a) Consider a stock whose current price is 50 and whose price at some ) &! fixed time T in the future may X be one of the following values:48,49,50, 51". Suppose we estimate that the probabilities of these stock prices are

p(48)=0.2 p(49)=0.4

p(50)=0.3

p(51)=0.1

If we purchase one share of the stock now, what is the expected return at T time ? What is the expected profit?

b Consider a derivative of the stock in part a) whose return is a D is a function of the stock price, say p(48)= 2

p(490= -1

p(50)= 0

p(51)= 3

Thus, the return D is a random variable on omega. What is the expected return of the derivative?