U.S. Equity Returns: History and Big ERN’s 10-Year Forecast

Expensive equities are a hot topic these days. Jack Bogle warned of lower expected equity returns recently (only 4% nominal!) and the CAPE has finally crossed 30 this month, according to Prof. Shiller. What does that mean for investors? What does it mean for early retirees? There has been a flurry of activity in the FIRE blogging world on this topic with posts by Physician on FIRE, JL Collins, Think Save Retire, and two consecutive ChooseFI Monday podcasts with JL Collins and with yours truly just two days ago discussing this topic, too.

I don’t think anyone has recommended selling equities and running for the hills. I certainly haven’t, and I am probably one of the more pessimistic FIRE bloggers. Please don’t buy gold coins! Personally, I would never bet against the U.S. stock market. If you had invested $1.00 in large-cap equities in 1871, your investment would have grown to over $13,000 by July 2017, even adjusting for inflation. In nominal terms, to more than $260,000! How amazing is that?

S&P500 Cumulative Returns
Real, CPI-adjusted S&P500 returns. $1.00 would have grown into over $13,000! (for full disclosure, the index didn’t exist back then and has been back-filled with historical stock return data by some smart economic historians)

So the good news is: Stocks have the tendency to go up, on average. The broad index not just recovered from every possible disaster we have ever encountered (2 world wars, the Great Depression, several financial crises, the Dot Com bust, 9/11, etc.) but rallied to reach one all-time high after the other. After every cycle of fear, we see a quick recovery back to economic fundamentals. But buried in the equity return chart above is one small piece of bad news; the flipside of the market bouncing back from disasters and returning to the trend is that stocks also underperform after long periods of above-average performance. And this is where Jack Bogle is coming from. He doesn’t forecast a new bear market – nobody can – but simply predicts a decade of underwhelming returns after the strong bull market over the last 8 years. How do you even make a forecast like that? That’s the topic for today’s post…

The Bogle Equity Return Formula

A good starting point to quantify equity expected returns would be to look at the Bogle Equity return formula, see a nice summary on Ben Carlson’s blog. Bogle accounts for historical equity returns splitting them into their three basic components:

  1. Earnings Growth,
  2. Multiples expansion (i.e., excess returns of the price index over an on top of earnings), and
  3. Dividend income (i.e., excess returns of the total return over and on top of the price index),
Bogle Return Formula
The Bogle Equity Return Formula: Total Equity returns are comprised of 1) Earnings Growth, 2) Multiples Expansion (Price index growing faster than earnings) and 3) Dividend Income.

I’m not 100% sure if Bogle even truly invented this formula because the decomposition of equity returns into the three components is not exactly rocket science. I wouldn’t be surprised if this concept is as old as the stock market itself.

In any case, what Bogle showed with this analysis is that earnings growth and dividends are relatively stable components and a lot of the noise in average equity returns each decade comes from the P/E change, see table below.

Accounting for average annual S&P500 returns by decade. Most of the equity volatility comes from the P/E Change (multiple expansion). Source: A Wealth of Common Sense blog.

Bogle believes that the P/E change has the tendency to revert back in the opposite direction after a strong surge or a strong decline and given the elevated P/E and Shiller CAPE right now, we’re in for slightly leaner equity returns going forward; only 4%!

I tend to agree with the Bogle analysis, but like to do the calculation slightly differently. And the good news: I will come up with a slightly more optimistic equity return!

Meet: The Big ERN Equity Return Formula

Here are a few things that I like to do differently from good old Jack Bogle:

  • I am exclusively interested in real, inflation-adjusted returns. Any comparison across time that looks at nominal-only returns is suspect (sorry, Bogle/Carlson!). Inflation can be so wildly different over time; around 2% for the last few decades, but it also reached double-digits in the 1970s/early 1980s, and negative inflation (deflation) in the 1930s. So for the sake of comparability, please, please, please, always calculate returns, earnings, etc. in real terms! We can always add back inflation later if desired, but the first step has to be done in real terms!
  • I like to drill down into the sources of earnings growth and thus split this component into two parts: Real GDP growth and Real EPS (earnings per share) growth. Again, with the emphasis on real rather than nominal figures. Corporate earnings are not manna from heaven. They are part of the macro-economy, specifically, part of National Income, see Table 1.12 in the National Income and Product Accounts (NIPA). Profits don’t grow in a vacuum, but because the economy grows!
Big ERN Return Formula
Big ERN’s equity return formula is an improved version of the Bogle Formula: a) I’m exclusively interested in real equity returns and b) I drill down into the Real EPS (earnings per share) growth and split it into Real GDP growth and EPS/GDP expansion.

And for the math geeks, here’s the derivation of the Big ERN Equity return formula:

Big ERN Return Formula Derivation
Derivation of the Big ERN Return Formula. (And if someone else has done this already before me, please give me the reference and I will give credit to the original source!)

So, let’s look at the history of real annual equity returns and their components. Here are the average annual growth rates by decade, see table below. This has a similar structure as the Bogle/Carlson table, but of course with some additional stats and of course with the 4 components of real equity returns rather than 3 components of nominal returns:

Big ERN Return Formula Table
Real annualized S&P500 returns (in logs) by decade and by components of Big ERN’s Equity Return Formula. Nominal returns for comparison.

