How To “Lie” With Personal Finance

“Lies, damned lies and statistics” (Mark Twain)

“Do not trust any statistic you did not fake yourself” (Winston Churchill)

There is a classic book called “How to lie with Statistics” that I read many, many years ago (actually decades ago!) as a college student. If you’re ever looking for an inexpensive but fun and impactful present for a young student/graduate with the hidden agenda of getting that person interested in math and statistics, this is the one! The book taught me to take with a grain of salt pretty much anything and everything number-related. Anywhere! Whether it’s in the news or in the Personal Finance blogging world and even (particularly?!) in academia. I’m not sure if I was already a severely suspicious (paranoid?) person before reading this or the book turned me into the person I’m today. So, inspired by that book, I thought it would be a nice idea to write a blog post about the different ways numbers are misrepresented in the FIRE/Personal Finance arena. And just to be sure, this post is not to be understood as a manual for fudging numbers, but – in the spirit of the “How to Lie With Statistics” classic – serves as a manual on how to spot the personal finance “lies” out there!

And there’s a lot of material! Probably enough for at least one more followup post, so for today’s post, I look at just four different way of how quantitative financial issues are frequently fudged in the personal finance world. And a side note about the slightly attention-grabbing title I used here: Well, I put the word “Lie” in quotation marks to show to the faint-hearted that this is a bit tongue-in-cheek. I could have written, “fudge the numbers” or “Enron-accounting” or “How we delude ourselves in personal finance,” or something like that. Also, Hanlon’s Razor (“don’t attribute to malice what can be explained by incompetence”) comes to mind here, but I’m not sure if those faint-hearted folks feel that incompetence is a significantly more benign explanation than malice.

So, let’s look at some of my favorite examples of how people lie to themselves (and others) in the realm of personal finance…

1: Using arithmetic, non-compounded average returns

If I wanted to lie to myself and others (or at least delude myself and others) and inflate my equity market return expectations, here’s a great way to fudge the numbers: Instead of using compounded average returns, simply use the arithmetic average returns over time. Huh? How can that make a difference? Aren’t the two the same? No, and here’s a simple example: If an asset returns -10%, +10%, +30%, respectively over three consecutive years then the portfolio evolves from $100 to $90, then $99, then $128.70. That’s a roughly +8.8% annualized return. The arithmetic average of the three return numbers is indeed (-10+10+30)/3=+10%. But where did we lose that one percent? Well, it’s apparent in the time series of portfolio values over time. After a +10% and -10% return we’re left with only $99! We never made it back to the initial $100 even though the +/-10% returns in the first two years average out to zero in the arithmetic sense! To make it back to $100 would have required a +11.11% return! That loss of one percent return after year 2 plus the fact that a 30% return in the third year is also slightly below 10% annualized, about 9.1% annualized to be precise, explains why the compounded returns lag behind the average returns.

How much of a difference does this make when we look at actual equity market returns? Quite a bit. Let’s take a look at the S&P 500 (U.S. large-cap stocks) since 1923 (apparently the start date used by Dave Ramsey). (side note for the history buffs: prior to 1957 this was the “Composite Index” and only in 1957 it became the S&P 500). In the table below are the results. Just for completeness, I do this in the following different ways:

  1. The CAGR (the correct way): 10.22%
  2. I first calculate the arithmetic average of the monthly returns (0.9596%) and annualize this by multiplying it by 12. 11.51%
  3. Take the monthly average but annualize it by compounding it to the annual number: 12.14%
  4. Take the arithmetic average of the calendar year returns: 12.11%

So, the arithmetic averages in 3 and 4 are roughly two percentage points above the CAGR!

How2LieWithPF-Table01
Different average return measures: S&P 500, total return index (dividends reinvested); 12/31/1923 to 12/31/2018.

And it’s quite common to mess up the average return calculations; Dave Ramsey is touting that 12% number very aggressively. And he even admits that his 12% figure refers to the arithmetic average. He doesn’t seem to comprehend the difference and he’s actually quite vocal and belligerent:

“…you can discuss all these freakin’ mathematical theories that you – some of you — financial nerds just sit around and crunch your numbers all the time and you do nothing to help people” Dave Ramsey, via Youtube (clip starts at the 2:44 mark)

Well, unfortunately, it’s not a mathematical theory. It’s just plain arithmetic. Dave Ramsey seems to even excuse fudging the numbers to “help people” – I guess – by getting them more excited about investing. I find this ethically troubling! I’ve also seen this 12% nonsense figure slowly making its way into the FIRE community. But a 12% return expectation is way above the historical norm. Be suspicious if anyone proposes a double-digit equity expected return!

Update 5/31/2019: Since this was requested by several people, below is the link to Ramsey’s page with the 1923 starting point. 12%+ returns over such a long period are only possible using arithmetic averages:

“The current average annual return from 1923 (the year of the S&P’s inception) through 2016 is 12.25%”   Source: Dave Ramsey

And if you go to the footnote 2 provided on Dave Ramsey’s page you land on the MoneyChimp page, where the “Average” return was indeed 12.25%. But even on this page, they put the word “Average” in quotation marks. The “True CAGR” was indeed two percentage points lower. So, Dave Ramsey is using a monkey business number from a site named MoneyChimp. You can’t make that up! 🙂

How2LieWithPF-Chart07
This is where Dave Ramsey got his 12% return. He used the arithmetic averages by calendar year, not the true CAGR. Source: MoneyChimp

 

How to spot this “lie” in the field: Always make sure that return numbers are CAGR. Sometimes that CAGR acronym is quoted explicitly. The phrases “compound,” “compounded” or “geometric average” would also be indicators that the calculation is done the right way. If no additional clarification is given, you might want to get your own calculator/spreadsheet out and confirm.

