Greg Hennessy wrote:

- quote -

Using Shiller's data it's a little over 2% per year. But given my
recent track record, you better check my math.

-Will

In article <42AB67F0.8060709[at]paragondynamics.com> ,
Will Trice <wwtrice[at]paragondynamics.com> wrote:
- quote -

Do you have any idea of the inflation rate for that time?

beliavsky[at]aol.com wrote:

- quote -

You're correct, I bungled the reinvestment of dividends (I forgot to
grow the amount of dividend received with the result of the dividend
reinvestment). This also puts the geometric average since 1932 at
12.5%. I'll just be quiet now and let you grown-ups carry on your
conversation... Thanks again, B.

- quote -

No.

- quote -

Yes, for Pete's sake, don't use the DJIA. It is a mathematically and
statistically meaningless index. It is also very difficult to calculate
dividends properly into the calculation, so it is likely that you did
not calculate them the same way.

- quote -

Go to the library and find the book Ibbotson Stocks, Bonds, Bills, and
Inflation. Almost all financial articles quote from this reference
book. It uses the S&P 500 (and equivalent) indexes. Their data starts
from 1926.

Annual total returns for large cap stocks:

1926-1999 11.35%
1926-2002 10.20%
1926-2004 10.43%
1930-2004 9.98%

Since many of the articles that we read were around 1999, the annual
return rate was over 11% at that time. After the bust, it dipped to as
low as 10.20% in 2002. Another reason was that in 1926-1928, there was
a big boom, so if you start counting in 1930, that lowers the
historical rate as well.

Will Trice wrote:
- quote -

I get a considerably higher number for the compound annual returns over
the period 1871 to 6/2004. I compute monthly log returns including
dividends using

monthly_log_return = log(new_price + annual_dividend/12)/old_price

Then, the compound annual return is

exp(12*mean_monthly_log_return) - 1

= exp(12*0.007277) - 1

= 9.12%

The "variance drain" due to fluctuating returns is 0.5*volatility^2,
which for annualized volatility of 15% (an approximate number) works
out to about 1.1%. The annual differential should be considerably less
than the you are getting.

beliavsky[at]aol.com wrote:

- quote -

You're right, using Shiller's spreadsheet, the average annual return for
the period 1871 - 2004, including dividends, is 10.7%, which nicely
matches the things I've read. Going back to the Yahoo DJIA data I
noticed that the "Adjusted Close" column, which is supposed to include
dividends, is identical to the "Close" column, so it must not be
adjusted. That was the problem with my calculations (thanks, B). But...

Just for fun, I looked at the annualized return for the entire period on
Shiller's spreasheet, reinvesting dividends. The annualized return is
only 5.7%! This is astounding that the geometric average would be so
much less than the arithmetic average. I know that in the presence of
volatility the arithmetic average is going to be higher than the
geometric, but this is a BIG difference. Using data from 1932 on (since
the Crash bottom) gives an annualized return of 8.8%, which is better,
but not close to 11%. This leads to the question, how did Shiller come
up with his benchmark data prior to WWII? The actual S&P benchmark
didn't start until after WWII, right? If this data is accurate, and if
future stock price increases will be something like the past, I think
many investors are going to be overestimating their returns, even if the
returns do average ~11%. Yikes!

So another question, why isn't the geometric average annual return used
more often for forecasting the price growth of an asset rather than the
arithmetic average? After all, it seems that the geometric average
builds in volatility which the arithmetic average does not.

-Will

Will Trice wrote:
- quote -

Will,
The 10%-11% figures you've seen reflect not only dividends but also
reinvestment of dividends - did you include that? With the high dividend
rates that were present during much of that time period, there's a lot
of additional money in the system...representing additional shares that
both gained in value and earned additional dividends.

-Tad

"Will Trice" <wwtrice[at]paragondynamics.com> wrote in message
news:42AA72E6.9030003[at]paragondynamics.com...

Further, the *maximum* 30 year average
- quote -

I'd always heard 10.8% for the last 30 years, very close to what you've
found in your research. I've only heard 11% on this newsgroup and that looks
to be rounding up, probably for simplicity's sake.

Elizabeth Richardson

Will Trice wrote:
- quote -

<snip
- quote -

Robert Shiller makes available at
http://www.irrationalexuberance.com/ie_data.xls a useful spreadsheet
with monthly data on stocks, bonds, and inflation, including the S&P
500 price level and dividend level. Using his data, I find that the
average MONTHLY total return on stocks from 1927 to 2004 is about
0.93%, using the formula

monthly_total_return = (new_price + annual_dividend/12)/old_price - 1

Annualizing the 0.93% monthly return gives an annual return close to
11%.

While reading anoop's thread, "understanding risk," I took the data
behind his chart (DJIA) and played with it in a spreadsheet. He
mentioned that the average annual return for stocks is 11%, a number
I've heard myself. But playing with the spreadsheet, I'm not seeing
that average. Looking at the data, using monthly closes and including
dividends, it seems that the average annual return for the period of
1930 through 2004 is only 7.4%. Further, the *maximum* 30 year average
annual return is 10.4% (for the period of 1970 - 2000), still short
(barely) of the often quoted 11%. Maybe this is an artifact of the
DJIA, but checking the Wilshire 5000 reveals similar results.

So is the 11% number an urban legend? Or am I just looking for answers
in the wrong places? What time period (and benchmark) is it necessary
to look over to reveal an average 11% return?

-Will