Creating synthetic index

Q2 part (B), p.136, CFAI vol 5 I understand part (A) but am a bit confused with part (B) I thought that at expiration ---- Portfolio value (if long the futures) = 1211 x (594.65-498.3) x 500 + 300 mil x 1.0235 ^ 0.25 = 360,087,102.5 Portfolio value (if invest in the actual stock index) = 300mil x 1.075^0.25 = 305,473,380.3 Now obviously the 360mil is much more than 305mil. I thought they should be similar, if not the same? Did I miss something? - sticky

I now know that my calculation for Portfolio value (if invest in the actual stock index) is wrong. It should be: = number of index units at expiry x $594.65 = (1211 x 500) x $594.65 = $360,060,575 This now agrees with the portfolio value (if long the futures). Now troubles seem sorted out but I still have a question. If we are really investing in the actual stock index at the very beginning, how can we be sure that we can buy 1211x500=605,500 units of index? - sticky