Stock XYZ is currently trading at $50. A JUN 60 call option on the stock is quoted at $12.65. The delta on the call is 0.5866, and its gamma is 0.0085. At the same time, a JUN 65 call option on this stock is quoted at $17.75 with a delta of 0.5432 and gamma of 0.0089. You currently have a short position on the JUN 60 call for 60 contracts. The risk-free rate is 5%.

(1) Construct a hedging strategy according to both delta and gamma hedging (delta neutral and gamma neutral at the same time). Please specific how many stocks and calls you buy/sell?

(2) How much initial investment do you need to construct this strategy?

(3) The following date, the stock closes at $52. The JUN 60 call is trading at 14.55, while the JUN 65 call is trading at $19.65. How much is your investment now worth? How much you would end up with if you had invested all the money in a risk-free bond in the very beginning? (Assuming continuous compounding).