*February 28, 2022*

What a difference a year makes! In late 2020, only about 16 months ago, I felt the urge to comment on the then-fashionable discussion of how **low inflation** would impact retirees. See Part 41 – Can we raise our Safe Withdrawal Rate when inflation is low? of my SWR Series. Feels like a lifetime ago, doesn’t it?

The takeaway back then: don’t get distracted by high-frequency economic fluctuations. Low inflation doesn’t necessarily mean we can all raise our safe withdrawal rates. Certainly not one-for-one. There is neither empirical nor theoretical economic backing for materially changing your retirement strategy.

Only a little more than a year later the tide has turned. We’re now facing the highest inflation readings in about 40 years. 7.5% CPI and potentially 8% year-over-year once the BLS releases the February figure in mid-March. So, people asked me if my inflation views are symmetric, i.e., high inflation is also a non-event? As I signaled in my inflation post last month, I’m not too worried. Here’s why…

Before we begin… a favor to ask: Please check out my recent podcast appearance on the White Coat Investor. It’s also available on YouTube. Talking about Safe Withdrawal Rates, Robo Advisers, Target Date Funds, Annuities, Trading Options, and more.

### Back to Inflation…

Today, I want to perform a type of analysis that had been on my mind for some time but I waited for the right occasion to talk about it: I have extensive time-series data on safe withdrawal rates and a bunch of macroeconomic and financial observables, like the CAPE Ratio, 10-year bond yields, inflation number, etc. The economist/econometrician/statistician in me would scream: “that calls for running a regression to determine how different macro/finance fundamentals impact your safe withdrawal rate!” Essentially, estimate an equation of the shape

SWR = a + b1*StockEarningsYield + b2*Bond Yield + b3*ShortTerm Yield + b4*CPI + etc.

Why did it take me so long to perform this analysis? Well, to be honest, there are a few “snags” in this type of analysis that make it mostly an interesting **academic exercise**, but maybe a little less useful as a **practical tool **for an early retiree “in the trenches” trying to pin down a withdrawal rate. More on that later. But I still believe that this type of analysis can educate us how – at the margin – higher or lower inflation would impact the safe withdrawal rate derived from my Safe Withdrawal Rate Toolkit.

### Data used

For the safe withdrawal rates, I generate twelve different series with my Google Sheet Toolkit:

- 3 different Stock/Bond allocations: 60%/40%, 75%/25%, 100%/0% Stocks/Bonds
- 4 different assumptions on the length of retirement and the final portfolio target:
- 30 years horizon, FV=100% of the portfolio (capital preservation, after accounting for inflation)
- 30 years horizon, FV=25% of the portfolio, i.e., only partial capital preservation, say because
- 30 years horizon, FV=0% (capital depletion)
- 50 years horizon, FV=0% (capital depletion)

I will use each one of the 3*4=12 combinations (one at a time!) as the dependent variable.

For the explanatory variables (=independent variables), I use the following eight series:

- The Shiller CAPE earnings yield, i.e., the inverse of the CAPE ratio, at the beginning of retirement
- The 10-year benchmark bond yield at the beginning of retirement
- The short-term yield (e.g. 3-month T-Bill) at the beginning of retirement
- The 1-year CPI inflation (i.e., rolling over the past 12 months)
- The 1-year
**future**CPI inflation - The 5-year
**future**CPI inflation - The 10-year
**future**CPI inflation - The 30-year
**future**CPI inflation

Notice that only regressors 1-4 would have been observable and available at the start of retirement (subject to a small caveat because the CPI comes out a few days after the month-end). But, again as an academic exercise, I can certainly include **future **realized inflation to see how a retiree would have changed his/her withdrawal rate if he/she had indeed had the perfect foresight and had known the future realized inflation rates.

Some more technical notes:

- I run the regressions from 01/1920 to 12/1991, at a monthly frequency. Thus the last retirement cohort is the final cohort that had 30 full calendar years of actual portfolio returns.
- The 50-year retirement horizons would include up to 20 years of calibrated/estimated return data toward the end. Thus, we want to use those results with a grain of salt. But, then again, as I pointed out in Part 14 and Part 15, due to Sequence Risk, the portfolio returns during the latter part of retirement have relatively little impact on the SWR.
- All regressions use the Matlab/Octave package “nwest” to calculate the Newey-West heteroscedasticty-adjusted t-statistics. Simple Ordinary Least Squares (OLS) slope estimates are indeed correct, but the t-statistics would have been overstated due to the overlapping windows!

### Warming up: Univariate Regressions

As a warm-up, let’s look at the **univariate **regression results (y = a + b*x) of one specific SWR Series: 75%/25% portfolio, 30-year horizon, and 25% final value target. I use this set of “favorite” model assumptions often because it’s a great baseline for both early and traditional retirees. It works for a traditional retiree with a 30-year horizon who wants to leave a quarter of the portfolio as a bequest. Or an early retiree who wants to bridge 30 years until Social Security and Pensions set in and keep the 25% final value target to supplement those cash flows later in retirement.

