Nestegg Cycle © Stretching the "4% Rule" to Manage Longer Retirements

Posting Date: July 09, 2023 (Revised July 13, 2023)

Origins of the so-called "4% Rule"
The so-called "4% Rule" (not actually a rule) grew out of statistical analysis of decades of financial market performance, by William Bengen in 1994
on a particular portfolio -- 50% US common stocks, and 50% US Intermediate Treasuries, rebalanced continually;
a particular retirement term -- 30 years;
and his discovery that over all fifty of the retirement periods on record, starting since 1926, that portfolio, and a 4% initial spending rate followed by annual COLAs, always SUCCEEDED, producing at least 33 years of payouts before running out of money.

In fact, in approximately 80% of the starting years for retirements, there was sufficient growth to provide payouts for 50 years (and possibly more in some cases, but the reporting was truncated at 50 years).

Some basics
From Bengen's paper: US Stocks averaged 10.3% compounded growth per year; the Intermediate Treasuries returned 5.1%;
The 50% mix produces 7.70%. This is the nominal rate but includes inflation which averaged 3.0%.
The adjustment for 3% inflation takes us to:
  1.0770 / 1.030 = 1.045631, thus an adjusted rate of 4.5631% above inflation.
  This rate, 4.5631%, is assumed in all calculations and illustrations below.

4% is the same thing as 1 part in 25, so that each $25 invested as specified will produce $1 per year in retirement payout.
As it happens, the online annuity calculator we used, gives much better decimal precision with larger input values, even though the proportions are the same, so we have adopted the convention of treating the iconic 4% case as 25000 of principal, and 1000 of annual payout.
  We will use the notation: [principal]:[payout] -- thus -- 25000:1000.

Because this key concept will be so frequently mentioned, we use the phrases "crash protection", "crash resistance", "crash support", and "crash buffer" interchangebly.

Now, using the annuity calculator to solve for the principal required to produce exactly 30 years of 1000/yr, at the inflation-adjusted interest rate of 4.5631%, we get 16168.65, which is a lot less than 25000. We'll call this the "bare-bones minimum" amount to supply the payments for 30 years.

Next, we use the same calculator to solve for the principal needed to produce the 1000/yr payments for 1000 years, as a good stand-in for "forever", and we get 21914.93, which is still a lot less than 25000.

So, WHY the interest in going as high as 25000, which will take a lot longer to save up, than will 16168.65 or even 21914.93?
The very shortest answer is that it has everything to do with "Sequence of Return Risk" (SRR).
SRR is the risk that, very early into one's retirement, the markets crash, causing unexpectedly rapid depletion of the invested principal, to the point where ongoing payouts of the expected amount, completely exhaust the account too soon.

Goals of this Posting
We will:
Delve into some engineering tradeoffs that can be used to manage "Sequence of Return Risk" (SRR);

Explore how this relates to the success of the choice of 25000 rather than 16169, per planned 1000 of annual payout.

Explore whether this remains a good choice for retirements longer than 30 years, with a special interest in 75 year retirements, relevant to the "FI/RE" community (Financial Independence / Retire Early) ... who regularly post articles about retiring in their 20's or 30's, based upon the "4% Rule".
Spoiler alert: DO NOT use the "4% Rule" to plan very long retirements! Details to follow.

We developed a simple way to express and explore a "simulated market crash", payouts during the crash, and a "simulated market recovery".
We assumed that the yield of 4.5631% continued during the crash, but applied to the reduced balance.
We worked with multiple sessions of this online savings calculator and this online annuity calculator and by degrees, incorporated most of these steps into more sophisticated routines in Windows Powershell scripts.
This, in turn, allowed us to easily run arrays of these calculations by invoking them from "foreach" loops with series of desired values.

Mostly we looked at the case of a sudden 75% drop in the value of the portfolio on Day One of retirement.

