Question

Three put options on a stock have the same expiration date and strike prices of $70, $80, and $90 are available at prices of $5, $7, and $10, respectively. Explain how a butterfly spread can be created. Construct a table showing the profit from the strategy. For what range of stock prices would the butterfly spread lead to a loss?

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Answer 1

Answer:

Long Put Butterfly options strategy- It is used to make profit from the neutral stock price action. When investor thinks that the stock will neither rise nor fall so much.

Construction- In this strategy, one put of higher strike is bought, two puts of litltle lower strikes are sold and one more put of lower strike is bought.  All Puts are of different strikes but same expiry. In this strategy, profit and loss both are limited.

Maximum profit- Difference between higher strike and middle strike prices (short puts) less the net cost of this strategy. Profit will be realized when the stock price is equal to the strike price of the short Puts (middle strikes)

Maximum loss- Limited to the net debit (net premium paid). Loss ocurrs when stock price is above the highest strike price at expiry date or stock price is below the lowest strike price.

Example- Buy 1 Put of strike 90 at $10, sell 2 Puts of strike 80 at $7 each and buy 1 more Put of strike 70 at $5.

(When Put is bought, premium is paid and when Put is sold, Premium is received.)

Net debit = Premium paid - Premium received

Net debit: (10+5) - (7*2)

Net debit = $1

Payoff Table (Payoff profile)-

Stock price at expiry	Strike 95	Strike 80 (2 Puts)	Strike 70	P/L	Net debit	Net P/L
70	+25	-20	0	+5	-1	+4
75	+20	-10	0	+10	-1	+9
80	+15	0	0	+15	-1	+14
85	+10	0	0	+10	-1	+9
90	+5	0	0	+5	-1	+4
95	0	0	0	0	-1	-1

Note:

• In strike 70 Put when stock goes above the strike then the maximum loss will be of net debit only (premium paid).
• In case of strike 80 Put (short) when spot goes above strike, profit will be limited to the premium received.