$($a$)$ Explain the meaning of the terms convenience yield and cost of carry. What is the relationship between futures price, convenience yield, and cost of carry? $(15$ marks$)$

Suppose a financial asset, ABC, 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; and the current six$-$month interest rate at which funds can be loaned or borrowed is $6\%.$

$($b$)$ what is the theoretical futures price? $(15$ marks$)$

$($c$)$ what action would you take if the future price were $$83?(10$ marks$)($d$)$ what action would you take if the future price were $$76?(10$ marks$)$