Hedge Ratios in two-period Binomial Model

I’m having an issue with getting the correct hedge ratio for the first period in these questions. Not sure where the numerator is coming from.

For example:

Stock trades @ $65, can go up 20% or down 17% for 2 periods. Strike price = $60. RFR=5

S+= 78




S–= 44.78

I have no problem getting the hedge ratios and applying them for the 2nd periods, but why is a hedge @ time 0 =

(20.86-2.68) / (78-53.95) ?

I have it as (28-0)/(78-53.95)

Thanks for insight, I’m sure I am just missing something small here.

I think you have not specified the risk free rate. Once you get that, calculate the up and down probablity and then arrive at the payoffs on Node 0. Remember on Node 1, one of the values is $64.74, which is > $60 and hence there is a pay off. Probably that is where the $2.68 comes from, which translates to a probablity of .56, I think. Net net, calc the up and down probablity and get the payoffs on Node 0.