This was expressed as a "crash_to" value of 25%, meaning that the portfolio was now worth 25% of its pre-crash value. In the simplest scenario, this meant that your 25000 is suddenly worth only 6250, but your expenses remain at 1000/yr. The table just below shows what happens to the portfolio's payout lifetime if the crash continues for years, and you make no adjustments to your spending:

25000:1000 retirements at 4.5631% RATE ...
 IMMED 75% CRASH of:  Limits Portfolio Lifetime to:
 ==================== ===================
 1 yr                 still good forever
 2 yr                 48.40 yr
 3 yr                 32.50 yr
 4 yr                 23.55 yr
 5 yr                 17.45 yr
 6 yr                 12.84 yr
 7 yr                  9.18 yr
Thankfully, as confirmed against Bengen's data, a 3 year crash like this, is equivalent to the largest ever seen in modern history. Keep in mind that in 80% of the years on record (at least, as of 1994) this does NOT HAPPEN, but if your timing is unlucky and it happens, what should you do?

We developed a method of successive approximations, to calculate a reduced payout amount for the duration of the crash. In each case, the starting value is clear, such as your 25000 suddenly dropping to 6250. The End-of-crash value cannot be allowed to fall below a value which would support the remaining years of payouts desired. If this was a 3 year crash, we'd need to support a remaining 27 years of a 30 year retirement, but a remaining 72 years of a 75 year retirement. We run the annuity calculator (or its equivalent financial function in Powershell) to determine this amount: solve for the Principal required to pay 1000/yr at 4.5631% for the 27 or 72 years or however many are needed in this case. This value, divided by 4, becomes the in-crash minimum limit.

The reduced payout DURING the crash, is squeezed between those two limits. It will be less than 1000 and more than 250. The lower limit of 250 would be due to having only 25% of the principal available for producing payouts.

We explored different starting amounts, centered on 25000, with several steps of 1500 more and less,
to produce payouts of 1000/yr
for retirement lengths of: 30, 40, 50, and 75 years.
For each retirement length, we calculated the reduced payout (crash mitigation) needed for a 3 year and a 4 year crash, down by 75%,
to enable the account to resume 1000/yr payments after the crash recovery, and through the end of the retirement period.

            Table of Crash Mitigations - Part 1 - 30 & 40 years

STARTING PRINC      30/3      30/4        40/3      40/4
---------------     ---------------       --------------
     29500          1000     1000         1000     1000
     28000          1000     1000         1000     931.35
     26500          1000     971.01       1000     826.67
     25000          1000     866.33       865.78   721.98   
     23500          917.53   761.65       729.20   617.30
     22000          780.95   656.96       592.63   512.61
     20500          644.38   552.28       456.05   407.93
            Table of Crash Mitigations - Part 2 - 50 & 75 years

STARTING PRINC      50/3      50/4        75/3      75/4
---------------     ---------------       --------------
     29500          1000     943.64       1000     833.20
     28000          1000     838.96       874.30   728.52
     26500          881.82   734.27       737.73   623.83
     25000          745.24   629.59       601.15   519.15       
     23500          608.66   524.91       464.57   414.47
     22000          472.09   420.23       328.00   309.78
     20500          335.51   315.54       --       --

               Each column header, such as "30/3" or "75/4", is a retirement length, a slash, 
                   and a crash length.
There is much to be gleaned from this table!

Some important quick observations:
* These necessary, temporary payout reductions are a lot more drastic than the standard breezy advice, to just not take your COLA in a down year. On the other hand, this strong medicine only applies in the most severe, protracted downturns, and NOT routine market corrections.

* The standard 25000 starting amount per 1000, paired with a 30-year retirement, is a great match for the worst cases recorded since 1926, and for up to three years of a severe and immediate crash, contains adequate reserves to "sail through" the storm with no cut in payouts!

* BUT as you move to longer retirements, this is no longer the case. In fact, to get a similar amount of crash resistance: a 40 year retirement needs to start with about 26500:1000; a 50 year retirement needs to start with about 28000:1000; and a 75 year retirement needs to start with about 29500:1000.

