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Index constituent weightings and implied volatilities
- Thread starter Grant
- Start date
segv , what do you mean by arbitrage ? A true arbitrage is not exists in dispersion , unless its full replication AND index IV is > than basket weighed IV ( which will never happens !). I offered ones to find a guarantee losing scenario ( on end of the month bases) in any dispersion position.
Quote from IV_Trader:
segv , what do you mean by arbitrage ? A true arbitrage is not exists in dispersion , unless its full replication AND index IV is > than basket weighed IV ( which will never happens !). I offered ones to find a guarantee losing scenario ( on end of the month bases) in any dispersion position.
I merely meant that the index arbitragers I know are not completely replicating the index.
-segv
This paper is excellent. I have read it before and it is good to read it again. I just wish the part on proxy hedging was as clear as the prior parts. I too am more visual than mathematical.Quote from segv:The methodology depends on the objectives. If you want spread risk, hedging, or simply index tracking you can use a cointegration approach to create a best-fit synthetic instrument. If you want correlation risk, you can use a weighted-sum approach using correlations. Based on your initial post, I think that you want the correlation risk. If thats true, see this dispersion trading guide for a quick tutorial: http://www.nuclearphynance.com/User...ueless 1.1.pdf#search="dispersion fdaxhunter"
My readings on cointegration have given me the understanding that it is used primarily for longer term applications, while the correlation calculation (faulty as it is) is usually done shorter term. Is this different in your experience?
I'll have to work up a little example of the "weighted sum approach" and see if it is the same as what you are familiar with, or perhaps Profitaker has one handy?
Obviously very few of here can do full index replications. My purpose in mentioning that as a first look was to simply find out what the bias of the spread has been. Of course the money and the risk is in the proxy selection, and this has not yet been talked about here.
It's not that I necessarily want correlation risk -- it just has come with the territory of dispersion. The cointegration alternative you mention (no correlation risk?) is intriguing and I wish you would say more about it. I'm not sure what you mean by a "best-fit synthetic instrument", but anything you can add on this alternative would be welcome.
Quote from mysticman:
My readings on cointegration have given me the understanding that it is used primarily for longer term applications, while the correlation calculation (faulty as it is) is usually done shorter term. Is this different in your experience?
While correlation measures the short term interdependence between two variables, cointegration attempts to measure the long run equilibrium or common trends. If a is correlated with b, then a tends to increase as b increases. If a is cointegrated with b, then some linear combination of a and b is stationary. Two variables that are correlated are not necessarily cointegrated. See this http://www.gummy-stuff.org/cointegration.htm and this http://www.ismacentre.rdg.ac.uk/nav2/pdfrequest/profcarolalexander/downloads/conf_sem/Rome1b.pdf
for more details.
So, we have two different measures, and two different risks. I said that correlation measures short term interdependence and cointegration measures long run equilibrium, but what is short or long term? The number of samples and the length of time are both important in cointegration models. It can be one second or one day data, but either way one needs a lot of it to detect cointegration with high confidence. One needs much less data to be convinced of correlation, but a lot of data is necessary to avoid small-sample bias (and other perils).
From the preceding explanation, I hope it is clear that a lot of data is always needed, but that neither methodology is restricted to a specific sample interval (1 minute, 10 days, 100 years, etc). Also, there is nothing inherently faulty about correlation as a measure, but correlation is not always a particularly good measure for the data in question.
The cointegration alternative you mention (no correlation risk?) is intriguing and I wish you would say more about it. I'm not sure what you mean by a "best-fit synthetic instrument", but anything you can add on this alternative would be welcome.
There is an abundance of research and published information. The two books below are good starting points:
Books:
Pairs Trading, Ganapathy Vidyamurthy
Applied Quantitative Methods for Trading and Investment, Christian L. Dunis (Editor), Jason Laws (Editor), Patrick Naïm (Editor)
Papers:
A Computational Methodology for Modelling the Dynamics of Statistical Arbitrage, Andrew Neil Burgess 1999 Phd thesis
The Cointegration Alpha: Enhanced Index Tracking and Long-Short Equity Market Neutral Strategies, ISMA Discussion Papers in Finance 2002
Testing Market Efficiency using Statistical Arbitrage with Applications to Momentum and Value Strategies S. Hogana, R. Jarrowb, M. Teoc*, M. Warachkad 2003
Statistical Arbitrage and Securities Prices, Oleg Bondarenko University of Illinois at Chicago
Inference And Arbitrage: The Impact Of Statistical Arbitrage On Stock Prices, Tobias Adrian MIT
High Frequency Pairs Trading with U.S. Treasury Securities: Risks and Rewards for Hedge Funds, Purnendu Nath London Business School 2003
Cointegration and Asset Allocation: A New Active Hedge fund Strategy, Carol Alexander 2001
Unit Roots, Cointegration, and Structural Change by G. S. Maddala, In-Moo Kim
New Directions in Econometric Practice: General to Specific Modelling, Cointegration, and Vector Autoregression by Wojciech W. Charemza, Derek F. Deadman
Using Cointegration Analysis in Econometric Modelling by Richard I. D. Harris
Cointegration, Causality and Forecasting: Festschrift in Honour of Clive W. J. Granger by Robert F. Engle (Editor), Halbert White (Editor)
Discrete and Continuous Systems, Cointegration and Chaos by Omar F. Hamouda (Editor), J. C. Rowley (Editor)
Essays in Econometrics: Casualty, Integration and Cointegration, and Long Memory, Vol. 2 by Eric Ghysels (Editor), Mark W. Watson (Editor)
Non-Stationary Time Series Analysis and Cointegration by Colin P. Hargreaves (Editor)
Practical Issues in Cointegration Analysis by Leslie Oxley (Editor), Michael McAleer (Editor)
Time Series, Unit Roots, and Cointegration by Phoebus Dhrymes
Workbook on Cointegration by Peter Reinhard Hansen, Soren Johansen
Recent Developments in Nonlinear Cointegration with Applications to Macroeconomics and Finance by Gilles Dufrenot, Valerie Mignon
Structural Changes in the Cointegrated Vector Autoregressive Model, P.R.Hansen, 2000
That should keep you busy for a while.
-segv
Given the above homework list, I suppose the thread will end now until sometime next year when somebody has read all that. The last paper is nowhere to be found, so why don't you post the pdf?
On the other hand, suppose one has mastered the use of cointegration and is able to create a basket that has a stationary tracking error. What could you do with that, hypothetically speaking?
On the other hand, suppose one has mastered the use of cointegration and is able to create a basket that has a stationary tracking error. What could you do with that, hypothetically speaking?
Quote from IV_Trader:
segv , are you actually trading dispersion (any) ? If yes , do you put position every month ?
does anyone trade dispersion profitably between constituents and an index? and if so how big do you have to go to make a decent profit? I assumed desks ended up in a dispersion trade as a sort of hedge.