Data: S₀ = 108; X = 115; 1 + r = 1.12. The two possibilities for S_T are 136 and 80.

a.	The range of S is 56 while that of P is 35 across the two states. What is the hedge ratio of the put? (Round your answer to 2 decimal places. Negative amount should be indicated by a minus sign.)

Hedge ratio

b-1.	Form a portfolio of five shares of stock and eight puts. What is the (nonrandom) payoff to this portfolio? (Omit the "$" sign in your response.)

Nonrandom payoff

$

b-2.	What is the present value of the portfolio? (Round your answer to 2 decimal places. Omit the "$" sign in your response.)

Present value

$

c.	Given that the stock currently is selling at $108, calculate the put value. (Round your answer to 2 decimal places. Omit the "$" sign in your response.)

Put value

$