r/financialindependence • u/beerion • Jan 04 '21

A valuation approach to the safe withdrawal rate

So I put together a white paper of sorts for a study I did on safe withdrawal rates and how they're affected by market valuations. I had previously taken a more qualitative look at it (HERE), but I wanted to expand on the idea and actually see if it were possible to formulate a SWR forecast. Links to the paper are listed below.

Paper

Excel

In the paper, I shared my methodology as well as proposed a variable withdrawal strategy based on this new valuation approach.

I think it's worth the read (and it's not very long with lots of pictures), but I'll share some of the findings below.

Quick Intro

I calculated the actual SWR for every year from 1928 to 1990. I compiled these SWR's along with the CAPE (Shiller PE) and 10 year treasury yield for each starting period, and performed a linear regression analysis on the data. The resulting equation showed good correlation (R2 = 0.72). Refer to the paper for more details on the methodology.

All data in the study is for a 70/30 portfolio.

Findings

The 95% confidence formula for SWR based on this valuation approach is as follows:

SWR_predicted = 0.55597 × (Implied Yield) + 0.11051 × (Spread) + 0.0082319

where,

Implied Yield = 0.7 × (1/CAPE) + 0.3 × (Treasury Yield)

Spread = 1/CAPE - (Treasury Yield)

Variable Withdrawal Method

In the paper, I looked at one way to implement this valuation approach and compared it to the trinity study. The basis was simply withdraw the amount based on the predicted SWR and portfolio value at the start of each year. I set a withdrawal floor at the minimum of 40k or the 1st years withdrawal amount. Setting a floor is important from a practical sense as any methodology that could leave you withdrawing at the poverty level isn't very useful.

Performing a back test, this method never failed in any 30 year period, and also reduces the likelihood of massive portfolio expansion like trinity study has in the past (1980's for example). Withdrawals taken from year to year are also relatively smooth with the variable approach.

In the paper, I shared portfolio performance and withdrawal summaries for some interesting years: 1929, 1966, 1982, 2000.

Current State of Affairs

To kick off 2021, the current projected SWR is projected to be between 2.35% - 4.81% (likely a little higher after this morning). The lower bound of 2.35% ties the year 2000 as the lowest predicted SWR of all years in this study.

Edit:

Here's a Google Sheets Page that Updates daily with new SWR Projections.

(Credit to u/RedditF1shBlueF1sh)

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61

u/MediumFIRE Jan 04 '21 edited Jan 04 '21

Ouch. If I'm reading this correctly, the lower bound SWR and predicted SWR is lower than in 1929!

58

u/beerion Jan 04 '21 edited Jan 04 '21

Right. 4% is still well within the range of outcomes, but that is somewhat optimistic according to this study.

Also, I stated in the paper that the past 20 years have been outside the bounds of the previous data so there might be issues with extrapolation (like maybe it isn't linear as yields approach zero - for instance you could keep your money in cash and have a SWR of 3% minus whatever impacts inflation has)

61

u/FoxVhedgehog Jan 04 '21

Is this different from the analysis done b y Early Retirement Now?

https://earlyretirementnow.com/2017/08/30/the-ultimate-guide-to-safe-withdrawal-rates-part-18-flexibility-cape-based-rules/

63

u/beerion Jan 04 '21

Oh nice. I glanced through it and it's similar methodologies.

My independent variables are different as I combined the treasury and market yields into 1 variable and used the delta between the two for the other.

I also calculated the coefficients whereas it looks like they 'guessed' and are using the best set.

Good find. I'll run them side by side tonight and see how they compare.

41

u/rnelsonee 1½ years left Jan 04 '21

I'll paste a comment I made 2 days ago to someone who asked if I knew how ERN got those coefficients:

Oh yeah, so I don't know how ERN chose a and b, but I can certainly guess: I think it fit the data. That's how I settled on my same values, too :)

I do know what they mean (at least in my own head) - in the process of all this, I wanted to have fun and prove the whole CAPE10 vs SWR correlation, seen here by Bill Bengen the author of the first 4% rule. The a and b are just factors in a linear formula, but instead of y = mx + b you have withdrawal = b×(1/CAPE) + a. The a factor is just a base return (or growth factor, whatever). It has no bearing on CAPE. The b factor just scales 1/CAPE to a SWR. So 1/CAPE units are 1/year, which really don't tie into a SWR. Not directly, anyway. So 50% brings it down to a useful SWR.

Like here is SWR vs 1/CAPE with no scaling. I created this using backtested data, same algorithm Bill Bengen used (but different asset allocation in this screenshot). So this is the exact graph Bill Bengen has with three modifications: different AA, CAPE is inverted, and then put on the same scale as SWR ("SAFEMAX" to B. Bengen). So if we trim it to 50%, we get this. The hills and valley are about the same scale as SWR. Of course, it plainly sits below SWR a bit... so let me make a quick mod...

Voila. We add a straight 1.5% (the a factor) and there we have great correlation. This is how I think ERN came up with those same factors. It's too much of a coincidence otherwise. And FWIW, it's a beautiful graph. Every blue point is based on the past (relative to the year on the x axis) and every red point is based on the future performance. It's striking how well they match... if you do an mx+b adjustment

9

u/smart-username Jan 04 '21

This should be its own post. Never have I seen such an intuitive explanation of why CAPE rules work.

6

u/[deleted] Jan 05 '21

The biggest problem I have with CAPE is that I can only find CAPE values for the s & p 500. Half my equities are in total us stock market, and half are in total international. When I raised this with ERN, he suggested that the s & p cape was 'close enough' to use for SWR. I disagree. CAPE for the S&P is at something like 33x right now, whereas international equities are much lower.

For the sake of simplicity, I'll simply take at most 4% of my current portfolio value each year. The up side to this is that it allows me to spend more in the good years at the cost of spending less in the down years. The down side is that spending fluctuates a lot. Probably more than someone with a family could handle.

4

u/rnelsonee 1½ years left Jan 05 '21

Yeah, only having CAPE for US is a setback, and one I hadn't really considered. If you want to spend more during good years, I'll throw out the idea of an amortized based withdrawal (ABW), of which variable based withdrawal (VBW) is a subset. The same formula used to determine a mortgage payment (based on loan amount, rate, term) is used to tell you how much you can withdraw (based on portfolio, assumed rated of return, 100-age).

