Question 1

Betty has initial wealth W₀ = $1200 and faces an uncertain future that she partitions into two states, s = 1 and s = 2. She can invest in two securities, j and k, with initial prices of P_j = $10 and P_k = $12, and the following payoff table:

Payoff

SecurityS = 1S = 2

J$10$12

K$20$ 8

(a) If she buys only security j, how many shares can she buy? If she buys only security k, how many can she buy? What would her final wealth, Ws, be in both cases and each state?(6 marks)

(b) Find the price of pure securities.(4 marks)