Equitizing cash/ creating cash out of equity

Finding it a bit confusing with the above topic. When do we use the fv of the amount divided by multiplier etc.Vs using the target beta of stock equal to 0/cash equivalent minus current beta devided by futures beta etc.?The way I do it is if the question does not include beta then the question asks for the fv of the amount formula. Why cant we use the beta formula to equitize our portfolio?

Equitizing Cash

bcos you do not have a portfolio

you have cash on hand.

now you want to get equity exposure with the cash on hand.

Long futures contract + Long Cash = Long Stock market exposure.

Converting Equity into Cash

Long Stock + Short Futures = Long Risk Free Bond (Cash)

and why is this different from the selling futures with a beta position – read the middle passage on Pg 334.

So is it safe to assume that we use the fv formula 1) when we do not have a portfolio 2) when we have an index we want to invest in?

what does long cash mean, if having cash on hand, i guess just use the cash to buy equity futures?

Long cash = long risk free bond.

Guys, i saw in a sample exam in 2013 the Mary Bing case scenario where it was giving a beta of the Future contract and when it made the calculation in equitizing 15million it did not include in the denominator the beta of the the future. Have you seen anything like this or should i suppose that it was a wrong solution?

In the cfa book in derivatives page 239 and 240 it uses a future contract without a beta so the calculation is easy. If we get a future contract with its own beta should we use it in the denominator?

i found this confusing too. I dont understand why the solution does not include the beta calculation

Aren’t there some topic tests questions that have a future beta assumed to be different than the portfolio and it’s used?