From: "jIM" 
Newsgroups: misc.invest.financial-plan
Subject: Re: Options for fixed payouts
Date: Wed, 20 Sep 2006 13:05:59 -0500
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> > "the volatility
> > of stocks decreases more rapidly than the volatility of
> > either bonds or T-bills. For holding periods longer than 20
> > years, a fully diversified stock portfolio is on average
> > less volatile than either a bond portfolio or a T-bill
> > portfolio... [T]his is even more true when the results are
> > adjusted for inflation."
> >
> These two sources seem to disagree.  The first has some major typos and
> shows no data: "If for example the anticipated rate of return for a
> portfolio is 10% per year (0.85% per month) with a standard deviation of
> 2.71 the reality is that the rate of return will be somewhere between
> 3.56% and -1.86% per month two-thirds of the time, and between 6.27% and
> -4.57% per month one-third of the time. There is a one-in-six chance
> that the monthly return will be below -1.86%."

Forgive me, it's been more than 15 years since I took statistics... I
believe the above analagy and the two posts which follow are comparing
Oranges to the performance of the Buffalo Bills...

"anticpated return of a portfolio is 10%" OK so far...
"standard deviation of 2.71" OK so far... my understanding would be
2.71 is the number of units (percentage points in this case) which the
10% will change 75% of the time (so 75% of the time the returns are
between 7.29 and 12.71%).  The 75% if the bell curve type deal...
 .85% per month- why use this number?- it is 10%/12 months, but the
assumption that all months have an "equal return" or "equal
contribution to return" is a little much.
"the reality is that the rate of return will be somewhere between
3.56% and -1.86% per month two-thirds of the time, and between 6.27%
and
-4.57% per month one-third of the time. There is a one-in-six chance
that the monthly return will be below -1.86%"- this is just BAD MATH.
If the .85 % per month is used, the standard deviation of 2.71 would
also needed to be divided by 12 (for deviation per month) correct?

I am an Engineer by degree, so any business types with a larger
knowledge than me can pick this apart (and feel free to show me the
error of my ways), but to me the error appears in how one determines
the deviation and to which numbers the deviation applies to.

The reason bonds have a higher "long term" volatility than stocks is
that returns will be confined in most probability to between 3-8% per
year for bonds.  Just guessing at these for what I would expect if I
invested in bonds.  However the change in returns would be "higher
percentages" of the overall return.  1 basis point difference for a
bond returning 8% is 12.5 (1%/8%=12.5%).  One basis point for a stock
returning 20% is a much less percentage of the overall return (5%,
1%/20%=5%).  CD's have an even more restricted return (probably between
0-5%), so a 1% change in return for a CD is an even higher volatility
than for bonds or stocks.

The primary goal of investing is probably overall return.  Volatility
is something used to measure the principal value of the portfolio
changing from year to year and is often used to measure risk of the
principle.

The goal of adding bonds is to reduce volatilty of the portfolio, even
if the bond returns in and of themselves are more "volatile".  Same
with CDs.  They are used primarily to keep the principal value of a
portfolio "relatively constant".