rudi

Capitalization Coupling: Major Indices at Correlation Highs

As you asked me for some links to studies of copulas:

www3.interscience.wile...

This here is about what is called tail-dependency (stock crash
together but in positive return times, they are less correlated
(indexes as well).

db.riskwaters.com/publ...
This is interesting as well but german.

www.imw.tuwien.ac.at/f...
This is an introduction to the topic, stating that conjunct negative
returns are more likely than conjunct positive returns. Also german,
sorry.

papers.ssrn.com/sol3/p...
This is a good study about copulas, but not within stocks, although interesting.

Googeling "tail-dependency" seems promising if you want to find more

Nevertheless: All this stuff is based on Embrechts (1999)
Embrechts P., McNeil A. and D. Straumann (1999), Correlation: Pitfalls
and alternatives, RISK

Link: www.ma.hw.ac.uk/~mcneil/ftp/risk.pdf !!


To d_teller:

This seems an interesting idea, as a non-parametric approach may deal
with the problem of non-normality of return distributions.
Have you had any success with that or any of the links to the studies?


In spite of that I have to repeat, that no approach is worth spending
time on, as long as it does not generate cash!

For this purpose, one should always lag the independent variables AND
split the sample in a test-sample and validation-sample.
Fit your model with lagged variables and apply it to the unused data
of the validation sample. It is only worth money if you find some
relation in the validation sample.
Keep in mind, that you bias the study if you use knowledge from the
validation-sample to alter your model. Best is to keep a (third) final
validation-sample until you are really sure with your model.

Michael, have you tried adding more variables and maybe
interaction terms to your model? E.g. include the lagged returns in
interaction with the correlation. I also would use a smaller time
frame than 100 days to calculate the correlation, to have a more
sensitive variable.


As an impetus: To generate cash, you could spend time to build models
that predict future correlations. One could use that to better
minimize the portfoliorisk and therefore absorb a higher lever. There
you get your free lunch. GARCH Models and Kalman filters are suitable for this purpose.

best regards
Rudi

Capitalization Coupling: Major Indices at Correlation Highs

Michael,

I replicated a part of your study. I selected DIA/IWM since it has the highest volatility and correlation. I used the past 100 days to calculate the correlations. In another replication of your study, I also used weekly data und based the correlations on the past 20 weeks.
On both occassions, there wasn't any significant relationship.
If there would have been one, I would have done the following (and suggest you try that for the set of data where you indeed found something): Lag the correlation-variable (differentiated) and do a regression analysis with the differences in returns.(Thus regarding the temporal structure.) Btw: A regression is not the best way in this case. A VECM would be a better choice, but it means a lot of work. Then try it vice versa. Lag the variable containing the returns and regress it on the future period of correlation. This may work. It should be even more significant if you shorten the period, to calculate the correlation. (Like 30 days e.g.)

Your R² statistics are random. You did not post any p-values and the negative (-1%) number for daily-based analysis suggests, that you are not able to reject the null-hypothesis. R² also increases with a shrinking N, so your increasing percentages cannot form the basis of any serious argument.

Capitalization Coupling: Major Indices at Correlation Highs

"In other words, as the correlation between indexes fell, the markets rose on average."
This is more likely to be explained by a higher correlation when markets crash. Your interpretation does not bear in mind the temporal causality, the interpretation should be the opposite, it is therefore worse than tassology.
The increasing correlation has been well established in conjunction with copulas.
en.wikipedia.org/wiki/...