Withdrawals With Fractional End-Balance Goals (Inflation-Adjusted)

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Withdrawals With Fractional End-Balance Goals (Inflation-Adjusted)

Previously defined Decumulation Factor AAFI & Systematic Withdrawal Rate SWRM are now modified for fractional end-balance Goals.

P = Original principal; normalized p.

Dj = Annual withdrawal for year j on December 31.

Aj = Monthly payouts during the year j; A1 = 0; A2 = D1/12,…,Aj+1 = Dj/12,...(j+1 is a subscript); A2 normalized is $1/month (Initial monthly payout).

Assumed initial payout (normalized) will be $1/month, uniform during the year, but inflation-adjusted at the end of the year. The start-year monthly payouts will be $0; the inflation-adjusted annual withdrawal at the yearend is deposited in a savings account or a money-market fund/account from which monthly payouts (1/12 of withdrawals) are made during the following year (interest rates for these accounts are ignored).

PV Inflation Factor IF = Final Balance/Final Balance (inflation-adjusted). This factor is over the entire term. In the discussion, annual inflation adjustment for year j is InflationAdjj.

f = Desired inflation-adjusted fraction of the original principal P (or P*IF), i.e. the end-balance goal = f*P*IF; f =< 1.

$AFI is the original principal amount needed to support $1/month initial payout that is inflation-adjusted annually; $AFI will be completely exhausted at the end of the term (dollar amount withdrawals).

$AAFI is the original principal needed to support $1/month initial payout that is adjusted annually, but at the end of the term, the leftover amount is inflation-adjusted fraction of the original principal, or f*AAFI*IF (dollar amount withdrawals).

PV SWR is the percentage of the original portfolio balance that can be withdrawn at the end of each year with inflation adjustment without the portfolio running out of money (dollar amount withdrawals).

New SWRM is the percentage of the original portfolio balance that can be withdrawn at the end of each year with inflation adjustment, but at the end of the term, the leftover amount is inflation-adjusted fraction f of the original principal (dollar amount withdrawals).

PV Cumulative Factor CF = Final Balance/Initial Balance. There is an information tab "i" that also provides inflation-adjusted final balance, and that gives inflation factor IF = Final Balance/Final Balance (inflation-adjusted).

PV Inflation-adjusted Cumulative Factor CFI = Final Balance (inflation-adjusted)/Initial Balance = CF/IF.

Monthly Payments and Annual Withdrawals

Start Year 1: Monthly payout A1 = 0; withdrawal on December 31 is D1 = 0.01*SWRM*Original Principal*InflationAdj1.

Year 2: Monthly payout A2 = D1/12; withdrawal on December 31 is D2 = D1*InflationAdj2.

Then, Year j+1: Monthly payout Aj+1 = Dj/12; withdrawal on December 31 is Dj+1 = Dj*InflationAdjj; j+1 is a subscript.
...

Calculation of AAFI & SWRM

Obviously, p > AFI. In fact,

(p - AFI)*CF = f*p*IF ,

or, (p - AFI)*CFI = f*p .

This p is AAFI,

AAFI = AFI*CFI/(CFI - f) ; f =< 1.

Note that,

SWR = 1,200/AFI , SWRM = 1,200/AAFI ,

so,

SWRM = SWR*(CFI - f)/CFI ; f =< 1.

All of the needed data (IF, CF, CFI, SWR) can be obtained from a single PV Backtest run with settings: Time Period “Year-to-Year” with most recent full end-year; Cashflows “None”; up to 3 tickers plus a benchmark. There is no trial-and-error involved. Be careful that SWR uses the last completed year, while IF, CF, CFI use the last completed month in free PV runs. Some of the definitions used here may seem unnatural but that is to conform to the PV convention used for SWR calculations.

After these calculations, results can be verified for each ticker by direct PV runs with annual withdrawals (inflation-adjusted) set to those indicated by SWR or SWRM. As only integer amounts are allowed for annual withdrawals, it is better to scale up the original principal amount to 100,000 or 1,000,000 (instead of default 10,000) to reduce errors.

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Examples - Withdrawals With Fractional End-Balance Goals (Inflation-Adjusted)

Method Summary

1. Start with a PV Normal Run with Year-to-Year (full end-years only) and without any withdrawals.

SWR is the percentage of the original portfolio balance that can be withdrawn at the end of each year with inflation adjustment without the portfolio running out of money (dollar amount withdrawals).

