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Correlations
Old 04-04-2007, 11:55 AM   #1
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Correlations

So, I've been going through my investments, reading investment books, thinking about slicing and dicing vs total market, etc. Being a little bored this morning I decided to put the last few years returns into a spreadsheet to see how the asset class correlations work out. Using the Excel CORREL() function, I get the following correlations (calculated on the yearly returns) between the S&P500 and the following assets:

2000 - 2006 (sorted)
===========
VTRIX (VG Intl val): 0.979
VGTSX (VG Intl): 0.961
NAESX (VG Small): 0.951
VWELX (VG Wellington): 0.905
VGSIX (VG Reit): 0.821
Dogs of the Dow: 0.813
DODBX (DC balanced): 0.790
VISVX (VG Small val): 0.782


Looking at just more recent data:
2002-2006 (also sorted)
=========
VGTSX: 0.999
VTRIX: 0.997
VWELX: 0.997
DODBX: 0.976
NAESX: 0.972
VISVX: 0.972
VGSIX: 0.901
Dogs: 0.820


From this data, asset allocation using the common slicing and dicing methods appears to be a waste of time.

I'm thinking this means the financial markets have become very efficient and it's easy for a person like me to buy into all these assets. Money flows easily around and around.

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Re: Correlations
Old 04-04-2007, 12:09 PM   #2
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Re: Correlations

http://etf.seekingalpha.com/article/24018 did something similar and its results show less correlation for int'l.

Note their "Beware the Black Box" section -- perhaps this happened with your results?
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Re: Correlations
Old 04-04-2007, 12:13 PM   #3
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Re: Correlations

Even though correlation coefficients of 0.8 - 0.9 can appear to be high, there can still be significant tracking error between the two portfolios. The tracking error (standard deviation of the return difference) for two portfolios is calculated from:

tracking error = S x ( 1 - R^2 ) ^ 0.5

where S = the portfolio volatility and R is the correlation coefficient

If R=0.9 and S = 15% (annual)

tracking error = 15 x ( 1 - 0.81)^0.5 = 15 x 0.44 = 6.5%

This means that there is about a 1/3 probability that the return difference between the two portfolios will be greater than 6.5% over a year.
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Re: Correlations
Old 04-04-2007, 12:30 PM   #4
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Re: Correlations

Quote:
Originally Posted by fluffy
http://etf.seekingalpha.com/article/24018 did something similar and its results show less correlation for int'l.

Note their "Beware the Black Box" section -- perhaps this happened with your results?
I just used yearly returns and a somewhat different time period. Maybe that's the source of the difference. Or, since I used only yearly data, maybe this is one of those errors when calculating the statistics from a small sample size.

For yearly returns I just used the yearly data from Morningstar in their total returns page.
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Re: Correlations
Old 04-04-2007, 12:57 PM   #5
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Re: Correlations

Quote:
Originally Posted by FIRE'd@51
Even though correlation coefficients of 0.8 - 0.9 can appear to be high, there can still be significant tracking error between the two portfolios.
Thanks!

Another thing I just noticed. 2003 was a big year for all of the indexes. Removing that year from the calculation reduces the correlations by a large amount. For example: DODBX goes from 0.79 to 0.62.
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Re: Correlations
Old 04-04-2007, 02:16 PM   #6
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Re: Correlations

5yrs is too small a period esp when you do yearly returns. Not enough data points. You might want to do monthly returns atleast. Also the last few yrs have been lights out for almost all asset classes. Everything went up a lot. And there haven't been any big negative events in specific asset classes. Extend it to 10+ yrs and you might start noticing stuff.

Also there is not rule which says the correlations should stay where they are right now

-h
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