If you take the historical serie of stock market returns I posted
above, the lowest 20-yr return period was 1929-1948 (the period that
covers the Great Depression), and it was an average return of 5.63
percent. For periods that do not cover the Great Depression years -it
is highly unlikely that such a market crash would be repeated ever
again- the lowest 20-year return was 7.74% during 1969-1978.

This means that one can safely plan a withdrawal of about 6% without
endangering to run out of money. Besides, if you own other assets like
a house, you can always put a reverse mortgage on it and get extra
money from your home.

By the way, if you do the same exercise -calculate the average 20-yr
return- with a portfolio of microcap deep value stocks, the lowest
yield was 18.2 percent per year (1955-1974), which is about the same as
as the HIGHEST 20-yr period yield of the stock market as a whole.
- quote -

Jose Bailen wrote:

- quote -

Jose - I think we're agreeing here. But again, randomly picking any
interval is meaningless. What Bill (woessner) posted first was the
observation that 1987-2006 could sustain a 7+%/yr drawdown. I ran those
years myself and found a starting withdrawal, and 3%/yr adder not only
survives 8.8%, but leaves principal at a inflation adjusted equal level,
i.e. $1M still leaves $1.8M after the 20 years.

As I look at the dividend adjusted S&P returns for the period, I first
have to note that 87 was a great year to sleep through. The return was
5.8% for the year. For a statistician working with year end data, 87 was
nothing. From 88-99 there was one negative year of -3.1%, but those 12
years averaged 19.7%, and rising withdrawals even starting at 8% can
survive such a period.

I then go to the 60's-70's, because that's hoe far back my data set
went, 1962-1981, those 20 years averaged 8.06%, but were sprinkled with
bad years. That period's starting drawdown, again with an eye toward a
break-even endpoint, is 3.4%. 4.75% will break even, but unadjusted for
inflation, lastly, 6.55% initial draw will run the account to zero after
20 years. This is a stark contrast to Bill's 87-2006.

I think the question come down to this: is it better to underestimate
the withdrawal number and find yourself with too much money at
retirement, or overestimate, and when that day comes, realize you may
need to work 5 years longer than you planned?

I am recalling Elizabeth's point that the flow isn't smooth, that Social
security may kick in for her then the spouse. That's fine, because it's
foreseeable and part of the planning. I plan to retire early enough to
be motivated to ignore SS, so if it's there, it's a bonus. While many
will have those income streams that start (SS, pension, inheritance,
etc) or stop (mortgage, paying for college, alimony), I'd think that
there's still that key number of first year withdrawal. Isn't that what
"The Number" by Lee Eisenberg is all about?
JOE

- quote -

The right way to find historical averages is to take a period as long
enough as to have good and bad years (i.e., bull and bear market
periods). On average, stocks yield about 7 percent in real terms over
long periods (see Siegel). The standard deviation of these returns (the
most commonly accepted measure of risk) is about 20.

On the other hand, if you take the smallest cap stocks and those with
the lowest price-to-book value, you may get as much as an average
return of 34.6 percent during 1927-2005, with a standard deviation of
57.1; i.e, returns that are 3 times higher but also volatility 3 times
higher (the 2006 portfolio with these micro cap/deep value
characteristics is composed by 261 stocks with an average market
capitalization of $86 million and an average P/B of 0.72). These data
are derived from the publicly available historical database maintained
by Ken French. They are summarized in another google forum -Small
Microcap Value-.

Jose Bailen wrote:
- quote -

I didn't nessasarily mean it as 'hugely good', but as 'not common'.
87-2000 averaged over 16%, and only the 11% or so post 3-year crash. I
suppose since every period is unique, my use of the word may be
meaningless, but my point remains, choosing one period is not a viable
method to back test.
JOE

"joetaxpayer" <joetaxpayer[at]nospam.com> wrote
- quote -

Despite my concerns about too much impractical mathematical
minutiae coming out of such exercises, one important point
that I think can be gleaned from them is the effect of
reinvesting dividends. It's a point guru Jeremy Siegel
really drives home in his books. Skip W. often makes it
here, too, though in a roundabout way, as he emphasizes
buying, holding and reinvesting steadily via mutual funds
and their distributions in one's retirement portfolio. Same
for Tad, though he's more explicit, as well as others.
Steadily reinvesting ensures buying a heckuva lot of stock
shares at low prices when times are bad. Particularly since
dividend distributions tend to rise over time, quite apart
from increases in the number of stock or mutual fund shares.
Steadily (1) buying low while (2) dividends keep rising has
a staggering, compounding effect on savings accumulation.