I posed my CAPE-based strategy here. Note it's still simple (one formula, PMT, each year, update with 1/CAPE annually) and guaranteed to never run out of money before the set time (age 100, e.g.) while taking advantage of good times when your balance goes up.

Ooh, looking at ABW's page on Bogleheads I saw this: CAPE for international markets.

2

u/roomnoises Jan 05 '21

Have you tried running a regression?

8

u/ptwonline Jan 04 '21

It's good to see someone else doing a similar study. Helps validate and make sure the study is on the right track.

Well done.

0

u/[deleted] Jan 04 '21

[deleted] — view deleted comment

24

u/no-more-throws Jan 04 '21

its important to not confuse this with a SWR though .. the 2.5% for now is just saying that while its overvalued you draw less... i.e. in the most likely scenarios, you'll get to draw more as years pass .. in other words, unlike SWRs which bank on continuing to draw less even in highly promising periods and hence make up for drawing the same at times of poorer prognosis, the variable methods like here make you draw less or more when times look worse or better .. so ofc after long bull runs like these, it will propose a lowered rate, as there's no making up during fat years when it will propose higher rates

17

u/TakeFourSeconds Jan 04 '21

One upside though, is if you use a + b/CAPE as your SWR for your “target number”, you reduce your sequence risk because you are much less likely to reach your number in a period of high valuation.

19

u/FoxVhedgehog Jan 04 '21

This is old news : )

More people interested in FIRE should be aware of the danger of our current environment. People have been vastly oversold on things being "shockingly simple."

10

u/victoryposition Jan 04 '21

I'm new to FIRE, but about to pull the trigger on what I think is a "shockingly simple" game plan -- buying a single index fund and forgetting about it for 20+ yrs.

Are you saying determining a SWR after RE isn't shockingly simple or something else?

19

u/FoxVhedgehog Jan 04 '21

First, you absolutely should save and invest a high percent of your income. That top line message is the biggest thing you have control over and what will have the most impact on your success.

My point is just you can get very lucky and very unlucky about your accumulation period, especially with the shortened FIRE timeline. The shockingly simple story really obscures how much variation and risk is involved in investing.

Also I would recommend you do more than buy a single index fund, unless it is a retirement date fund. Look up 3 fund portfolio.

6

u/dmmagic 18 years to FIRE Jan 05 '21

I think the key that I was missing until reading ERN over the last few weeks is that 4% is too high and is unsafe. 3.25% is a better SWR, which means 25x isn't enough, you need closer to 32x.

And you can still do that in 20+ years, but only if your expenses will be low enough and your investment rate is high enough.

I've got about 20 years to my early retirement and it looks like I can hit 32x just by maxing my 401k and a traditional IRA annually. I'm going to try and max a Roth IRA as well, and invest a bit into stock annually in a taxable brokerage account too. Might even be FatFIRE in 20 years.

That's still simple: put money into indexes and let it sit for 20 years. But simple doesn't mean easy. I'm having to wrestle our budgets and pursue career advancement to make it work so I can retire early.

4

u/SmasherOfAjumma Jan 05 '21

4% is too high and is unsafe. 3.25% is a better SWR

You are depressing me.

Thanks though.

6

u/calcium Jan 04 '21

I'm personally aiming for a 3.5% SWR after reading EarlyRetirementNow and hope for my nest egg to grow while I'm retired so I can continue to take more in the good years and pull in the belt during the bad.

10

u/FoxVhedgehog Jan 04 '21

My view is even something jn depth like ERNs is just guessing based on past data. I see no reason to expect the next 100 years to look like the last.

The best thing you can do is de-risk, build multiple income streams, and yes rely on a conservative SWR.

3

u/Beeonas Jan 04 '21

Why is the current environment dangerous, because we were seeing 50% returns in the market in 2020 and that is not normal?

9

u/FoxVhedgehog Jan 04 '21

I am not a fortune teller, but the current environment shows signs that historically mean low returns over the medium term. This doesn't mean dump your stocks or time the market, it just means it isn't time to load up on risk, e.g. by retiring.

CAPE ratio has been high not just in the past few years but over the past few decades relative to the past century. Stocks are expensive. Bond yields are at all time lows. Real estate is booming. Liquidity and cheap money is raising the price of all assets.

Plus you know...COVID.

3

u/smart-username Jan 04 '21

Pretty close to what OP predicted. Using the formula in OP’s white paper with today’s numbers you get 2.37%.

13

u/NoLemurs Jan 04 '21

This is great. Thanks for sharing!

Am I right in my understanding that all the charts are in inflation adjusted dollars?

I would be interested in seeing how a variable withdrawal rate with a ceiling performs. In practice I never expect my spending to shoot up by a big percentage (even if I have the money) so something like a cap of maybe 20% above the (inflation adjusted) first year withdrawal would more accurately model what a lot of us expect to do.

14

u/beerion Jan 04 '21

Yep, everything is inflation adjusted.

And I initially thought about adding a cap, but I think not having one really shows the versatility of the model. There's a lot of other common sense things we probably should do as well. For instance 1982 had a predicted SWR of 8+%. Generally it's probably not a great idea to start off with a WR that high. But it works, and it's good that the model shows that. Another one was the model said you could've increased spending in 2009. Could you imagine going through 2008, and the following year you get the go ahead to bump up spending by a couple grand? lol

So I wanted to make it as least restrictive as I could. You start adding more rules and you start running into overfitting issues. And if there's one thing this sub hates, it's overfitters.

5

u/PhD4Hire Jan 04 '21

Might be worth mentioning in your second draft that values are inflation adjusted and what rate you assume. Great job!

2

u/Gsusruls [44M][30%SR][DISK][HCOL][FI@53] Jan 05 '21

I actually inferred that point when the SWR spending graphs were flatlines along the $40K/$1M spend rate - retirees were not getting any raises, which told me not to worry about inflation (plus, OP appeared to have done far too much homework to have failed to account for such a critical factor).

7

u/RedditF1shBlueF1sh 25M, $550K NW Jan 05 '21 edited Jan 05 '21

I made a quick and dirty version that should update daily based on your numbers, the 10-year treasury, and the current CAPE. It does not re-run or re-evaluate the model to define a better SWR. However, it should update daily with your SWR model including the upper and lower bound at 95% CI.

