Forward-Spot Parity

FIGURE 6.2 Forward Contract Profit/Loss Prnfiln  

Buy forward contract CASH FLOWS STARTDATE 0 EXPIRY Pr-F 

Borrow zero present-value of forward price F/1.05 F 

By design, the portfolio has a payoff that is identical to the forward s [Px - f). The cost of setting up the portfolio must therefore equal the current price of the forward if one were cheaper than the other, a trader could make a risk-free profit by buying the cheaper instrument and shorting the 

The forward strategy can be used to imply the forward price, provided that the current price of the underlying and the money market interest rate are known. FIGURE 6.2 illustrates how this works, using the one-year forward contract whose profit/loss profile is graphed in figure 6.1 and assuming an initial spot price, P, of 50, a risk-free rate, r, of 1.05 percent, and a payout yield, R, of 1 percent. 

FIGURE 6.3 shows that the payoff profile illustrated in figure 6.1 can be replicated by a portfolio composed of one unit of the underlying asset 

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The futures price can be analyzed in terms of the forward-spot parity relationship and the risk-free interest rate. Say that the risk-free rate is r-. The forward-spot parity equation (repeated as (6.8a)) can be rewritten in terms of this rate as (6.8b), which must hold because of the noarbitrage assumption. 

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