Suppose Mr.T comes to you via a broker with the following proposition: You will give me $1,600 today. In return, 18 months from now I will guarantee to pay you whatever the square of the stock price of ABC is at the time. For example, if the stock price ends up at $80, I will pay you $80 x $80 = $6,400. The current stock price of ABC is $20. You know that each half-year the stock price will either increase by 100% or decrease by 50%. The risk-free discount rate is 9.76% per annum.

a) What is the annualized volatility for ABCs stock price? (2 marks)

b) Assume that the ABC stock pays no dividends in the next 2 years. Would you accept this offer? Why? (8 marks)

c) Continue to assume that the stock pays no dividends. Suppose upon receiving the payment from Mr. T 18 months from now, you will need to pay $100 to the broker. That is, if the stock price ends up at $80, you will receive $80 x $80 $100 = $6,300; if the stock price ends up at $2, you will receive a net payoff of $2 x $2 - $100 = -$96. Assume that you are very risk-averse, explain how this additional cost will affect your calculation of the lowest acceptable offer price in b)? (4 marks)

d) Assume that the stock pays a $2 dollar dividend in half-year time, what is the lowest offer price that you will accept? (6 marks)