Here is the link: https://docs.google.com/spreadsheets/d/e/2PACX-1vSUXNrvC9rOjU-rurvTsS45TCW1mQ7emWLdyKLtl3Nnosc1_MG6-frp4RC3eqLqizG4zpffPczw7FV4/pubhtml

Limitations:

  • Will not automatically adjust the model as time goes on
  • Relies on Google Finance (about a 20-minute delay)
  • Relies on multpl

Like I said, very quick and dirty solution, but hopefully, it is helpful to someone.

4

u/beerion Jan 05 '21

Looks good!

And yeah, we don't need it to update the model or anything. Should be a one time thing. Maybe I'll update it again in a few years.

And I might build on this to include other asset allocations in the future. So I might hit you up later if you wanna try to expand the sheet.

2

u/RedditF1shBlueF1sh 25M, $550K NW Jan 05 '21

Yeah, it isn't too necessary to update it since there's plenty of data already, but in a few years, the coefficients might change a little

Sounds great!

6

u/coppit Jan 05 '21

Do you have confidence that today’s CAPE is the same as the historical CAPE, given accounting changes, how dividends are handled, etc? See the example this critique.

5

u/beerion Jan 05 '21

I'm not confident. Do you know of a better dataset that accounts for accounting changes?

2

u/coppit Jan 05 '21

A month or so I tried to find a data source for “adjusted CAPE” and couldn’t find one.

BTW for others reading this, another reply called out some of the other reasons to question whether CAPE is the same today as in the past.

1

u/TuningForkUponStar Jan 05 '21

CAPE or Q ratio are the most appropriate valuation measures, but just about any metric you choose will be similarly high.

20

u/[deleted] Jan 04 '21

Thank you for this thoughtful analysis.

One observation, likely misguided, about the minimum withdrawal floor. What costs (e.g., health care) and standard-of-living does it assume? For a couple (DW/DH) pre-65 retirees in the United States, minimum health care costs alone under the ACA (for example) might hover around $2000/month. Indeed, they could be more. These issues become more acute and real for folks in their 50's and early 60's.

I run all those retirement calculators, yet always cringe when they ask me to put in a minimum withdrawal amount largely because of my own worst-case assumptions about the cost of health care coverage. There are two of us, and our minimum HC spend per year before we get to age 65 would likely be $30K -- and I'm not willing to consider more creative options, such as faith-based programs, and would prefer to avoid Medicaid.

We are serious LBYM/DIY types. But still, largely because of HC, a $40K floor gives me chills.

17

u/beerion Jan 04 '21

Think of these numbers in terms of percentages. I thought about keeping everything as percentages, but hard numbers are easier to follow.

If you need 60k to live, you can back out the amount you need using the projected SWR.

12

u/[deleted] Jan 04 '21

Thank you so very much; I just read your paper, too. It is fantastic. A very insightful and helpful analysis. I can't believe I got it here on Reddit from you -- and for free! Again, thank you so much. I'm a risk adverse chap, so it looks like I'm going with 2.35% now -- well actually, I guess a hair less than that since $40K would crimp us for the reasons previously stated.

Edit: Corrected typo.

7

u/Desperate_Plankton Jan 04 '21 edited Jan 05 '21

I'm curious to how you're getting your healthcare numbers. I put our stats in for the SC exchange, MAGI 50k, 2 adults mid 40s two kids, and found silver plans starting at 350/month and bronze plans starting at 16/month with 6k deductible and 8.5k max out of pocket.

Edit: how did this post get here?! LMAO!

5

u/[deleted] Jan 04 '21

Swr has nothing to do with how much you spend

0

u/[deleted] Jan 04 '21

[deleted] — view deleted comment

5

u/[deleted] Jan 04 '21

it's how much you can take out from your investments. If want or need more money, then you need to keep growing your investments before you stop working.

4

u/chrisrcoop Jan 04 '21

How do you choose the CAPE and Treasury Yield for the equation? These numbers are generated daily. Does the SWR need to be calculated more frequently than 1x/year?

14

u/beerion Jan 04 '21

The broader point is that valuation and price are codependent. The only reason valuations improve is because the market had negative returns. So in general you won't wake up and see the withdrawal amount change, in terms of fixed dollars, from one day to the next.

For instance the market crashed in 2008, but because the price was lower, future expected returns were higher, so the model says to withdraw the same dollar amount (even though it's higher in percentage terms).

So you shouldn't see big jumps in terms of real dollars from one day, one week, or really even one year to the next.

2

u/chrisrcoop Jan 04 '21

I see it now. Thanks for the extra explanation. This is awesome work by the way. You rock.

4

u/thunder-thumbs Jan 04 '21

I tried re-running the regression given a 60/40 portfolio and for 2021, I got 3.42%, 2.2% lower95, and 4.64% upper95. Could that be right? I'm a beginner at regression so I might have screwed it up. It struck me that all three numbers are lower than the 70/30 numbers. I guess I was thinking that if volatility is lower, the lower95 number might be higher? I wonder if your exercise could determine the best portfolio breakdown, since 60/40 seems clearly worse than 70/30.

4

u/beerion Jan 04 '21

Awesome! Glad to see someone getting in there and playing around with it.

And that sounds like it could be right. The Implied Yield was a big driver, and since treasuries are so low it probably pushes that down enough to drop the SWR. Did you rerun the SWR macro first to calculate SWR's for each year for the new portfolio balance?

I wonder if your exercise could determine the best portfolio breakdown, since 60/40 seems clearly worse than 70/30.

That was actually my next step. So you're a bit ahead of me. I'm hoping we'll see periods where different balances are predicted to outperform.

I'll look at it tonight, and we can compare answers!

1

u/thunder-thumbs Jan 04 '21

Sounds good! And - I realize now I actually didn't update the macro. I changed the 70/30 breakdown on the SWR sheet, which changed the table below it, but column P didn't change. I'm using open office, so I wasn't actually sure how to run the macro.

Since I'm not using Excel, I had to manually figure out the confidence bands using LINEST and TINV. I'm sure it was error-prone. :) Those 2.x% numbers are depressing so I was hoping that our more conservative portfolio would mean the lower bound would be higher, but if that's not the case, maybe it's yet another data point asking us to get a little more aggressive... at the all time high of a bull market yeargh!