Let’s look at the scatter plots of the independent variable (x-axis) and the safe withdrawal rates (y-axis). I group these into 4 charts with scatter plots each. Let’s start with the stock earnings yields and the 10-year bond yields, see below:

- The Shiller earnings yield has a strongly significant slope parameter (β=0.55, t=4.98) and a very impressive correlation of ρ=0.84. All the failures of the 4% Rule happen when the CAEY is below 5%, i.e., when the Shiller CAPE is above 20. Regular readers will know that I’ve been “preaching” that since 2016!
- The intermediate-term bond yield also has a positive impact on the SWR, but the relationship is certainly not linear. And it’s not even monotone either! For very low bond yields, historical SWRs were elevated again. The sub-4% withdrawal rate all occur in the “middle region” between 3% and 6.5%.
- By the way, regular readers will recognize the two charts (though updated with newer data) as part of my analysis debunking troll-extraordinaire Financial Sumoguy’s claim that we need to pin our withdrawal rate to the 10-year yield, and the 10-year yield
**alone**: “Do we really have to lower our Safe Withdrawal Rate to 0.5% now?” (August 31, 2020). The lesson back then: That’s really dumb. The 10-year yield is not very useful when determining a safe withdrawal rate of the average Stock/Bond portfolio.**Equity valuations matter most!**

Moving on to short-term yields and inflation:

- Short-term yields (3-month T-bill) indeed correlate a little bit with the current SWR. The t-stat is 1.9 which would qualify as significant at the 5% level for a one-sided test. But also notice that all of the failures of the 4% Rule occur between 3% and 7% short-term yield, not really when yields are low. You’re looking at a range of the blue cluster of +/- 4 percentage points around the red line. As a standalone regression to learn about SWRs, this is utterly useless. But this regressor might be useful in the multivariate regressions below.
- If we try to relate the trailing inflation rate with the current SWR, not only is the relationship statistically insignificant (t=1.30). The very small slope actually goes in the wrong direction: a
**positive(!)**relationship between past inflation and future SWRs. That flies in the face of all those running around in panic in light of the high CPI numbers now.

Next, let’s look at how the benefit of perfect foresight about future inflation could have “predicted” the SWR. Let’s start with the first chart and look at the 1-year and 5-year annualized CPI rate on the x-axis and the SWR on the y-axis. There’s pretty much no relationship. It doesn’t take an economics Ph.D. to figure that one out! So, quite amazingly, future inflation over a short-to-medium horizon seems uncorrelated with future SWRs.

And, finally, the 10-year and 30-year future realized inflation (annually):

- The 10-year realized inflation rate has a negative slope, but it’s only about -0.20. But the negative slope is statistically significant (t=-2.21). But again, there’s a huge band of blue dots around the red line. On a standalone basis, even knowing the future 10-year inflation rate is useless!
- The 30-year future realized inflation rate has the best statistical association with the current SWR. That’s pretty impressive: a slope of about -0.94 (so, indeed, the realized inflation rate reduces your SWR almost one-for-one!). The slope parameter is highly significant (Newey-West t-stat of -2.75) and the correlation is also not too shabby. But notice one fly in the ointment? Between 1929 and 1959 we had modest inflation, just under 2%, and that’s when the 4% Rule failed. So, 30 -year realized inflation rates are not very useful when pinning down SWR on a standalone basis.

### Summary so far…

Equity valuations matter the most. And recall, the CAEY is something that’s actually **observable **at the start of retirement. Trailing inflation has a **positive (!) **impact on the SWR and even with the perfect foresight of the future 30 years of inflation you can only hope for a whacky, not exactly monotone relationship between inflation and the safe withdrawal rate.

Hence, my assessment of the current macro and financial conditions: we should certainly be worried about the future and choose a conservative safe withdrawal rate. But that has nothing to do with inflation, and has **everything **to do with lofty equity valuations!

### Warm-up 2: Univariate regressions of all SWR time series on the CAPE Yield

One other exercise before we jump into the multivariate regressions (i.e., multiple explanatory variables at the same time). Let’s look a the univariate regression results of regressing all the 12 different SWR series on the Shiller CAPE yield. Please see the table below.

- I marked the 75/25, 30Y horizon, 25% FV target because we will use this SWR series in more detail later.
- All slopes and intercepts are highly statisitcally significant.
- Quite intriguingly, the slope estimate for the CAPE yield is always just about 0.5. If you ever wonder why the CAPE-based safe withdrawal rate rules (see Part 18) work so beautifully with a slope parameter of 0.5, this is the reason!
- Of course, if the equity portion is all the way at 100%, then you ‘d increase the importance and thus the slope of equity valuations. Makes perfect sense, too!
- Playing around with different horizons of final value targets for a given asset allocation, mainly impacts the intercept, not the slope. For example, in the 75/25 example, you’d use a 1.61% intercept and 0.541 slope with capital preservation. But if you want to deplete your portfolio you’d keep roughly the same slope (0.557) and shift up the intercept to 2.73%.

