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..?
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Index constituent weightings and implied volatilities
- Thread starter Grant
- Start date
Quote from rosy2:
i am referring to principal component analyis. eigen values/vectors can be obtained from a covarince/correlatin matrix of your basket constituent returns. they tell you which stocks in your basket move more/less with the whole.
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
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.
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.
âHow do you derive the 19.12% figure?â
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 thatâs 49 values and for a 100 stock index it becomes 4950 values !
I canât 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 âthat hereinafter will be referred to as the main formula.â
âHow is the "implied index correlation (IIC)" determined (please use my examples)?â
Index Vol
IIC= -----------------
(Weight x Vol) + (Weight x Vol)
For formulae when correlations are other than +1, zero, or -1 see above paper.
âRe 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%?â
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 youâre 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 youâre going to trade. In any event, you need up-to-date Vol info, although it wonât change significantly by 10 minutes or so, real-time Vol data isnât really necessary.
I've always thought, if you see an arbitrage opportunity, ignore it because it doesn't exist
I agree itâs 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, itâs 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.
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 thatâs 49 values and for a 100 stock index it becomes 4950 values !
I canât 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 âthat hereinafter will be referred to as the main formula.â
âHow is the "implied index correlation (IIC)" determined (please use my examples)?â
Index Vol
IIC= -----------------
(Weight x Vol) + (Weight x Vol)
For formulae when correlations are other than +1, zero, or -1 see above paper.
âRe 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%?â
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 youâre 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 youâre going to trade. In any event, you need up-to-date Vol info, although it wonât change significantly by 10 minutes or so, real-time Vol data isnât really necessary.
I've always thought, if you see an arbitrage opportunity, ignore it because it doesn't exist
I agree itâs 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, itâs 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.
We have discussed this last year in the EGAR thread. Didn't know you were doing work in this area.Quote from ElectricSavant:Excuse me for butting in, but I work in this field for my personal trading and find these discussions few and far between.
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?Quote from ElectricSavant:I have found correlations to be ranges representing deviations measured numerically..
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?Quote from ElectricSavant: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..?
We are still in two dimensions are we not? So how does this improve on the correlation between each stock and the index?Quote from rosy2:
i am referring to principal component analyis. eigen values/vectors can be obtained from a covarince/correlatin matrix of your basket constituent returns. they tell you which stocks in your basket move more/less with the whole.
What is the synthetic asset? The weight of each stock is given and does not need to be determined.Quote from segv:
One might also consider cointegration techniques as an alternative for determining the constituent weights of the synthetic asset.
Quote from mysticman:
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.
it doesn't improve correlation. it does allow for a better weighting in your basket
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?Quote from rosy2:it doesn't improve correlation. it does allow for a better weighting in your basket