Suppose there is a financial asset ABC, which is the underlying asset for a futu

Question

Suppose there is a financial asset 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:

a.                 In the cash market ABC is selling for $80.

b.                 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.

c.                  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? What is the profit?

c.   What action would you take if the futures price is $76? What is the profit? ?

Suppose there is a financial asset 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: What is the theoretical (or equilibrium) futures price? What action would you take if the futures price is $83? What is the profit? What action would you take if the futures price is $76? What is the profit?

Explanation / Answer

If you borrow money today to buy ABC your cash flow in 6 months is

$4 - $80(3%/2) = $2.80

If you purchase the futures contract your cash flow in 6 months is

S - F = $2.80

where we equate the cash flows.

F = S - $2.80 = $77.20

So the futures price is $77.20

If the futures price is $83 I would short the futures contract and buy ABC. The profit would be $5.80 since that is the difference between the actual and correct price.

If the futures price is $76 I would buy the futures contract and short ABC. The profit would be $1.20.

This is assuming that ABC is priced correctly and that there are no transaction costs.

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