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# Futures Pricing Problem

Suppose there is a financial asset, a bond ABC, which is the underlying asset for a futures contract with settlement six months from now. You know the following about this financial asset and the futures contract:

-In the cash market ABC is selling for \$80.
-ABC pays \$8 per year in two semi-annual payments of \$4, and the next semi-annual
payment is due exactly six months from now.
-The current six-month interest rate at which funds can be loaned or borrowed is 6%.

Respond to these questions:

a. What is the theoretical (or equilibrium) futures price?
b. What action would you take if the futures price is \$83?
c. What action would you take if the futures price is \$76?
d. Suppose that ABC pays interest quarterly instead of semiannually. If you know that you can
reinvest any funds you receive three months from now at 1% for three months, what would
the theoretical futures price for six-month settlement be?
e. Suppose that the borrowing rate and lending rate are not equal. Instead, suppose that the
current six-month borrowing rate is 8% and the six-month lending rate is 6%. What is the
boundary for the theoretical futures price?

#### Solution Preview

a) What is the theoretical futures price?

The theoretical futures price (F) is given by:

F = P[1 + t(r - c)]

where P = cash market price, t = time, in years, to the futures delivery date, r = financing rate, and c = current yield (coupon rate divided by the cash market price).

Inserting our values, we have:

F = P[1 + t(r - c)] = \$80[1 + 0.5(0.06 - 0.08)] = \$80[0.99] = \$79.20.

(b) What action would you take if the futures price is \$83?

You would sell the futures contract at 83, purchase the bond at 80, and borrow 80 for six months at 6% per year.

(c) What action would you take if the futures price is \$76?