Sensible Withdrawals or go with the flow ...

When people talk about Safe Withdrawal Rates
(see Bylo's
list)
they usually assume certain Rules like
 rebalancing your portfolio at fixed intervals (annually, for example)
 maintaining some
fixed allocation of assets (like 80% stocks + 20% bonds, for example)
 withdrawing a certain percentage of your portfolio each year (like 5%, for example)
 increasing withdrawal amounts with inflation (at 3%, perhaps)
Then they check to see whether your portfolio will survive for umpteen years (like 30 years,
for example) and ...
>Get to the point!
Okay. I submit that this is cyberfiction and real people don't do that. If, after a few
years of withdrawing at some safe rate (say 4%) your portfolio has grown from $1M to $6M, do you
continue to withdraw at 4%? Also, if there's a severe market downturn, do you continue at 4%?
Or, suppose you only withdraw 1% in a given year. Can you then withdraw 7% the following year
(so the average is 4%)? Also, if you withdraw nothing in a given year (because you won the
lottery or postponed your retirement), then do you still withdraw that magic 4%, because
it ignores the size of your portfolio (which may be larger  or smaller  next year)? Also,
shouldn't your variable financial needs be considered, so that ...
>Get to the point!
Okay. I'd like to consider a different scenario where we decide upon some
Minimum annual withdrawal rate ... just enough to pay the
bills (and live on bread and water) ...then only withdraw beyond that if the market is good
to us.
>Which means?
I'm suggesting that after we've withdrawn, say 3% for example (to pay the bills), we check to see if our
portfolio has increased since a year ago (even after withdrawing that 3%) and,
if it has increased by at least the inflation rate, we withdraw some more ...
>For that new car?
Or a holiday in the Bahamas. Of course, we forgo any of these pleasures after a
bad year.
>How much more do we withdraw, after a good year?
Oh, I don't know. Maybe 25% of the extra monies.
>Extra monies?
Yes, we withdraw our 3%, then see how much is left in our portfolio. If the resultant
portfolio has increased (compared to a year ago) by at least the inflation rate  that's
the extras  then we withdraw an additional fraction of these extras.
>But that means you're withdrawing MORE after a good year. Isn't that dangerous?
Because the market may very well tank the next year? But after a BAD year, would you want to withdraw any extras?
Maybe your philosophy should: Don't withdraw extras after a BAD or after a GOOD year.
I don't think that's a good idea. If your portfolio took off, then your current withdrawal rate is low, so that's when
you should consider withdrawing more.
>In your opinion.
Yes. In my opinion.
>I assume there's a spreadsheet ...
Uh ... I'm working on it. It looks something like this, where (for example) we maintain a
sliceanddice
portfolio and withdraw 4% to pay the bills
and withdraw 10% of the extras after a good year, to a maximum of $50K:
>What if I have to pay taxes on annual gains, huh?
Uh ... there's a place where you can stick in some tax percentage and any positive annual return will be reduced by this percentage.
>So what's that "Best" button?
If you're willing to wait for it, the spreadsheet will run through a bunch of allocations and pick the Best.
If you want to play with the spreadsheet, Rightclick on this picture and
"Save Target" or "Save Link". In addition to Large and Small Cap Growth and Value
data, from 1928, it also has T bills, 5year treasuries, Gov. Long Bonds, S&P 500 and Total
Stock Market ... and you can choose any four as well as the range of years as well as ...
>But, in Monte Carlo, doesn't one normally assume a fixed Standard Deviation and Mean Return and ...
Yes, and some kind of Return Distribution, Normal or Lognormal, which stays fixed for the next
umpteen years. Let's, instead, use actual annual returns.
>What's that MRW stuff?
I'll explain in Part II.
>So you like this Monte Carlo stuff, eh?
It's great fun ... but don't take it seriously. It's an easy way to see what effect certain
parameters have on portfolio evolution. It's one of many toys that Financial Planners have
at their disposal. Used with discretion, it can be helpful in getting a feel for what might
happen, in the future, if we did this or that.
>Okay, but what are those "Average Annual Extras" ... in Today's Dollars?
Actually they're the extra annual withdrawals, over and above the 4% (in the above example),
averaged over a thousand
Monte Carlo
portfolio simulations. However, an "extra" $10K
forty years from now may sound
good, but at 4% inflation it'd be equivalent to about $2K, today, so the
spreadsheet gives the equivalent amount in "Today's Dollars" ... for example $2K
instead of the $10K.
>And that skinny red curve? The one without the dots?
That's the Average Portfolio value, averaged over a thousand Monte Carlo simulations.
>It's huge!
Yes. In fact, at each year (for the situation illustrated in the spreadsheet, above),
we can estimate a Maximum Annual Income which would reduce this
"Average Portfolio" to the specified Minimum Final Portfolio over the remaining years.
That, too, is huge ... like so:
>Mmm, those extras are lookin' good ...
Bahamas, anybuddy?
>There's Explain sheets. What do they look like?
Like
this and
this and
this and
this.