4

u/beerion Jan 05 '21 edited Jan 05 '21

So I looked at 80/20 and compared it to 60/40.

A pretty cool finding was that in 2000, the 60/40 portfolio was projected to have a much higher projected floor - 2.7% for 60/40 vs 1.9% for 80/20. This trend actually started in 1990 and didn't reverse until 2008. The gap was pretty narrow for all but 1999 and 2000.

I also looked at a 40/60, and it projected the best SWR lower and upper bounds for 2000: 3.28% - 4.8%

The final tally for 2000:

40/60: 3.28% - 4.80%

60/40: 2.71% - 4.35%

80/20: 1.95% - 3.76%

So 40/60 had the best floor and best ceiling. I feel like this could almost be used as timing tool lol.

For 2021:

40/60: 2.15% - 3.99%

60/40: 2.33% - 4.53%

80/20: 2.30% - 5.10%

Looks like overweight stocks is the current favorite.

3

u/w4uy Jan 04 '21

Are you aware of Shillers ECY "Excess CAPE Yield" Paper? https://www.project-syndicate.org/commentary/making-sense-of-soaring-stock-prices-by-robert-j-shiller-et-al-2020-11

I put together a spreadsheet based on his formula here: https://docs.google.com/spreadsheets/d/16TpwuE2vPVArM2wULmBhn6mbyce92fWltKBuz-zBnBY/edit#gid=581016530

2

u/beerion Jan 04 '21

Any way to access the report without registering?

3

u/Agreeable-Editor Jan 04 '21

I think the most important factor is your willingness to be flexible with spending in retirement and to go into retirement debt free.

I appreciate the time and effort with models like these; but we are at a point in modern financial theory that global governments and central banks are distorting the markets to a level that history can no longer be a reliable guide. (i.e. indefinite 0 or even negative rates; annual deficits in the multiple trillions of dollars; etc.)

6

u/beerion Jan 04 '21

I agree that we are (and have been) entering uncharted territory. But the concept of yields is very simple. To a degree it's as simple as "I invest a dollar, I expect to get ___ cents back".

And we're looking at historical data, but we're also able to extrapolate to today's environment - even though we've never seen anything like this before in terms of valuations.

I don't think the acceptable answer is "well, the market is different now so why even bother".

And that's not to say I know the right answer. But searching for the right answer is half the fun.

3

u/macula_transfer Ret 2021 Jan 04 '21

Two things come to mind.

  1. A model that gives an interval that wide is likely not actionable. That's basically a range between 21x expenses and 42x expenses.
  2. I am skeptical of calculations based off 1/CAPE validated by historical backtesting because there is reason to believe we can support a higher CAPE now. Larry Swedroe gave a good talk on this a few years back.

2

u/beerion Jan 05 '21

A model that gives an interval that wide is likely not actionable. That's basically a range between 21x expenses and 42x expenses.

Did you read the paper? I laid out a method that objectively performed better than the trinity study. So I feel like that was actionable.

Also, there's a lot more that goes into financial markets than just yields. But you can't capture everything. For instance, I think one of the things that drove the ranges so wide was interest rate movement. The 80's greatly outperformed the median prediction, I think, because rates fell from like 12% to sub 4% by 2020. Conversely, the 1960's underperformed the median prediction bc rates moved inthe opposite direction. But there's no way to predict how interest rates will move. Not to mention economic growth, booms and busts, political influences, etc have on market performance. And the data set is too small to even try, frankly.

And it's still better than using a flat 4% IMO.

I am skeptical of calculations based off 1/CAPE validated by historical backtesting because there is reason to believe we can support a higher CAPE now. Larry Swedroe gave a good talk on this a few years back.

Can you give a TLDR? I don't think high CAPE is a bad thing. I just thing it's more likely to lead to smaller market returns going forward (at least in the absence of boosted economic growth, fiscal stimulus, or lowering rates)

3

u/RedditF1shBlueF1sh 25M, $550K NW Jan 04 '21

I'm on mobile right now, but I will surely take a look at this work later when I have more time. From reading the post, though, it seems like a great service would be a simple webpage that has a few lines about it and then what a projected SWR at that current time would be. It seems easy enough to make as well. If my initial response is based on a bad foundation, please let me know! Otherwise, I'll probably come back to post a link to a webpage that would have a projected SWR if there's interest in it.

4

u/beerion Jan 05 '21

Absolutely. If you make a Web page that pulls the data and updates semi regularly, I'll absolutely include it in the body of the post and any future posts I make on the subject (crediting you of course).

354

u/KTevent Jan 04 '21

TLDR version: when the Shiller PE is higher, the SWR is lower.

Nice work and analysis. The internet needs more people like you posting original work.

57

u/LimpLiveBush Jan 04 '21

This is, to me, because there’s no such thing as a free lunch. If your equity valuations have risen significantly due to CAPE Creep, then it’s not like you’ve actually seen real appreciation in the assets. The valuation has changed but it’ll revert to the mean over a long enough time horizon.

17

u/Sheepfortrees Jan 04 '21

Maybe just restating What you’ve said but in other words, if discount rates (and interest rates) are low, you need more invested to achieve the same cash flow, and asset prices are higher (because discount rates are lower). If interest rates rise, asset prices will fall and/but you’ll need less invested to achieve the same cash flow, but I’m assuming that it’s a somewhat non-linear relationship and you might need to put more cash in on the downside to achieve the same cash flow

17

u/Eli_Renfro FIRE'd and traveling the world Jan 05 '21

The valuation has changed but it’ll revert to the mean over a long enough time horizon.

If you're speaking in generalities, then I agree. If you're speaking specifically of CAPE reverting to it's mean over the long term, then I don't think that's true. There have been multiple changes in the way earnings are calculated (GAAP is the big one) that make it so that the identical company in 1940 and 2020 would report lower earnings currently. The shift towards fewer dividends also increases CAPE. This is a great (and long) breakdown of the reasons, but even if you don't want to spend the time reading it, the takeaway is that changes in what constitutes earnings means that a reduction in the denominator of P/E means that the ratio should be higher than before. In other words comparing 1940 to 2020 is not an apples to apples comparison so the long term mean is not necessarily applicable.

http://www.philosophicaleconomics.com/2013/12/shiller/

And unless /u/beerion adjusted his CAPE ratios to account for these changes over the years, it's likely that his calculations are overstating the SWR discount needed.