By the way, what kind of SWR would be recommended from the above regressions using today’s CAPE yield? If we assume a CAPE of around 35 as of 2/25/2022, then the 75/25-30Y-25%FV regression would imply a safe withdrawal rate of 2.45% + 0.553/35=4.03%. Whoa, that’s awesome! The 4% Rule works, even in today’s environment? Well, not so fast! Remember that the good-old regression draws a line **through the center** of the scatter plot, trying to minimize a squared-deviations loss function. With a 4% withdrawal rate, we’d then risk a failure rate of 50%, gasp! And the spread of the blue dots around the red line is huge, with a standard deviation of 1.12% for this model. We might need to reduce that SWR quite substantially, to lower that probability of failure. We can gauge from the scatter plot that we’d need to shift down the red trend line by probably roughly 1.25 percentage points to capture the **lower edge** of the scatter plot. 2.88%! That doesn’t sound so hot anymore!

### Multivariate Regressions

Since the different SWR assumptions mainly impact the intercept, not so much the slope, let’s fix one specific SWR time series, i.e., our good-old 75/25 portfolio 30-year horizon, 25% final value target, and study how multiple regressors would jointly account for the safe withdrawal rate variations. I propose 8 different regression models

- Baseline univariate regression with the CAPE yield only
- Add the 10-year bond yield
- Add the short-term yield
- Add the 1-year trailing inflation
- Add the (perfect foresight) 1-year future inflation
- Instead of the 1-year, use the 5-year future inflation rate
- Instead of the 5-year, use the 10-year future inflation rate
- Instead of the 10-year, use the 30-year future inflation rate

In the table below are the regression results:

Going through the regression results as we add and change regressors, here are a few intriguing results for the 8 different models:

- Model 1 is again the baseline univariate model. Not much new here. The R^2 of the regression is 0.707.
- Adding nominal 10Y bond yields, we get a slightly positive but not significant slope. Not a shocking result;
*nominal*bond yields don’t matter much for*real*SWRs. - Adding short-term yields we now make both fixed income slopes significant, and of opposite sign. That’s very intuitive! Nominal bond yields don’t matter much, but the slope of the yield curve does. The R^2 is improved somewhat. But, again, notice that 70% of the SWR variance is already captured through the CAPE yield. Only an additional 0.07 come from the yield curve!
- Adding the trailing inflation adds nothing! The slope is negligible (0.005, much lower than the 0.07 in the univariate regression). The R^2 is unchanged.
- Adding the 1-year forward realized CPI also doesn’t add much.
- If we use the 5-year forward inflation rate instead, we indeed get a little bit of extra R^2, now at 0.818. And the slope of the 1-year trailing CPI is positive (albeit not exactly significant) while the future inflation gets a negative beta. That makes sense! The
**level**of inflation is not that crucial. It’s more the**direction**! In other words,**moderating inflation is actually beneficial for the SWR!**Which bodes well for out current situation, because I can’t see how inflation will move much above 7.5% and certainly not for an extended period. - If we replace the 5-year forward CPI with the 10-year forward figure, we get the highest R^2 overall. All slope estimates are significant now of 5 years or even 10 years!
- Quite intriguingly, if we knew the entire 30-year future inflation average, we lower the R^2 again relative to knowing only the first 10 years. And the t-stat on the 1-year trailing CPI deteriorates somewhat. It’s an intuitive result again; due to Sequence Risk, it’s actually the first ten years of your retirement that decide about success vs. failure, not so much the entire history.

### Statistical vs. economic significance

Let’s look at the results from Models M6, M7, and M8, i.e., the regressions with the highest R^2 and the most significant t-stats for all the regressors. What happens if we were to plug in today’s observables for the stock earnings, bond yields and trailing inflation, as well as some inflation forecasts? Notice that we know from above that the absolute numbers may not be that useful because the regression line goes *through *the data cluster and will likely create more of a mid-point SWR with a 50% failure rate, not so much a failsafe withdrawal rate. But the changes in SWR give us an idea about how – purely at the margin – changing some inputs will change the SWRs.

For the CAPE, I use an estimate of 35.05 as of the 2/25/2022 close. The bond yields are from Bloomberg.com and even though I pulled the numbers on 2/25, they seem to be the 2/24 closing quotes. But close enough for government work. The 1-year CPI estimate (not used in M6/M7/M8, but just displayed for fun) is the Michigan Survey 1-year ahead CPI estimate. The 5, 10, and 30-year CPI estimates are the TIPS-implied rates, also from Bloomberg, also for the 2/24 close.

Here are the results: First, start with a Goldilocks economy: Not too hot, not too cold. A CAPE of 20, i.e., an earnings yield of 5%. 4% yield for 10Y, 3% for short-term. And inflation at a steady 2%. The 3 different regressions give you an initial SWR of between 5.12% and 5.97%. Knock off another 1.25% to get to a failsafe estimate and that’s a nice generous initial withdrawal rate!

