Which position is the most risky

[qin841121]

a) Gamma negative Delta positive
b) Gamma negative Delta negative
c) Gamma positive Delta negative
d) Gamma positive Delta positive

OA is a). I don't understand.

 

[David Harper CFA FRM]

Provocative question, can I ask the source? I'll be interested in Alek's reaction. FYI, GARP would never phrase an (new, recent) FRM question this imprecisely. My view is:

• positive gamma is always less risky (exclude c and d)
• however, cannot assert that delta positive or negative is less risky (answer either a or b); e.g., i don't like it when "position Greek" isn't used b/c percentage (per option) gamma is always +, but position gamma is negative for the short, but: both long call and short put are position delta positive, while short call and long put are position delta negative. I don't see a basis for suggesting that long call/short put is riskier than short call/long put, as all have M2M value risk?
• Intention could be: (a) implied by short put (-gamma, +delta) and (b) be implied by short call (- gamma, -delta) and .... hmm... actually, that doesn't lead to (a), you might argue that leads to (b) due to unlimited exposure of short call ... yea, actually, that doesn't work ... i don't even understand the intention of (a)

 

[qin841121]

I saw this randomly on a china tuition provider website. They list the source as 2001 FRM real question.

May I know why positive gamma is less risky? Is it because gamma is similar to convexity?

 

[David Harper CFA FRM]

oh, what a great source thanks for availing us of such a precious resource as a random question from a random chinese site, which i am sure they stole from some un-named source i am delighted you value our time so highly

yea, gamma is like convexity: the curvature mutes the loss in value to the long call or long put option holder (percentage gamma is always positive such that positive position gamma implies long option position). thanks,

 

[qin841121]

I stumbled onto this question while I was searching for answers to other questions to the official mock exam. I was unable to do it and I thought this may be a good question to discuss. I apologize if I have offended you

 

[David Harper CFA FRM]

can you please source any future questions you post (just say where they came from, to help us -- with even a minor citation, it might help prevent myself or somebody else from engaging time into a hopeless question. If you had noted "pulled this randomly from the internet" I would know better than to engage with it, although it is still a provocative question!). plus it has the ancillary benefit of not enlisting us into copyright violation (a lot of those sites, for a fact, are just stealing content anyway ... i mean no ethnic bias but, it's just an empirical reality that a disproportionate share of the copyright violation emanates from the Asian sites). Thanks for your understanding,

 

[qin841121]

Noted.