Relationship Between Forward and Futures Prices

For the strategy employing forwards, contracts are bought, where r is the daily return (or instantaneous money market rate) and T the maturity term in days. The start forward price sF=X, and the payoff on expiry 

The futures strategy is more involved, because of the margin cash flows that are received or paid daily during the term of the trade. On day one, r contracts are bought, each priced at F. After the close that day, Fi — F is received. The position is closed out, and the cash received is invested at the daily rate, r, up to the expiry date. The return on this investment is Thus, on expiry the counterparty will receive rfi - 

The next day, futures contracts are bought at a price of F. At the close, the cash flow of F2 — F[ is received and invested at generating a return on expiry of r ( 2 This process is repeated until the 

This is also the payoff from the forward contract strategy. The key point is that if equation (6.3) below holds, then so must (6.4). 

---