Index constituent weightings and implied volatilities

Discussion in 'Options' started by Grant, Aug 26, 2006.

  1. Can any of you look at "a day of trading" in the S&P 500 and re-weight more accuratly based on a sector strength analysis..?
     
    #21     Aug 26, 2006
  2. segv

    segv

    For the interested reader, there is a nice tutorial on PCA here:

    http://csnet.otago.ac.nz/cosc453/st...nts.pdf#search="principal component analysis"

    One might also consider cointegration techniques as an alternative for determining the constituent weights of the synthetic asset.

    -segv
     
    #22     Aug 26, 2006
  3. Grant

    Grant

    Rosy2 and segv,

    To the uninitiated, eigen vectors and conitergration are meaningless without context. They may well be the path to eternal beauty and fortune but do I need to start from scratch through to post-graduate level maths to find out? What about a few examples?

    (I will read the ref to PCA, though.)

    And what are we doing here on a Saturady night? Sad.

    Grant.
     
    #23     Aug 26, 2006
  4. ”How do you derive the 19.12% figure?”

    For correlation between components stocks of +1, zero, and -1 the portfolio (index) volatility calculation is straight forward;

    Correlation +1 = (Weight x Vol) + (Weight x Vol)
    Correlation 0 = Square Root of ((Weight x Vol)Squared)) + ((Weight x Vol)Squared))
    Correlation -1 = (Weight x Vol) - (Weight x Vol)

    For other correlation values the calculation is much more complex and involves a correlation matrix with values between each and every stock. For a 10 stock index that’s 49 values and for a 100 stock index it becomes 4950 values !

    I can’t write the formula here, so have a read of this paper;

    http://www.egartech.com/research_dispersion_trading.asp

    The index volatility formula can be found where they say “that hereinafter will be referred to as the main formula.”

    ”How is the "implied index correlation (IIC)" determined (please use my examples)?”


    Index Vol
    IIC= -----------------
    (Weight x Vol) + (Weight x Vol)

    For formulae when correlations are other than +1, zero, or -1 see above paper.

    ”Re your FTSE IIC of 0.44, does this mean that for a 1% change in the IV of the constituents, the FTSE IV will change + 0.44%?”

    No. It means that, given the component weights and volatilities, for the index volatility to be X% then the component average correlation must be 0.44.

    if no option is traded, then extrapolation becomes increasingly problematic(al?).

    True. But in the case of the FTSE100, the total weight of stocks without options is just 6.55%, and I suggest therefore fairly insignificant. I use an arbitrary 20% vol for these stocks. If you’re really keen you could always input the statistical Vol.

    But to actually nail the IV's of the sum of the constituents and index at the point of execution may be a nightmare

    It depends how big how big a basket you’re going to trade. In any event, you need up-to-date Vol info, although it won’t change significantly by 10 minutes or so, real-time Vol data isn’t really necessary.

    I've always thought, if you see an arbitrage opportunity, ignore it because it doesn't exist

    I agree it’s unlikely, but you can find near riskless trades (IIC near zero or +1).

    Do you use any software.

    I know my way around Excel and have some VBA knowledge, it’s all I need.

    Are you in the UK (where)? I'm in a sleepy fishing village called Manchester.

    10 miles north of Brighton.

    Good luck.
     
    #24     Aug 27, 2006
  5. Grant

    Grant

    I really appreciate what you've done, here and the amount of work involved.

    I've kept the previous replies. These will form the basis for further research. I'll keep you informed

    Thank you, once again.

    Grant.
     
    #25     Aug 27, 2006
  6. We have discussed this last year in the EGAR thread. Didn't know you were doing work in this area.
    Last year we determined that dispersion trading can be done on the Dow for example with an account of modest size (within the reach of most traders).

    Could you explain exactly what you mean by that? Yes correlations have ranges, but how to ranges represent deviations?

    Again this question is somewhat obscure but enticing.On any given day certain sectors would be stronger than others. But you can't trade sectors unless you are thinking of going to ETFs, and actually that would be the only practical way you as an individual could do dispersion on the SP500. So can you explain what you meant here?
     
    #26     Aug 27, 2006
  7. We are still in two dimensions are we not? So how does this improve on the correlation between each stock and the index?

    What is the synthetic asset? The weight of each stock is given and does not need to be determined.
     
    #27     Aug 28, 2006
  8. Grant

    Grant

    Works in practise, let's see if it works in theory.

    Why keep things simple, when they can be complicated. Maybe some are trying to justify their salaries.

    Grant.
     
    #28     Aug 28, 2006
  9. rosy2

    rosy2

    it doesn't improve correlation. it does allow for a better weighting in your basket
     
    #29     Aug 28, 2006
  10. Wouldn't it be great if we could change the weighting in the basket to whatever we wanted it to be? But you don't seem to get the point. The weights in the basket are given. They are fixed. They cannot be changed willy nilly by traders. For our purposes they cannot be "better", and they cannot be worse. They are not synthetic. Do you understand?
     
    #30     Aug 28, 2006