Futures Contracts

OK I am actually pretty decent on using futures contracts BUT I think I just confused myself. Can someone remind me when the ‘value’ part of the formula below needs to get ridden at the risk-free rate for the period in question- lets call it three months.

So to create synthetic EQ for 3 months- # contracts= beta-beta/beta * value ridden / value of contract used

BUT- if they change it to we want to ‘pre-invest’ $3M, we do NOT need to ride that $3M in this case, correct?

Essentially, can someone summarize when that ‘value’ needs to be ridden at the risk-free rate in the formula above?

thnx!