Inflation-adjusted Cumulative Factor CFI = Final Balance (inflation-adjusted)/Initial Balance

2. SWRM is the percentage of the original portfolio balance that can be withdrawn at the end of each year with inflation adjustment, but at the end of the term, the leftover amount is fraction f of the inflation-adjusted original principal (dollar amount withdrawals).

SWRM = SWR*(CFI - f)/CFI


Period 01/2000 - 12/2022 captured the dot.com bubble burst and was possibly the worst start for withdrawal programs in the recent history.

                                              SWRM
FUND        CFI          f = 0     f = 0.25    f = 0.50    f = 0.75     f = 1
VWELX      2.9844    7.25%    6.64%      6.035%     5.43%      4.82%
FBALX       2.8961    6.83%    6.24%      5.65%       5.06%      4.47%
ABALX       2.9187    7.40%    6.77%     6.13%        5.50%      4.865%
VFINX       2.2346    4.34%    3.85%      3.37%       2.88%      2.40%

Note that the previously considered cases are when f = 0 or f = 1.

So, one can plan for lower withdrawals during the term with the goal of ending with a desired fraction of the inflation-adjusted principal. When there is no specific end goal, f = 0.25 may be used just for additional safety - after all, things may not turnout as expected.

PV Run  www.portfoliovisualizer.com/backtest-portfolio?s=y&sl=QDsE4vD8ubI49eilxiauU 

Edit/Add. TwitterLINK

YBB Personal Finance
@ybb_Finance
(11/21/23)

#SWRM #hashtag has multiple meanings. The use HERE is as Systematic Withdrawal Rate - Modified.
It's an obvious extension of #SWR = Safe/Sustainable/Systematic Withdrawal Rate.

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Withdrawal Programs with Adjustments

With modified systematic withdrawal rates SWRMs, it is possible to split withdrawal programs. For example, a long withdrawal program for 30-40 years can be split into two programs with 15-20 years each. Rationale is that these programs tend to be conservative and actual results may be better than expected. So, one may reevaluate them after 15-20 years for possible improvements in the payout rates.

Program 1, 15-20 years, SWRM with fraction f = 1 (i.e. full inflation-adjusted original principal). Using 01/2000-12/2022 SWRM values for conservative design with VWELX, that is the SWRM of 4.82%.

Program 2, subsequent 15-20 years. Although the full inflation-adjusted original principal is on hand, the actual balance P2 may be higher. The value of f may be changed too if the situation has changed. Again, using 01/2000-12/2022 SWRM values for conservative design (or alternative values, if available) with VWELX, for the new principal P2, use the SWRM of 6.035% for f = 0.5 (only half of the inflation-adjusted principal P2 at the end for legacy or inheritance), or the SWRM of 7.25% for f = 0 (exhaustion of principal); a fund other than VWELX or a portfolio of funds may also be used.

Even if the payouts cannot be improved, these interim reviews can lead to adjustments based on realized performance results.

Shorter programs for, say, 10 years each may be used. However, there is the danger that programs with shorter periods may be more exposed to large market swings and the applicable SWRMs may be low or N/A. For example, if the calculations were made from PV run for the period 01/2000-12/2009 (dot.com bubble to GFC),

VWELX (hybrid)  SWR = 12.31%, SWRM = 3.61% (for f = 1),
VFINX (all-stock)  SWR = 7.42%, SWRM N/A (for f = 1).

So, while a hybrid like VWELX could work, all-stock VFINX failed. Also note that SWRs are misleading as the original principal is exhausted in 10 years; even a fund with 0% return will give the SWR of 10%. This issue is eliminated with SWRM and f = 1.

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Stress-Testing Periods

The recent 10-year bad stretches for stocks were 01/1999-12/2009 (10 years; SWRM invalid/NA for VFINX/SP500), and for bonds or bond-proxies 01/2012-12/2022 (10 years; SWRM invalid/NA for VBMFX/total bond market).

