Consider the following options on stock X:

Option	Delta	Gamma	Vega
A	0.5	2.2	1.8
B	0.8	0.6	0.2
C	-0.4	1.3	0.7
D	0.7	1.8	1.4

A bank is long 1000 units of Option A, short 200 units of Option B, short 2000 units of Option C, and short 500 units of Option D. The following two options are also available in the market:

Option	Delta	Gamma	Vega
E	0.6	1.5	0.8
F	0.1	0.5	0.6

1. a) Design one strategy that would make the banks portfolio delta neutral.

2. b) Design one strategy that would make the banks portfolio delta and gamma neutral. Explain why this strategy provides a better hedge with respect to changes in the price of stock X than the strategy you constructed in part (a).

3. c) Design one strategy that would make the banks portfolio delta, gamma, and vega neutral.