delta-gamma neutral

Discussion in 'Options' started by mynd66, Mar 25, 2009.

  1. mynd66


    I was just reading how this works and I still don't see where the catch is. Of course there is no strategy, un-managed, that will generate continuous profits without the relative risk.

    You buy 100 calls of xyz SK25. Gamma= 0.1
    Long Call has a gamma of 1000

    You sell 125 calls of xyz SK30. Gamma= -0.08
    Short call has a gamma of -1000

    Gamma Neutral

    Long 100 calls of xyz SK25 who's delta is 0.6. Delta =6000
    Short 125 calls of xyz SK30 who's delta is -0.4 Delta =-5000

    Position delta thus far= 1000
    So now you short 1000 shares of xyz bringing the position to Delta Neutral.

    Theta on the long calls is -.01
    Theta on the short calls is .02

    Net theta= 150
    Position generates $150/day

    I am having trouble determining the hypothetical captial required based on margin requirements but relative to similar examples it would seem you would need in the areas of 30K to implement this trade.
    Using 30K will generate a 2.5% gain/5days.

    Now... factoring in commissions the only thing left to worry about is IV(?). What is the magnitude and likelyness of a change in IV that will compromise this position? How would you hedge vega and would it be rational?

    Finally, because there must always be a buyer for every seller, why would anyone take the other side of this trade?

    I hope I made sense.
  2. dmo


    What's missing in your example is, well, an actual example - a real world example of a position where you are neutral gamma but long theta.

    Generally speaking, if all your options have the same expiration, and you are neutral gamma, you will be neutral theta and vega too.

    Of course, gamma neutrality in options is a very temporary phenomenon, and can change the moment the underlying moves or IV changes. Even if nothing moves, time will pass - which affects gamma neutrality as well.

    So maintaining a position gamma neutral becomes more and more difficult as expiration approaches, and eventually (with ten days or so remaining until expiration) becomes impossible.

    The more time remaining, the more "stable" option gammas are (the less they change with a change in the underlying), so the easier it is to maintain a gamma neutral position.

    So if you could find a position with significant time remaining where you are gamma and vega neutral (and of course delta neutral) - but long vegas - you would indeed have a cash machine. But I doubt if you can show me an example.
  3. mynd66


    Yes it is contradictory as I couldn't be gamma neutral yet long gamma at the same time... which would justify why taking the other side of this trade may be the perfect set up for a particular outlook.

    If everything was neutralized the only thing that is 100% is commission. lol
  4. How much profit is generated when the stock is 45?
  5. heech


    Quite a bit:

    So now you short 1000 shares of xyz bringing the position to Delta Neutral.

    The real challenge of this strategy, as earlier poster mentioned, is maintaining gamma neutrality as you get closer to expiration. (Assuming price is close to the strike.)
  6. Reread Natenberg. Thank me later.

    FWIW, you are definitely on the right track. Miles ahead of 99%.
  7. Come on, you should give other options traders a bit more credit than that --or at least a bit more of them. ;-) How many options traders are there? I mean traders that are not using options as an equivalent to the underlying for leverage. I would think this group would represent a bigger proportion than you are implying ...but then again, out of that group, how many of them trade wisely or make money? I can't argue against that percentage well can I? :cool:
  8. mynd66


    Is this a trick question or did I screw up? If the stock climbs to 45 within a relatively short period of time and if IV doesn't change change I would have to say zero.

    But I guess (granted my math is right) that if the stock goes to 45 in a short period of time IV might not be the same because that might be considered volatile in which would essentially be the risk associated with this strategy.

    I don't know but would be interested in how they calculate IV. As a matter of fact I'm going to google it now.

  9. First, I think you have to consider the financing of the whole portfolio (interests earned/paid on the purchase/sale of shares/options).
    Then, the negative skewness of the daily price change distribution implies the existence of a volatility skew. For instance, XYZ 6-month 75% put IV > XYZ 6-month 100% call IV.
    As a result, your neutral-gamma long-skew strategy means negative theta (no free lunch).
    Your strategy is mainly dependent on the volatility skew (the skew changes according to IVs i.e. offers/demands).

    Last, other risks to consider:
    Positive gamma when the underlying is close to the lower strike, negative gamma when the underlying is close to the higher strike.
    There might be second-order convexities due to change of spot/change of IV (negative convexity if you have to sell additional shares lower).
    Short options might be exercised.

    One last thought about the classical neutral-delta neutral-gamma positive-theta strategy: conversion (long underlying contract short synthetic position), beware of the dividend risk.
  10. 1) You sold stock all the way up - to remain neutral. That doesn't help.

    2) If you sold no stock,

    the 100 longs are worth 20 each; +20,000

    the 125 shorts are 15 each; -18750

    the stock is up about 20 points; -20,000

    Please tell me how that = "quite a bit" of profit?????

    #10     Mar 25, 2009