Doubt- Calculating contracts by creating synthetic cash position out of equity

CFA Level III Derivatives
#1

Hello Guys Please somebody have a look at this Question which is about Creating cash out of equity

Question image: https://ibb.co/dsovZS

Based on Exhibit 1& 2 how many contracts are needed to sell to execute strategy 2" ?

I calculated As [V (1+r)t] / q*f

i,e [350M (1+0.5% )2] / 2157 *250

I get answer as 650 contracts, but the answer given is 793 contracts. and the method they used here is [(Bt - Bs) / Bf]* S/f

Why the ans using the method i solved is wrong and why there is inconsistency in these two methods?

Thanks

#2

You left out the betas in the formula. You should multiply by [B(cash) - B(equity)] / B(futures)

Note that B(cash) is zero because cash doesn’t move with the market.

So it’s -B(equity) / B(futures) = (-1.1 / 0.9) = -1.22

Multiply your answer by -1.22 and you get 794.

The reason they give 793 is that they don’t multiply by (1+r)t

Why don’t they multiply by (1+r)t to get the future value? I don’t know why they sometimes do and sometimes don’t. And it looks like other people have the same question:

https://www.analystforum.com/forums/cfa-forums/cfa-level-iii-forum/91365209

#3

I don’t get it either, I calculated 794 as well. From what I read you don’t calculate FV if it’s about preinvesting a future amount (i.e. it is already in FV terms). In this case it looks like the 350 million is a PV amount so the number of futures contracts should be based on 350*(1.005)(3/12)…

#4

Yes it’s very unclear. I use FV only when synthetic equity/cash is asked, otherwise for changes in asset allocation, preinvesting of cash,… I use the formula with the betas.