Book review / Correlation analysis / Matlab, page-5

Ok so getting this thread started...

This book is obviously about stock market crashes.

An interesting point that this book makes (pages 41 - 45) is that;
1) Information leads to randomness
2) A lack of information leads to regularities

I sense the value in this is that genuine market trends driven by real information are by nature random;
- New, tangible information is immediately priced in
- Future price returns have no correlation to past returns.

The author provides some insightful examples on page 41.

It had me thinking that a useful tool might be to avoid situations where returns are correlated as this might signal "flocking" by investors who are creating trends out of no real information.

In terms of finding returns that are correlated, the author has an example on page 36;
- Link to page 36

What the graph on that page shows is that;
- After about 2 minutes, information is priced in
- After 2 minutes you can not use past information (on this particular day anyway) to predict future returns

Interestingly the author makes the point that the reason why there is a 2 minute correlation window is because the brokerage costs exceed the available gain that could be obtained by this correlation. Therefore markets with low brokerage costs will be more efficient.

The math behind this graph seems to come from this journal article;
The sharp peak-flat trough pattern

in particular;





So this is where I've gotten up to with this part of the book and I've been too lazy to do that Math.

The formula in yellow seems similar to the formula the author has on page 37.

It seems the method to create the graph on page 36 of the book is to;
- Download price data (say 5min interval) and calculate the return between each period
X = Price returns
- C = The correlation matrix X*X' (assuming 0 mean return)
- Find the inverse of this correlation matrix = C^-1
- Sum and multiply each (i,t) element by the return at i, summing from 0 to t-1
- Divide each sum by C^-1(t,t)
- By collection the result from each sum (0 to t-1) should produce a graph similar to page 36

Anyone else have any input as to whether I have the math here right?

My intention is to then apply this on a daily, monthly scale etc and see what happens.