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:
Q1. What is the theoretical (or equilibrium) futures price?
Q2. What action would you take if the futures price is $83?
Q3. What action would you take if the futures price is $76?
Q4. 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?
Q5. 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?