Risk Management of Forward and Futures Strategies Reading 28

Guys in R28 of CFA level 3 Volume 5 there are two types of formulae to use to use for reallocation and risk management of equity futures.

Does any one know in which case to use for equities the Nf = [V(1+rf)T]/(qf) and when to use the:

beta T x S = beta S x S + Nf x betaf x f

it seems like for each question you have to use either one or the other but which one to use in which case i am confused.

does any one know which to use when?

I thought based on the reading you would use the beta for reallocation and pre-investing but if you wanted to convert an equity to a risk free asset you would use the first one

but it seems like in the examples in the official study book they use one formula and in the practice questions they use a different formula. e.g. for p267 question 8 the strategy is to convert to synthetic cash so i use Nf = -V (1+rf)T / (qf) formula to get answer but they use the beta formula instead which i understand but on page 238 exhibit 5 and generally section 3.4 they should use Nf = -V * (1+rf)t / (qf)

at the same time question 3 of the reading is also to convert an equity portfolio to synthetic cash (i.e. exactly same question as 8) and there they use Nf = -V (1+rf)T / (qf) formula

the deal is that the official text book even says that turning an equity portfolio to beta zero is similar to converting equity to synthetic cash but it is at least to me not clear when to do which formula. certainly the two formulas give you a different number of futures contracts

any help much appreciated!!