(a) Shares of XYZ stock cost $50 today and will sell for either $125 or $50 next year, with equal probability (1/2,1/2). A one-year zero coupon bond with face value $150 is selling for $100 today. What is the replicating portfolio and the price of a European put with strike equal to 2 $72.5?

(b) Derive the risk-neutral probability implied by the prices provided in the previous point. Clearly explain why the risk-neutral probability may differ from the actual (1/2, 1/2) probability.

(c) Derive the price of a security whose payoff next year equals √ S1, where S1 is the payoff of one share of XYZ stock next year.

(d) What is the expected return of XYZ stock under the “risk-neutral” probability measure? Is this expected return different from the “true” expected return of stock XYZ? Explain why.