Two longer stress-testing periods are 01/2000-12/2022 (22 years) and 01/1999-12/2022 (23 years) that include the dot.com bubble, the GFC 2008-09, the Covid pandemic 2020, and a historic selloff in the bond market (when after pandemic easing, the Fed raised rates very rapidly). The latter period (01/1999-12/2022) is also interesting as it includes the entire 10-yr period 01/1999-12/2009 within it, and eventually, VFINX/SP500 did OK, but initial bad 10 years caused it to lag.

If strategies “fail” (i.e., SWRM is invalid/NA) or have very low SWRMs for these stress-test periods, then their prospects for reasonable withdrawal rates for the next 30-40 years must be questioned. This despite some examples where some “fails” may rebound if given more time. The term “failure” as used here is not based on any particular withdrawal level, but is simply when the SWRM is invalid/NA, i.e. there is failure to produce the desired inflation-adjusted original principal (0 =< f =< 1) at any withdrawal level (>= 0). Also, "boring" hybrids tend to do better than other exotic options.

Periods less than 10 years shouldn’t be used for this stress-testing. Although the SWRM eliminates the principal-exhaustion/loss effect, the security markets are very volatile over short-terms, and the SWRM values may be quite low to be useful or be invalid/NA. This is seen for the 8-year period 01/2000-12/2008 (dot.com bubble to GFC). It is suggested that long withdrawal programs of 30-40 years can be split only into 2 smaller programs of 15-20 years each, if desired for interim reviews and adjustments; more splits than that may be counterproductive.

The prior worst periods for withdrawal program starts were in 1930s, 1960s, etc, but investors often say those times were so long ago and things are very different now. That is why the use of these recent worst periods ending in 2022 is suggested. These stress-tests may suggest withdrawal rates a bit higher than those suggested by Bengen's Rule (4% w/COLA), but not lot higher as some wild-eyed optimists may suggest.

Edit/Add, 12/3/23. An interesting observation is that PV PWRs are comparable or lower (for longer runs) than SWRMs; for longer periods, the SWRMs approach SWRs as CFIs become larger. Both produce inflation-adjusted original principal at the end but have very different payouts. But this means that often a quick look at PWRs may be enough to guess SWRMs before calculations.

PV Run 01/1987-12/2022 (35 years)   www.portfoliovisualizer.com/backtest-portfolio?s=y&sl=6fWnO8vgZHplkLlkND1keH
SWRs VWELX 7.89%, FBALX 7.43%, ABALX 7.63%, VFINX 8.82
SWRMs VWELX 7.035%, FBALX 6.545%, ABALX 6.70%, VFINX 8.106. (f = 1)
PWRs VWELX 5.98%, FBALX 5.74%, ABALX 5.68%, VFINX 6.75 (worse than SWRMs)

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Rebalancing 60-40

PV Runs, 01/1987-12/2022 (max possible at PV w/indexed OEFs), Stock Index VFINX, Bond Index VBMFX, 100-0, 0-100, DIY slice-and-dice 60-40 allocation with various rebalancing, 60-40 RA (annually; default), 60-40 RQ (quarterly), 60-40 RM (monthly), 60-40 RN (never), 60-40 Calc (simply calculating 60%-40% from final values from VFINX and VBMFX runs). The Initial Value is 10,000; shown are Final Values (FV), CAGR, SD. Also included are some active hybrids.

                       FV         CAGR           SD

VFINX          331,775   10.22%      15.36%
VBMFX           60,065    5.11%        4.07%
60-40 RA     189,687     8.52%        9.57%
60-40 RQ     191,290     8.54%       9.54%
60-40 RM     185,932     8.46%       9.59%
60-40 RN     223,091     9.01%      11.74%
60-40 Calc   223,091     8.176%    10.844%

Active

VWINX        166,136     8.12%       6.65%
VWELX       247,948      9.33%     10.21%
FBALX        225,373      9.04%     10.31%
ABALX        220,635     8.97%       9.56%

www.portfoliovisualizer.com/backtest-portfolio?s=y&sl=1NiBtn39hCRKEbErdLiFXM
www.portfoliovisualizer.com/backtest-portfolio?s=y&sl=6yvRNdorzEkxPfLGtl8d9D
www.portfoliovisualizer.com/backtest-portfolio?s=y&sl=45OgHVjtdbqnRDkkJLoI4g

Note that 60-40 Calculated from the final values for VFINX and VBMFX has the SAME FV (linear superposition is valid) as for 60-40 RN (never rebalance), but the CAGR and SD are different (linear superposition not valid). While not seen in this timeframe, very frequent rebalancing is not good (more effort, possible trading restrictions, little expected improvement), and quarterly or annual rebalancing may be the best compromise; PV also has semi-annual and customizable +/- bands rebalancing options that weren’t tested.