* No mitigations are shown for 75-yr retirements starting with 20500, because the bare minimum for this retirement is higher than 20500.

So there are tradeoffs:
* While the 75-yr retiree can "sort of" use the 4% Rule, it is not optimal, as it is for a 30-yr retiree. His/her crash mitigation pay would need to be harshly cut to 601.15/yr for 3 years, or 519.15/yr for 4 years.

* You can NOT compromise on the crash mitigation pay cuts, especially for 75 years.
For instance, if you try to "split the difference" thinking you could substitute 800/yr for 6 years, instead of 601/yr for 3 years, in the above 75-yr case, you would NOT be even CLOSE.
Here are some of your alternatives after the partially mitigated 3 year crash:

  1 - Take payments of 1000/yr starting immediately post-crash BUT! run out of money in 42 years: 30 years too soon!
  2 - Continue taking 800/yr for 19 post-crash years. THEN you can resume payments of 1000/yr.
  3 - Take payments of 600/yr for 8 post-crash years. THEN resume payments of 1000/yr.
  4 - Take payments of 400/yr for 5 post-crash years. THEN resume payments of 1000/yr.
  5 - Take NO payments for 3 post-crash years. THEN resume payments of 1000/yr.
  6 - Take payments of 881.29/yr starting immediately post-crash and for 72 years.

* Going into a severe crash situation, there's no way to know how long it will persist before recovering.
Therefore, the only prudent course is to assume defensive payout cuts for the maximum expected crash length.
But how long is that, really?
From the historical record of 1926 thru 1994, that number is 3 years. Could it ever be worse?
There is no good way to know for sure, so you might make a case for adopting the even more drastic payout cut required for a 4 year crash, just in case.

Is Crash Protection Worth the Cost?
Consider: bare bones minimum principal to provide 1000/yr for 30 years, is, as already mentioned, 16169. At this amount, there is no crash buffer at all, and during a 75% crash, you'd need to reduce your payout by 75% to match: take only 25% of the 1000/yr, or 250/yr. You would need to make up the other 750 some other way. Otherwise your money will be exhausted well before 30 years.

Roughly, this means you'd need to come up with 2250 for 3 years or 3000 for 4 years, PER 1000 of desired annual payout.

Compare this with the extra approximately 8800 (25000 - 16169 = 8831), PER 1000 of desired payout, to be accumulated pre-retirement, to reach 4%. Don't forget that in a realistic situation, where you might want something like a 100K/yr payout, each number must be multiplied by 100 -- you'd need to come up with 300,000 from elsewhere, in exchange for the 880,000 extra which you did not invest.

Here is a Table for 75 Year PAYOUTS of 1000/yr, with 0 to 4 years of crash protection:

-----------------   --------------
     0              21143.39
     1              24012.47
     2              26756.35
     3              29380.48
     4              31890.10
Here again, for the 75-year retirement, we see a similar pattern: bare-bones payouts require 21143, while 3 years of crash protection require 29380, a difference of about 8200. And the standard 25000 of principal, in this case, affords us less than a year and a half of crash protection. Scaled up 100-fold to a more realistic payout of 100K/yr, we require an extra 820,000 invested, to protect 300,000 in payouts during a crash, something which has only about a 20% historical likelihood of being needed.

One big difference between the 30 year old retiree starting a 75 year payout, versus the 67 year old starting 30-40 years, is that the younger person could reasonably suspend retirement and go back to work for a few years, to survive the crash; whereas, the older person probably could not do this.

Odds and Ends
We ran some mitigation calculations for a prolonged crash of 50% -- in which one's payout-producing principal were cut in HALF.
The impact is much less than that of the 75% crashes discussed above.

Here, for the 75 year payout, a starting amount of 25000 will support a 4 year, 50% crash completely; and require a payout cut to 940/yr for a 5 year crash.

