Consider the model of a stock where it either goes up by 7% or down by 4% each year. Let p(up) be the probability that stock goes up and p(down) the probability that stock goes down.

(a) Suppose that p(up) = 52% and pdown = 48%. Recall the expected rate of return is defined as the number which satisfies the equation E[S1] = S0e ^(1) where S0 is the known asset spot price and S1 is the unknown asset price in one year from now. What is the expected rate of return of the stock?

(b) If the risk-free rate is 5%, what probabilities pup and pdown lead to an expected return equal to the risk-free rate?