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Correlation Part II
Old 03-01-2011, 05:30 PM   #1
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Correlation Part II

I have been involved in several discussions on the potential benefits of low correlation investments in an aggregate portfolio. I believe I can do all the calcs except one, and have displayed my work in other threads. Anyone know how to calculate weighted correlation for a portfolio? All I can do is correlation between all investments and average correlation - which represents a portfolio with equal % of each investment. Much obliged if one of you wizards can help, haven't gotten there with Google yet...
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Old 03-01-2011, 05:52 PM   #2
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here's a little tutorial that explains (among other things) weighted correlation:

Portfolio Characteristics
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Old 03-01-2011, 06:12 PM   #3
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All the required mathematics can be found here: Variance - Wikipedia.

Basically, the variance of the sum of N random variables is the sum of the N x N covariances. Note that Cov(X,Y) = Cov(Y,X), so that not all N x N covariances are unique (the covariance matrix is symmetric and positive semidefinite).

Before we carry this kind of work out too far, we need to be sure that the subject random variables have stationary statistical properties. Do we know that the correlation between assets stay constant with time, or even if their variances are time invariant?
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Old 03-01-2011, 06:25 PM   #4
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Before we carry this kind of work out too far, we need to be sure that the subject random variables have stationary statistical properties. Do we know that the correlation between assets stay constant with time, or even if their variances are time invariant?
That's the model, that past is prologue. And from past asset correlation values, one could (feasibly) construct an optimum portfolio going forward. This is but one of those variations on Modern Portfolio theory.

Whether it's true or not remains to be seen. personally, I would throw in a healthy dose of skepticism.

Your mileage may vary.
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Old 03-01-2011, 06:47 PM   #5
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I have been involved in several discussions on the potential benefits of low correlation investments in an aggregate portfolio. I believe I can do all the calcs except one, and have displayed my work in other threads. Anyone know how to calculate weighted correlation for a portfolio? All I can do is correlation between all investments and average correlation - which represents a portfolio with equal % of each investment. Much obliged if one of you wizards can help, haven't gotten there with Google yet...
Other than an interesting discussion, does all this statisical mumbo-jumbo have anything to do with FIRE? It certainly isn't needed to build a FI enabling portfolio. And RE is just something you want to do and therefore do it. Where does all this calculating and statistics play into it?

It's a great thread, an interesting read. But it's just a theoretical discussion, right?
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Old 03-01-2011, 07:02 PM   #6
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Some people think that there is some determinable portfolio which optimises the risk-reward continuum.

If nothing else, it gives you something to talk about at cocktail parties. When you tell em' all about how you constructed your portfolio (whilst swirling a glass of white wine), the birds will sing, men will envy you, and women will want to have you.
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Old 03-01-2011, 08:51 PM   #7
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Some people think that there is some determinable portfolio which optimises the risk-reward continuum.

If nothing else, it gives you something to talk about at cocktail parties. When you tell em' all about how you constructed your portfolio (whilst swirling a glass of white wine), the birds will sing, men will envy you, and women will want to have you.
That sounds good. I doubt that the last outcome will occur, however. They may find the subject boring.
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Old 03-01-2011, 08:54 PM   #8
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and women will want to have you.
Yes; they will want to have you committed.

Ha
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Old 03-02-2011, 12:51 AM   #9
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Before we carry this kind of work out too far, we need to be sure that the subject random variables have stationary statistical properties. Do we know that the correlation between assets stay constant with time, or even if their variances are time invariant?
No, in fact we know that the correlation between asset classes changes over time. I think about all one can say is that asset class A and asset class B have over time tended to have high, or low, correlation.

And of course, in a bad bear market, all correlation values approach 1 (i.e. everything tanks at the same time).
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Old 03-02-2011, 07:35 AM   #10
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If nothing else, it gives you something to talk about at cocktail parties. When you tell em' all about how you constructed your portfolio (whilst swirling a glass of white wine), the birds will sing, men will envy you, and women will want to have you.
Good luck with that MB.
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Old 03-02-2011, 08:53 AM   #11
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Other than an interesting discussion, does all this statisical mumbo-jumbo have anything to do with FIRE? It certainly isn't needed to build a FI enabling portfolio. And RE is just something you want to do and therefore do it. Where does all this calculating and statistics play into it?

It's a great thread, an interesting read. But it's just a theoretical discussion, right?
You might read this http://www.indexuniverse.com/publica...-round-ii.html and decide for yourself. This author explains why he thinks it's useful during accumulation, but even more important during distribution, so there is a FIRE connection. There are other discussions on this topic as well, just check Google.

I don't believe it's a be all, end all - but I think it's well worth being aware. We just had a member on this forum express concern that all his holdings were moving together (too highly correlated?), correlation may be a good insight. I also think it's more useful in selecting holdings for your portfolio, and not something that needs to be tracked ongoing if at all. YMMV

As with all investing discussions, what works is what lets you sleep at night...
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Old 03-02-2011, 09:28 AM   #12
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Although it is not the pure number you are looking for, it is directly reflected in the aggregate portfolio standard deviation. But portfolio SD has as additional factors the individual asset SDs. This is one use of a mean-variance portfolio optimizer. I posted a demo optimizer in another thread that could be used to examine this specifically.
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Old 03-02-2011, 03:16 PM   #13
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You might read this The Benefits Of Low Correlation: Round II - JOI Articles and decide for yourself. This author explains why he thinks it's useful during accumulation, but even more important during distribution, so there is a FIRE connection. There are other discussions on this topic as well, just check Google.

