So the formula I’m working with for the butterfly spread with puts is: (XL-St) -2(Xm-St) +(Xh-St) - PL + 2Pm - PH. I got this from a Scheweser book from 2013 and their example problem works out using that formula.
In CFAI text examples in the reading (volume 5,pgs 298-299) they have reversed the second part of the equation and are using +PL - 2Pm+PH and their example problem works out using that formula.
I suppose I should use the CFA book formula but can someone confirm which one is correct?
(XL-St) -2(Xm-St) +(Xh-St)
this indicates you bought XL Sold 2 XM and bought Xh
so you ended up paying PL, PH and got 2 PM
so payout at the beginning = -PL + 2 PM - Ph
and net payoff would be
which is + PL -2PM + Ph
The high and low put are covers for your loss, so you buy these, and you sell two puts with an inbetween strike price to benefit from a non-moving price.
In your profit formula, the Ph and Pl are preceeded by a negative sign, as you paid a premium for the long, while the Pm is a short, a positive sign.
The first formula is correct