Question

1.A butterfly spread is the purchase of one call at exercise price X₁, the sale of two calls at exercise price X₂, and the purchase of one call at exercise price X₃. X₁ is less than X₂, and X₂ is less than X₃ by equal amounts (i.e., X₂ – X₁ = X₃ – X₂), and all calls have the same expiration date. If X₁ = $10, X₂ = $15, X₃= $20, what is the minimum and maximum payoff of this strategy?

	A.	Minimum: 0; Maximum: $5
	B.	Minimum: 0; Maximum: $10
	C.	Minimum: 0; Maximum: $15
	D.	Minimum: unlimited; Maximum: $5
	E.	Minimum: unlimited; Maximum: unlimited.

Answer 1

Answer :

FOR CALL OPTIONS :

In options , the person who buy the right "TO BUY " is called Call Buyer and for the right call Buyer pays the Premium which is called Option Premium whereas the person who sells such right of Buy is known as Call Seller and Call seller receives the Option Premium.

Further , FOR PUT OPTIONS

the person who buy the right "TO SELL" is PUT Buyer anf for the right PUT Buyer also pays the Premium which is called Option Premium and the person who sells such right of Sell or not is known as Put Seller.

In the given question, we have given the details for Call Options.

Now, Call Buyer will exercise the right only when "Current Market Price as on Expiry Date " is greater than the Exercise Price .(Call buyer bought the right , therefore, he has the right to decide whether to exerise or not the option).

And if the Call Buyer exercise then call seller has to exercise and so, Call seller will end up making loss.

So, One of the Party either Call Buyer or Call Seller will make profit and other will incurr loss.

FOR CALL BUYER :

Now, Net Profit of Call Buyer if Exercised will be :

= Current Market Price as on Expiry - Exercise Price - Option premium paid

So, the difference of CMP (Current Market Price ) and EP (Exercise Price ) will be profit for Call Buyer less by the Option Premium paid for obtaining right.

Breakeven for Call Buyer will be = Exercise Price + Option Premium Paid .

Maximum Loss for Call Buyer = OP Paid because if chooses not to exercise even then this amount has to be paid off by the Call Buyer .

Maximum Profit for Call Buyer = unlimited

Since in the Question we have not given Option Premium details so, we are going to ignore it for our calculation.

NOW FOR CALL SELLER,

Maximum Profit is Option Premium received .

Maximum Loss is Unlimited

Butterfly spread is a type of strategy in which :

1. Buy One call at Low Exercise Price (EP)

2. Buy one call at High Exercise Price

3. Sell the two Call at Average EP of High and Low EP

Table of Profit / Loss

CMP as on Expiry	EP = X1 = $ 10 (a)	EP = X3 = $ 20 (b)	EP = X2 = $ 15 (c)	Net Profit/Loss (a+b+c)
	Call Buyer	Call Buyer	Call Seller
Suppose , $ 6	0 (will not exercise as CMP of $ 6 is less than the EP of $ 10)	0 (will not exercise as CMP of $ 6 is less than the EP of $ 20)	0 as Call Buyer will not be excercised	0
$ 7	0 (will not exercise as CMP of $ 7 is less than the EP of $ 10)	0 (will not exercise as CMP of $ 7 is less than the EP of $ 20)	0 as Call Buyer will not be excercised0 as Call Buyer will not be excercised	0
$ 8	0 (will not exercise as CMP of $ 8 is less than the EP of $ 10)	0 (will not exercise as CMP of $ 8 is less than the EP of $210)	0 as Call Buyer will not be excercised0 as Call Buyer will not be excercised	0
$ 9	0 ( Call Buyer will not exercise as CMP of $ 9 is less than the EP of $ 10)	0 ( Call Buyer will not exercise as CMP of $ 9 is less than the EP of $ 20)	0 as Call Buyer will not be excercised0 as Call Buyer will not be excercised	0
$ 10	0 (as Breakeven at EP is $ 10 which is equal to CMP of $ 10 ) so Profit will be 0 , whether exercise or not	0 ( Call Buyer will not exercise as CMP of $ 9 is less than the EP of $ 20	0 as Call Buyer will not be excercised0 as Call Buyer will not be excercised	0
$ 11	Exercise (Profit of $1 = $ 11 - $ 10)	0	0	$1
$ 12	Exercise (Profit of $2 = $ 12 - $ 10)	0	0	$ 2
$ 13	Profit = $ 3	0	0	$ 3
$ 14	Profit = $ 4	0	0	$ 4
$ 15	Profit = $ 5	0	0	$ 5
$ 16	Profit = $ 6	0	loss of $ 2 as 2 call sell	$ 4 ($6- $2)
$ 17	Profit = $ 7	0	Loss of $ 4 ($2 loss * 2 call)	$ 3
$ 22	Profit = $ 12	$ 2 profit ($ 22 -$20 )	loss of $14 ($7 loss * 2 call)	0 ($14 - $14 )

So, Maximum Payoff will be at CMP of $ 15 (as on Expiry)

and Minimum Payoff will be 0. as we can check from above that at CMP as on Expiry of $ 22 the NEt profit is 0.

as Minimum cannot be les than 0

So, OPTION A. is Correct.

A.	Minimum: 0; Maximum: $5

where , CMP = Current Market Price

EP = Exercise Price

Note : 1. CMP as on expiry have been supposed , assumed to compute our answer.  

2. OP (Option Premium ) have been ignored since not given in Question.