7. The Greeks (20 points) Note: these parts are not related to each other. You can do them separately. For this problem, suppose the current stock price is $100, and suppose your firm's proprietary options pricing model gives you the following prices and Greeks: (a) (10 points) For outside reasons, you are required to hold 1,000 shares in the firm and you cannot change this. However, your firm does not wish to take on the price risk, and so you are asked to find a delta- and gamma-neutral portfolio. How many calls and puts must you go long or short in order to achieve this goal? Assume each option is on a round lot of shares, which is 100 shares. (b) (10 points) You put together a delta- and gamma-neutral portfolio. Your boss is disappointed that the expected return on this portfolio is the risk-free rate. Explain (using at most four sentences) why this low expected return is reasonable. (You may assume we are in a Black-Scholes-Merton type of world.)