A trader creates a long butterfly spread from options with strike prices $60, $65, and $70 by trading a total of 400 options. The options are worth $11, $14, and $18. What is the maximum net gain (after the cost of the options is taken into account)?单项选择题
A
$100
B
$200
C
$300
D
$400

Question

A trader creates a long butterfly spread from options with strike prices $60, $65, and $70 by trading a total of 400 options. The options are worth $11, $14, and $18. What is the maximum net gain (after the cost of the options is taken into account)?单项选择题

A

$100

B

$200

C

$300

D

$400

BlackTom AI · Accepted Answer

To tackle this problem, I’ll break down the butterfly setup and then evaluate the payoff vs. cost step by step.
First, identify the structure: a long butterfly with strikes at 60, 65, and 70 implies you buy 1 call at 60, sell 2 calls at 65, and buy 1 call at 70 for each unit of the spread. With 400 options in total, this corresponds to 400 / 4 = 100 butterfly units since each unit requires 4 contracts (1 + 2 + 1).
Next, compute the net premium paid per butterfly unit: you pay 11 for the 60 strike, you receive 2 × 14 for the two 65 strikes (a credit of 28), and you pay 18 for the 70 strike. Net premium = 11 − 28 + 18 = 1. Therefore, the total upfront cost for 100 units is 100 × $1 = $100.
Now assess the maximum payoff at expiration: a long butterfly typically peaks when the underlying price is at the middle strike (65). The payoff per butterfly at expiry is the distance between adjacent strikes, which is 5 (65−60 = 5 or 70−65 = 5), so the maximum payoff per butterfly is $5. For 100 butterflies, the total payoff when P = 65 is 100 × 5 = $500.
Finally, determine the net gain: maximum payoff ($500) minus total cost ($100) equals a net gain of $400. 
Evaluating the other options:
- If you had only $100 as the net gain, that would imply a substantially smaller payoff or higher cost than provided by the setup; with the $5 per unit peak payoff and the $100 cost, you get $400, not $100. 
- If the net gain were $200 or $300, that would require either fewer contracts or a smaller peak payoff than the defined strikes and quantities would yield, which contradicts the given 400 options and the 60/65/70 structure. 
In summary, the combination of a peak payoff of $500 and a $100 total cost leads to a maximum net gain of $400, aligning with the last option.

A trader creates a long butterfly spread from options with strike prices $60, $65, and $70 by trading a total of 400 options. The options are worth $11, $14, and $18. What is the maximum net gain (after the cost of the options is taken into account)?单项选择题

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