Welcome back to the 20th installment of the Safe Withdrawal Rate series. Check out Part 1 to jump to the beginning of the series and for links to the other parts! This is a follow-up from last week’s post on equity glidepaths to address a few more open questions:

- Some more details on the mechanics of the glidepath and why it’s so successful in smoothing out Sequence of Return Risk.
- Additional calculations requested by readers last week: shorter horizons, other glidepaths, etc.
- Why are my results so different from the Michael Kitces and Wade Pfau research? Hint: Historical Simulations vs. Monte Carlo Simulations.

So, let’s get to work …

### More on the glidepath mechanics

In last week’s post, we got a bit ahead of ourselves, simulating glidepaths without digging deeper into the intuition for **why** a glidepath should cushion the effect from Sequence of Return Risk. So let’s look at a simple case study to understand the benefits of an upward-sloping equity glidepath in retirement:

- A 10-year horizon, withdrawals are made annually at the beginning of the year. The initial portfolio value is $1,000,000, the initial withdrawal is $35,000, which is then increased by 2% every year to keep up with inflation.
- We look at one glidepath from 70% equities to 90% and one fixed 80% equity allocation.
- In the first case study, equities drop by 30% in year 1, then another 5% in year two before starting another nice 8-year-long bull market. Also, notice that the bond market returns are modeled to reflect a negative correlation with equities!
- The rebalancing to the target weights occurs every year at the same time as the withdrawals. In other words, post-withdrawal the portfolio displays exactly the target weights.

Let’s look at how the (nominal) portfolio values, withdrawals, and the rebalancing evolve over the ten years, see table below. The top panel is for the glidepath, the bottom panel is for the constant equity share.

- With the glidepath, you actually withdraw much more from bonds, especially during the first few years. Over 60% of your total withdrawals during the first 10 years come from bonds. On the other hand, with the fixed equity weight more than 85% of your withdrawals come from equities. That’s even higher than the target equity share! Because you withdraw so much more from equities while equities are cheap the fixed asset allocation is more exposed to Sequence of Return Risk.
- The benefit of the glidepath comes from the fact that we not only plow money
**into**equities on the way down (two years of negative withdrawals!). But during the bull market, we withdraw only about $25k p.a. from equities and the rest from bonds! That gives the equity portfolio more room to enjoy the bull market! - Compare that to the withdrawals with the fixed equity shares: You withdraw about $17k from the equity portfolio at the bottom of the stock market (ouch!) and then during the bull market, you withdraw more than the necessary consumption level from the equity portfolio to replenish the bond portfolio every year. During the bull market, the equity weight is constantly dragged above its target. Thus, you hamper the recovery of your portfolio when you constantly shift away from the well-performing asset (equities) and into the relatively low-performing asset (bonds).
- Also notice that after two years, the glidepath beats the static allocation by about $42k ($733,314 vs. $691,746). After ten years that gap has increased to almost $80k ($1,074,558 vs. $995,378).
**Almost half the advantage of the glidepath came from the bull market that followed the drop!**

Of course, if the returns were to occur **in the opposite order** – a continued equity bull market eight years and then a crash at the end – results will look quite different, see table below:

- All assumptions are the same as before. I only reverse order of returns.
- Now the glidepath performs worse than the constant equity weight. But that’s expected: Because you start with only 70% equities you participate less in the bull market and you have the highest equity share when the market falls in years 9 and 10!
- Of course, even though the glidepath underperforms the static allocation ($1,089,990 vs. $1,162,099), you are still better off than with the glidepath when the bear market hits you in the first two years ($1,089,990 vs. $1,074,558)!

To summarize the case study results, let’s look at the final values for the glidepath and the constant asset allocation, see chart below. The variability of final asset values is lower with the glidepath. True, you underperform the constant 80% equity portfolio when you have a long bull market early in retirement, but the glidepath performs significantly better when it really counts, i.e., when there’s a bear market during the first two years of retirement!

### Back to the historical simulations: more glidepaths

The table below is almost the same as last time, but with a few changes:

- I added eight more glidepaths. The first is inspired by the work of Michael Kitces who, relying on the Monte Carlo simulation study with Wade Pfau (see Table 6), suggested a 30 to 70% equity glidepath over 30 years, which optimized the success probability of a 4% Rule using historical average returns. So I used that glidepath (30->70% with a 0.111% passive slope). But I also use glidepaths with larger slopes (0.2%, 0.3%, 0.4% per month) and the same for a lower starting and end point (20% -> 60%).
- Instead of high CAPE vs. all CAPE scenarios, I split the percentile stats into high CAPE (>20) and low CAPE (≤20).

