The delta and gamma of the portfolio held by an option dealer are – 4 000 and + 1 400, respectively

The portfolio has positive gamma. Call and put options, both have positive gamma.

In order to make the portfolio gamma neutral, we need to add to the portfolio, a short position in either the call options or in the put options.

Put options have negative delta while call options have positive delta. Hence, a short position in Put options will have positive delta while a short position in call options will have negative delta. Our portfolio has a negative delta.

Hence, if we add:

• Short position in call options to the portfolio to make it gamma neutral, we will end up creating a resultant portolio with much higher negative delta. So, we will now need to add long position in underlying shares to make the resultant portfolio delta neutral. Since, shares have a delta of 1, we will need to go long (buy) on larger number of shares to make the portfolio delta neutral.
• Short position in put options to the portfolio to make it gamma neutral, we will end up creating a resultant portolio with much lower negative delta. So, we will now need to add long position in underlying shares to make the resultant portfolio delta neutral. Since, shares have a delta of 1, we will need to go long (buy) on relatively smaller number of shares to make the portfolio delta neutral.

Hence, short position in put option along with long position in underlying shares will be the most cost efficient way to make the portfolio delta-gamma-neutral as it involves going long on (buying) relatively lower number of underlying shares.