CFAI EOC Chapter 36 # 3c - synthetic cash

Others had posted similar questions in years past and no one could clarify…

$25,000,000 position in equtiies. They short a # of futures to create synthetic cash and effectively get the RFR. Makes sense. I understand what the value of the futures contracts will be at the end. Futures net payoff = +$2,990,650. Easy peasy.

I do not understand how they come to the value of the underlying stock loss. They simply say…

“Netting the futures payoff against the stock position produces $25,157,150.” Yet they do not show the actual stock position or loss. Just taking $25,000,000 and giving it the dividend and return of the index does not come out to this “netting” position.

The example in the chapter does the same thing. ANYONE SEE THE SAME ISSUES?

In four 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.

Netting the futures payoff against the stock position produces $25,157,150, equivalent to investing $24,930,682 at 2.75 percent for four months. The short futures position has thus effectively converted equity to cash.

you invest 24930682 for 4 months at 2.75% = 24,930,682*(1.0275)^(4/12) = 25,157.149.81 …

My broswer crashed at the end of my first anwser so Ill write something quick :

Fo = Value of the future at time 0

St = Value of the equity index at time T= end of contract

Ft and St is always the same since future converge to the spot price of the index at the end of the contract

your total position is :

Future position at time t =

-86(250)( St - Fo(1+Rf)^(4/12)) = -21500St + 21500Fo(1+Rf)^(4/12) = -21500St +25157150

Your Equity position at time t is :


net those 2 out :

total portfolio at time t = -21500St +25157150 +21500St = 25157150

no matter what St is.