As I mentioned in previous
posts, the web is replete with columns about sequence of returns (SOR) risk
showing that the order in which we experience market returns matters when we
begin spending constantdollar amounts from our portfolios.
I previously showed how you can eliminate the SOR risk from
terminal portfolio values (TPV) — the amount of money in your portfolio at the
end of retirement — by basing your retirement spending on a constant percentage
of remaining portfolio balance. But, I didn’t talk about the payouts of spending strategies, which is
an important point missed by every other SOR risk column I have read.
Using the six annual returns:
19.76%

9.37%

7.96%

0.86%

27.33%

14.88%

let’s look at both TPV’s
and their payouts from both spending strategies (constantdollar
withdrawals and percentage of remaining balance withdrawals) using the 720
possible orders of these six returns.
In the first scenario, a retiree has a stock portfolio
valued at $1M and she withdraws $25,000 a year. The second is identical, except
the retiree withdraws 2.5% of her portfolio’s remaining balance every year.
Here are the results[i] for the 720 sequences for $25,000
withdrawals in graph format.
With constantdollar withdrawal amounts, the annual payout
is always $25,000 (by definition) but the terminal portfolio value depends on
the order of returns. TPV’s ranged from
$931,049 to $1,015,467.
Remember what we are doing here is not looking at different
sets of market returns, but at the 720 different ways this set of six returns
can be ordered.
And, here are the results[ii]
for 2.5% withdrawals of remaining portfolio balance each year.
With percentage withdrawals, TPV is $979,537 no matter how
the annual returns are ordered, but annual payouts range from $16,553 to $36,986
and the present values (PV) of those annual payouts discounted at 2% range from
$108,000 to $182,000.
SOR risk affects payouts but not terminal portfolio values
when spending is based on remaining portfolio balance. It affects terminal portfolio values but not
payouts when spending is based on anything else. So, SOR risk is going to show
up somewhere.
We get to decide which place by picking a spending strategy.
You might expect that eliminating SOR risk with respect to
terminal portfolio values simply generates the same amount of wealth while
varying the payouts and holding the TPV’s constant, instead of the reverse.
It doesn’t.
When we transfer SOR risk from terminal portfolio value to
payouts, we don’t transfer an equal amount of risk. Here’s an example.
Since both terminal portfolio values and annual payouts are
important, I measure retirement wealth as the present value (PV) of all payouts
in retirement plus the present value of the terminal portfolio, as if it were
paid back to the retiree after 30 years. I use a 2% discount rate and consider
the two scenarios above (2.5% withdrawals and $25,000 withdrawals).
First, I looked at all 720 possible sequences of the six
annual market returns.
PRESENT VALUE OF
RETIREMENT WEALTH WITH ALL PERMUTATIONS OF SIX ANNUAL RETURNS
PV of Terminal Portfolio

PV of Payouts

Total PV

Average Total NPV

Std. Dev.


2.5% Withdrawals

869,801

107,853 to 182,068

977,654 to 1,051,869

1,010,627

16,621

$25,000 Withdrawals

826,745 to 901,705

140,036

966,780 to
1,041,741

1,008,407

16,789

The ranges of outcomes are the result of SOR risk. They use
the same 6 annual market returns, but in every possible combination. In
particular, look at the Total PV column. These are the ranges of 720 possible
outcomes as measured by the combined present values of payouts and terminal
portfolio values.
The results aren’t very different after 6 years. Percentage
withdrawals do only a little better by every measure. But recall from my earlier
post that SOR risk grows exponentially with time and these differences
might be much more pronounced over longer periods.
Next, I looked at a thirtyyear sequence. Fortunately, we
don’t have to run all 2.65 x 10^{32} permutations of 30 years of returns (when is
the DWave
quantum laptop hitting the market?) because we know the bestcase scenario is
when the annual returns are ordered highest to lowest and the worstcase scenario
is the reverse.
I looked at the sequence of real market returns from 1979 to
2008 from Robert Shiller’s website
and ran both spending strategies with that data for the best and worstcase sequence of returns. Here is
what I found:
PRESENT VALUE OF
RETIREMENT WEALTH
BEST AND WORSTCASE
SEQUENCES FOR MARKET RETURNS 1979 TO 2008
PV of Terminal Portfolio