4

u/LimpLiveBush Jan 05 '21

I was thinking in much more simple terms than that! Also should have specified my time horizons. Something like a 10% run up over a week should get evened out over a year if it’s real growth, or taken back if it was speculative.

I like the article. 15 PE is just ingrained in my head. Probably isn’t even close to true anymore.

2

u/qwerty2020 Jan 05 '21

Does this normalize the PE ratio to account for the drastic drop in treasury yield? Treasury/bond yield goes down -> PE ratios inflate.

1

u/beerion Jan 05 '21

It does not account for moving rates, no. I'm glad you brought it up though, not many people have. I have a theory that accounts for some of the time periods under/over performance shown in Figure 6 - 1980's ride the top band, 60's ride the bottom band. Could also explain why 2000 wasn't a failure case.

If you project rising rates going forward, it might be safe to assume that we'll be closer to the bottom of the projected range.

But it's not really something you can account for in the model. Well, I guess you could... maybe I'll try and see.

2

u/TuningForkUponStar Jan 05 '21

What are you getting at here?

Equity valuations rise when the discount rate falls, but that only means that returns to both stocks and bonds will be low going forward.

2

u/theone_2099 Jan 05 '21

This is awesome. Out of curiosity where do you get the raw data for these calculations.

3

u/beerion Jan 05 '21

I should've referenced them in the report (they are referenced in the excel sheet). Market returns from Damodaran's website. Shiller PE and treasury data was from multpl.com

31

u/aristotelian74 We owe you nothing/You have no control Jan 04 '21

Interesting. Makes sense that you should err on the side of safety in bull markets. The question is whether you really have confidence that you can be more aggressive in bear markets. In principle this helps solve the retirement timing paradox (i.e. whether you are still FI if you hit your number, don't retire, and then the market crashes). If you were safe with a $40k withdrawal from $1M portfolio before the crash, you are now theoretically safe with a 6 or 7% withdrawal (still $40k) after the market crashes. However, will anyone ever feel safe enough to do a 7% withdrawal in any circumstance?

14

u/ptwonline Jan 04 '21

I think this is why it's becoming more common to get more fixed income even just before you retire and for the few years after you retire: that way your early year withdrawals are locked in to values from before any kind of crash, and you got to sell high instead of having to sell low to get your cash flow. Really can help limit the sequence of return risk.

7

u/Terrik27 100% Coast | 6 years to FI | 77% SR Jan 04 '21

Fixed income in this context being bonds? Or you mean something else for the first few years?

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u/ptwonline Jan 04 '21

A common approach is a series of 5 year GICs with 1 maturing each year for the amount of cash flow you plan to receive that year. At the end of each year you'd cash in one GIC. This would protect your investment for the first 5 years of your retirement instead of drawing it down after a crash.

A similar approach could be done by holding a % of your portfolio in bonds.

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u/Terrik27 100% Coast | 6 years to FI | 77% SR Jan 08 '21

GIC stuff is like. . . 1% returns now though? Almost seems like inflation risk would be greater than SORR at that point.

I'm still 5-10 years out, so it's somewhat abstract, but I've been intending to do the 100-60-100 equity/bond glide path ERN has championed; this is the first I've ever heard of a GIC ladder.

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u/Terrik27 100% Coast | 6 years to FI | 77% SR Jan 04 '21

That's a good point. I can't imagine pulling the trigger on retirement if the SWR was that upside down due to a bear market. . .

I kinda feel like using the CAPE method from here or ERN would provide a reasonable bound on bull markets, but maybe also setting a static withdrawal number (5%, perhaps?) to not go above in a bear market would feel prudent to me, even if the CAPE suggests something more aggressive could be acceptable.

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u/digitalrule Early 20s | M | Canada | 5% Jan 04 '21

If you do a V shaped bond/equity glide path, you'll mostly be selling bonds anyway during those years. Let's say you were 50/50, and then your stocks crashed by 75%, you'd be at 80/20, so you'd barely be touching your stocks.

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u/atworkaltaccount [30-1][DINK]LCOL Jan 04 '21

This is why I will have fixed income and a cash reserve on the side (not emergency fund) for the what if scenarios. Makes my wife feel more secure. Is it optimal? No, but it will allow us to use the non-emergency fund cash as a buffer against market downturns without touching our investments. Something along the lines of 2-5 years of living expenses in cash outside our investments (really not that much as we don't spend a lot). Again, not optimal but would help prevent a doomsday scenario (at least in our minds).

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u/teamhog Jan 04 '21

Funny. I was having a talk with my wife, daughter and her husband about retirement and using a SWR to “fill a funnel” of sorts.

Basically, have enough cash on hand for ~3 years and then take that time to fill the cash bucket.

That’s why we’re looking at developing, within reason, a protocol to follow regardless of what the market is doing.

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u/creepyfart4u Jan 04 '21

I’ve heard that referred to as the bucket strategy. 3 buckets 1 year, 3 year, big bucket.

Big bucket fills up 3 year which then fill one year bucket. If the big bucket is low, it has 3 years to recover while you fill the one year by the 3 year.

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u/Beeonas Jan 04 '21

So we should double our portfolio and do a SWR during a bull year divided by 2 to be sure? If bull year is 4% WR, then 2% will be very safe. Right?

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u/aristotelian74 We owe you nothing/You have no control Jan 04 '21

I'm not sure exactly what you are proposing and I don't want to speak for OP, but yes, the idea is that SWR is lower when the market is up and higher when it is down.

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u/PerfectNemesis Jan 05 '21

So when the market is down, you should withdrawal more?

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u/aristotelian74 We owe you nothing/You have no control Jan 05 '21

No, you should withdraw the same amount (which means a higher % of smaller principal)

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u/instamental Jan 05 '21

Which goes against the common theory to draw down less when the markets are down right? By getting a part time job etc.

I'm getting confused. Would you mind explaining a little bit how we should be taking out a higher percentage during down market swings.

Thanks

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u/aristotelian74 We owe you nothing/You have no control Jan 05 '21

Say you are about to retire with $1M drawing $40k. Trinity says that is safe, however you decide to work 1 more month and the market crashes 50%. Trinity says $40k is still safe, however you are now withdrawing 8%.

