Delta/Gamma hedging

[crablegs]

Hello again,

Embarrassing question given this was a topic covered over and over again when I took my charter a couple of years ago....

One thing truly disapointed me today (or should I say I truly disapointed myself....), I really thought I had that Delta hedging thing under control and my whole world got rattled after working on the 2011 GARP exam. May I bother someone with this?

This is in short what I thought....

• When you buy calls, you add positive delta (vice versa have negative delta if you sell calls)
• When you buy puts, you add negative delta (vice versa have positive delta if you sell puts)
• When delta hedging, if you buy calls (add positive delta) then you need to short the underlying by : delta x # of options
• When delta hedging, if you buy puts (add negative delta), then you need to buy the underlying by : delta x # of options
• When you gamma hedge and need to reduce gamma then you need to sell options . If you sell calls, delta will then be reduced and you need to buy the underlying by delta x # of options sold. If you sell puts, then delta will increase and you need to short the underlying by delta x # options sold
• When you gamma hedge and need to increase gamma then you need to buy options. If you buy calls, delta will then increase and you need to sell the underlying by delta x # of options bought. If you buy puts, delta will decrease and you need to buy the underlying by delta x # options bought

Did I get this completely wrong?

The one that completely threw me off was Q. 18 of the 2011 GARP practice (Exam #2). The trader bought 200 call options contracts (each on 100 shares of GM). The delta of the option is 0.50. The answers states that in order to delta hedge the trader needs to buy 10,000 shares of GM.

I thought that when long calls (positive delta), one would need to short the 10,000 GM shares?

Thank you in advance.

Glen

 

[David Harper CFA FRM]

Hi Glen,

The Q.18 is a mistake, it's awful, but they got that wrong. You are, of course, right that shares need to be shorted in that case
(search "General Motors" for prior discussion threads)

Your summary looks PERFECT to me.

In case it helps, can i point you to my ProTip here (orange at top) @ https://forum.bionicturtle.com/threads/l1-t4-7-dynamic-delta-hedging.4839/

it may just perfect your understanding to distinguish between POSITION Greek and PERCENTAGE GREEK; e.g.,
For example, to sell (short) puts then looks like:
- quantity * -percentage delta = + position delta

This is robust, and lets you keep straight, for example, that percentage gamma is always positive but position gamma is negative if we short call/puts b/c: -qty * +gamma = - position gamma

Hope the vocab reinforces what you've already go there, thanks, David

 

[crablegs]

Thank you very much. I feel relieved. This rocked my world for a second. Will definitely make use of the ProTip!