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Synthetic Cash position with Equity Futures

Scratching my head at this one….

There is a formula to temporarily reduce equity by using futures. That formula to find out how many futures contracts to do this synthetic cash position :

Formula 1: Nf=((βT−βS)/βf)x(S/f)
Set βT = 0

And then there’s another formula that says: 

Formula 2: Nf= S(1+ Rf)n/(f x multiplier) 

Then I run into a practice problem that uses Formula #2: [An investment management firm has a client who would like to temporarily reduce his exposure to equities by converting a $25 million equity position to cash for a period of four months. The client would like this reduction to take place without liquidating his equity position. The investment management firm plans to create a synthetic cash position using an equity futures contract.] 

And then a few questions later, I run into another problem that uses Formula #1 rather than Formula #2: [Create a synthetic cash position by temporarily converting the US equity exposure in the fund into cash for a period of three months.]

Which formula is the right one, and why didn’t formula #2 work for the 2nd question? I tried formula #2 for the 2nd question and it was way off compared to formula #1

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Figured this out… They’re essentially the same formulas. Formula 2 assumes beta of 1 while formula 1 lets you plug in the betas. Schweser notes was helpful in this explaining this part.