You hold one share of IBM stock. The current stock price is $56. You are worried that the stock price may decline. Your objective is to get at least $50 from the stock at the end of one year. Assume the volatility of IBM stock (sigma) is 30% and the risk-free rate is 8%. 

(i) How will you hedge using put option on IBM stock to make sure that you receive at least $50 at the end of the year? 

(ii) Suppose put option on IBM stock is not available. How can you create a portfolio using only IBM stocks and a risk-free bond that has exactly same payoff as the portfolio in (a) at the end of the year? [Hint: You need to use Black-Scholes formula for put option. Calculate d1 and d2 (show your calculations). Then, use N(d1) =0.79 and N(d2)=0.69].