A hedge fund has a portfolio of OTC options on a particular stock. The portfelos Delta is -400 and its Gamma is -1200. Furthermore, an exchange traded option on the same stock is available to trade which has a Delta of 0.6 and a Gamma of 0.4. (a) What position in the above exchange traded option and the stock itself would make the hedge funds overall portfolio both Delta neutral and Gamma neutral at the same time?

(b) What are the benefits of creating a portfolio which is both Delta neutral and Gamma neutral?