How I deal with this issue here on the ERN blog: I actually don’t even mention CAGR explicitly very often but rest assured that everything is A-OK here! 🙂

2: Ignoring inflation (i.e., confounding nominal and real returns)

OK, so let’s assume we’re smart and careful enough not to mess up the average return calculation. 10% equity returns, that’s still quite impressive! But unfortunately, that’s still a bit too high because that was the nominal return. If we’d had 10% inflation over that time span then a 10% nominal return doesn’t look so hot anymore. Of course, in most Western economies we’re talking about 1.5% or 2% CPI inflation per year today. What difference does that make if we ignore inflation? Admittedly, a negligible difference in any given year but it adds up over time. Even 2% inflation will erode your purchasing power over time. $100 today will become only $55 after 30 years and only a bit more than $30 after 60 years. Ignore that in your FIRE calculations and your fat-FIRE budget might slowly turn into lean-FIRE!

How2LieWithPF-Chart01
Erosion of a nominal $100 over time under different inflation rates. Note that we’ve seen around 2% inflation over the last few decades, but there were some 30-year windows with 5+% average inflation (e.g. 1960s to 1990s)!

And this slow erosion of purchasing power is what makes inflation so dangerous. Not doing any inflation adjustment to your retirement budget in any given year seems innocuous. But over time you’d accumulate a dangerous cut in purchasing power. My blogging buddy Fritz called inflation the Silent Killer of Retirement, quite appropriately if you look at the chart of inflation erosion in the chart above! So, in any case, if we take out inflation from the S&P500/Composite return we’re now down to 7.15% for average returns 1923-2018. I still find this really impressive. Using the Rule of 72, that means your money doubles every ten years!

How2LieWithPF-Table02
S&P 500, total return index (dividends reinvested): 12/31/1923 to 12/31/2018, Nominal vs. Real (CPI-adjusted).

Of course, bungling the nominal vs. real returns isn’t always that obvious. Sometimes the nominal vs. real lie is very elegantly hidden. Here are some examples:

Example 1: “The 1980 and 1982 recessions weren’t all that bad for the stock market”

For someone like me, who has a morbid fascination with all the things that can go wrong in (personal) finance, the 1970s and early 80s are really intriguing. Funny thing is, if you look at the nominal equity performance between, say 1972 and 1982, the S&P 500 performance (total returns = dividends reinvested) doesn’t look so bad. Sure, there was a 43% drop in 1973/4, but a swift recovery followed and the two recessions in 1980 and 1981/2 saw only a very shallow drop in the stock market. Seems like a pretty benign period, right? Wrong! First, the drop in 1973/4 was over 50% when adjusted for inflation, roughly in line with the dot-com bust and the 2008/9 meltdown. Then the peak-to-bottom drop in the early 80s was 27%, which is a bit higher than the 17% drop in nominal terms. But even this 27% drop disguises the fact that the bottom in 1982 was still a whopping 40% below the CPI-adjusted 1972 peak.

How2LieWithPF-Chart05
What a difference the CPI makes: Nominal stock returns over the 10-year period 1972-82 don’t look so bad. But in real, CPI-adjusted terms, both the 1973-75 and 1980/81/82 events look devastating!

By the way, adding to the pain during this period was the fact that bonds didn’t offer any diversification benefit because yields went up and caused both stocks and bonds to lose exactly at the same time. So, from a personal finance point of view, the 1970s/80s were a total unmitigated disaster, by some measures even worse than the Great Depression! But believe it or not, I’ve seen material from otherwise trustworthy bloggers who make the indefensible case that recessions aren’t really that bad for the stock market, pointing to the experience during the 70s and 80s. A little bit of soul dies every time I read that!

Example 2: “The year 2000 retirement cohort would have done just fine with a 4% withdrawal rate because they’d recovered their initial portfolio value by now”

This claim is often based on Michael Kitces’ case study of the 2000 retirement cohort. Kitces very accurately points out that an imaginary retirement portfolio would have recovered its $1,000,000 value by 2015 even with annual $40,000 withdrawals, adjusted for CPI inflation. But make sure you read the entire post, otherwise, you’ll miss this important piece of information:

“Of course, an important caveat to the chart above is that it’s based on ‘nominal’ dollars, not adjusted for inflation. Which is important, because it means that retirees who had similar portfolio balances after the first half of retirement were not necessarily going to have the same buying power with those dollars for the rest of retirement” Kitces.com, accessed May 18, 2019.

Adjusting for inflation, your portfolio would still be significantly under its starting value, just around $674,000 as of 4/30/2019. If you keep withdrawing $40,000 a year out of that portfolio you’re now looking at a 5.9% effective withdrawal rate. Probably fine if your horizon ends in the year 2030, but likely a reason for concern if you had been an early retiree in 2000 and you’re looking at another 30+ years going forward from here!

Well, at least you can’t blame Michael Kitces. He clearly states that the portfolio value was in nominal dollars, visible for anyone who wants to see it. The “lie” is mostly a result of confirmation bias running amok, i.e., the 4% Rule cheerleaders in the FIRE community ignoring the disclaimer about nominal returns and touting this as a great success of the 4% Rule even for early retirees.