Though of course I think most of us agree here that thee
most successful savers are the ones who regularly invest a
portion of their paycheck and live within their means.

- quote -

Aside: Shiller somehow extrapolated back to 1871 for his S&P
500 data. I do not know if it is meaningful to go back
/that/ far. Just saying.

woessner[at]gmail.com wrote:

<snip
- quote -

Doing a simulation with the historical time series of monthly returns
illustrates how a withdrawal strategy will perform if history repeats
itself exactly. I think it's more realistic to "bootstrap". If you have
have a set of N monthly returns, sample with replacement from this set
by
(1) generating random integers between 1 and N and
(2) using the random integer to select the return from the set.

This amounts to assuming that the DISTRIBUTION of future returns will
be the same as the historical distribution and that successive returns
are independent. If you think that future returns will be lower than
past returns by X, you can subtract X from each historical observation.

By bootstrapping one can generate many synthetic data sets and estimate
the probability that an (initial X% of capital + inflation) rule will
work for M years.

- quote -

There is nothing extraordinary to the 1987-2006 average returns of
stocks or the S&P 500.
The average return of stocks during 1928-2006 has been 11.77 percent
per year, versus 3.9 percent for T-bills and 5.2% for T-bonds
(downloadable data available here:
http://pages.stern.nyu.edu/~adamodar.../histretSP.xls)

Elle wrote:

- quote -

I copied data from;
http://pages.stern.nyu.edu/~adamodar...ile/spearn.htm

Elle's further remarks about accuracy are right-on. The link I provided
offers annual dividend data along with S&P index values. Make any
assumption you wish, but to keep the math easy (to my own way of viewing
this) I:
Treat the S&P as the dollar price of a stock, and start with X number of
shares.
In year 1, I begin with some amount of cash, therefore the annual S&P
delta applies 100% to 'shares' I am tracking.
I add the dividend at year end by adding to the 'shares', and have a
variable for expenses.
You can then make any assumptions you wish, pre-tax such as 401(k) will
tax at withdrawal, post tax accounts have the 15% tax on the dividend, etc.

My 'shares' method lets you view the distinction between the S&P index
growth vs the reinvested dividends. You can see (if you write the sheet
this way) that we are back to break even from before the crash (S&P
1500) due to dividends. The data I link to also goes back to 1960, so
you get to see impact of a number of ten and twenty year periods.

Later.

JOE
JoeTaxpayer.com

<woessner[at]gmail.com> wrote
- quote -

No, you're not. I see your point. The Shiller database is
probably best by far for this effort. Though, guys, IMO the
sort of "accuracy" you are pursuing is not very practical,
and so it's not really accurate in a meaningful sense. It is
a good exercise for newbies, of course, introducing a
multitude of financial planning concepts, from how stocks
beat inflation; how one can live off income from stocks
(both dividends and by cashing in principal periodically);
historical behavior of economies; etc. It's also a good
exercise for the math-obsessed, something that serves
engineers well in college, then one gets to real engineering
post-college and largely post-academia, and realizes so much
of accomplishing things is based on guesstimating, with a
mind for margins of error. Otherwise, numerology will taunt
and tease the unversed, and compel them to say things with
little-to-no-or-possibly-negative value in actual financial
planning. At least, from where I am sitting.

joetaxpayer wrote:
- quote -

Point taken. I'll try to redo this with the data Elle suggested. The
availability of data is the only reason I restricted myself to this
period.

- quote -

Mathematically, it's the same as inflating the withdrawal. You either
keep everything in constant (in this case, 1987) dollars or inflate
everything with time. I found it a lot simpler to keep everything in
constant dollars. I could reproduce the spreadsheet with inflating
dollars, but the results would be the same.

- quote -

You're absoultely correct. In fact, the simulation is unrealistic,
because it uses (nearly) daily dollar cost averaging. The driving
factor here was laziness. The data set I used provided daily data
points and I didn't bother to decimate the data. The data set Elle
suggested provides monthly data points.

Elle wrote:
- quote -

I looked at this. I rejected it because it doesn't include dividends.
Maybe I'm missing something?

Thank you both for your input.

--Bill

"joetaxpayer" <joetaxpayer[at]nospam.com> wrote
- quote -

Indeed, this is what leapt out at me. I know Bill is pretty
sharp, so I figure this was a bit of a post-on on his part.
Or perhaps he figured the correction c. 2000-2001 (and that
in October 1987?) made this realistic enough to ponder.