I don't believe it's a be all, end all - but I think it's well worth being aware. We just had a member on this forum express concern that all his holdings were moving together (too highly correlated?), correlation may be a good insight. I also think it's more useful in selecting holdings for your portfolio, and not something that needs to be tracked ongoing if at all. YMMV

As with all investing discussions, what works is what lets you sleep at night...
I agree; this is one of my favorite papers. In particular the author discusses diversification's impact on portfolio recovery, which most would consider vital for FIRE.
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Old 03-02-2011, 06:18 PM   #14
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You might read this The Benefits Of Low Correlation: Round II - JOI Articles and decide for yourself. This author explains why he thinks it's useful during accumulation, but even more important during distribution, so there is a FIRE connection. There are other discussions on this topic as well, just check Google.
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I agree; this is one of my favorite papers. In particular the author discusses diversification's impact on portfolio recovery, which most would consider vital for FIRE.
+1. I do not currently have any commodity indexes or REITS in my portfolio. I have been relying on my second house as a real estate holding. But the more I think of it I believe my "regular" portfolio should be more broadly diversified to reduce the volatility pertaining to the SWR I want to pull from it. Other assets could be liquidated in a crunch but why not smooth out the primary returns from the portfolio.

With that in mind what do folks around here think are the best vehicles at Vanguard and Fidelity to cover commodities and REITs?
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Old 03-02-2011, 07:20 PM   #15
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+1. I do not currently have any commodity indexes or REITS in my portfolio. I have been relying on my second house as a real estate holding. But the more I think of it I believe my "regular" portfolio should be more broadly diversified to reduce the volatility pertaining to the SWR I want to pull from it. Other assets could be liquidated in a crunch but why not smooth out the primary returns from the portfolio.

With that in mind what do folks around here think are the best vehicles at Vanguard and Fidelity to cover commodities and REITs?
We're still in the accumulation phase, and also have no exposure to commodities or REITs in my 401k because they are not offered. Our taxable investment account is at Vanguard and includes the Vanguard REIT Index Fund (I know, it's not tax efficient). As a pseudo (i.e. not very good) proxy for commodities, we also have a small position in Vanguard Precious Metals and Mining.

There have been several discussions on this board regarding commodities, and many do not believe that there is an efficient ways to invest in them. However, I think the consensus is that if you do invest in them, then ETFs are the way to go. Unfortunately for us, I don’t think investing in ETFs is very cost effective because of the transaction fees incurred with regular periodic investing.
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Old 03-02-2011, 11:43 PM   #16
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+1. I do not currently have any commodity indexes or REITS in my portfolio. I have been relying on my second house as a real estate holding. But the more I think of it I believe my "regular" portfolio should be more broadly diversified to reduce the volatility pertaining to the SWR I want to pull from it. Other assets could be liquidated in a crunch but why not smooth out the primary returns from the portfolio.

With that in mind what do folks around here think are the best vehicles at Vanguard and Fidelity to cover commodities and REITs?
If you happen to hold a small cap value fund, you may already have a position in REITs. That sort of overlap and potential for overexposure (beyond your asset allocation plan) is something to look out for in adding sector specific funds.
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Old 03-03-2011, 12:15 AM   #17
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+1. I do not currently have any commodity indexes or REITS in my portfolio. I have been relying on my second house as a real estate holding. But the more I think of it I believe my "regular" portfolio should be more broadly diversified to reduce the volatility pertaining to the SWR I want to pull from it. Other assets could be liquidated in a crunch but why not smooth out the primary returns from the portfolio.

With that in mind what do folks around here think are the best vehicles at Vanguard and Fidelity to cover commodities and REITs?
If you happen to hold a small cap value fund, you may already have a position in REITs. That sort of overlap and potential for overexposure (beyond your asset allocation plan) is something to look out for in adding sector specific funds.
However, if you do decide you want to buy a mutual fund specifically for REITS, Vanguard has one called VGSIX. I don't know the Fidelity funds. They may have one too.
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Old 03-03-2011, 03:07 AM   #18
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I also think it's more useful in selecting holdings for your portfolio, and not something that needs to be tracked ongoing if at all.
I'm a strong proponent of diversification. I understand correlation and measures of variability. I just haven't found detailed calculations of those parameters within and between the categories of my portfolio to be all that useful. It seems to result in measuring with a micrometer and cutting with an axe, at least for me.

Are you actually doing detailed correlation and variability calculations and fine tuning your portfolio to correspond? Or just looking for broad trends and nudging portfolio composition gently from time to time? I'm in the later camp.
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Old 03-03-2011, 03:19 AM   #19
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With that in mind what do folks around here think are the best vehicles at Vanguard and Fidelity to cover commodities and REITs?
Regarding REITs, about two yrs ago I was investing DW's rollover IRA funds and when I got to REITs I couldn't decide between ICF and VNG, so I bought her equal dollar amounts of both. Both are set up for automatic reinvestment of dividends. Two yrs later, they've both done very well and are still equal in value. So I guess I could have bought either and had similar results.
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Old 03-03-2011, 05:32 PM   #20
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With that in mind what do folks around here think are the best vehicles at Vanguard and Fidelity to cover commodities and REITs?
No recommendation to anyone, but I have VGSIX for REIT's and VGENX (energy, not broad commodities, but energy is a no-brainer to me - the world is hopelessly addicted for the near future IMO) at about 3% and 4% respectively of my overall AA. And I'd be comfortable with more VGENX, but REIT's are not as timely these days IMO (and evidently Dr. Bernstein recently agreed) so I'll probably stand pat there.
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