The Mathematics of Financial Modelingand Investment Management

2-Financial Markets Page 61 Wednesday, February 4, 2004 1:15 PM

Overview of Financial Markets, Financial Assets, and Market Participants 61

Profit = Total proceeds – Total outlay

= F + yP – (P + rP)

The theoretical futures price is where the profit from this strategy is

zero. Thus, to have equilibrium, the following must hold:

0 = F + yP – (P + rP)

Solving for the theoretical futures price, we have:

F = P + P (r – y)

Alternatively, consider the following strategy called a reverse cash

and carry trade:

■ Buy the futures contract at F

■ Sell (short) the underlying asset for P

■ Invest (lend) P at r until the settlement date

The outcome at the settlement date would be:

1. From Settlement of the Futures Contract

Price paid for purchase of the underlying asset to settle = F

futures contract

Payment to lender of the underlying asset in order to borrow = yP

the asset

Total outlay = F + yP

2. From the Loan

Proceeds received from maturing of the loan investment = P

Interest earned = rP

Total proceeds = P + rP

The profit will equal:

Profit = Total proceeds – Total outlay

= P + rP – (F + yP)

Setting the profit equal to zero so that there will be no arbitrage profit

and solving for the futures price, we would obtain the same equation for

the theoretical futures price as given from the cash and carry trade.