Medium correlation coefficient for a Portfolio

Hello,

In an Excel workbook I reported 10 time series of 10 titles that should cover the past 15 years. After i calculated the returns and the statistics (mean, std. dev, var, etc.) I'd like to calculate the medium correlation coefficient of the portfolio. I don't mean the correlation matrix, but a single number for the entire portfolio.

Is that possible?

Thanks.

[Oleg Komarov]

Yes, it is. Are you referring to http://www.jstor.org/stable/2328653?

[Fabrizio Marinelli]

Yes, exactly! Matlab has any function that allows the calculation of that coefficient?

[Oleg Komarov]

Well, but it's just the average of the lower diagonal correlation coefficient matrix.

With 10 time series, there is not much computational effort spent on calculating the correlation coefficient matrix first.

[Fabrizio Marinelli]

So, let's say that the time series is about 5 titles; correlation coefficient matrix is, for example:

1,0  0,7  0,1  0,0  0,1
0,7  1,0  0,3  0,0  0,3
0,1  0,3  1,0  0,6  0,6
0,0  0,0  0,6  1,0  0,5
0,1  0,3  0,6  0,5  1,0

The average correlation coefficient is just [(0.7 + 0.1 + 0.3 + 0.0 + 0.0 + 0.6 + 0.1 + 0.3 + 0.6 + 0.5)/10]?

[Shashank Prasanna]

Do you have the formula for the medium correlation coefficient? I can't find anything online.

[Oleg Komarov]

Sorry, not the lower diagonal but the average of all off-diagonal elements. Thus you need to multiple your calculation by 2 since the matrix is symmetric:

(0.7 + 0.1 + 0.3 + 0.0 + 0.0 + 0.6 + 0.1 + 0.3 + 0.6 + 0.5)/5

@Benji: I posted a link in first comment.

[Fabrizio Marinelli]

Ok ok i understand, thank you!

[Shashank Prasanna]

Thank Oleg, I thought it was for purchase only, appears there is free online view.