Creating Synthetic Cash different, position, question, selling, convert

invic

Hello - I am somewhat confused by a problem in Schweser 2012 Practice Test Book 1; Test 2; Afternoon question 37 (page 133). This question asks to convert a $3 billion position into synthetic cash by selling futures contracts. As I was working on this question, it dawned on my that I have two different ways to create synthetic cash in my head.
#1) [(Target Beta - Portfolio Beta) / Futures Beta ] * ( V / (Pf)*multiplier )
       (using a Target of 0 or .25)
#2) - V * (1 + RF)^T / (Pf)*multiplier
The answer to the question uses the second formula. However, I used the first when I saw the question. Of course my answer was there as a wrong answer. The answer key doesn’t provide any information as to why. If someone can please let me know when to use which formula, I would be most grateful
Thank you very much.

HuskyGrad2010

one is for hedging and the other is to create synthetic cash, both question and answer are clear.

ayodayo

I intutively work it backwards.
At the expiration of future liability to settle = [ St - F]  x N* x q—–> So we owe  = N*q F, it would be worth St x N* x q
Now equations # of contracts N = V (1+Rf)^ t / q F
Effective amount required (due to round off)
V * = N* x q x f / (1+Rf)^t………we put this much money in risk free bond which grows to V* (1+Rf)^t—> equivalent to our liability at expiration of future..
Now at expiration we will receive St (price at expiration) x N* x q……..here due to dividend reinvestment
# effective no of stocks = N* q / (1+delta) ^ t…….which will grow to N* x q due to reinvestment of dividends
I hope i made sense & have got it right!

wizofoz

hi jana in this example could you explain how do we arrive at no. of units of stock.
I understand that no. of stock units = (V/S) * (1+delta)^T       ———- (A)
how does (A) equal to -(N*q) / (1+delta)^T ?

wilslm

Page 361 of book 5 of CFAI text has an example

Andreas42

#1 changes the portfolio exposure using futures.  #2 creates synthetic cash.  the question asks for synthetic cash.  do what they ask.