>Do you have a name for this kind of
Monte Carlo Simulation?
I mean, everybuddy's talking about MCS these days so ...
I call it DMC which stands for ...
>Dynamic Monte Carlo?
You got it.
Now here's something interesting.
Suppose we have a $1,000,000 portfolio and ...
>A million bucks! Holy ...
Pay attention. We'll withdraw 4% every year (that's 4% x $1,000,000 = $40,000), increasing
each year by, say, 4% due to inflation. So what's the value of this
$40K withdrawal, after
forty years ... expressed in today's dollars?
>Huh?
In today's dollars, it's always worth $40K.
Although it increases by 4% every year,
its buying power is always just $40K.
>Okay. In today's dollars we're withdrawing
$40K. Now what?
Now we run this through our spreadsheet and find that in 92% of the thousand Monte Carlo
simulations our portfolio will survive for forty years. Ah, but now we ...
>Wait! Don't tell me! We reduce the 4% and grab some of those "extras".
Aah, how clever. In fact we reduce the withdrawal rate to 3% but withdraw 50% of the excess
gains, over and above the 4% inflation. As it turns out, there's still a 92% survival rate, over
the thousand Monte Carlo simulations.
>So what have we gained? Nothing!
>If reducing the fixed percentage is better, then what about ...?
Here's some pretty pictures:
2% withdrawal and 100% of 'extras' 
1% withdrawal and 200% of 'extras' 
>I was thinking Hawaii, maybe Maui. What about you?
You're supposed to ask what the percentage withdrawals actually are, with these 'extras' and ...
>I was just thinking ... what are the actual ...?
Here's some more pretty pictures:
2% withdrawal and 100% of 'extras' 
1% withdrawal and 200% of 'extras' 
Note: The percentages are average total withdrawal as a percentage of the
Average Portfolio value.
>In the spreadsheet you pick a year at random and use the annual
returns from that same random year. But, you're ignoring the possibility of correlations
between one year and the next. I mean, maybe, in the real world ...
Aah, I know exactly what you mean ... serial correlation. Maybe the returns in
1953 influenced the returns in 1954 so that ...
>Yeah, yeah. So what are you going to do?
Fagedabawdit.
Pearson Correlation
However, the serial correlation between successive inflation rates is significant
(about 0.65 for 1928  2000), so, if you ask nicely (by putting an "x" into cell B5
rather than specifying an inflation rate)
the spreadsheet will pick a random year, after 1928, and will select 30 (40? 50?)
successive inflation rates, starting at that year.
Thanks to Dave L. for this idea.
>But then you're ignoring any correlation between market gains and inflation rates, eh?
Uh ... yes, but they're so small ... a percent or three (or less).
Let's do a bit of mathematical stuff.
>No, please, fagedabawdit.
Pay attention.
We let the growth factor of our portfolio, during the n^{th} year, be denoted by
g_{n}. That means, if our portfolio grew by a factor of 1.23 over the fifth year,
then g_{5} = 1.23 and if it grew by a factor ...
>Okay, I get the idea.
Very good. Further, suppose the inflation factor for year n is i_{n}. That means that ...
>For an inflation rate of 4.56% in year n, then ... uh ...
Then i_{n} = 1.0456, namely 1 + inflation rate.
Okay. If we started with a portfolio worth $P and withdraw a fraction
f of this
original portfolio (that's fP), and each year this amount
increases by the inflation factor for that year, then:
at the end of Year  Portfolio  Withdrawal  Balance

1  Pg_{1}  fPi_{1}  Pg_{1}  fPi_{1}

2  Pg_{1}g_{2}fPi_{1}g_{2}  fPi_{1}i_{2}  Pg_{1}g_{2}fPi_{1}g_{2}  fPi_{1}i_{2}

3  Pg_{1}g_{2}g_{3}  fPi_{1}g_{2}g_{3}  fPi_{1}i_{2}g_{3}  fPi_{1}i_{2}i_{3}  Pg_{1}g_{2}g_{3}  fPi_{1}g_{2}g_{3}  fPi_{1}i_{2}g_{3}  fPi_{1}i_{2}i_{3}

etc. etc.  ...  ...  ...

