Reading 41 EOC q 2b and 3c

In these calculations I don’t understand how the shown calculation shows how the synthetic position produces the same result as an investment in the actual index (2b) or how it’s equivalent to investing the risk free asset (3c). For example, with 3c I understand that investing the actual amount committed (24,930,682) @ the risk free rate of 2.75% for 4 months = 25,157,150 This appears to be the same as the right part of the futures contract calculation (-86)(250)(1170.1). What confuses me is that the solution says “NETTING THE FUTURES PAYOFF AGAINST THE STOCK POSITION produces 25,157,150, equivalent to investing 24,930,682 at 2.75% for 4 months.” Isn’t the futures payoff the (-86)(250)(1031 - 1170.1)? If you net this against the stock position of 24,930,682 it doesn’t equal the 25,157,150. How does the calculation for the number of shares (21,411.16) come into play? This is really confusing me

Oh boy - stared at this question for an hour last night. Look forward to an answer! I thought I had this chapter down no problem…until the EOCs confused the heck outta me!

Remember the manager owns stock in Q 3, which also appreciates . In fact the price mentioned is for the index. So the profit from the futures ( due to shorting and subsequent decline in price) is offset against the loss in the stock he owns This is different from Q2 where he is equitizing cash and doesn’t own physical stock

Q2 deals with creating a synthetic equity position, Q3 deals with creating a synthetic cash position. For both of them I don’t understand the calculation that shows the equivalence of being in the synthetic vs. the underlying

for Q2, assume the future that was purchased was a 3month future, so that in 3 months time the futures price = index price because you’re at expiry. So what happens is, you invest the right amount of cash in order to settle the futures at 498.30 (as payment is settled at expiry), that way in 3 months time you pay up as the future has expired, and receive 605500 units of index. Which is the same as just buying 605500 in the first place

And then for Q3: At expiry You will receive cash in the amount of 86*250*1170.1 And you ‘deliver’ 86*250 of the stock (currently priced at 1031) This leaves you with a ‘cash’ position of $86*250*1170.1

resurrecting this thread, does anyone agree that the end scenario is not detailed clearly in the questions enough to prove success of the synthetic transaction?