock by the price increase is offset by the loss in
18-16. This problem repeats the previous one except the collar requires that the investor have a
cash outflow. The purpose of the problem is to illustrate that constructing a collar protects
against a decline in the price of the stock. The executive buys the put with the strike price at $35
The profit/loss profile:
Price of Profit on the Net
the stock Stock Call Put Profit
$50 $11.75 ($6.62) ($1.94) $3.19
45 6.75 (1.62) (1.94) 3.19
While the executive has not lost an opportunity for further gains if the price of the stock were to
rise above $41.44, the objective of the position was to protect against a price decline. As the
profile indicates, the position achieves its objective, since the maximum loss is $1.81.18-17. The
a, b, and c. The straddle: buy the call at $40 for $3 and the put at $40 for $1. Total cash outflow
is $4.
Price Intrinsic Intrinsic Gain/loss Gain/loss Net
of the Value of Value of on the on the
Stock the Call the Put Call Put
$30 $0 $10 ($3) $9 6
35 0 5 (3) 4 1
36 0 4 (3) 3 0
The maximum loss is $4 at a price of $40, and the range of price that produces a loss is $36 - $44
The strip: buy the call at $40 for $3 and two puts at $40 for $1. Total cash outflow is $5.
Price Intrinsic Intrinsic Gain/loss Gain/loss Net
of the Value of Value of on the on the
Stock the Call the Put Calls Put
$30 $0 $10 ($3) $18 15
35 0 5 (3) 8 5
The maximum loss is $5 and the range of price that produces a loss if $37.50 - $45.
The strap: buy two calls at $40 for $6 and one put at $40 for $1.
Total cash outflow is $7.
Price Intrinsic Intrinsic Gain/loss Gain/loss Net
of the Value of Value of on the on the
Stock the Call the Put Call Put
$30 $0 $10 ($6) $9 3
The maximum loss is $4 and the range of price that produces a loss is $33 - $43.50.
18-18. This problem illustrates the butterfly spread which combines the bull and bear spreads.
The butterfly requires three options; in this illustration the strike prices of the three calls are $57,
60, and 63. The prices of the calls are $6, 3, and 1. The investor buys one call at $57 for $6 and
one call at $63 for $1 and sells two calls at $60 at $3 each. The total cash outflow is $1.
a.
Price Intrinsic Intrinsic Intrinsic
of the Value of Value of Value of
Stock the Call the Call the Call
at $57 at $60 at $63
$50 $0 $0 $0
55 0 0 0
Price Gain/loss Gain/loss Gain/loss Net
of the on the on the two on the
Stock Call Calls Call
at $57 at $60 at $63
$50 ($6) $6 ($1) ($1)
55 (6) 6 (1) (1)
b. The maximum possible loss is $1 if the price of the stock fluctuates.
c. The maximum possible gain is $2. Since the cash outflow is only $1, the percentage return is
d. Range: $58-62
e. If the investor expects the price of the stock to be stable and not fluctuate, the butterfly
achieves the objective of generate a profit when the price of the stock is stable.
18-19. This problem is the result of a student asking about possible strategies with different
combinations of options. While there are virtually unlimited possibilities, I asked the student to
give me at least one, and he suggested the first two (a and b). I added c through e, obtained the
prices of IBM (renamed HBM) and several options. Each strategy was assigned to a student to
work through and present in class. This assignment generated a large amount of class
participation. The answers provided by the students are given below.
1. The cash inflows (outflows):
a. Buy the 180 and 210 calls and sell the 190 and 200 puts:
b. Buy the 180 and 210 calls and sell the 190 and 200 calls:
c. Buy the 180 and 210 calls and buy the 190 and 200 puts:
d. Buy the 180 call and the 210 put and sell the 190 call and the 200 put:
e. Buy the 180 put and the 210 call and sell the 190 put and
the 200 call:
2. Profits and losses at various stock prices:
a. Buy the 180 and 210 calls and sell the 190 and 200 puts:
Prices 180 call 210 call 190 put 200 put Net gain
of the purchased purchased sold sold or loss
stock
$180 -17.45 -3.20 -1.45 -4.85 -27.05
This strategy generates large gains if the price of the stock rises but large losses in the price of
the stock declines.
