Delta Gamma Neutral Portfolio - Hull Question 24

[bhar]

Hi
I came across this assignment problem in Hull. I tried to solve it but would like to get a correct answer to this problem. Could you please help. I have ignored the vega neutralising requirement from the original question as it is low testability.

The answer I got - Gamma Neutralising trade - -6000/1.5 = 4000 Long Call Options.
Delta Neutralising trade = 4000 * 0.6 = 2400 short the underlying security.

Could you please correct me.

 

[David Harper CFA FRM]

Hi bhar, the first trade correctly neutralizes gamma: 4000 options *1.5 = +6000 which neutralizes the portfolio's (prior) -6000. Since the full security (full sterlings) have zero delta, the second trade won't impact this, so this is good to neutralize gamma.

However you forgot the portfolio's existing (initial) -450 position delta (which you already have correctly in yellow). The first trade of +4,000 long call options will add +4,000 * 0.6 = +2,400 position delta to the -450, such that you need to neutralize 1,950 position delta with the second trade. So the second trade is to short 1,950 sterlings. Thanks,

 

[bhar]

Thanks David. That helps a lot.