Question

A call with a strike price of $44 costs $4. A put with the same expiration date and a strike price of $40 costs $3. Calculate the profit/loss the investor makes from a short strangle at expiration date stock prices of (i) $38, (ii) $42, and (iii) $46. For what range of expiration date stock prices will the investor make a profit?

Answer 1

=> Short strangle is the option strategy in which we short a call option of out of the money strike price and put option of out of the money strike price.

=> By shorting the call option we will have a premium of $4 and by shorting the put option we will have a premium of $3.

=> Here our net premium credited will be $4 + $3 = $7

=> In case of call option ( 44 strike price), we can keep the entire premium ($4) as profit if the stock price expires below or equal to the strike price of $44 and if the stock expires above $44 then our profit will be reduced. But when the price moves above the breakeven of $48 (44+4) then we will start to make losses on the call option.

=> In case of put option ( 40 strike price), we can keep the entire premium ($3) as profit if the stock price expires above or equal to the strike price of $40 and if the stock expires below $40 then our profit will be reduced. But when the price moves below the breakeven of $37 (40-3) then we will start to make losses on the put option.

=> By implementing this strategy we will have upper break even of $ 51 ( Call strike price + net premium credited) and lower break even of $33 ( Put strike price - net premium credited)

=> Now we can move to the answers

1) When the stock price expires at $ 38

=> We will have $4 profit in case of call option ( because it expires below the strike price $44)

=> In case of put option, it expires below the strike price of $40 , so we have to reduce $2 ( $40-$38) from the put premium of $3

* profit from put option = 3-2 = $1

=> Total profit from the strategy = 4 + 1 = $5

market expiry	call profit	put profit	strategy profit
38	4	1	5

2) When the stock price expires at $ 42

=> We will have $4 profit in case of call option ( because it expires below the strike price $44)

=> We will have $3 profit in case of put option ( because it expires above the strike price $40)

=> Total profit from the strategy = 4 + 3 = $7

market expiry	call profit	put profit	strategy profit
42	4	3	7

3) When the stock price expires at $ 46

=> In case of call option, it expires above the strike price of $44 , so we have to reduce $2 ( $46-$44) from the call premium of $4

* profit from call option = 4-2 = $2

=> We will have $3 profit in case of put option ( because it expires above the strike price $40)

=> Total profit from the strategy = 2 + 3 = $5

market expiry	call profit	put profit	strategy profit
46	2	3	5

=> Above we have discussed that by implementing this strategy we will have a upper break even of $51 and lower break even of $33 , so in the range of $33 to $55 (price of stock on expiry of the options) the investor can make profit.