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.
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!
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 improvement 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.
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.
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