Neutralizing Equity Exposure different, position, question

leadcfa

I am referencing problem 40, Practice Exam II, Vol 1 Afternoon but the question is relevant more generally.
When asked to neutralize the exposure to equities it seems there are two methods that produce different results.
Say I have a long position in equity $1 Bn.
Method 1: I can hedge this via futures : Nf = [ (Beta Target - Beta Current)/Beta Future ] * (Stock $ Value / p*q).
Method 2: I can turn the position into synthetic cash also by using futures. Here the formula is slightly different: Nf = V(1+r)^T / p * Q
These produce different results. Logically they should be equivalent since they both produce a zero beta exposure that should earn the risk-free rate. What am I missing here?

Daniel1985

Nicely put – all makes sense now

prashantsahni

2 differences. Assuming you are talking about the same equity position to be converted into cash
Method 1, is an instantaneous hedge, in the sense it acts as a hedge from the time you enter into the Futures contract. Any upside you gain from Beta in you lose because of the short Future contracts leaving you with Zero Beta exposure. Any portfolio with Zero beta is basically Cash.
Method 2, is when you set up a hedge from effect in the future (T periods). The amount of Future/Forward contracts needed in the future will be different than required at present.