Lets denote the price of stock X today (t = 0) as S0 and the price of a stock tomorrow (t = 1) as S1. We know that S0 = 50. We also know that S1 = (1 + r )S0, r is the rate of return, which is uncertain. For simplicity, assume that tomorrow, the return r can either go up (r = 0.10) or down (r = -0.15). The probability of going up is 2/3 in t = 1. You plan to potentially hold the stock for 2 periods, so you did some research to try and figure out the price of the stock at t = 2 (S2). You found out that after an up market in t = 1, the probability of the market improving in t =2 becomes 3/4. Also, after a down market in t = 1, the chances of going down again in t = 2 become 2/3. a) Create the payoff tree to map out the potential stock prices two periods ahead (S2). On the payoff tree indicate i. The probability of the final potential prices (4 points) ii. The potential S2 price levels (4 points) b) Calculate the expected price of the stock, two periods ahead (that is, E(S2 ))