PV of Payouts

Total PV of Retirement Wealth


Worst Sequence of Returns


2.5% Withdrawals

3,100,060

487,892

3,587,951

$25,000 Withdrawals

431,240

559,911

991,151

Best Sequence of Returns


2.5% Withdrawals

3,100,060

4,893,631

7,993,691

$25,000 Withdrawals

5,604,748

559,911

6,164,660

Percentage withdrawals are significantly better in both the best and worst cases.
Now, a couple of important points. First, while I had been using 4.5% and $45,000 in previous examples, I had to change the withdrawals to 2.5% and $25,000 in this step because the constant withdrawal portfolio failed in its twelfth year with $45,000 withdrawals in the worst case.
Now, a couple of important points. First, while I had been using 4.5% and $45,000 in previous examples, I had to change the withdrawals to 2.5% and $25,000 in this step because the constant withdrawal portfolio failed in its twelfth year with $45,000 withdrawals in the worst case.
This brings out an important point regarding the two
strategies. The constantdollar withdrawal strategy, as is well advertised,
leaves the retiree flat broke before retirement ends 5% to 10% of the time.
Percentage withdrawals never do, though payouts will decline as the portfolio
values drops.
This is the worst case
of SOR risk. Not that constantdollar withdrawal strategies cost more, or
that we aren’t compensated for the risk, but that portfolio failure[iii] is a real
possibility.
Second, I am not trying to show that one of these two
spending strategies outperforms the other. There is plenty of research to show
that constantdollar withdrawal strategies underperform. At these two extremes,
in this specific example, percentage withdrawals look much better, but there
are plenty of sequences in the middle where constantdollar withdrawal shows
better results, including the actual 1979 to 2008 order, where $26,842
withdrawals generated a PV of $5M
compared to $4.7M for 2.5% withdrawals.
I will note, however, that I have tried many 30year
sequences of returns and I am yet to find a set of returns where percentage
withdrawals did not dominate constantdollar withdrawals in the best and
worstcase sequences using present value of combined payouts and TPV’s.
What I am trying
to show is that shifting SOR risk from terminal portfolio values to annual
payouts isn’t a wash.
Given the 30 annual market returns in this example, 2.5%
withdrawals provided outcomes from $3.6M in the worst case to $8M in the best.
That’s the range of outcomes if we remove SOR risk from terminal portfolio
value.
$25,000 withdrawals generated about $1M in the worst case
and $6.1M in the best. So, switching from constantdollar to percentage
withdrawals not only switched SOR risk from TPV to payouts, it provided higher
value and lower risk. And it completely avoided portfolio failure.
That’s consistent with the many studies that show
constantdollar withdrawal strategies underperform.
Notice that the differences in sequence of returns risk is
much more pronounced at 30 years than at six. Since SOR risk is partially the
result of the uncertainty of stock prices along the path (it isn’t present in a
buy and hold strategy) that is what we should expect.
So, we can eliminate SOR risk from terminal portfolio values,
or eliminate it from annual payouts, but not both. If we eliminate it from
annual payouts, we introduce the risk of portfolio failure.
By basing our spending strategy on a constant percentage of remaining portfolio values, we can shift SOR risk to annual payouts, where it seems to do less harm.
By basing our spending strategy on a constant percentage of remaining portfolio values, we can shift SOR risk to annual payouts, where it seems to do less harm.
Personally, I’d prefer risking my annual income to risking
the source of all future annual
income, even if it were an even trade, but it is not.
Next up: Sequence of Returns Risk or Something Else?
Next up: Sequence of Returns Risk or Something Else?
CONSTANTDOLLAR WITHDRAWALS OF $25,000 ANNUALLY
Year 0

Year 1

Year 2

Year 3

Year 4

Year 5

Year 6


Market Return

19.76%

9.37%

7.96%

0.86%

27.33%

14.88%


Portfolio Balance

1,000,000

777,400

679,558

708,650

677,556

837,732

937,387

Payout

25,000

25,000

25,000

25,000

25,000

25,000

[ii]
2.5% OF REMAINING BALANCE WITHDRAWALS
Year 0

Year 1

Year 2

Year 3

Year 4

Year 5

Year 6


Market Return

19.76%

9.37%

7.96%

0.86%

27.33%

14.88%


Portfolio Balance

1,000,000

777,400

685,123

722,530

698,253

871,630

979,537

Payout

25,000

19,435

17,128

18,063

17,456

21,791

[iii]
By “portfolio failure” in this case, I’m referring to depleting a portfolio
before the end of retirement.
Mr. Cotton,
ReplyDeleteWonderful explanation. I was wondering what your thoughts might be about the possibility of increasing the constant percentage withdrawal to compensate for the payout fluctuations. Seems like this could be done and still be safe from portfolio failure.
Michael
I did notice while I was comparing 4.5% withdrawals with $45,000 withdrawals that I could increase the percentage a bit and still come out ahead. For example, 5% withdrawals might favorably compare with $45,000 withdrawals.
DeleteI chose 4.5%/$45,000 solely because they are numbers familiar to the SWR crowd.
Increasing the percentage would be fine, of course, if the market mostly goes up. If you increase the percentage and the market doesn't go up enough to justify it, you will primarily be shifting payout value from the end to the beginning of retirement because you will later be taking that same larger percentage of a declining portfolio. A larger percentage is going to reduce the value of your terminal portfolio, which might not be a bad thing.
It will still be safer than constantdollar withdrawals, and cheaper, because you're less likely to go broke.
I would have to add, though, that my gut feeling is that efforts to fix the problems with spending down a volatile portfolio of stocks in retirement by either method will ultimately be unsatisfying.
As Wade Pfau once told me, "You simply can't expect to spend a consistent amount periodically from a volatile portfolio."
You might get away with it, but you shouldn't expect it.
Thanks for the question!
Dirk