You are given with the following information. You have a stock portfolio that consists of 1000 shares of Apple computer's stocks, where the stock does not pay dividend. Suppose the risk-free rate is 1.5%, and the current stock price is $172 per share, and the monthly volatility of the stock is believed to be 12%.

a) Suppose you want to apply the "Delta" hedging for a week by buying a European put option that entitles the holder the right to sell 100 shares of Apple Computer's stock with strike price as $171.60 per share. Show how you will construct a delta-hedging portfolio by using the above information. (Hint: apply the Black-Scholes model of put option).

b) In performing the above hedging strategies, do we eliminate all risks in the portfolio? Why or why not? What are the assumptions for the analysis?