In Butterfly Put Spread (buy one put with low exercise price (Xl) and one with high (Xh) and sell two puts with medium exercise price (Xm)), should we always assume: Xh-Xm=Xm-Xl ? If not, how do you show that max profit is Xm-Xl-(price of low put+price of high put - 2xprices of medium puts)? I.e. profit is maximized when St=Xm and put with high price is exercised => max profit =Xh-Xm-(price of low put+price of high put - 2xprices of medium puts)
this came up in another thread and was explained well there. search.
I did before posting! Can’t find it though 
Your profit will be: Max(0,(Xl-S) - 2*Max(Xm-S) + Max(0,XH-s) If you remember the formulas then you dont’ have to worry about the rest as you can just plug in numbers.
remembering the formula’s is too much work for me. i remember them by understanding the profit of each option… http://www.analystforum.com/phorums/read.php?13,626595,627169#msg-627169 that was the thread before - not as helpful as i remember…
If you remember that a Call’s profit is Max(0,S-X) and a Put’s profit is Max(0,X-S) then everything else is easy you just have to remember what a butterfly, straddle, bull spread, bear spread, etc are and you can setup your formula. For instance a Straddle is Buy a Call and Buy a Put at the same strike price so, Max(0,S-X) + Max(0,X-S) - Premiums. You know the max profit is unlimited, but the loss is limited to the premiums paid. Ok, I’m rambling and need to stop.
Like striker, there is no way I can remember all those equations. I just draw myself a line, and figure out the profit/loss, breakeven price.
put it’s really only 2 equations and subsitute one of the equations in for each put or call and a “+” for long and “-” for sell or short. :).
Understanding how to calc the profit is rather easy, like you guys said you need to know the position and understand put/call payoff. I have a hard time conceptualizing the breakeven, max and min so I may have to just memorize those. Which I am none too pleased about…
Strikershank, thanks for the link. I only searched 90 days and this post was back to November. My question remains though :(. I refer to the same pages CFA Dreamer mentioned in the old post (p166-167 in Reading 39 in CFAI): maximum profit is given as Xm- Xl -(Pl-2Pm+Ph). where as if you substitute S=Xm in the profit equation (see bigwilly post above), you get: Xh-Xm-(Pl-2Pm+Ph). The two equations are equal if Xh-Xm=Xm-Xl, so should we assume this relationship always holds?
The way I am looking at it - I will be thorough with Covered call S-C, Protective Put S+P, Collar S-C+P, Straddle (+C+P or -C-P) Interest Rate Cap/Floor/Interest Rate Collar Butterfly spread, BullCall Spread et al - I was advised to stay light
From the formula for profit of butterfly spreads how do you get max profit?
max profit occurs at St = Xm, seems like only one short call is assumed to be in money?
I wrote a series of articles on option strategies, including one on the butterfly spread. You’ll find them here: http://www.financialexamhelp123.com/option-strategies/
Full disclosure: as of 4/25 I’ve installed the subscription software on my website, so there’s a charge for viewing the articles.
full disclosure as of 4/25 I got sad. If there was more time until the exam and a few more level 3 articles, I’d buy in, but at this point, not worth it. Thanks for 2.75 great levels of free articles s2k!!!