Comparing with active allocation funds, 38-62 VWINX does the worst in the group of moderate-allocation funds (as expected due to its lower equity exposure), 62-38 VWELX does the best (possibly due to its low ER), while FBALX and ABALX have strong showings.

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Allocation Index Funds

There aren’t many choices for indexed allocation funds for stress-testing if one excludes TDFs that have glide-paths. For active allocation funds, there are many choices.

There is the old VG VBINX (1992- ; NA for purchase)/VBIAX (2000- ).

Then, there is the iShare series (2008- ) with ERs of 15 bps that takes quite a bit of liberty with the use of terms/names – AOA (aggressive; 97.42% equity), AOR (growth; 93.84% equity), AOM (moderate; 87.52% equity), AOK (conservative; 81.95% equity). There is also a corresponding ESG series (2020- ) with ERs of 18 bps – EAOA, EAOR, EAOM, EAOK.

Fido has FFNOX, ER 11 bps, 84.83% equity, 1999- .

WisdomTree has an active 1.5x leveraged 60-40 for 90-60 effect, NTSX, active, ER 20 bps, 2018- ; it uses stock selection plus Treasury futures for bond exposure and leverage.

These may be used for PV Backtesting and none shine. The simplest way to backtest DIY slide-and-dice allocation is with VFINX (1976- ) and VBMFX (1986- ).

[Admin/YBB]

Asset Allocation & Withdrawal Strategies in Retirement – Bolin
www.mutualfundobserver.com/discuss/discussion/61869/asset-allocation-withdrawal-strategies-in-retirement-bolin 

yogibearbull
(1/6/24)
Asset Allocation & Withdrawal Strategies in Retirement – Bolin

There is an interesting article by Charles Lynn Bolin ( @lynnbolin2021 ) on withdrawals in the January 2024 MFO issue. In the SUPPLEMENTARY information presented here, portfolio # won’t be used as they can cause confusion.

In Bolin’s Table #1 with 4 portfolios tested with 6% withdrawal rates, be aware that those are 6% withdrawals from the YEAREND balances every year. So, the amounts withdrawn will fluctuate widely with the market. The residual balances are shown in Figure #1 to indicate whether those kept up with inflation.

Interestingly, PV has a parameter PWR (under the Metrics tab) that provides max % withdrawals from YEAREND balances that will also leave inflation-adjusted residual at the end.

A reference is made to “the time-tested 4%”, but that so-called Bengen’s Rule has a different withdrawal regime – 4% of the INITIAL lump-sum that is subsequently adjusted annually for inflation; the PV run settings also allow for this and the related PV metric SWR is the max % withdrawal in this scenario (that will EXHAUST the portfolio).

One can also deduce from the PV run data the max % of the INITIAL lump-sum that is subsequently adjusted annually for inflation AND leaves inflation-adjusted initial lump-sum at the end, and that % is SWRM.

The table below shows PWRs, SWRs, SWRMs.

Portfolio;                                                PWR;      SWR;      SWRM
50%VFINX + 50%VTRIX;                        5.59%;   7.71%;    6.79%
70%VFINX + 25%VBMFX;                       5.92%;   7.77%;    6.96%
50%VFINX + 25%VTRIX + 25%VBMFX;   5.40%;   7.46%;    6.50%
VFINX;                                                  7.06%;   8.77%;    8.19%

Bolin’s conclusions about inflation adjusted residual balances are consistent with whether the PWR is less than, or greater than, 6% in the table above. It is also interesting that all could support Bengen-style 4% (w/COLA) and even higher (note SWRs). In fact, all would leave more than inflation-adjusted initial lump-sum even with 6% w/COLA (note SWRMs).

Of course, all the data and conclusions are for the period 01/1987-12/2023.

www.mutualfundobserver.com/2024/01/asset-allocation-and-withdrawal-strategies-in-retirement/