Next, keeping all the bond and inflation inputs the same, let’s change *only *the CAPE to 35.05 and thus the CAEY to 2.85%. Bummer! the SWR drops by between 99 and 118bps. That may not sound like much, but that could be a quarter or a third of your retirement budget!

Third, if we also adjust the bond rates and inflation numbers to match today’s environment, we change the SWR by about…, uhm, nothing. In fact, the model estimates **go up** by a few bps. Not really anything to write home about either, but contrary to popular belief, our current inflation landscape has essentially no bearing on the SWR.

And again, I’m not saying we should ignore macro fundamentals. We should pay close attention to the one macro fundamental that matters, equity valuations. But everything else is a rounding error in your SWR! Sometimes you get *statistically *significant parameter estimates. But if you play with inputs the results are not really *economically *significant.

That’s not to say that inflation is totally irrelevant. If our current TIPS-implied estimates are wrong and I plug in the historical **worst-case** numbers for 5/10/30 years we certainly get that SWR moving. Down by another 103-155bps. Tighten your belt by another 26-35%, just based on inflation. But I have trouble justifying 8.84% inflation for another 10 years. Unless we have a replay of the 1972-1982 inflation runup.

### A 1965 case study

For the 75/25 portfolio, 30-year horizon, and 25% final value target, we observe the lowest SWR in the mid-1960s. November 1965, to be precise. This means the retiree used the 10/31/1965 observables and starts withdrawing on that date for a Nov 1 retirement. Plugging in the 10/31/1965 CAEY, fixed income, and CPI data, we get a regression-predicted SWR of 3.79%, please see the table below. That’s not too far away from the actual 3.58% SWR. Let’s plug in today’s observables and attribute the **changes** in the overall SWR (+0.63%) to the different components:

- The S&P500 is significantly more expensive today, as measured by the CAPE. All else equal, that would account for a 64bps lower SWR.
- The yield curve is much steeper, which gives you slightly positive net impact on the SWR: -165bps + 189bps = +24bps
- The inflation shock 1965->1975 was much worse than what’s predicted for us today. The realized CPI inflation 5.66% was much worse that what the bond market predicts right now and the shock relative to past inflation (only 1.7%) was also much worse. That’s a +102bps impact on the SWR.
- All of the “marginal” impacts sum up to a 63bps
over the 1965 worst-case scenario. This would imply a 4.41% SWR from the regression or a 4.21% SWR if we add the 63bps to the actual 3.58% fail-safe.**improvement**

Of course, the calculations look a lot worse if we apply the post-1920 historical worst-case inflation rate of 8.84%. With that input, we reduce the SWR by 92bps. That gets you to 2.86% if simply plugging into the regression equation or 3.58%-0.92%=2.66% if we apply the marginal adjustments to the actual 11/1965 SWR. That’s a painfully low withdrawal rate.

And the last thought experiment: How bad would inflation have to be over the next 10 years to match the same SWR, i.e., the historical failsafe WR? That’s in the table below. Even with a 5.10% CPI rate over the entire next 10 years, we’d still get an SWR only as bad as the historically worst SWR in 1965. I find it hard to believe that we’ll see a CPI realized rate that high and even if we do, we move the SWR “only” back to the historical failsafe.

### Conclusion

Looking back at historical data, the previous worst-case scenarios for retirees, either the 1929 cohort or those around 1965-1968 generated some pretty conservative safe withdrawal rates. Certainly below 4% but not really that much below 4%. What’s currently predicted for the inflation path is all well within historical norms, thus, a failsafe calibrated to historical data should easily hold up in the future. I don’t see a reason to throw in the towel and change anything in my methodology.

Expensive equities are the gorilla in the room. It’s certainly possible that the Federal Reserve in an inflation-fighting mood could trigger a large sell-off, like in 1982. But again, that episode is already part of my simulation toolbox. Unless the inflation shock is much worse than in the 70s and 80s, I’m still sticking with my methodology. If that ever changes, I’ll write about it here!

### Thanks for stopping by today! Please leave your comments and suggestions below! Also, make sure you check out the other parts of the series, see here for a guide to the different parts so far!

*Title picture source: pixabay.com*

Thanks for doing all that work! The subject is very interesting.

The article is pretty Geeky though. You may want to consider writing a summary in layman’s terms and then go through the “math”. I am 1 class short of being a math major and I struggled with it (I’m a math-based Computer Science graduate). I am getting old though and my abilities to follow math has been degraded significantly.

MFPOSA’s comment is understandable! – but I for one would like to counterbalance it with a vote of encouragement for the geeky math. It’s what distinguishes this blog – it’s not just about having an author with fancy credentials, it’s about presenting sophisticated analysis in detail.