Results:

- When the
**CAPE is below 20, there is no benefit from a glidepath.**Any 90-100% static equity weight will give you the highest, or at least close to the highest fail-safe withdrawal rate. The same is true when targeting slightly higher failure rates (1%-25%). - But glidepaths are useful when equities are expensive (CAPE>20), as we already saw last week! The 60 to 100% glidepath had consistently the best withdrawal rates for all failure probabilities studied here. 40->100% and 80->100% are close behind. The active vs. passive glidepaths and the exact slopes don’t make that much of a difference if you get the correct start and especially the endpoint (100%!) of the glidepath.
- Quite amazingly, the glidepath recommended by the Kitces and Pfau study (30 to 70%) is consistently one of the worst. It not only underperforms pretty much all of the other ERN-designed glidepaths. It’s actually so bad that
**it even underperforms most of the static asset allocation paths**in the historical simulations! At first, I thought this is because of my 60-year horizon, but as we will see in just a minute, the Kitces and Pfau glidepath is pretty universally inferior, even over a 30-year horizon!

### How about a shorter retirement horizon?

Glad you asked! Here’s the same table but with a 30-year horizon:

- The same result as before:
**Glidepaths are of no use when equities are cheap to moderately valued (CAPE below 20).** - Notice how among the fixed equity weights, you achieve the most attractive SWRs between 65 and 75% when the CAPE is above 20, a bit lower than the 75-80% optimal equity weights over the longer horizon. But
**wh****en the CAPE is below 20 you’re still better off using 100% equities, regardless of your failure probability!** - The glidepaths that did best over 60 years, moving from 60% to 100%, are still consistently very good performers. Quite intriguingly, the 40->100% glidepaths are now even slightly better!
- The Kitces and Pfau glidepath is still one of the worst performers. Both in its original form (slow transition over 30 years) and with faster transitions. The 20->60% specification is even worse.

### Failure Rates of specific SWRs

Another way to slice that data. Instead of targeting a specific failure rate and then calculating the withdrawal rate, we can also look at the different withdrawal rates between 3 and 4% and calculate the failure rates, see table below:

- I do this only for the high CAPE regime (>20) to save space.
- Notice the unacceptably high 60-year failure rates for the 4% rule!
- Also, notice that the failure probabilities are lower with the glidepaths but the effect is only marginal. For example, even with the “best” glidepath will not miraculously rehabilitate the 4% rule. All you can hope for is to make the 3.5% rule a lot more secure!

### Higher Final Value Targets

As requested by a reader last week, here’s the table with SWRs targeting specific failure rates but for different final value targets and using fail-safe and 1-5% failure probabilities. The reader asked for 1% steps, but I report only fail-safe, 1%, 3% and 5% to save space. If you want the 2% and 4% SWR percentiles you simply take the midpoints!

Results are roughly the same. But I noticed that the benefit of the 60-100% glidepath goes up vis-a-vis the static allocation. For example, the fail-safe SWR improves by 0.22% (3.47% vs. 3.25%) under capital depletion. But it improves by 0.29% under capital preservation (3.34% vs. 3.05%). Again, it doesn’t miraculously make the 4% Rule viable again but you’ll get a noticeable improvement in the sustainable withdrawal amounts!

### Why do I get different results than Michael Kitces and Wade Pfau?

First, I thought that the main driver was the shorter retirement horizon in the Kitces/Pfau paper (30 years). But I showed above that even over 30-year windows their proposed rule, 30->70% linearly over 30 years (=0.111% monthly steps) is consistently one of the worst glidepaths. You can improve it a little bit by accelerating the pace of the glidepath to 0.2, 0.3, or 0.4% monthly steps, which gets you to 70% equities after 200 months, 133 months and 100 months, respectively. But even those glidepaths stink compared to some of the other paths that I proposed. They are even worse than some of the fixed asset allocations. What’s going on here?