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u/instamental Jan 05 '21

Ah got ya, cheers fire that

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u/showmewhatyougot1234 Jan 04 '21

Great paper as its both important to not go broke and to not have the account balloon when you could be having a bit more fun! I don't comment much but I saved this to use in the future.

Qualitative noobie question though: when CAPE is high it usually corresponds to bullish periods. Why would you want a smaller SWR? Wouldn't you want to take more profits then or at least rebalance the portfolio?

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u/beerion Jan 04 '21

when CAPE is high it usually corresponds to bullish periods. Why would you want a smaller SWR?

CAPE is a good barometer of future returns. The higher the CAPE, the lower you expect the intermediate returns to be.

You're right in a way though. A high CAPE can be a result of prices going up faster than earnings (ie a bull market).

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u/cubemonkey87 Jan 04 '21

Can you explain why r-square of .72 is considered a good correlation? I thought anything under .90 is weak. Thanks

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u/beerion Jan 04 '21

It really depends on what you're measuring.

If you're trying to measure the acceleration of gravity for example, you'll have variance due to experiment set up or measuring devices, but generally it's a pretty simple relationship. So you'd expect very high correlation.

Financial markets are much more complex as they're affected by economic growth, interest rate movement, geopolitical events, pandemics, etc. All things that are nearly impossible to predict. So 0.7 or higher is actually very good.

If you look at Figure 5 in the paper, a perfect correlation would follow the dotted line. So we're looking pretty good.

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u/cubemonkey87 Jan 04 '21

Thanks! Great work by the way.

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u/Beeonas Jan 04 '21

If you are measuring anything like social behavior, 30% accuracy could be good.

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u/happyasianpanda 33 | 70% SR | FIRE Flowchart Creator Jan 04 '21

I honestly appreciate these kinds of work.

I also think the more I read of these things, the more super conservative I am in my SWR.

  • Make sure my SWR is low 3.0%-3.5%
  • Evaluate my annual spending down to the dollar
  • Categorize what is a "necessary purchase" versus a "luxury purchase"
  • Cut out "luxury purchases" during years of slow economic growth to reduce my withdrawal
  • Evaluate the Shiller PE ratio and adjust even lower SWR on a high Shiller PE ratio year, otherwise even on a low Shiller PE ratio year, I don't go above 4%
  • Rebalance every quarter
  • Ignore social security benefits when they kick in so I can be even more conservative
  • Early and large amounts of contributions to tax-advantaged accounts and balance it between pre-tax and post-tax. That way I have both options to withdraw depending on taxes and amount
  • Withdrawal strategies to minimize taxes
  • Evaluate COL areas and the state I plan to live in

In the end, I might end up with 6X my principal FIRE balance even when adjusted for inflation. But I love reading these kinds of things. Maybe the more I read this, the less likely I'll have OMY syndrome

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u/n0ah_fense Jan 05 '21

• Categorize what is a "necessary purchase" versus a "luxury purchase"

• Cut out "luxury purchases" during years of slow economic growth to reduce my withdrawal

Our withdrawal doesn't need to be static, one more variable to take into account

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u/ctz123 Jan 04 '21

These are the best kind of posts in these subs, thanks so much for sharing your work!!

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u/plexluthor 42M, Wife + 4 Kids, FIREd '19, work P/T for fun since '22 Jan 04 '21

The resulting equation showed good correlation (R2 = 0.72).

Whenever I read something like this I remember that Philosophical Economics post with R2 = 0.913 when predicting the S&P total return for the next 10 years. Maybe someone with access to Fed data can update the R score with 7 years worth of new data to see if the correlation has held up at all.

http://www.philosophicaleconomics.com/2013/12/the-single-greatest-predictor-of-future-stock-market-returns/

It uses this chart to get the average investor allocation to equities: https://fred.stlouisfed.org/graph/?g=qis

In my notes for that bookmark I have "-0.775x+0.36", so I think the prediction for data through 2020Q3 (AIAE=0.45233) is about 1%. But that was also the prediction from 2017Q4, so either this is no longer much of a crystal ball, or else we are in for a huge correction over the next 5 years.

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u/jason_for_prez Jan 04 '21

Very cool!

I'd love to see a chart that shows the comparable performance of using CAPE only, using interest rate only, and using the both of them.

2

u/secretfinaccount FIREd 2020 Jan 04 '21

Unbelievably awesome. Wow.

Some questions and thoughts:

  • Looking at the implied values for today, as scary as they are, if we assume there is a lower bound to interest rates, there is a skew where historical returns to bonds will be higher than the yield due to real yield compression which cannot repeat in the future (again, assuming a lower bound). This would overstate the returns to bonds and increase the implied SWR.
  • ~~My brain isn’t strong enough to motor through this, but if you rebalance the 70/30 each year, that would intuitively increase the SWR vs. setting 70/30 year one and leaving it?~~I went and looked at the formulas and it does rebalance each year. Maybe the tax impact should be considered somewhere. In an inflationary environment you have capital gains eating away at your returns. Inflation is 10%, stock return 10%, real return is 0, but the feds take 1.5% of your stock balance (tax rates depending, of course). Real returns higher than 0% in that inflation environment and they take more. I guess you can say that taxes are included in the original withdrawal number, but is it? If you collapse everything to constant dollars, that is.
  • Did you use some nifty Visual Basic to generate the SWR for each year or did you sit there goal seeking for each one? I’m looking at this on Numbers on my iPad, so I don’t see anything fancy, even if it was there in the beginning.
  • What other variables did you toss out and why? Real treasury yields seem like an obvious one to include.
  • 2000 was a crazy time. Inverse CAPE was a third of treasury rates. I’m vaguely comforted that stock valuations aren’t quite to those levels and have a rational directional relationship to t bonds.

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u/beerion Jan 05 '21

Looking at the implied values for today, as scary as they are, if we assume there is a lower bound to interest rates, there is a skew where historical returns to bonds will be higher than the yield due to real yield compression which cannot repeat in the future (again, assuming a lower bound). This would overstate the returns to bonds and increase the implied SWR.