I like the ‘geeky’ math as well. It is a lot harder to do the ‘geeky’ math than throw out some poorly thought out hand-wavy types of analysis that will cause people to waste years of their lives toiling away in cubicle, or Zoom, hell. This is how you get the best recommendation vs. idiotic alternatives like the “Financial Samurai” which has devolved into clickbait with his idiotic 0.5% SWR recommendation.

Thanks for the kind words! 🙂

Geeks rule! Thanks for the words of encouragement! 🙂

I re-read the article today and laughed again so hard at “Financial Sumoguy” 👍😂😂

I’m sure Sam had to laugh about that one too.

My ability to follow math was always degrading 🙂

But you still come here and read this! So, you’re well above average! 🙂

Well, I skipped all the tech details. 3500 words for the laymen is what my blog is all about. 😉

I agree with MFPOSA who commented regarding the mathiness. Way too much for me to digest on 1 cup of coffee and 20 years out from college statistics. 🙂 ha ha

I appreciate the conclusion at the end though. “This time it’s NOT different. Probably”. Shooting from the hip, I agree. Higher inflation means higher nominal stonk returns. At least we can all celebrate with easy double digit nominal returns (in spite of watching Dollar Tree prices jump from $1 to $1.25).

Thanks, Justin! THat’s what I’m here to do: do the hard work and report the findings so not everyone has to go through the math!

And, yes, the inflation is obvious. I guess the Dollar Tree can still go up to 1.99 and still call itself Dollar Store, right? Nothing to worry until we go to $2 and above! 🙂

Hey ERN, I’m curious if you’ve come across this article in the past and what your reaction to it is. https://www.philosophicaleconomics.com/2013/12/shiller/

Nice link. I’ve made my own adjustments and will write a post on that some time in the future.

But yes, absolutely: the CAPE likely needs an adjustment.

Awesome! I’m looking forward to the future post. I always value you’re insight and have learned a ton from your blog.

Great link, Trent!

Great link! Are you aware of anyone who is tracking the “Pro Forma CAPE”? Did a quick Google search and couldn’t find it anywhere online

Another great addition to your body of work – and very interesting that at the point of retirement only the CAPE really matters!

OOI, have you given any thought to what sort of nasty inflation regime would have to kick in around ten years after retirement to put a spanner in the works?

Thanks!

Well, forecasts get more opaque the furhter you move away from historical norms. We can obviously plug in some crazy numbers, like 10+% for the future CPI but the error bands around those SWR estimates will also be huge.

So, I stick to my guns, plus in a “reasonable” historically normal CPI estimate (slightly elevated) and everything will be fine. 🙂

I hear you.

For info, the UK worst case 30 year and 10 year RPI values are 8.3% and 14.2% respectively!

I am not an econometrician but any means, but wouldn’t it be more appropriate to use time series methods like the “xreg” regression implemented in the “auto.arima” function in Rob Hyndman’s “forecast” R package? [See here](https://towardsdatascience.com/time-series-analysis-with-auto-arima-in-r-2b220b20e8ab).

No you wouldn’t. This is not a seasonality issue.

For clarification, does this answer mean that:

a) the sequence of inflation is in no way similar to the sequence of returns and, stand-alone, inflation impacts are commutative; and

b) the overall combined effect (SOR, inflation, etc) is another thing though.

Sequence of inflation matters just like the the sequence of returns. In fact, since I use real returns, the inflation sequence is in the returns already when I talk about SoRR. But since the volatility of nominal equity returns is so large,, most of SoRR is due to nominal equity returns. But we shouldn’t ignore inflation either.

Thanks.

I guess this conclusion from your part 15 probably applies: “Precisely what I mean by SRR matters more than average returns: 31% of the fit is explained by the average return, an additional 64% is explained by the sequence of returns!” leaving, by my calcs, around 5% for all the other variables, including inflation.

Sorry, maybe that particular link I posted emphasised the seasonality issue too much. I’m sure you’re right that seasonality specifically isn’t an issue here!

But wouldn’t financial time series have all sorts of other issues with serial autocorrelation/non-stationarity of various flavours that violate the assumptions of non-time-series regression methods? I’m more than willing to defer to you as the expert in this field!

I just know that in my work, when I analyse non-financial time series datasets it usually requires use of ARIMA models and similar approaches (depending on what ACF plots and similar tools say about stationarity, etc). But I have no experience with financial modelling!

On another note, does the Newey-West method you used accommodate those super-weird-looking residuals?

How are return and SWR data, measured in % non-stationary? Are they at risk of wandering off to +/- infinity?

OLS betas are efficient estimators but the std errors need to be adjusted. You use Newey-West to deal with the overlapping window issue, and that’s it.

But you are welcome to use your techniques. Let me know if you find anything worth publishing.

Data Series in a Google Sheet, in case you want to run your analysis:

https://docs.google.com/spreadsheets/d/1TxZvuZrn1agi6QBkPxMow3IDWGKmYb8oRoDhKo_wUK8/edit?usp=copy?

It’s great that inflation doesn’t have a statistical impact on our SWR but doesn’t it destroy our real purchasing power during retirement? My brain is telling me that having to hold our SWR steady during rising inflationary periods means the quality of retirement is going down!

