d. Consider a stock with a current price of P $27. Suppose that over the next 6 months the stock price will either go up by a factor of 1.41 or down by a factor of 0.71. Consider a call option on the stock with a strike price of $25 which expires in 6 months. The risk-free rate is 6%. (2.) Suppose you write 1 call option and buy Ns shares of stock. How many shares must you buy to create a portfolio with a riskless payoff (which is called a hedge portfolio)? What is the payoff of the portfolio? We can form a portfolio by writing 1 call option and purchasing Ns shares of stock. We want to choose Ns such that the payoff of the portfolio if the stock price goes up is the same as if the stock price goes dowm. This is a hedge portfolio because it has a riskless payoff P(u The Hedge Portfolio with Riskless Payoffs Strike price: X- Current stock price: P up factor for stock price: Down factor for stock price: d Up option payoff: Cu MAXIoPlu-X) Down option payoff: Cd MAXO,P(d)-X] Number of shares of stock in portfolio: Stock price Portfolio's stock payoff: # P(u)(NS) Subtract option's payoff: Cu Portfolio's net payoff current stock Stock price Pide S0.00 Portoflio's stock payoff:-P(d(Ns) Subtract options payoff: Cd Portoflio's net payoff