But I’ve also seen some bloggers obfuscating this nominal vs. real issue a lot more blatantly. For example in this blog post on Ben Carlson’s blog “A Wealth of Coming Sense” (which I generally like, just not this one blog post), there are similar calculations as in the Kitces case study – notice the $1m+ portfolio value for the year 2000 retirement cohort – but now there is no mention at all of the fact that the final portfolio values being reported in nominal terms only! In fact, phrases like this one:

“but inflation did take a monster bite out of the ending balance in the 1973 start date”

…suggest to the unsuspecting reader, that all numbers were CPI-adjusted: withdrawals and portfolio values. But again, only the withdrawals, not the portfolio values are adjusted for inflation! How sneaky! And a side note: there are at least two additional data fudging problems in Ben’s calculations:

  1. He starts the 1929 retirement cohort in January rather than in September – the true market peak and over 30% above the beginning of the year level. This greatly obscures the true danger of “retiring at the market peak!”
  2. He displays only the 1973 cohort but ignores the 1966 market peak where retirees actually would have run out of money after 30 years due to the horrendous 1970s and early 80s recessions and bear markets!

So, to sum up, if you were to do this exercise the right way, then the portfolio values after 30 years look a lot less appealing. Instead of preserving or even growing your capital after 30 years it looks more likely you may run out of money (1966) or almost run out of money (1929, 1973) to the point where your portfolio won’t last for the fourth decade. Which would be a bit of a problem for early retirees!

How2LieWithPF-Table04
Final value comparison. for different retirement cohorts after 30 years. Notes: Ben uses 1/1929, I use 9/1929 cohort. The 1966 cohort would have run out of money in 1993. Ben: 2000 retirement cohort is up to 2018, ERN: 2000 cohort up to 4/2019. Ben uses 5y Treasuries, I use 10y.

Example 3: “[After 30 years,] the [4%] safe withdrawal rate actually has a 96% probability of leaving more than all of your original starting principle [sic].” Source: Mad Fientist podcast with Michael Kitces

Again, the final portfolio values are not adjusted for inflation. This gives the false impression to a gullible FIRE fan that since you preserve your capital for 30 years with such a large probability, you can easily tag on another 20 or even 30 years and you can thus “extrapolate” the 4% safe rate from 30 years to a FIRE-style retirement horizon. But that’s not true. Using the inflation adjustment both for withdrawals and for the portfolio value over time you run a much larger risk of shrinking or even depleting your capital over 30 years. In the table below, I display the failure probability calculations for a 60/40 portfolio, 30 years horizon, monthly withdrawals, 1/1871-4/2019, all calculated with my SWR toolbox. You would have failed to maintain your purchasing power in the portfolio over 30 years with a 42.8% probability. And an almost 60% probability conditional on an elevated CAPE ratio (above 20. Note: Today’s CAPE is 30!!!). In fact, in the historical simulations, you faced an 8.9% probability of totally depleting your money after 30 years, conditional on an elevated CAPE (>20). This shows you how totally senseless the alleged 4% failure probability for capital preservation is! If it sounds too good to be true it probably ain’t!

How2LieWithPF-Table03
Failure probabilities of the 4% Rule over 30 years. Stock=60%, Bond=40%. CPI-adjusted withdrawals and portfolio values. 1/1871-4/2019.

How to spot this “lie” in the field: Without any further clarification, one would almost always assume that return figures are nominal. Every time a study states that withdrawals are inflation adjusted but there is no further mention of what was done to the portfolio values over time, one could almost safely assume that the portfolio value over time is not inflation adjusted (and is thus a completely useless statistic, more on that below).

How I deal with this issue here on the ERN blog: In safe withdrawal simulations it is an absolute must to use the double inflation adjustment, i.e., inflation adjustments to both withdrawals and final portfolio values to use comparability of final portfolio values across time. I try to be really, really explicit about what I do: Unless explicitly stated, the default position is that all calculations here on the blog in general and the Safe Withdrawal Rate Series, in particular, are done using real, CPI-adjusted returns. It’s the only sensible way to do it.

3: Ignoring different inflation regimes

Notice that none of the issues in item #2 above would be that much of a concern if the U.S. economy simply had had a constant inflation rate over time. If we’d faced x% constant inflation every year then everyone can just easily transform some nominal median portfolio after y years back into real numbers. But inflation rates do differ wildly over time, see the chart below. Not adjusting for inflation would have melted a $100 nominal dollar amount to anywhere between $20 to $85 since the existence of the U.S. Federal Reserve:

How2LieWithPF-Chart06
The inflation impact over 30-year windows varies wildly over time!

To demonstrate why we should be cautious about summary stats that rely purely on the nominal final portfolio value, let’s look at the following numerical example. There are 5 (completely fictional) observations of retirement cohorts with their final portfolio value after 30 years. They are conveniently ordered from cohort 1 = highest to cohort 5 = lowest. The median among the nominal values is exactly $1m. If we now deflate the nominal values by their corresponding average inflation rate, i.e., Real = Nominal/(1+Inflation)^30, then we get the real portfolio values anywhere between $356k and $662k. But do you notice something peculiar? The ranking is completely different for the real portfolio values:

  • The cohort that has the median nominal value now has the lowest real portfolio value.
  • The median real portfolio value is $416,479, which is the portfolio of the cohort that has the highest nominal value
How2LieWithPF-Table05
Numerical example: Don’t trust nominal final portfolio values!