The major difference between my work and the Kitces/Pfau study is that I use historical returns and they use Monte Carlo simulations. How can that make such a big difference? In my view, there are (at least) three features of real-world return data that are impossible to replicate with a Monte Carlo study a la Kitces/Pfau:

**1) Short-term Mean Reversion:** After each major drop in equities, we are bound to observe a strong recovery, see, for example, our post on the 2009-2017 bull market from a few months ago. The theory is that investors overreact on the downside (remember March 2009?) before a nice new bull market ensues. A Monte Carlo study will not replicate this feature. A Random Walk means that returns have no memory, i.e., the distribution of returns going forward after a 50% drop is the same as after 50% gain. But with real-world data, you’d benefit from a glidepath with a much steeper slope to better capture the bull market that will likely follow the initial drop. Remember, in the first year after the 2009 trough, the S&P500 went up by 72.3% (nominal total return, March 9, 2009, to March 9, 2010)!

**2) Long-term Mean Reversion:** The non-random-walk nature of equity returns is even more pronounced if we look at longer windows, say, 15 years. In the chart below, I plot the average annualized real S&P500 return over two consecutive (neighboring) 15-year windows. Notice the negative correlation? If the previous 15-year return was poor then the next 15 years had above-average returns! This has profound consequences on the glidepath design: It’s the main reason why the glidepath has to shift to its maximum much faster than over 30 years and it’s also the main reason why in the historical simulations, the preferred long-term equity weight is 100%.

**If you get unlucky during the first 15 years of your retirement due to poor equity returns you benefit greatly from going “all in” during years 16-30 of your retirement!**

In fact, that might be the only way to salvage an underwater portfolio that has been taken to the woodshed due to bad equity returns and 15 years of withdrawals. If you base your optimal glidepath design on Monte Carlo simulations you’ll find much lower optimal long-term equity weights!

**3) Correlations:** Kitces and Pfau have to pick one single stock-bond correlation in their Monte Carlo Study. However, in real-world return data, this correlation has been all over the map during the last few decades. We’ve had the 1970s/early-1980s where the correlation was strongly positive (both stocks and bonds lost value), but we also had the 2000s onward where stocks and bonds had a strong negative correlation and bonds were a great equity diversifier. The optimal glidepaths calibrated to that one single correlation are clearly suboptimal when using historical data.

### What now?

I’m the first to admit the weaknesses of working with historical return data. We don’t know what the future holds. CAPE ratios are hard to compare over time, and I can come up with theories for why the returns going forward can be much more attractive than in the past. But I also have a theory for why they could be worse. So, using the historical simulations as a midpoint to gauge average returns is not a bad starting point.

In my personal view, a Monte Carlo study for retirement glidepath design is the worst of all worlds. You *still* have to make an assumption about future mean returns and there is no telling whether that assumption is better or worse than the historical return assumption. But you also lose all the interesting return dynamics that are due to equity valuations occasionally deviating and then returning to economic fundamentals. That’s why I will always stick with historical returns despite the limitations!

### Conclusions

1: In retirement, an equity glidepath with a positive (!!!) slope helps you during an equity bear market. But not just on the way down! A lot of the benefit from the glidepath comes from better rebalancing dynamics during the subsequent bull market!

2: A glidepath can alleviate some of the sequence of return risk. But the effect is still relatively small. Don’t even start to think that a glidepath can miraculously make the “4% Rule” feasible again over the next 60 years! Expect an increase in the sustainable withdrawal amounts by about 5%, or a slight to moderate decrease in the failure probability of any given SWR.

3: A successful glidepath in retirement should ratchet up the equity share pretty rapidly and reach the maximum equity weight roughly over the length of one complete bear plus bull market. Dragging out the glidepath over 30 years or more is not recommended!

4: Historical simulations show that an equity glidepath is useful when the CAPE is high at the commencement of retirement. As it is today! If the CAPE is below 20, glidepaths are of no use and an aggressive static equity allocation (close to 100%!!!) has performed best in historical simulations!

5: Monte Carlo simulations miss important elements of real-world data, i.e., mean reversion of equity valuations and changing asset return correlations. Hence, glidepaths that were calibrated to do well in Monte Carlo simulations (Kitces and Pfau) tend to do poorly in historical simulations. Unless we believe that the past observed dynamics of equity returns no longer apply in the future, we should disregard the Kitces/Pfau glidepaths because they’d likely perform worse than even most static asset allocations.

Hi Karsten,

I’m doing a second read through of your SWR series. I haven’t gotten up to the glide path articles yet but I have a question that popped up in my mind.

