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?
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?
You would buy the ...
This posting answers five questions regarding a financial asset, ABC, which is the underlying asset for a futures contract with settlement six months from now.