In other words, the ranking is completely reshuffled when adjusting for inflation. (For the math geeks, it’s because the median operator and the inflation adjustments are highly non-linear operations) Consequently, reporting any stats on the nominal portfolio value (median value, the probability that we exceed a certain threshold, etc.) is a completely moot exercise. The only figure that’s not impacted is the probability of hitting $0 because – you guessed it – a 0$ final portfolio value is the one single value that’s the same in nominal and real dollars! So, we can’t deduce anything about the real, inflation-adjusted numbers from the nominal values. And by the way, it’s also of no use to, for example, “guesstimate” the median real value through MedianReal = MedianNominal/(1+MedianInflation)^30, which would be $1,000,000/1.02^30 = $552,071 in this case. Very different from the actual median value.

So, not only do we overestimate the final portfolio value by looking at the nominal values (see item 2 above) but by looking only at the nominal final portfolio values we lose so much important information about the distribution. I have to roll my eyes every time I read how the Trinity Study elaborates on median nominal final portfolio values. Or how FIRE bloggers parrot senseless stats like “the median portfolio value using the 4% Rule would have been 2.9x the starting value” or “you’d have a 96% chance of preserving your initial capital” (see item 2 above). These are totally useless junk statistics when derived from nominal values alone! That’s why I’m such a stickler on doing my analysis with double-CPI-adjustment: withdrawals and portfolio values have to be inflation-adjusted over time to make them comparable across different inflation regimes! Everything else is junk science!

How to spot this “lie” in the field: Again, the gold standard in quantitative financial/economic research is to do the inflation adjustment period by period. It’s also quite common in Finance to adjust returns by calculating the excess return over a risk-free benchmark (i.e., 3-month T-bill, etc.) instead of CPI inflation. If nothing is mentioned, one can assume almost for sure that these are again nominal returns.

How I deal with this issue here on the ERN blog: Again, I always do the inflation adjustment period by period with the exact inflation number in that month. I wrote a nice little summary about how exactly I do the inflation-adjustments in my SWR Series, see this post, especially the appropriately named section “How I account for inflation in my Safe Withdrawal Rate Series!”

4: Pick the “right” Start/End Points

Notice that in my own calculations I always work with return data going back to 1871. The average real stock return since 1871 has been about 6.6%, see the chart below. Notice that due to the y-axis log-scale, the red CAGR return line is one straight line!

How2LieWithPF-Chart03
Cumulative real S&P500 returns (total return, i.e., dividends reinvested). The mean return since 1871 is the CAGR!

Looking at the picture above I can come up with a nice new opportunity of number fudging numbers and data malfeasance. If we start the equity return interval at the trough of the market in 2009, we’d have observed a 14%+ average equity return, see the chart below. And that’s above inflation! Quite impressive but likely not repeatable indefinitely. But starting at some of the other market troughs, like 1975 or 1982 we can still boost the average return by 1 to 2 percentage points. Notice a problem here? We are now taking the average over x bear markets and x+1 bull markets. And that can move up your average return to values that are unlikely to be repeated going forward from today’s perspective. Especially after we’ve now experienced 10+ years of a very impressive bull market!

How2LieWithPF-Chart02
Picking the “right” starting points: We can significantly boost the average return if we start at the bottom of the bear market!

How to spot this “lie” in the field:

  1. I always ask myself, is the return series long enough to include at least several up and down markets? If there’s never been any downmarket, be careful about extrapolating returns. We’ve had 14% annualized returns since March 2009 but nobody in their right mind would believe that this trend will continue long-term. That said, some folks who entrust their money with some of the new lending platforms (e.g., debt, mezzanine debt or equity investments, personal, business and real estate loans) should ask themselves how those investments will perform if we go through another recession again.
  2. Even if the return series includes multiple up/down cycles, check if the starting point was “conveniently” picked right at the bottom of a down market while the endpoint is many years into the bull market. If an average return is calculated with a starting point later than the earliest available date, always ask yourself if there’s a sensible reason to do so.

How I deal with this issue here on the ERN blog: Some folks use data starting in 1926. I use data going back to 1871. For all intents and purposes, the results of safe withdrawal rate studies will be very similar. That’s because of the really scary Sequence Risk episodes (Great Depression, 1970s/80s) all happening after the 1926 cutoff. Also, because 1926 was more or less in the middle of the 1920s bull market the average real return 1926-today is strikingly similar to the one using data starting in 1871.

Conclusion

Whoah! That’s a lot of material for one post already. And we’re just getting started! I got another set of “lies” for a future post.

In any case, we started with 12% average equity returns (actually 12-18% according to the great finance genius Dave Ramsey) and now knocked it down all the way to 6.6% if we look at the very long time trend of real total equity returns. That’s still extremely impressive! Multiple percentage points above the average real GDP growth! It’s also significantly higher than many other major asset classes: Bonds, gold, silver, etc. so, please don’t misinterpret this post as trashing stock investments. I hold way too much (and I mean waaayyyy too much!!!) equity percentage in our portfolio to be a stock market trash talker. Quite the contrary, I’ve gone on the record recently that the whole scare about the yield curve inversion was exaggerated. I’ve also gone on the record in early January, both here on the blog and on the ChooseFI podcast, episode 109R, saying that the equity drop in Q4 of 2018 was likely overdone. Looks like good advice so far! I’m neither a cheerleader nor a doom-and-gloom guy. Just a realist.

And then, finally, be cautious about some of the cheerleading about the 4% out there. I’m a skeptic, as you all know, see the Ten things the “Makers” of the 4% Rule don’t want you to know (SWR Series Part 26). If people using the exact same return data as I come to very different conclusions I’d get very suspicious!