Do you see how it's going?
>NO!!
Well, we'd like to determine the withdrawal rate (that's f)
such that, at the end of Year N, our Portfolio is reduced to zero. That means that:
Pg_{1}g_{2}g_{3}...g_{N}
= fPi_{1}g_{2}g_{3}g_{4}...g_{N}
+ fPi_{1}i_{2}g_{3}g_{4}...g_{N}
+ fPi_{1}i_{2}i_{3}g_{4}...g_{N}
+ ...
+ fPi_{1}i_{2}i_{3}...i_{N}
which we can also write as:
1/f =
i_{1}/g_{1}
+ i_{1}i_{2}/(g_{1}g_{2})
+ i_{1}i_{2}i_{3}/(g_{1}g_{2}g_{3})
+ ...
+ i_{1}i_{2}i_{3}...i_{N}/(g_{1}g_{2}g_{3}...g_{N})
>I don't like this one bit. I mean ...
Wait. Our final result is much simpler.
We'll let the nyear Portfolio gain factor be G_{n}, so
G_{n} = g_{1}g_{2}g_{3}...g_{n}
and we let the nyear inflation factor be I_{n}, so
I_{n} = i_{1}i_{2}i_{3}...i_{n}
>The nyear inflation factor? I never heard of that.
Think Consumer Price Index, or CPI, which we assume starts at CPI = 1 when we start our Portfolio.
Anyway, we get a Magic Formula:
f
= 1 / (
I_{1}/G_{1}
+ I_{2}/G_{2}
+ I_{3}/G_{3}
+ ...
+ I_{N}/G_{N}
)

>So?
So, if we use a 4 x 25 sliceanddice Portfolio ...
>25% devoted to each of Large & Small Cap Growth stocks and ...
... and Large & Small Cap Value stocks.
Yes, and if we consider the CPI and stock returns for 40 years, starting in 1928, we get
f = 0.047 meaning ...
>Meaning a 4.7% withdrawal rate would have reduced our Portfolio to $0, right?
Right.
>Why start in 1928? What about ...?
Before we consider starting at some other year, you're supposed to ask what this
CPI/Total_Gain looks like ... these I_{n} / G_{n}, as the years go by.
>I was just thinking. As the years go by, what do these ...?
Here's a typical scenario for a 4 x 25 portfolio:


Then the sum, like I_{1}/G_{1}
+ I_{2}/G_{2}
+ I_{3}/G_{3}
+ ...
is the area under the curve, when drawn as a column chart, like so
for another period, from 1950.
The smaller the area, the larger the withdrawal
f.


Of course, we might assume a constant Annual Gain, say 10% (g = 0.10)
and a constant Inflation Rate, say 3.5% (i = 0.035)
and a number of years, say N = 30 years
... and get a formula for f,
namely:
(1  x)/{ x (1  x^{N})}
where x = (1+i)/(1+g)
and we'd use decimal equivalents, like
g = 0.123 for an Annual Gain of 12.3%
and
i = 0.0345 for an Inflation of 3.45%.
You can play with the formula here:
>So, there's a lot of Risk in big withdrawal rates and ... uh, by the way, how many definitions of "Risk" do you have?
Jillions. Here's a couple:
See
Risk Measures
See
Slice and Dice
>What about that Magic Formula for Maximum Rate of Withdrawal ... using Monte Carlo?
Good question, but before we do that, notice that we can check out 12 month price targets.
You set up the spreadsheet, as noted
here, and you get the Monte Carlo Probability
that the target will be achieved :^)
Now, let's continue in Part II
Click for Part II
A simpler spreadsheet
If you want a spreadsheet much simpler than the Sensible Withdrawals spreadsheet
noted above ... one that selects returns at random (with the specified asset allocation) and allows you to devote
a fraction of your initial portfolio to a fixed, immediate annuity ... then tells you how often you might expect your
portfolio to survive ... well, just take a peek at what it looks like,
here, and if you want to download,
RIGHTclick HERE (older version zipped here) and Save Target ....