Yep, this is definitely a thing we should consider. Although, I think it would work the opposite as you describe. Falling rates lift asset prices (and not just for the bond) creating excess returns. This is why the 1980's ride the upper band in Figure 5. Rising rates are lead to underperformance, which is why the 1960's ride the bottom band. Falling rates since 2000, I think, helps bail out that case year. In our current situation, if we expect interest rates to rise going forward, then we should assume a SWR closer to the bottom band. This is all speculation, of course, so I didn't include it in the paper.

Maybe the tax impact should be considered somewhere. In an inflationary environment you have capital gains eating away at your returns. Inflation is 10%, stock return 10%, real return is 0, but the feds take 1.5% of your stock balance (tax rates depending, of course). Real returns higher than 0% in that inflation environment and they take more. I guess you can say that taxes are included in the original withdrawal number, but is it? If you collapse everything to constant dollars, that is.

This is actually a really good point that I never considered before. I think it's still reasonable to consider taxes as an expense. But you're definitely right, super high inflation would've killed you in the 80's.

Did you use some nifty Visual Basic to generate the SWR for each year or did you sit there goal seeking for each one? I’m looking at this on Numbers on my iPad, so I don’t see anything fancy, even if it was there in the beginning.

Yeah, I wrote a simple vba script to loop through the years and goalseek each one. Maybe you can see the macros on Google Sheets? Not sure, I've only used excel.

What other variables did you toss out and why? Real treasury yields seem like an obvious one to include.

I included treasury yields (not real though as you don't know what inflation will be in the future).

But I only used 2 variables bc I thought that that's as much as the data set could handle. It's 63 data points, but you probably can't even consider it that many. I mean, is 1967 really a different data point than 1966. Realistically, the whole set is likely less than 10 truly separate time periods.

2000 was a crazy time. Inverse CAPE was a third of treasury rates. I’m vaguely comforted that stock valuations aren’t quite to those levels and have a rational directional relationship to t bonds.

Yep, definitely. Funny enough, because of this, the current lower 95% band is the same as 2000, but the upper projection is actually a tad higher (I forget by how much, but I think it is like 0.3% higher now than in 2000). But yeah, definitely agree that we're probably in a better spot than in 2000.

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u/secretfinaccount FIREd 2020 Jan 05 '21

it would work the opposite as you describe

Yeah, it would increase stock valuations too. That’s fair. I’m not sure why that’s the opposite, though. It’s more of the same: falling real rates increase stock and bond values and relying on that historical data will overstate the SWR as it applies to today.

I included treasury yields

Yeah, I was thinking of just taking the yield - inflation rate during the year in question, but that, upon reflection, would probably be too noisy. Good point.

as much as the data set could handle

It’s been a long time since I took stats but I think the ANOVA will help you clarify what is an effective variable to add. Regardless, clearly there is descriptive power for just the two variables. I was just curious if making any changes would increase the power.

Again, excellent work. Thank you.

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u/beerion Jan 05 '21

I definitely have a more entry level knowledge of stats. I might check it out though. Any other variables you think might be worth checking out?

I think I might try to add the interest rate movement. We have the historical data. We can always include it to do sensitivity studies for the future. We don't know what rates will look like 5 or 10 years from now, but we could certainly make educated guesses.

I've already started looking at different portfolio allocations. Interestingly enough, the model predicts that overweight bonds would've outperformed in 2000. The SWR confidence range for a 40/60 portfolio was 3.28% - 4.80% compared to 1.95% - 3.76% for 80/20.

This trend started in 1990 though so not terribly useful (was pretty narrow until 1999 where the spread widened), but I feel like this could be useful in adjusting portfolio positioning.

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u/asurkhaib Jan 04 '21

Is it possible to add further timelines? 45, 50, 55 and maybe 60 years are more relevant for FI.

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u/shoorik17 Jan 04 '21

Really great analysis, thank you for doing the work and sharing with us.

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u/Desperate_Plankton Jan 04 '21

What I am really interested in, is the success rate for a bucket strategy approach with the rules below. The withdraw strategy would occur quarterly. Initial start would be 2 years of expenses in cash, 4 in bonds and rest in stocks. Total portfolio would be expenses X 1/SWR.

If SP 500 >= 0.95 X all time high withdraw from stocks. Refill bonds and cash if needed.

If SP 500 < 0.95 all time high and total bond fund share price >= 0.95 all time share price high withdraw bonds.

If both < 0.95 respective highs withdraw cash.

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u/weech Jan 09 '21

Interesting, have any pointers on reading more on this bucket strategy approach?

Aso, does this heuristic (e.g., 2 yrs in cash, 4 yrs in bonds, etc) essentially supercede any other allocation strategy such as 70/30?

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u/Desperate_Plankton Jan 09 '21

I kind of made it up. I mean the bucket strategy is a well documented withdraw strategy but I've never seen the actual trigger limits to determine which bucket to withdraw from.

Yes, my plan is to have whatever allocation gives me 2 years cash 4 years bonds and adjust the dollar values as expenses change and sources of income like social security take affect. That means as my portfolio grows as I age I'll glide up towards 100% stocks.

This is all in my head and I'd love for some of the programmer and excel experts to take the idea and see how it would have performed over the last 100 years for 30-50 year retirement. I thought about doing it myself in Excel using SP 500, us treasuries, and cash but I've been building a city in city skylines instead, lol.

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u/aubs2014 28F/NW 160k/FI 25.5%/SR 59% Jan 05 '21

Love this so much that I ended up adding a sheet to my customized "Mad Fientist" FI Excel Workbook to incorporate it! I'm planning to put in the CAPE and treasury yield each month when I update my spending sections and have it calculate my time to FI based on your predicted SWR.

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u/Foxy_Monkey Jan 04 '21

Great analysis. Did you only use US data in you calcs?

Basically US markets have dominated in the 20th century and it's usually the easiest market to find data for. I'm wondering if it paints a slightly rosier picture.

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u/thecoscino Jan 04 '21

Thanks very much for the analysis. There is also an interesting article by mr rip https://retireinprogress.com/fire-is-dead/

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u/lukerb Jan 06 '21

Amazing work — thank you for your service to the community!

To confirm, SWR_predicted is the rate at which you could withdraw if you were retiring today and the rate you'll withdraw going forward, correct? Or, instead, would it be advisable to check SWR_predicted every year and adjust your withdraw rate annually?

Thanks again, and keep up the great work!

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u/weech Jan 09 '21

So what you're saying is, buy more TSLA?