Hope you enjoyed today’s post. Please share your own favorite finance “lies!”

99 thoughts on “How To “Lie” With Personal Finance

  1. Great post as usual, Big ERN. This explanation of how numbers are “crunched” in the personal finance/FIRE world serves to further validate the salient points highlighted in your SWR series. Very informative stuff. IRT Dave Ramsey; I’m a fan of his “get out of debt” and live responsibly crusade but cringe every time he mentions stock market averages of 12% or gives INVESTMENT advice. The historical compounded return you mention of 6.6% makes doom and gloom forecasts of 5% returns over the next decade seem not so bad if the 5% is compounded using expected inflation numbers. Thanks for the post.

    1. Yeah, same here. I like Dave Ramsey for what he’s doing getting people out of debt. After people graduate from Ramsey, it’s best to look for another expert to move on to the next stage in life! 🙂

  2. ERN, I love this post as a fellow skeptic who is persnickety about math (especially when the stakes are high, i.e. with regard to personal finance and retirement!) Question: do you know of a Retirement Calculator that allows the user to adjust inflation as well as returns? I use the Personal Capital Retirement Calculator, but I notice that their built in assumption is that returns are quite rosy, and that is not something that the user can adjust. In my modeling, I try to compensate for this by raising the inflation rate (which is adjustable on PC). Any suggestions?

    1. @LW in my FI spreadsheet course I have a big section devoted to inflation adjusted returns to make it as flexible as possible for users. However the tool itself might be a bit simple for you – but it’s got a 30 day return 🙂
      [Karsten apologies for the product placement, feel free to delete!]

    2. Well, my calculator (SWR series part 28) does everything in real return space based on historical real returns. Just for the reason you mentioned, rosy returns, not enough levers to change assumptions, I stay away from most other calculators out there!

  3. It’s the real/nominal confusion that upsets me the most. Like you say it does not have much impact in the short term, but for the length of periods we consider for retirement it needs to be taken into account. It’s no good telling someone they will certainly still have $1M left after many decades if that $1M is only enough to buy rice and beans.

    To your point about the 70’s, I really had not appreciated how stunningly bad that period was (and I’m not talking about the hair and fashion) until I started doing my own projections with historical data. It’s not an obviously bad period but the inflation is a total killer! It still mystifies me why QE did not produce the inflation bomb everyone predicted after ’08, but the recent decade could have turned out so differently and wiped out these great real returns we’ve had.

    1. Thanks, AoF!
      We shall see how QE will work out in the future. I cross my fingers we won’t repeat the 1970s. Even half the inflation shock would wreak havoc on today’s stock/bond portfolios!

  4. Hi ERN, yet another throughly researched and evidence based article de-bunking some of the more outrageous claims on stock market performance. The sad thing being that the ‘truth’ is actually a very good news story in itself and does not need exaggeration.

    On the 4% SWR point, or indeed any SWR percentage, do you feel that the number itself is mis-leading or is it more the context that it is presented in is inaccurate? My view based on using your excellent spreadsheet, is that the answer as often is “it depends”. As a late-comer to FI, I have a shortened time horizon in retirement, as well I can live with capital erosion as our children are well setup for the future based on their education and career choices. So 4% or even higher could work for me.

      1. Great article.
        But I would love to see the rationale behind “4% can be too low for many early retirees.”. If anything this seems too high to me. I start with knowing that it came from various studies that looked at a ‘normal’ 30 year retirement time frame. Extending that to longer, as an early retiree would need to do, should drop it down to lower.

        Using ERN’s spreadsheet (its great… thank you!) and plugging in a typical 60/40 asset allocation, and even a modest 40 year time horizon, and even adding in some SS benefits for 2 earners… it shows a 4% SWR failing ~5% of the time, and above 4% failing 10+%. Maybe that is an acceptable level in this discussion. But not to me.

        I am worried every time I see a 30-something use the 4% rule, knowing they have 60 years of retirement and it was based on a 30 year analysis.

        1. Google “Doug Massey FTI”. He answers this question frequently on Quora. He developed a formula that looks different, but essentially is the SWR as a function of retirement age, where retiring at 30 has it at 3%, at 40 it is 4%, at 50 it is 5%, and so on….The older you retire, the higher your SWR can be, according to his formula, which I agree with. I’m 52, and in my retirement spreadsheet I’ve concluded that I have an 80% chance of success with a starting withdraw rate of over 6%! But I’ve tightened it by factoring in many variables like the actual cost of taxes, health care, social security, future downsizing, and spending that reacts to market crashes.

          1. Nice! I still like that the CAPE adjusts bu equity valuation regime. I would like to see a better way of taking into account the age of the retiree as well and maybe combine the CAPE with the FTI. That would be cool!

            1. Actuary Evan Inglis you can google him has come up with a “feel free” SWR. Take age divided by 20. Then divide by 100. So for me age 63 / 20 / 100 = .0315. Using your formula if I take the CAPE 30 yield multiply by 0.5 slope and add 0.015 intercept / 100 = .0317. How cool is that?! 😀

              1. Oh the CAPE calc doesn’t need to be divided by 100. Hey it’s 1am here and I’m a bit sleepy. You get the idea.

                1. And then would you recalculate the CAPE SWR either monthly or annually, adjusting your withdrawal accordingly, or would you use it to establish the initial SWR at the start of retirement , thereafter increasing the withdrawal dollar amount by monthly or annual COLA?

