Derivs - Synthetic Cash

Hey guys,

Hopefulyl someone has their CFA book handy… Volume 5… page 267.

I’m having a hard time understand the last part of these questions. FOr quesiton 3, part C: Assume that the stock index is at 1031 when the futures contract expires. Show how this stratey is equivalent to investing the risk-free asset, cash.

In the answer it says:

in 4 months when the futures contract expires, the stock index is at 1031. The payoff of the futures contract is -86 (250) (1031-1170.10) = -$21,500(1031) + $25,157,150 = $2,990,650. ( How does this math work?? ) The formula they are doing is number of futures contracts * mutiplier *(new index price - old futures price). First they use that fomrula, then the 1170.10 dissapears and they just use 1031.

second part of answer: Netting the futures payoff against the stock posiiton produces $25,157,150, eqiv to investing $24,930,682 at 2.75% for 4 months. The short position has thus efectively converted equity to cash.

Been spending a few days on this, and just don’t how the math works there… Any help would be appreciated. Thanks!