b. Buy the 180 and 210 calls and sell the 190 and 200 calls:
Prices 180 call 210 call 190 call 200 call Net gain
of the purchased purchased sold sold or loss
stock
$180 -17.45 -3.20 11.43 6.35 -2.87
This strategy generates modest gains if the price of the stock remains stable (i.e., a variation on
selling a straddle).
c. Buy the 180 and 210 calls and buy the 190 and 200 puts:
Prices 180 call 210 call 190 put 200 put Net gain
of the purchased purchased bought bought or loss
stock
$160 -17.45 -3.20 21.55 24.85 25.75
This strategy reverses the previous one and generates a gain when the price of the stock moves
sufficiently in either direction. While at $170 and $220, the strategy generates a gain of $5.75,
the gain rises to $25.75 if the price falls to $160 or rises to $230.
d. Buy the 180 call and the 210 put and sell the 190 call and
the 200 put:
Prices 180 call 210 put 190 call 200 put Net gain
of the purchased purchased sold sold or loss
stock
$180 -17.45 8.50 11.43 -4.85 -2.37
This strategy is another variation on selling a straddle that works if the price of the stock remains
stable.
e. Buy the 180 put and the 210 call and sell the 190 put and
the 200 call:
Prices 180 put 210 call 190 put 200 call Net gain
of the purchased purchased sold sold or loss
stock
$180 -5.55 -3.20 -1.55 6.35 -3.90
The strategy generates a profit if the price of the stock declines and a modest loss if the price of
the stock rises.
3. If it is anticipated that the price of the stock will rise, strategy (a) generates a very large return
compared to buy the stock. For example, if the price of the stock is $192 and rises to $200, the
4. The anticipation that the price of the stock will be stable argues for strategies (b) and (d). As
always, the risk is that the expectation will not fulfilled and the price of the stock moves in either
Teaching Guides for the Financial Advisor’s Case: Profit and Losses from Straddles
In this case, the possibility exists that a merger price war could erupt and drive the stock price
up. Conversely, the proposed merge could fail, and the price of the stock would fall.
The student is asked to develop three profit-loss profiles using different options on the same
stock. The three strategies illustrate types of straddles in which the buyer of the straddle expects
the price of the stock to move but cannot determine the direction.
Strategy 1: purchase the cheapest options:
Price of the call at $80: $1.00
Price of the put at $60: $1.00
Price of Intrinsic Profit Intrinsic Profit Net (total)
the stock value of on the value of on the profit
the call call the put put
$50 $0 ($1) $10 $9 $8
55 0 (1) 5 4 3
While the potential loss is small, the price of the stock has to rise to $82 or fall to $58 for Herrara
to profit.
Strategy 2: purchase the options with the $70 strike price
Price of the call: $8.00
Price of the put: $3.50
Price of Intrinsic Profit Intrinsic Profit Net (total)
the stock value of on the value of on the profit
the call call the put put
$50 $0 ($8) $20 $16.50 $8.50
55 0 (8) 15 11.50 3.50
60 0 (8) 10 6.50 (1.50)
65 0 (8) 5 1.50 (6.50)
The potential loss is much larger while the price range that generates a profit barely improves.
Essentially this strategy is inferior to the previous one.
Strategy 3: purchase the options with the $60 strike price
Price of the call: $17.00
Price of the put: $1.00
Price of Intrinsic Profit Intrinsic Profit Net (total)
the stock value of on the value of on the profit
the call call the put put
$50 $0 ($17) $10 $9 ($8)
55 0 (17) 5 4 (13)
1. If a bidding war erupts and the price of the stock rises, the third strategy generates the most
2. If the merger is defeated and the price of the stock falls, the first and second strategies start to
generate profits if the price of the stock falls to $58 and $58 1/2. For the third strategy to
3. If the original offer price of $72 becomes the final price, all three strategies generate losses.
The first strategy generates the smallest loss.
4. If the worst case is defined as the largest absolute loss, which occurs in the third strategy
5. Herrara's analysis suggests that the stock is overpriced. If he is correct, constructing the
straddle using the first strategy makes the most sense. If he is right and the merger fails to go
(You may wish to have students consider other combinations such as buying the call with the $80
strike price and the put with the $70 strike price. One possibility is to assign a different strategy