                2. In simulations it’s actually easiest to calculate the SWR every month. But in practice, I can see that it’s not really necessary. Maybe adjust every quarter. Certainly at least once a year!
                  And again: you don;t adjust by CPI/COLA. The CAPE rule determines the SWR, multiply by current portfolio value and that’s the withdrawal amount. And that will (hopefuly!!!) keep up with inflation!

        2. Hi Gary,

          May I suggest you have a look at Firecalc, it allows for the setting of a SWR, against a time horizon and the size of the pension pot. This can then be customised to include Social Security payments, etc. In my case, the simulation shows an outcome of zero failure cycles against a SWR of 5%. Of course, it is my choice whether to act on this, but it gives me a sense of the maximum SWR that I could achieve.

          All the best.

        3. The 4% fails in “naked” and “academic”-style SWR simulations. A lot of actual FIRE folks in their 40 or 50s have sizable pension and Social Security income relatively early in their retirement. Factor that in and you’ll get a >4% SWR.
          But you’re right: for the extremely early retirees in their 30s or even 20s, you might want to discount that future income very heavily and stay at SWR<4%.

  5. ‘Statistics are like bikinis. They show you a lot, but can cover up some very important things.” -My Junior High Shop Teacher

    Dave Ramsey has some incidents of giving pretty horrible advice. My favorite was him doubling down on “If your investments average 8% a year and inflation is 3%, you can safely take out the remaining 5% a year indefinitely!”. I had had that same retirement plan once – when I was 19.

    But the 12% he touts is based on AIVSX, which indeed has returned about 12% since inception 85 years ago. I wouldn’t plan on that going forward, but it’s true. His “recommended family of mutual funds” is American Funds, and you’ll find their domestic stock funds making up the .3% of funds that outperform the market over many decades.

    1. Be careful about several issues regarding that 12% figure for AIVSX. There is survivorship bias to factor into the discussion, there is style drift to consider (a ‘feature’ of American Funds), and also the fact that the vast majority of purported outperformance was prior to the turn of the century. I have nothing against Ramsey (he has a great message, but is wrong on this Investment topic)… nor American Funds, they are well run and can do well for you as long as you aren’t paying loads and high fees to own them.

  6. In your first example you’ve switched the -10% and +10% returns in terms of the portfolio value at the end of the year. Also your graph of capital preservation vs depletion for CAPE’s under and above 20 does not make sense. The percentages in both the under 20 column and over 20 column do not sum to 100%.

    Just a few things I noticed along the way. Otherwise, I very much enjoyed this post!

    1. Item 1: Indeed the +/-10% were switched in the taxt vs. the calculation. Didn’t make any difference in the final result of course.
      Item 2: The table with the failure probabilities for different CAPEs indeed makes sense. Not sure why it doesn’t make sense to you…

  7. Wow, seriously good post. I feel like I learned a ton from it! The real returns vs inflation adjusted returns discussion always gets to me too, with mentions of “you should use 9% for all your calculations” (or higher!). It’s interesting to see that 6.6% is closer to the target.

    That makes me wonder about MMMs “shockingly simple” chart of years vs savings rate to get to 4%. That chart uses a 5% a year rate of return – even below the market avg. That’s probably not a bad thing for a diversified portfolio that would return closer to that. If 6.6% is closer for an all stock portfolio, what might a diversified portfolio (take your pick on asset allocation) look like percent wise?

  8. Thank big ERN! I always wondered exactly why the Fidelity retirement calculator (Monte Carlo simulation one) used a 6.6% inflation adjusted, “average market return” figure for an all stock portfolio in that tool.

      1. Hi ERN and Philip, I’ve actually told my Fidelity rep that I think their retirement planning software is too rosy with not enough levers to pull – too much of a black box. For example can’t adjust for CAPE regimes. But it does use real returns and discounts to today’s dollars which is good. Interestingly the rep recommended I put half my account (half my net worth) in an immediate annuity at my current age of 63. The software shows I will have 2x the remaining portfolio in today’s dollars at age 98 vs. no annuity. I would never do this. Sounds like their looking for some nice commissions off me.

  9. Biggest lie in personal finance right now? A family with young children can have a 50+ year worry-free retirement with no additional earned income, no pension, and minimal social security on a nest egg of 25 times current annual expenses.

  10. Thanks for the post. I have a question: Instead of using inflation-adjusted real returns to project future retirement buying power, what if you use nominal returns, but give your projected spending an “annual raise” in the amount of inflation. Would this be more-or-less equivalent or is this thinking flawed in some way? Also, is there a commonly accepted value for the standard deviation of inflation to reflect its volatility?

    1. I don’t recommend that either. Goes back to point #3: different inflation regimes. If you use the historical returns of 10+% and deflate them only by 1.5-2% inflation we had recently then the real returns are again articially inflated.

  11. The biggest lies are generally the ones we tell ourselves. This category moves quickly beyond ‘lies’, I think it critical to focus on the behavioral biases (which I guess you could say are really about being fooled by our own senses.) The tendency to fix on certain numbers of little real import in our investment process, immediacy bias, confirmation bias, etc, etc.

    I think it’s a little over the top to refer to many of these items as lies, unless done with purpose to deceive. In many cases, the intent of analysis was something other than the point you chose to highlight, which I’m glad you mentioned. It’s good to break down such things, but in the case of both Kitces and Carlson it would have been better to do so without the character aspersion associated with the label. If you are going to focus on lies, I’d request that you choose real attempts to deceive. Ramsey, otoh, has at least kinda earned a spot on this list by stubbornly refusing to do his homework and modify his message, and he earns money from his recomendations to use his approved advisors. Now, someone like Madoff could likely provide several post’s worth of data.