FWIW – I really enjoyed the mathiness. I didn’t bother to verify any of it, but I understood the analysis.

The analysis is done in real terms.

People always fall for the fallacy and assume that nominal returns are fixed. Then higher CPI is bad and lower CPI is bad for retirees. But nominal returns are not set in stone. Also see Part 41 for another example of this fallacy (Brazil stock returns in the late 1990s).

Thank you for this post. I love that the modeling and statistics support the intuitive conclusions! As I consider the practical implications (in my second year of retirement), I’d like to ask about recommended frequency of calculating SWR. Most of your analyses assume annually, which is fine for illustration. As you note, conditions have rather drastically changed over the past few months. Given that economic swings must be expected, would a monthly SWR calculation be best for a person with fewer than 10 years of retirement? Or would perhaps more of an event-driven approach be suitable, with re-calculation of SWR when it is clear conditions have significantly changed since last calculation? I apologize if I’ve missed discussion of this issue elsewhere in your body of work. If I have, please point me in the right direction. Thanks again.

I think recomputing the SWR every year or so is sufficient. Unless there’s a huge move in a short time (March 2020).

I thought the whole point of a *Safe* WR is that you need not recalculate it “ever”.

In particular, if the market is down 20% and your portfolio is down 15%, the SWR was already designed to incorporate that. If your portfolio goes *up*, you can safely *increase* your withdrawal amount, but you need not decrease it just because the market and portfolio are down.

If you choose a WR above the historical failsafe, that’s a different story, of course. Or if you’re going with the CAPE-based approach (which isn’t actually generating a SWR).

And of course if your portfolio falls precipitously and you’re concerned that you could experience something *worse* than anything historically, that would be a good reason to revisit the WR downwards.

Correct.

The reassessment would be useful in at least two instances:

1: can I now raise my SWR in light of recent performance that’s been better than the historical worst-case? Pretty likely!

2: Could the drawdown be worse and/or longer than in the past? Unlikely but possible.

You are able to casually state “… I can’t see how inflation will move much above 7.5% and certainly not for an extended period.” Isn’t the reason you can say this due to the evolution of monetary policy in response to the ’70s inflation shock? This evolution is incorporated into the latter part of your dataset, but how has monetary policy changed over the entire dataset? Some of your readers lived through the ’70s (my first home mortgage was something like 9%) and may wonder if an earlier generation Karsten might have said the same thing in, say, 1972. Just wondering if there is some confounding going on here amongst the input variables.

Great post as always, by the way!

We’re not talking about one single year. We’re talking about the 10-year or even 30-year average.

So, yes, with today’s monetary policy and the understanding of economics (see Nobel Prices for Lucas, Sargent, Prescott) that we have today that we didn’t have before in the 1970s, I believe we will not make the same mistakes.

But I grant you that: maybe our newly-woke Federal Reserve (now worrying more about climate change than monetary policy) will squander that knowledge. See last month’s post with the phases of strong/weak men creating good/bad times.

What about the PWR (Perpetual Withdraw Rate) in these periods?

If you use the the 30-year, 100% final value target, you notice that the intercept is about 0.80-1.00% lower. That would be a haircut to apply.

All your backtest data is generally in a low to rising debt to gdp environment. That rising debt also juiced returns. I doubt the future will mimic the past at this point with high debt. It will act as a big drag.

True. And we will see how this bedt burden will work out in the future.

Will it create stagflation? possible, but we’ve already had stagflation in the past as well. So unless the stagflation is worse than the past, I’m still safe using my backtests.

Inflation in 2022 will depend on whether the dis-inflationary forces of:

1) the end of QE and pandemic stimulus

2) rising interest rates, and

3) the usual outflow of dollars from the US real economy into foreign/rich people accounts that has caused low inflation for years

Are greater than the inflationary forces of:

1) commodity shortages due to the Ukraine war and other issues,

2) prolonged manufactured goods shortages due to COVID in China, (HK just had more cases than the entire US, and will probably end up locked down)., and

3) rising inflation expectations amid a delayed and too-small Fed response

Basically, nobody knows if we’ll end the year with 10% inflation or -2%. There are so many new variables to consider, and that’s why the Fed is taking a cautious stance toward rate hikes. I think the 2008 vs. 2020 helicopter drops demonstrated the difference between dropping the cash on banking institutions vs. dropping it directly on the people. The later was an adrenaline shot to the heart, Pulp Fiction style. Now that it’s being withdrawn, there are more ways for the Fed to be wrong than for them to be right.

Yeah. Investors don’t have worry about the inflation itself. It’s the root cause, i.e., gweo-political uncertainty.

Also, in hindsight, the whole monetary easing during the pandemic was uncalled for. This wasn’t a liquidity freeze like 2008/9. The Fed should have reversed course already in late 2020 or early 2021 at the latest.