Bill, for S&P 500 data going way back, see Robert Shiller's
downloadable data set at
http://aida.econ.yale.edu/~shiller/data/ie_data.htm . It
also has info on dividend yield and inflation (see the CPI
data). I downloaded this on a spreadsheet a few years ago I
guess and refer to it often. Like Joe, my heart beats nearly
through my chest every time I use the Shiller spreadsheet
for an analysis.

One may also put in the symbol ^GSPC and extract S&P 500
data from Finance.Yahoo's historical site back to 1969.

- quote -

You sentimental financial advising fool you. I love it.
;-)

Little aside: I continue to think the costs of health care
throw such a wrench into things that "rules of thumb" like
the 4% drawdown rate should be assigned a "high" margin of
error indeed. Of course, the Kennedy-Shriver-Schwarzenegger
coalition may be succesful sooner rather than later. Which
means maybe I should ponder my taxes going up lots, rather
than my health care costs. But don't touch my Roth IRA,
Arnold!

woessner[at]gmail.com wrote:

- quote -

I pulled the sheet, here are my remarks;
The 20 years 87-07 were extraordinary. S&P rising from 242 to 1400. This
is 9.2% without reinvested dividends, over 11% with. This in a unique
period which contained 2 crashes. One can still debate that the nature
of the 90's run-up may never be repeated. The point that Elle continues
to make, which isn't lost on me, is that analyzing past data is one
element of planning, but assumptions that are based on a continuation of
that data going into the future is likely to fail. A number of studies
suggest that we are at a point where future returns are likely to lower
than past averages, I've seen 6-8% as the 15-20 year forecast.

I am real sorry here. How do you account for inflation? It appears you
de-flated the mutual fund price instead of increasing withdrawals. That
seems wrong. At best, it obfuscates the impact of inflation, and the
true way we look at it. John never suggests a burger will continue to be
$2.00, but his $2 million dollar portfolio will deflate to $500K. It's
the cost of the burger that rises.

Lastly, I have great respect for a good spreadsheet. The best can bring
a tear to my eye. I don't get the advantage of a 20 year spreadsheet
with daily withdrawals. A point can be proven with one line per year. If
the difference between success and failure is the missed compounding by
having the years' expenses taken to cash in advance, well, maybe things
were running a bit tight. In the end, you are correct, that time period
could survive the withdrawal rate. Monte Carlo would tell you what would
be if 2000-02 happened to occur prior to the 90's.

In the end, a 7% drawdown requires $570K for the first year to generate
$40K as compared to the $1M I use (for 4% withdrawal). What ever
strategy one uses at final retirement, I'd prefer to err on the side of
caution. The misses believes that whatever number I figure, the Gods
will conspire to crash the market the day we quit work. Therefore, I
need 50% more than I even suggest. How's that for conservative?
JOE

OK, so all the recent talk about draw down rates made me run this,
myself. Here's what I did:

1) I started with Vanguard's S&P 500 index fund. I got the data from
Yahoo. I like Yahoo's data because it includes the adjustment for
dividends and capital gains. Unfortunately, Yahoo's data only goes
back to 1987. I know the fund goes back to 1976. Does anyone know
where to get price data with dividend adjusments going back to 1976?

2) I took the closing prices from the data and adjusted them for
inflation. The inflation rate is variable, but I used 3.01%. I got
that number from the Bureau of Labor Statistics. Of course, this
assumes constant inflation, which isn't realistic. But I think it's a
reasonable approximation.

3) For every trading day, I compute the number of days since the
previous trading day. I multiply that by the daily draw down, which is
based on the annual draw down rate and the initial account balance.
The daily draw down is kept constant through the whole scenario.

4) After subtracting the draw down, I update the account balance based
on the closing price of the fund.

By monitoring the account minimum and end balance, I determined it the
maximum drawdown it could sustain over the period 1987-present is 7.22%
(after inflation). At that rate, the account had approximately the
same value at the end as at the beginning and the account was never
negative.

Then I decided to run the account dry. I upped the draw down rate to
9.61%. This left me with a ending balace of essentially $0.
Interestingly, the volatility in the fund was not a limiting factor in
this scenario. That is to say, even though I drove the ending balance
to $0, the account was never negative. Toward the end, when the
account is running dry, I think that's just due to luck. But the fact
that the account never runs negative at all says something about the
volatility of the S&P 500 (or lack thereof).

Anyway, if anyone would like to play with this, I've made it available
at:

http://woessner.dyndns.org:8080/~bill/vfinx.xls

Please feel free to comment.

--Bill