Is the bond allocation 10-year treasuries or does it not matter? I remember you saying how Kitches used different bond allocations to sort of fudge the results so I wanted to clarify.

Also I never hear anyone recommend TIPS or other inflation-linked bonds as the bond allocation. What’s the downside to using inflation-linked bonds as part of the bond allocation instead of treasuries?

Big ERN,

Thank you so much for this series! The rigorousness of your analysis is very helpful.

I am about 2 years away from ER and have been looking for some insurance against sequence of returns risk. I’ve decided to implement a 60->100 glidepath with 0.4% active shift and could use your advice on a few practical questions:

1) In modeling how to implement this, should we use a “buffer” to decide if equities are at their peak? In other words, if I’m looking at the value of the S&P 500 on a specific day each month, to decide if some funds should shift from bonds to equity, it would be unusual to pick a day where it is EXACTLY at its high. Should I have a rule like “if the S&P is within 1% of its 52-week high, do NOT shift” to deal with day-to-day fluctuations?

2) My equity portion is 70% domestic, 30% international. This month, if I look at the price for VTI as a proxy for S&P 500, it says not to shift anything. However, VXUS for international is 10%+ below its peak. Do I shift if EITHER is below? Both?

3) Is there a safety valve CAPE value where it makes sense to change the allocation more quickly? You mention no value to the glidepath at CAPE < 20… at that point, does it make sense to start moving large chunks each month? Everything?

Thank you again for all your work!

I like the buffer method in 1).

2) I would probably shift 0.3×0.4% =0.12% in that case

3) so you want to be a market timer? Great for you! I doubt that the CAPE will easily drop below 20 again, but yes, absolutely if we get to the low 20s and below 20 I would accelerate that glide path!

Best of luck!!!

I came here to ask the same question #3 as Emily. It seems as though an analysis could be run with accelerated or deceleration glidepath % based on CAPE for best results.

Or perhaps more simply, it would be interesting to see results for every time the CAPE dropped to 20(?) or every time market dropped by 30%(?) and your entire bond allocation was shifted to 100% equities at that moment, how you’d fare relative to the static 0.3% or 0.4% glidepaths.

Have to leave that you though. I’m just a caveman, your world frightens and confuses me.

I’m very curious about how your bond portion is invested. I’m also concerned about all of the capital gains I would incur shifting my current allocation (mostly equities) into a 40% bond allocation. The equity-to-bond conversion would need to happen in taxable accounts, since I won’t have penalty-free access to retirement accounts for many years.

I have no bonds. Well, I have some Muni bonds to hold the margin cash for my option trading. But without that I’d have no bonds.

I assume, that for us non-US based investors, with a glidepath we would also want to reduce currency risk on the glidepath? Obviously a big exchange rate drop on the international investment side of the portfolio could be just as bad as a market crash (though often those are related).

I am an Australian and have about 50% in AUD denominated bonds/equity and 50% in non-AUD denominated bonds/equity. So I assume my glidepath should probably increase bonds pre-FIRE and then increase equity post-FIRE (as per the above), but also increase AUD denominated assets pre-FIRE and then slowly return to target weighting (eg. 50/50) post FIRE.

Does that sound about right?

Sounds about right. I would simply hold the bond portion in Aussie bonds. For equities you certainly want the diversification with non-Aussie stocks.

Great piece and series!

Another difference between the methodology of your study to the Pfau/Kitces one is that you calculate the SWR (or SAFEMAX as they call it) and they take the WR as an input/constant (either 4% or 5%) and calculate the success rate of that. I wonder if this can also cause the difference in results.

That shouldn’t make a difference. When I calculate a SWR <x% for one cohort it should happened if and only if the Pfau/Kitces calculations find failures of the x% Rule.

Maybe I’m talking nonsense, but it seems to me that they try to find the glidepath that minimizes failure rates at WR of 4% and you try to find the glidepath that maximize the SWR. Not sure if it should result in the same glidepath.

That may indeed make a (small) difference. But I showed that their optimal GP is still suboptimal for a 4% WR when using historical data. Monte Carlo vs. historical return patterns will have the biggest impact.

Sorry I missed that you showed this in the table for CAPE>20. Probably you had the same results for all CAPE’s. Keep up the good work!