Just to prove that I read it all… “2.45%*0.553/35” should probably read “2.45% + 0.553/35”. Do I get a gold star? 🙂

P.S.: I do read — and appreciate — it all. Thank you!

Correct! Thanks!

I enjoyed the post, makes me feel less nervous about inflation. Personally, I didn’t think the post was too geeky, and I thought the conclusion summarized the results well.

However, in your CAEY vs. SWR graph I understand you’re trying to determine a low-fail SWR by reducing the y-intercept by 1.25%, but that leaves most high CAEY values as failures (below the green line). Additionally, most of the low CAEY are tightly bunched together suggesting less variability i.e., maybe a higher low-fail SWR than the green line suggest? I’m just wondering if there’s a more precise way to look at it, maybe that’s not as important for the purposes of this post.

I know. I shifted the green line down to capture the lower edge of the scatter plot at least in the RELEVANT range of the CAEY.

Hi, Reading through your analysis…

In section Warm Up 2, you mention “the 75/25-30Y-25%FV regression would imply a safe withdrawal rate of 2.45%*0.553/35=4.03%.” Something is wrong with this calculation. Shouldn’t this be a y=a + bx calculation, but the numbers don’t work either, although I can read off the graph to see a 1/35 CAEY should be about 4.5% SWR.

I don’t want to be pedantic, just trying to understand what the numbers mean. Feel free the berate me if I have this completely wrong.

BTW I love your whole SWR series, I have based my retirement plan on it!

Hi, Another question.

I understand the the methodology of calculating inflation in the US significantly changed in the 1980’s (I think). There is anecdotal evidence from a respected website which calculates the current US inflation rate is much higher ~10-15% using the old 1980’s methodology.

Would the changes in calculation of inflation make comparisons between today’s inflation and 1965 etc difficult?

Probably they are referring to hedonic indexing, quality adjustments.

First: 10-15% doesn’t mean a 2% CPI is now 12-17%. It means a 2% rate would be 2.2-2.3% under the old methodology.

I don’t think that reclaculating the old inflation rates under the new method would make any difference, because the quality improvements of tech gadgets wasn’t as repid back then.

His numbers are right. 2.45%*0.553/35=4.03% is correct and it is a y = a + bx calculation. This for the average SWR (half of cases would fail at this rate), not the fail-safe SWR. I would read that section again. Also ERN has cut off the graph so it does not display CAEY = 0. So based on the graph shown 1/35 CAEY is about 3.05%.

Hi Michael, My calculator does not give that answer. If it is a y=a+bx calculation then where is the plus? Reading from the graph should give the same answer as the calculation. Perhaps big Ern could comment when he has a chance.

Sorry I mistyped that. Y-intercept is 2.45%. Slope is 0.553.

2.45% + 0.553/35 = 4.03%.

Yes, it’s 2.45% + 0.553/35=4.03%

Corrected the typo! 🙂

Lastly a comment.

In my country, inflation is calculated with a trimmed mean, weighted average, with cyclical adjustments etc etc. The standard basket of goods for a family is such the they almost never eat meat and buy $50 of cleaning products weekly. This is clearly not representative of the average person (I definitely don’t clean that much!). Inflation calculations are too politicised and are fiddled with constantly.

I think the main take out is that SWR is heavily dependent on CAPE, which is clearly stated in your SWR series. Inflation has a small effect and is somewhat unreliable.

Thanks for sharing! That’s scary. Sorry to hear that. Certainly, trimmed means are useful in some circumstances, but a basket is a basket. e can’t just ignore rapid food and energy inflation. If the CPI is used to adjust benefits, especially retirement benefits, the whole basket,should be used, not just a trimmed mean!

I think it’s about time we stop trying to math real life. No model in the world can predict what’s gonna happen so Ill stick to 3.25% SWR and go on with my life. I recommend you all do that same

Please read Part 46 of the series. If you still think that way, don’t let the door hit you on the way out…

Wow. I didn’t mean to be rude, it’s just that the more I read your posts the more lost I get with so much math and analysis on something that is not a exact science. You did a great job getting us to 3.25% SWR but now it’s ok, let it go or you’ll have SWR part #597 soon !

Haha, no offense taken

3.25% might be too conservative if you’re an early retiree in your 40s or 50s. It’s always better to do the math right. You don’t want to be too aggressive, but not too conservative either.

Ok. Give me a final number then.3.5%? 3.33%?

Never mind. I calculated here for the 100th time and I’ll stick to 3.25% because I’m on a conservative 60/40 portfolio

IMO you are the one taking a big risk in 2022 keeping fully 40% of your portfolio in bonds, given the negative real interest rates (or *maybe* barely-above-zero real rate if you believe inflation falls back below 3% soon) and all the debt the government and the Fed’s balance sheet has taken on.

Such an asset allocation in today’s worlds is anything but “conservative”.

Whatever WR you choose.

Separately, it’s impossible for anyone to give you “a final number” when you indicate neither duration in years nor target final value.

