Suppose now you are short 100 units of the butterfly spread on AAPL described using Portfolio A defined in question 1. You want to delta and gamma hedge your short butterfly position using Ns shares of AAPL stock, Nc units of an an at-the-money European call option on AAPL with 2 years to expiration, and NB dollars of borrowing (NB 0). To be clear, specifically the position you wish to hedge is -10011 A which is: Long 100 at-the-money call options with 1 year until expiration Long 100 at-the-money put options with 1 year until expiration Short 100 put options with strike price $160 with 1 year until expiration Short 100 call options with strike price $200 with 1 year until expiration AAPL is currently trading at $180. Assume the stock does not pay any dividends. Assume there is no arbitrage in the market and the Black-Scholes framework for option pricing holds. For this problem you are given the continuously compounded annual risk-free interest rate r = 8% and the volatility o = 0.3. Specify the numerical value for Ns for the portfolio which provides the desired delta and gamma hedging. Round your answer to the nearest integer number of shares. Suppose now you are short 100 units of the butterfly spread on AAPL described using Portfolio A defined in question 1. You want to delta and gamma hedge your short butterfly position using Ns shares of AAPL stock, Nc units of an an at-the-money European call option on AAPL with 2 years to expiration, and NB dollars of borrowing (NB 0). To be clear, specifically the position you wish to hedge is -10011 A which is: Long 100 at-the-money call options with 1 year until expiration Long 100 at-the-money put options with 1 year until expiration Short 100 put options with strike price $160 with 1 year until expiration Short 100 call options with strike price $200 with 1 year until expiration AAPL is currently trading at $180. Assume the stock does not pay any dividends. Assume there is no arbitrage in the market and the Black-Scholes framework for option pricing holds. For this problem you are given the continuously compounded annual risk-free interest rate r = 8% and the volatility o = 0.3. Specify the numerical value for Ns for the portfolio which provides the desired delta and gamma hedging. Round your answer to the nearest integer number of shares