    1. First, I pointed out that Kitces isn’t the liar, but the people who misread his work are.
      Second, Carlson’s work is so poorly done and so misleading, and it’s done by someone who – given his background/CFA charter – should know better. I’m being generous keeping the word “lie” in quotation marks.
      Third, I did point out Ramsey here and on other places on this blog.

  12. They haven’t closed a fund in over 45+ years so survivorship bias isn’t a factor. I’m also not sure what you mean about style drift as a “feature” of American Funds. They’ve consistently stuck mostly with value investing, especially when it was severely out of favor like the tech bubble.

    As far as loads go, pay a load and get the advisor’s help or buy them no load and do it yourself.

    1. I’m glad I don’t get my investment advice from Dave Ramsey. I wonder how many of his followers are assuming 10% would be a safe withdrawal rate since they can count on 12 to 18% returns.

      Do you remember Tony Robbins? He did infomercials back in the 80’s promoting his self-help audio tape program called Personal Power. I thought there was a lot of good information in the series, but he was way out of line when it came to investment advice. He claimed that 20% annual returns could be had pretty easily by educating oneself on investing. I ended up majoring in Finance in college but I was never able to find those “easy” 20% returns. If I had, my net worth would be nearly a billion dollars now and I wouldn’t be stressing over SWR.

      1. What, wait, a billion dollars? With a CAGR of 20%, over 35 years, you would have started out with a net asset value of $1.6m in ca. 1984. With a NAV of 1.6m just after college, I wouldn’t have been stressed out about anything.
        I’d have founded my start-up in a garage, Jobs-like, probably failed gloriously, shrugged it off, come to my senses and invested the remainder sensibly once the youthful exuberance had worn off a bit. Of course, ETF had not been invented yet in the 1990s, so I’d have to navigate an investment course between mutual funds with usurious expense ratios.

        1. Okay, so maybe not a billion, but remember Tony Robbins said 20% was easy, and I was prepared to try hard, so maybe I could have achieved 25 or 30% annual returns after getting myself some investing edumication. 😉

        2. Edumacation is the process by which one becomes edumacated, the achievement of which is generally marked by a gradumacation ceremony. Edumacated people know a lot of things, though the process of how they came to know them mostly remains a mystery to onlookers.

  13. Dang dude, you pretty much schooled me on this math. Good post ERN. Some very good points to consider. Inflation is an interesting beast – not only is it inconsistent, but various depending on what you’re talking about. Construction inflation, for example, tends to be about 4-6 percent per year (avg of course) and that can impact things such as municipal tax rates and other areas that would affect someone’s expenses.

    This is all good for the math nerds but most folks need to it be simple. So the long and the short of it — build a little cushion beyond the 4% rule, yeah? (or keep a fun side hustle?) Anyway, I’ll stick to writing about the FOI (Fun on Investment) of riding bicycles while building toward FIRE.

    1. Oh yes, I haven’t even covered that: different folks have different personal infaltion rates. Depending on what’s your personal consumption basket.
      Better keep a little extra cushion, as you suggest!

  14. Great Article! So much mumbo and so much jumbo in FIRE land all without taking inflation and tax policy into account in disbursement, is going to lead to a lot of failed purchasing power even in the face of some kind of portfolio survival.

    1. Harrison: You’re barking at the wrong tree here. Among the FIRE bloggers I’m not one of the dogmatic ones who clai that there’s no way to beat the market. Remember, I used to work in finance/asset management.
      So, I’d never say that outperforming the S&P500 is impossible. The blog post was about how the S&P500 has trouble fetching 12% nominal over extended periods.
      But back to your list of funds: I think we can at least agree on this: It’s a heck of lot easier to identify the funds outpoerforming the S&P ex post than ex ante, right?

  15. Thank you so much for being deep in the weeds. This (and your other posts) have been both practically helpful and emotionally reassuring. I’ve felt a bit hesitant about the FIRE math these past few years, and am delighted to have found someone so happy to chew through the tough details.

    That said, a question! Why is the median resulting real value in your inflation chart $416,479, but in the narrative its $552,071? Apologies if I’m missing some obvious distinction between the two here, but I’m not tracking the difference. Based on the formula you provided, starting with the median $1m and applying the median 2% should result in the latter figure, right?

    Thanks again for all you do!

  16. ERN, Thanks for another quality article; looking forward to Part 2.
    Your comments on inflation are particularly welcome as most people seem to have forgotten (or perhaps just do not know) about the potentially devastating impact of inflation. I can just about remember the double digit inflation of the 1970’s. One of the best articles I ever read on this and how serious it can be (versus say, sequence of returns) was written some years ago by Jim Otar – see “Determinants of Growth in Distribution Portfolios ……” under <> at the following link http://retirementoptimizer.com/. There are many sobering examples, and perhaps the most interesting points he makes relates to what he calls luck factors and “the sequence of inflation”.

      1. Yes, I think it is a very good paper as, indeed, is his referenced 500+ page book from 2009. I kind of hoped the white paper might trigger your curiosity e.g. what do you think of Fig 1 therein? Or, to be even cheekier, whilst many acres of text and diagrams have been written (by yourself and lots of others) about sequence risk the coverage about spending patterns and inflation – both generally and personally – falls way behind this. Just a thought!

        1. It’s a different approach. I prefer mine, especially working exclusively with real returns.
          I find his Fig 1 is 99% mumbo jumbo. But I have to admit that I’d like to construct something like this, only with different categories: How much of the final value dispersion is due to a) average returns vs. b) sequence of returns, for example…

          If my work is insufficient for you I suggest you run with his approach, though.