For the 30 year payout, a starting amount of 25000 will support an 11 year, 50% crash completely; and require a payout cut to 986/yr for a 12 year crash.

We also explored the effects of 3-year crashes, down 75%, occurring progressively later in the retirement cycle, all starting at 25000:1000 -- the leftmost column shows years into retirement: 0, 5, 10, etc.
  "Zero" years into retirement, is the "Day One" crash we've been discussing.
                 1000/yr          Mitigated Pay during crash
75% CRASH YR     Pay
                 Longevity        40yr    50yr    75yr
------------     ----------       -----   -----   -----
0                32.5             866     745.2   601
5                42               --      869.0   689
10               52               --      --      798.5
15               66               --      --      936
20               97               --      --      --
23               forever          --      --      --

From this study we see that after 5 years:
  a 40-yr retirement can absorb the 3 year crash without a payout reduction,
  a 50-yr retirement needs to reduce the payout to 869/yr during those 3 years,
  a 75-yr retirement needs to reduce the payout to 689/yr during those 3 years.

So this is a previously unrecognized issue for the "FI/RE" community -- that a "4% Rule" retirement, intended to make payouts for 75 years, requires a much longer period of "hand-holding" than does a shorter retirement starting with the same 25000:1000 setup. Even 15 years in, a crash would require a modest reduction to 936/yr during the three bad years.

By twenty years though, even the 75-year retirement at 25000:1000 is safe from the 3 year crash.

To be crash resistant to a 3-year 75% down crash within five years:
  A 40-year retirement is fine with 25000:1000
  A 50-year retirement requires 26500:1000
  A 75-year retirement requires 28000:1000

And if IMMEDIATE crash resistance is desired -- as already built into the 30-year retirement:
  A 40-year retirement requires 26500:1000
  A 50-year retirement requires 28000:1000
  A 75-year retirement requires 29500:1000

Be aware! After such a major crash, even with the mitigation shown, you have consumed the crash resistance that had been designed in, and are now running with a "bare-bones" portfolio. Hopefully, a bull market arrives to raise you up again!

LINKS to our Calculator and Other Blog Articles

We have shown:

1 - Why 25000 is very nice for 30 years at 1000 payout -- survives an immediate, severe, 3 yr crash

2 - Why 16169, the minimal annuity calculated principal amount for 30 years, provides ZERO crash resistance
	and in fact, requires FULL payout cuts to match the crashed principal cuts! 
	Payouts must be reduced from the usual 1000/yr, to 250/yr during the crash.
3 - Why 21915, theoretically enough to support 1000/yr forever, is still weak on crash resistance.

4 - Why crash resistance comparable to what 25000:1000 provides for a 30 year retirement, calls for about:
	26500:1000 - for 40 year retirement
	28000:1000 - for 50 year retirement
	29500:1000 - for 75 year retirement
5 - Why crash resistance is SOMETIMES worth the cost; When it is, when it is NOT.

6 - Why, for longer retirements at 25000, stronger mitigation pay cuts are required during a crash.
7 - Why, in an IMMEDIATE, severe crash (down 75%), mitigation pay cuts for 3 years (worst case in modern history), 
	or possibly 4 years (in case of worry that a new worse-yet case could occur)
	need to be self-imposed, full strength, right away: delayed mitigation is surprisingly painful.
For #6 & #7, and starting with 25000:1000 -- 

	30 yr retirement is covered thru 3 yr crash; 4 yr crash mitig: 866.33
	40 yr retirement is covered thru 2 yr crash; 3 yr crash mitig: 865.78; 4 yr 721.98
	50 yr retirement is covered thru 1 yr crash; 2 yr mitig: 976.77; 3 yr 745.24; 4 yr 629.59
	75 yr retirement is covered thru 1 yr crash; 2 yr mitig: 765.32; 3 yr 601.15; 4 yr 519.15