Question about deltahedging

TskTsk · Feb 28, 2012

Upon a rehedge, you in essence lock in a profit or loss, so if you determine your gamma/delta PnL by the formula 1/2gamma*S^2, you lock in this profit if you rehedge. Is it then safe to assume that if you rehedge your deltas by 70%, you lock in 70% of the PnL that 1/2gamma*S^2 would give you? It seems that way but I'm asking just in case, as I've been caught by surprise by these things before.

PS: By 70% I mean if you got 100 long deltas, you sell 70 shares and in essence rehedge 70% of the deltas.

TskTsk · Feb 28, 2012

Anyone?

Martinghoul · Feb 29, 2012

TskTsk · Feb 29, 2012

Alright thanks

babutime · Feb 29, 2012

Quote from TskTsk:

Alright thanks

What I've learnt here is to ask questions that are simple to understand.

Answers might be complex, but the questions definitely have to be simple...

TskTsk · Feb 29, 2012

Quote from babutime:

What I've learnt here is to ask questions that are simple to understand.

Answers might be complex, but the questions definitely have to be simple...

Not sure what you're getting at...anyways no worries my question was answered by Martinghoul

babutime · Feb 29, 2012

Quote from TskTsk:

Not sure what you're getting at...anyways no worries my question was answered by Martinghoul

I got the feeling that maybe you wanted a more elaborate answer... that was all...

TskTsk · Mar 2, 2012

Quote from Martinghoul:

Yes

Actually on further thought, are you sure this is the case? Remember the formula 0.5*G*S^2 is not linear in nature.

Let's look at an example:
If I have 200 gammas and spot moves 1, I've made 0.5*gamma*1^2 = $100 and my deltas are now +200. If I now rehedge my deltas from 200 to 100, I've hedged 50% of my deltas and have thus made 50% of $100, which is $50.

However this is not the case. Consider that after the rehedge I'm 100 deltas long. My gammas are still 200. Thus the spot price in which I'm delta neutral would be 100/200 = 0.5. If we now use the PnL formula, we get the following result: 0.5*200*0.5^2 = $25. So if I now rehedged the remaining of my deltas, I would make $25, in addition to the $50 I made previously. Total PnL is $75. However had I rehedged everything at once, I would've made $100. So something is off. Maybe it's my calculations...wouldn't be the first time.

Martinghoul · Mar 2, 2012

Quote from TskTsk:
Actually on further thought, are you sure this is the case? Remember the formula 0.5*G*S^2 is not linear in nature.

My gammas are still 200.

I am normally not sure of anything... However, there's one thing that I am relatively sure of: gamma doesn't remain the same after the underlying moves.

I don't really understand the argument you're making. Just do the actual arithmetic and see if you disaagree.

babutime · Mar 2, 2012

Quote from TskTsk:

Actually on further thought, are you sure this is the case? Remember the formula 0.5*G*S^2 is not linear in nature.

Let's look at an example:
If I have 200 gammas and spot moves 1, I've made 0.5*gamma*1^2 = $100 and my deltas are now +200. If I now rehedge my deltas from 200 to 100, I've hedged 50% of my deltas and have thus made 50% of $100, which is $50.

However this is not the case. Consider that after the rehedge I'm 100 deltas long. My gammas are still 200. Thus the spot price in which I'm delta neutral would be 100/200 = 0.5. If we now use the PnL formula, we get the following result: 0.5*200*0.5^2 = $25. So if I now rehedged the remaining of my deltas, I would make $25, in addition to the $50 I made previously. Total PnL is $75. However had I rehedged everything at once, I would've made $100. So something is off. Maybe it's my calculations...wouldn't be the first time.

Isn't the formula for delta and gamma PnL:

$d*(dS/S) + G*[(S^2)*(ds/S)^2]/2

where d is delta

ds/S is stock return

G is gamma

?

That's what I thought...