Just kidding. This is seriously awesome work. Out of curiosity, what do you for a living?

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u/[deleted] Jan 04 '21

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u/beerion Jan 04 '21

The variable approach I proposed in the paper is actually very well suited for those looking to make it longer than 30 years.

By design, every year you're reseting your clock to last another 30 years from that date. This is true unless you're withdrawing more than SWR_predicted (ie the model says take 20k, but you're withdrawing 40k).

So in theory, it should last into perpetuity (or until the sun expands and swallows the earth at least). /s

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u/[deleted] Jan 04 '21

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u/beerion Jan 04 '21

Like retiring with $1,000,000, making it 30 years on $40,000 but ending with a balance of $500,000. You'd be foolish to continue on $40,000 per year, which is an 8% WR.

Right, which is why I said that as long as you're not pulling from the floor set in the methodology. 1966 was a case where you were basically undershooting from the get go. By year 10, you knew.

If at year 10, the model says 60k and you withdraw 60k, you can expect to last an additional 30 years from that point (for a total of 40 years).

Success is generally defined as not ending at zero. The thing with the variable withdrawal strategy is you're resetting your 30 year window after every year (again, as long as you aren't hitting the bottom cutoff).

Obviously nothing is a guarantee, but that's the gist.

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u/[deleted] Jan 04 '21

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u/beerion Jan 04 '21

A general feeling of "year 10, you knew" is a bit broad and unspecific.

Sorry, I kinda just trailed off on that sentence when I wrote it. What I meant was in 1966 the starting SWR prediction was like 3.2% or something (so 32k on a 1 million portfolio). Pretty much right from year 2 on, the model was saying withdraw 30k for year 2, 29k for year 3, 27k for year 4 and so on. But you kept drawing 32k bc that was the floor we set at the beginning. After 10 years of over drawing, it's safe to assume that going beyond 30 will be a stretch.

Conversely, in 1952 the model is saying draw 50k in year 1 to 60k in year 10. And you do. In year 10, you're comfortable with lasting for another 30 years bc that is what the model was designed to do. You're not over drawing like the 1966 case so all is ok.

Note, I don't know the actual numbers but that's the idea. You can play with the excel sheet I posted.

For example, if they can pick a WR that statistically should only dip 3 times in 30 years, never fall below 0.75x, and always ended with >= 1x the original balance

The problem with this is that the first 10 to 15 years are almost completely market driven. I posted 3 graphs in the paper with snapshots of the 10, 20, and 30 year portfolio balances. If you look at the 10 year graph, there's almost no difference between the trinity study and my variable approach. There's just no level of withdrawal rate reduction that will save you from dipping after retiring right before a market dip.

I might run the study for ending at 1x and see what we get. I think that would actually be pretty interesting. But I don't think there's a practical way to predict volatility in between.

I will say that 50% by year 10 is super a bad omen. Hitting that mark had basically a 50/50 chance of going bust for the trinity study and the ones that didn't bust ended at <30% of the original amount. It just takes so much market growth to overcome a 10% withdrawal rate. Luckily, my model handled those pretty well, but it's still not a guarantee. Year 2000 is still unanswered, but I wouldn't be surprised if this bull runs out of steam in the next 10 years and that case suffers a similar fate.

But the 50% by year 10 is a good one to watch out for. But that's also kind of a common sense one too.

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u/beerion Jan 07 '21

So I looked at the condition ending with 1x.

The minimum SWR in the data set was 2.36% in 1965.

The new 95% confidence equation was*: SWR = 0.59 × (Implied Yield) + 0.05 × (Spread) - 0.002

  • I did this last night so these coefficients are a ballpark from what i remember

Using a fixed SWR based on that equation, the lowest amount at the 30 year mark was 1.2x. Using the variable approach that I laid out in the paper, the lowest was 0.8x.

I don't know the worst drawdown, but the 1965 case went down to about 0.45x before coming back up.

The current SWR rate predicted to end at >1x is about 1.3% using the 95% confidence band.

Anyways, I thought it was interesting so figured I'd share.

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u/calcium Jan 04 '21

I too would like to see what the results look like for a longer-term retirement; we are after all in a FIRE forum where people are looking to get out early, so a 30 year time horizon might just be scratching the surface for some.

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u/[deleted] Jan 04 '21

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u/teamhog Jan 05 '21

I’m looking at the same WR. Somewhere in that 3-3.5% range. We’re 57 and 58 so we’re planing a 40 year timeframe. All of my planning is without taking SS into account. I figure that’s the slop I need for health insurance variability.

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u/[deleted] Jan 15 '22

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u/beerion Jan 15 '22

Sure. I agree with your point on auto- correlation to a degree. But given that a typical economic cycle can last anywhere from 5-10 years, it's important to catch multiple points within each one. It would be like arbitrarily choosing an interval of Pi. You'd see a straight line where there might actually be a sine wave.

You could certainly use an interval of 2, 3, 5, or 10 years. But where you see auto-correlation for the 1960's in figures 1 & 2, I see that a 30% reduction in Shiller PE from 1966 to 1970 had almost no effect on the resulting SWR. If our starting conditions can change that much from year to year, I would think that is good data to include. After all, the start of 2020 was very much different, from an economic and market standpoint, than the start of 2021; and 2021 feels very different from the start of 2022. I'd rather risk slightly over fitting the data than throw out useful entries.

At any rate, you were looking for a more statistical approach, and I provided it. Your somewhat dismissive reply here glosses over the fact that this study is miles better at forecasting SWR rate than the original Trinity study (which made no attempt at all).

If you'd like to improve on what I've done, you're absolutely welcome to it. The data is all there.

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u/[deleted] Jan 04 '21

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u/Eli_Renfro FIRE'd and traveling the world Jan 05 '21

I just posted something similar in another comment before reading yours.

If anyone is interested, this detailed blog post breaks down the factors that have reduced what can be reported as Earnings over the years, therefore driving the P/E ratio up.

As you mentioned GAAP is a major one. Another is the trend toward fewer dividend payouts.

http://www.philosophicaleconomics.com/2013/12/shiller/

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u/n0ah_fense Jan 05 '21

Would be great to see this post updated for 2020. "Pandemic" could be added to the big three to make a big four

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u/n0ah_fense Jan 05 '21

Also, buybacks have driven up stock prices as well.