Hi ERN, love your work. Thanks for the 30-year timeframes. Was wondering if you would consider breaking the CAPE categories into smaller ranges? E.g. 30… in my view there’s a big market valuation difference between a CAPE of 21 and a CAPE of 33. If I see a 3.8% withdrawal rate in the CAPE >=20 section, and maybe that applies when the CAPE is 22, I wonder if I should take it down 10% for a CAPE 30 environment? i.e. 3.8% x .9 = 3.42% when the CAPE is 30ish? Thanks!

I would advise against using too many CAPE ranges/categories. The number of independent observations will become so small that the SWR stats become unreliable.

Looks like some of my previous comment wording regarding CAPE ranges got cut off. I meant having CAPE ranges of under 20, 20-25, 25-30, 30-35. Unless there isn’t sufficient historical data for those ranges? Or to put it another way, how would we adjust the SWRs in a low 30s CAPE environment vs a low 20s CAPE environment? Recently it was in the low 30s.

Do you have any insight into Warren Buffett’s 90% stock 10% cash allocation? One study by a finance professor at IESE suggests this 90-10 allocation has a 2% failure rate using the 4% rule: https://www.ieseinsight.com/doc.aspx?id=1815&ar=7&idioma=2_blank.

Not a bad allocation. It increases the risk of some really bad outcomes, though. The 4% unconditional failure probability is lower than for a 60/40, but the failure probability is higher (>10%) when you condition on a CAPE>20. So, that’s a caveat!

When using the Glidepath and your SWR toolbox calculator together, should we use the SWR of the initial portfolio allocation? If so, do we change it when we have reached

For Example: at a 40/60 for 30 year horizon its showing SWR = 4.38% (CAPE+30), but when the glide is completed (assuming CAPE didn’t change) at an 80/20 its showing SWR = 3.54%. Should we recalculate each year based on current CAPE and new portfolio allocation?

If the bear market occurred during the time you went through with the glidepath then the CAPE will have very well changed. So, you definitely want to check how your current asset mix and your current WR performed when the historical CAPE was similar to your current CAPE.

Did you incorporate expense ratios into the total return computation in your model? If so, what values of expense ratios did you use? (Expense ratios would play a relatively big role in the final SWR, so curious to understand if/how they are incorporated here.)

In my Google Sheet (part 7 and 28) there is a field where you can enter your ER. I use 0.05% p.a. as a weighted expense ratio for the stock/bond portfolio in all of my calculations here.

I tried your SWR Toolbox v2.0 spreadsheet, and it seems to give different results than this article. For example, for 80% fixed stocks allocation over 60 years to 0% final target valuation, the failsafe SWR given by the Toolbox spreadsheet is 3.29% while this article lists 3.14% as the failsafe for the same set of params. Any idea why the discrepancy?

Set the additional cash flows in the “cash flow assist” tab to zero and you also get the same 3.14% failsafe in the Google Sheet

Would be intrigued to see research on optimal glide paths into the bind tent during accumulation as well!

Yeah, I’ve looked at some simulations. It will be a future blog post! 🙂

I’m very interested as well!

What’s your take on the following path-independent dynamic asset allocation strategy? https://www.bogleheads.org/forum/viewtopic.php?t=293469

I don’t interact/discuss with the Bogelheads. Too many trolls there, so I don’t try to respond to any posts there. The post starts with “The optimal asset allocation for a 4% withdraw rate with a 30 year horizon is 50% stocks.” which is not true. Not sure if I want to go through the rest after the post starts with an incorrect premise.

I have proposed path-dependent AA for the withdrawal path (=active glidepaths where the glidepath slope depends on the equity returns). They seemed to work pretty well.

Thanks for taking a look. Mainly, I was thinking that their high-level strategy of having a lookup table that maps (portfolio-size-divided-by-annual-spend, years-left-in-retirement) to (success-probability, optimal-allocation) seems like a very useful way to represent a (path-independent) strategy to guide rebalancing. I was also wondering if there’s some nuanced flaw in their constant shifting of allocation as the portfolio grows and shrinks over time. It “feels” similar to the fallacy about SWR that you pointed out in your recent post (i.e., no need to reset SWR when the market drops because of conditional expectations), but I can’t quite put my finger on it, so maybe I’m wrong about that.

Yeah same feeling here. Looks fishy, can’t put my finger on it.

Also, nobody can ever claim that they can provide a table where retirees can just look up their # in a table. Retirement is too personal. We all have other cash flows and spending constraints that will push the true # mich higher or lower.