OK, good luck! But maybe you’ll find some other content here you find interesting! 😉

There is no set final number. If you’re a 30yo retieree with not much SocSec, then yes 3.25% is a good number.

If you’re a 50yo early retiree with a corporate pension and SocSec around the corner? Probably above 4%…

Did you just cancel Applied Maths?

Hey Big ERN, random thought/question on SWR, and that’s about reserves. Hypothetically if my calc’d SWR is 4%, I really can’t spend 4% can I. I need to take some value haircut on that each month/year to allow for periodic big ticket items like replacing a car, or the house AC unit, etc. Otherwise I risk blowing past my allowed spend, exceeding my SWR over time, as if these are “unplanned”. How do you think about reserves in this context? Thanks.

Bad budgeting! You’re supposed to create a baseline budget factoring in all those additional “surprise” expenses. Sometiems the expenses will be higher, sometimes lower.

The natural fluctuations around that baseline should not have a meaningful impact on your SWR calculations. See mu post SWR Series Part 47. Especially the first two sections:

“1: Intra-year fluctuations in withdrawals? Wing it!”

“2: Fluctuations in annual withdrawals? Wing it!”

If I am tracking this correctly, then 2.66% is the SWR for a 75/25 portfolio with a 30-year horizon and a 25% bequest, assuming the worst historical inflation experience. Is that correct?

I don’t think so. When I plug those numbers into ERN’s sheet, I see 3.58% as the SWR – with the low point occurring in the 1960s, right before high inflation began.

The SWR by definition covers all conditions, so there’s no need to look at “worst historical inflation experience” separately.

[FWIW, if you swap out 10% gold for stocks (65-25-10), you raise that to a 3.97% SWR since 1926 (although lower going back to 1871).]

The global min is 3.58 (Nov 1965).

First, thank you for this series! It has been tremendously helpful on my FIRE journey. I have one question that I hope you can address.

A huge amount of your work uses CAPE/CAEY as an input. However, since the changes in how goodwill is accounted for after FAS 142 in 2001 radically changed the value of the “E” in CAPE resulting in persistently higher CAPE values. A CAPE of 30 today represents market valuation that corresponds with a significantly lower CAPE value from the 1990s or earlier. This can be seen by the fact that CAPE has only briefly spent time near its historical values in the teens since the changes in GAAP.

I think the easiest way to frame this is with an analogy. If my car gets 30 miles per U.S. gallon and the U.S. changes to Imperial gallons (which are 25% larger) then I can’t suddenly say I am getting 25% better mileage. My mileage is the same even if the MPG number has jumps to 37 MPG. The change is due to the change in the definition of the denominator. The same thing happened with CAPE – the definition of earnings changed to make the reported earnings lower even though nothing in the real world changed. That means that all calculations based on CAPE since FAS 142 went into effect are no longer valid for direct comparison.

I haven’t seen you address this, but it seems to me that it makes all the work you’ve done based on CAPE unnecessarily pessimistic.

I think you’ve done tremendously valuable work, even if I think this may indicate one flaw. I wouldn’t have spent dozens of hours reading and admiring your work if I didn’t have the highest respect for it.

see https://www.philosophicaleconomics.com/2013/12/shiller/ for more details on the problems with CAPE.

I know. I run my CAPE numbers both the Shiller designed it but I also account for share buybacks, earnings retention and different corporate taxes over time. And there are other adjustments like treatment of goodwill. There’s no perfect measure but we can certainly improve Shiller’s method.

Thank you for the response! I realize you have better things to do than answer randos on the internet.

Can you point to a post where you describe these adjustments that you referred to in our reply? I have read every entry in the series at least once but I don’t recall seeing this discussed (I may have missed it!). Rather, I recall seeing you refer to CAPE of 15-20 as slightly elevated and 20-30 as moderately elevated in SWR #3 and in SWR #18 and many other places you refer to equities being expensive. Yet at the time #18 was posted CAPE was 30, not much higher than average CAPE since 1990 (26) and the since 2000 (27). The S&P 500 was around 2,500 when SWR #18 was posted and it’s now around 4,000 as I write this. Perhaps this is a case of the markets being irrational for a long time, or perhaps what constitutes fairly valued CAPE needs to be re-examined given the data from the past 30+ years as well as the reasons to suspect the data may be sending a valid message.

It seems like CAPE and CAEY are so fundamental to your SWR calculations that I’d love to see how you adjust those values and if you still believe that CAPE of 15-20 is elevated, or if we should treat CAPE in the 25-30 region as fairly valued given all the changes over time.

Again, thank you for everything you’ve written! You’ve been a huge benefit to the FIRE community. Some additional clarity on your treatment of CAPE/CAEY, given their importance to your work, would be of tremendous value.

Thanks! I run my own calculations, and they are close to what this guy is doing:

https://nucleuswealth.com/articles/trump-broke-the-shiller-pe-here-is-a-simple-fix/

I will do an update blog post to the CAPE calculations some day. It’s on my to-do list! 🙂