Suppose a stock is trading at $50. Further suppose that we have the follow- ing information on the Black-Scholes prices of three European call options with 3 months to expiration:

K	45	50	55
C	6.86	3.60	1.61
	0.83	0.60	0.35
	0.034	0.052	0.049

(a) Write down the equations which one needs to solve to make a zero- cost, Delta-neutral portfolio with a convexity of 0.05 using the three types of calls. You do not need to solve these equations.

(b) What is the sign of the portfolios Theta? Briefly discuss the intuition behind your answer.

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