          1. I think your work is excellent and I did not intend to ever suggest otherwise; apologies if that did not come across. My main point is that the sequence of returns (SoR) is just one of the factors that determine the outcome. And whilst it is true that SoR can be very influential, in some circumstances other factors, such as, say, inflation, may well dominate. Interestingly, an inflation article was posted just a couple of days ago at http://www.theretirementcafe.com/

  17. Yes! Great post! Thanks for calling out these issues. This stuff bugs me as well, especially with the recent mainstreaming of FIRE. A much needed post, which I will be sure to share! Thanks BigERN!

    1. I concede that inflation may feel different for different folks consuming different consumption baskets. But I doubt that this will raise the inflation rate by 4% points (top chart) or even 7-8% points in the lower chart. I wouldn’t trust that source.

  18. Vielen Dank Karsten für deinen tollen Blog den ich mit Begeisterung verfolge. Die FIRE Community wächst langsam aber stetig auch hier in Deutschland 🙂

  19. >Dave Ramsey is touting that 12% number very aggressively. And he even admits that his 12% figure refers to the arithmetic average.

    I looked at S&P funds in my 401k and Roth, and my wife’s 401k. Both list average annual growth above 11% since the fund’s inception.

    Why is Dave Ramsey singled out for so much hate on this topic when Fidelity and Vanguard both fail to use CAGR? Ramsey is just repeating the same info that all the major investing firms use in their prospectus sheets. But nobody rages against Fidelity, Vanguard, American Funds, T Rowe Price et cetera when they neglect to put an asterisk near the average annual return charts explaining the precise details of their calculation method.

    1. To my knowledge, Fidelity, Vanguard, American Funds, T. Rowe Price, etc., just like all trustworthy financial companies use the CAGR.

      The 11% number, though, is again subject to lies #2 and #4: it’s a nominal figure and it’s a (likely) a relatively short horizon.

      So, that’s why I quite appropriately single out Dave Ramsey! 🙂

  20. FIRE investors want to minimize their risk of portfolio failure and minimize the time to retire. To some extent, we are just simpletons asking the numbers what to do.

    For this simple purpose, inflation adjusted returns vs nominal returns are kind of like measuring in inches vs centimeters EXCEPT when comparing across asset classes such as equities, bonds, annuities, cash instruments, and mortgage payoff. The issue is that you have to deflate them all equally, but stock total returns are generally quoted as the arithmetic average, bonds as yield to maturity or coupon rate, cash as simple interest, and mortgage payoff as the APY or APR. I suggest you recommend the metrics to use so that an investor can align all their options with comparable expected returns, coming up with their own return for investments of different risk profiles. One must at least use compounding metrics before starting on a forecast.

    Have you considered a portfolio application of economic value added (EVA)?

    Regarding the debate about inflation adjustments in retirement, there is evidence to suggest most of our expenses will actually decline over time. Retirees of a frugal mindset (which by necessity should include almost all early retirees) buy less fancy clothes for work, drive less, have more time to cook for themselves, and may pay off their mortgages.

    Healthcare is the big worry, but it is debatable what exactly you get by working 5 extra years as a middle aged person so you can treat yourself to open heart surgery or a boutique cancer drug when you’re 80, and survive 10 more months as a result. Perhaps it’s better to steal years of youthful freedom and face the death panels of capitalism when the time comes, rather than to sacrifice years of adventure for months of being elderly and bedridden. A few thousand dollars per year still buys a person about the same level of care that was available 30 years ago when life expectancy was peaking.

    1. “but stock total returns are generally quoted as the arithmetic average”
      Not sure that’s true. WHere would they be quoted like that? Say, if you go to Fidelity and look at the past return tables, they HAVE to be quoted in CAGR, not arithmetic average.

      Where would I use EVA? No, I guess I never considered EVA for personal finance, only in accounting.

      It’s the age-old debate about expenses going down. I rely less on average numbers and more on what I see people around are doing. I see a lot of older folks spending more due to health issues, the need for more household help, the need to travel in more confort, etc. And that doesn’t even take into account the large unpredictable risk of nursing home care.
      But you can certainly account for lower expected expenses in the SWR Google Sheet!

  21. This is why I trust your FIRE blog above all others, Big ERN! I’m good enough with math that I usually distrust other people’s calculations, but not good enough to trust my own FIRE calculations. It can be very complicated! I’m glad someone as meticulous as you is out there! 😁

    Personally, I take Ramsey’s advice with a grain of salt. I used to read his website, but at some point I got tired of his preaching against credit cards. I have no debt, and I rather enjoy the cash back I get from my card. Plus, I consider it safer than using a debit card. It would be silly for me to switch to debit!

  22. Hi ERN. Great article as usual!

    I’m a little unclear about some of the math in point 3. I’m guessing that the inflation rates in your data are computed as the mean of a backward looking 30 year sliding window? Why take the mean inflation and not the CAGR? I would assume that the purchasing power chart directly above is (implicitly) using CAGR inflation, isn’t it?

    1. The average annual CPI rates over the 30-year windows in the chart are also calculacted like a CAGR:
      (CPI(t) / CPI(t-360months))^(1/30)-1
      Again, I would only use CAGR calculations unless otherwise stated, even for inflation rates.

  23. Great conversation in the comments. Am I missing something from the post? All I see is a TBA before the 4 points are titled with no discussion.

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