Futures Pricing Problem:?

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Futures Pricing Problem:

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:

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

路 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.

路The current six-month interest rate at which funds can be

loaned or borrowed is 6%.t

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?

Futures Pricing Problem:?

You calculate the futures price by arbitrage. To do this you calculate the cash flows assuming you purchase the future today and compare it to the cash flows assuming you purchase the futures contract today and havbe the asset delivered. The futures price is determined by equating your position.

I am assuming here that if you purchase ABC at t=0 you get the $4 payment but if you purchase the futures contract at t=0 you do not.

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.

Futures Pricing Problem:?

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