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gammas 31. You hold two types of calls and two types of puts on a given stock. The deltas and of the respective types are (+0.40, +0.03), (+0.55, +0.036), (-0.63, +0.028), and (-0.40, +0.032). You have a long position in 1,000 of the first type of call, a shon position in 500 of the second type of call, a long position in 1,000 of the first type of put, and a short position in 500 of the second type of put. (b) Suppose you decide to gamma hedge your portfolio using only the first type of call. (a) What is the aggregate delta of your portfolio? The aggregate gamma? What is the resulting delta of the new portfolio? What position in the underlying is now required to create a delta-neutral gamma-neutral portfolio? gammas 31. You hold two types of calls and two types of puts on a given stock. The deltas and of the respective types are (+0.40, +0.03), (+0.55, +0.036), (-0.63, +0.028), and (-0.40, +0.032). You have a long position in 1,000 of the first type of call, a shon position in 500 of the second type of call, a long position in 1,000 of the first type of put, and a short position in 500 of the second type of put. (b) Suppose you decide to gamma hedge your portfolio using only the first type of call. (a) What is the aggregate delta of your portfolio? The aggregate gamma? What is the resulting delta of the new portfolio? What position in the underlying is now required to create a delta-neutral gamma-neutral portfolio