Date: Sun, 21 Nov 2004 21:41:48 CST
From: Rich Carreiro
Newsgroups: misc.invest.financial-plan
Subject: Re: Where to look data for asset allocation
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Karen Younge writes:
> What I would like to know is, how/where to find out the correlation
> between various sorts of investments.
How is actually procedurally simple:
1) Find annual total return series for all the asset classes in question.
2) Compute the mean and standard deviation of each series.
3) Regress each series against every other one to find the
correlations between all pairs of assets.
Once you have the data, (2) and (3) can be done by a decent spreadsheet.
Of course, since many of the entities that generate such returns
data like to sell it to financial institutions, getting the data
(for free, anyways) might be a bit tricky :-)
You may well have better luck trying to find tables of average
returns of asset classes and correlations between asset classes.
I don't know where you've looked, but be it online or in
dead-tree locations, consider looking more at places geared
at advisors, financial institutions, and academia.
Also, I believe there are even places that sell poor man's MVOs (with
a more limited set of asset classes and probably not as much returns
history as the very expensive stuff sold to the big boys). But if you
plan to go the MVO route, I recommend you crack a stats book and
understand the mathematical underpinning of MVO (it's actually not
that hard to understand the basics). I'm a firm believer in
understanding what a tool does before using the tool.
> investments? How does one take multiple kinds of investments into
> account when looking at correlations?
You pull out a computer and have it do the dirty work :-)
For example, the second simplest portfolio there can be -- just
two assets -- results in the following:
* Return of the portfolio = f*Ra + (1 - f)*Rb
* Std dev of the return = sqrt[f^2 * Sa^2 + (1-f)^2 * Sb^2 + 2*f*(1-f)*Sa*Sb*C]
[where Ra, Rb are the average total returns of assets A and B
where Sa, Sb are the standard deviations of the returns of A and B
where C is the correlation between the returns of A and B
where f is the fraction of the portfolio invested in A
and therefore (1-f) is the fraction invested in B]
Now imagine a portfolio with 10 assets in it....
> tween (for example) gold bouillon and a portfolio with 50% in a stock
> index fund and 50% in medium term Treasury bonds?
You can compute that from the correlation between gold and the index
fund and the correlation between gold and the bonds.
> Also, I need to know how to calculate the overall return for a portfolio
> from the expected returns of its various components.
Return is easy enough -- it's just the weighted average of the returns
of the assets in the portfolio.
But it is standard deviations of portfolio returns and correlations
between portfolios that gets complicated (and hard to do without a
computer).
> Also, I intend to use "socially responsible" funds for most if not
> all my stock based investments (I might buy a few individual stocks,
> or maybe not). It seems to me that SRI funds might have a different
> correlation value than an index fund that invests in about the same
> size companies and with the same objectives, because the SRI fund
> will include less of some kinds of stocks (e.g. tobacco, nuclear
> power, or weapons) but more of other kinds (e.g. alternative
> energy). Wouldn't this cause the SRI fund to have at least a
> somewhat different correlation with other investments than an
> equivalent non-SRI fund?
While I'm not sure what's so "socially irresponsible" about companies
who manufacture products vitally important to the survival of our
society, such as weapons, and those would will vastly reduce
greenhouse gases if widely accepted, such as nuclear power, yes,
excluding them will change the numbers. My guess, though, is not it
won't change them by much and you could just use the asset class's
numbers in your decisions. If you're concerned, you could compare the
annual total return numbers (year-by-year, not just multi-year average
numbers) of an SR fund with those of an index fund in the same asset
class (you don't want to compare just to the index itself, since the
published indexes are price-only indexes, not total-return indexes).
By comparing the annual total return series of the SR fund to the
index fund, you can compute the correlation of the SR fund to the
index. If the SR fund highly correlates to the index fund, then you
can just use the index's numbers in calculations. If not, you'll have
to roll your own correlation numbers.
> I am trying to figure out about what sort of rate of return I can
> generate on the house proceeds, in order to figure out how much
> other income I will need up til whenever I am able to shed jobs
> altogether.
Well, you can make some reasonable guesses without having to go
through any of this. For example, given that 10-year T-bonds are
running around 4.2%, you can be guaranteed of doing no worse than a
4.2% return (assuming you're not forced into selling before the bonds
mature!). On the high side, you wouldn't be wise to count on anything
over 10% (8% is probably more realistic). So if you can't get your
plan to work with an 8-10% return, there's not too much point in doing
all the grindy stuff, since the grindy stuff isn't going to give you
anything that significantly beats that. But if you discover that you
only need a 6.5% return to make things work, then you can use the
grindy stuff to see (a) what's the least risk you can get that 6.5%
with and (b) what asset class combinations are needed to implement
the plan.
--
Rich Carreiro rlcarr@animato.arlington.ma.us
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