A few technical comments about the table (skip if you’re not a math geek):

  • All returns are in (natural) logarithms, i.e., calculated as ln[X(T)/X(0)]/T. The reason is that now the 4 individual components add up to the total real equity return without having to worry about compounding effects. To transfer the logarithmic % back into actual % we’d have to calculate exp(x)-1. For example, the average log-% real equity return is 6.48% in this table, which equals exp(0.0648)-1=6.70%.
  • I report one (equal-weighted) mean over the different rows. But since not all rows are full 10-year decades I also report the time-weighted mean, which is the true point to point 1871-2017 average compound return.
  • You will notice some subtle differences between my calculations and Bogle’s. For example, the dividend component by decade doesn’t quite match. For the reasons mentioned above, I calculate the dividend component as the compound average growth rate of the total return divided by the price return. If you just took the average dividend yields you might get slightly different results, which is what Bogle/Carlson might have done. I definitely prefer my methodology.
  • For the economics geeks: What I call “Real GDP” here is not the Real GDP from the NIPA. I calculate my numbers as nominal GDP divided by the CPI. I’m aware that the CPI is not identical to the GDP deflator, but for the calculations here I decided to deflate all nominal numbers by the same inflation measure, CPI. Results wouldn’t change much if I had further decomposed the GDP components into NIPA-style real GDP and the GDP-Deflator/CPI ratio.

Some observations from the return table:

  • Over the very long-term, only two of the four components of real returns have the potential to provide a consistent positive contribution to equity returns: a) Real GDP growth and b) dividend income. This is similar to Bogle’s result. I merely show that the stable part in the Bogle earnings growth comes mostly from the GDP growth. Earnings are a lot more volatile, as we will see below.
  • The two other components, earnings growth over GDP growth and earnings multiples expansion, have a low or even negative contribution over time (-1.52% and +0.51% respectively). Moreover, they have a much higher standard deviation over time and a “negative serial correlation” which means observations in two consecutive decades are negatively correlated. In other words, a high contribution in one decade foreshadows a low, even negative contribution in the next decade.

What explains the low average contribution and negative serial correlation in the EPS/GDP and SPX/EPS ratios? Very simple: The stock market returns to macroeconomic fundamentals. Earnings can’t grow much faster than GDP forever. And even if they do for a while, they will mean-revert and grow slower than GDP the next decade.

Likewise, the equity price index can’t grow much faster than earnings forever. A notable exception was the back to back growth for two consecutive decades in the 1980s and 90s, somewhat of the golden age for equities, though that came to a screeching halt when the 2001 recession helped normalize the lofty equity valuations. After the earnings multiples had quadrupled over 20 years they were in for an adjustment period.

As a side note: The negative serial correlation even flows through to the real total returns. The average equity return has a -0.48 correlation between two consecutive decades. This means there is statistical evidence that, gasp, wait for it …

The stock market is not a really Random Walk!

If you look at the cumulative return chart above, it may look like a random walk with “drift,” i.e., an upward trend, but it follows the red trend line a little too close to be a real random “Random Walk.” This convergence back to economic fundamentals represents itself visually as the total return index closely “hugging” the red trend line and the negative correlation of average returns in two consecutive decades. But can we use this to forecast equity returns?

Forecasting equity returns? It’s a Catch-22!

What I’ve learned from the historical return data is that forecasting equity returns is still tough. It’s a catch-22:

  • Over short horizons, say, 10 years, I may have a pretty good handle on near-term GDP growth and dividend yields but there is so much noise from the two volatile components (EPS/GDP and SPX/EPS expansion) that nobody can forecast returns with any degree of certainty.
  • Over longer horizons, (say, 30, 40, 50 years) the two noisy components might average out to zero again, but I don’t have a very precise view on longer-term GDP growth and dividend yields.

But not forecasting might be an even worse forecast!

Throwing up your hands and saying forecasting is hard is one solution. But keep in mind that if you believe the stock market returns 8% no matter what (strict Random Walk hypothesis) then that’s a forecast, too, but I don’t think it’s a very good forecast. You are intentionally ignoring the mean-reversion, so you’ll be too conservative if stocks valuations are cheap (March 2009) and too optimistic when stocks are expensive (March 2001).

Attempting a forecast of 10-Year equity returns

So, looking at the decomposition of real equity returns into the four components, let’s attempt to assign some “reasonable” numbers to those components and see how the real equity returns look like. In the central/moderate return forecast, I use the following assumptions:

  • Real GDP growth of 1.75%. That’s lower than the last few years, but keep in mind that this is averaging over expansions and recessions. True, the 2010-2017 partial decade so far had 2% growth. But that was in absence of a recession. The previous decade had two recessions with the resulting average GDP growth of only 1.3%, so averaging the two decades I arrive at 1.75%.
  • I believe that the real EPS can still continue to outpace GDP growth. In the baseline, I use a 1% faster growth for earnings than for GDP. Why? Shouldn’t this mean-revert after a 6% growth rate over the last 7 years? Strong corporate earnings growth over the decade so far was mostly a recovery from rock-bottom earnings after the 2008/9 recession. Earnings growth was a bit underwhelming recently so there is some additional earnings growth potential going forward!
  • But I also believe that the P/E will very slowly shrink, by 1% p.a. In my baseline forecast, I don’t assume any kind of exaggerated and drastic walk-down in the P/E. In fact, the P/E will stay at over 21 after 10 years. I may be conservative, but I’m not a grinch! For the record, I believe that the P/E can stay above its long-term average going forward (a topic for a separate blog post). Just not all the way up at 23-24 for the P/E and 30+ for the CAPE!
  • I think dividends will continue to contribute 2% p.a.

With all of that and none of the assumptions particularly crazy pessimistic, we get an expected real equity return of +3.75%. Add to that my personal 2% inflation forecast and I get just under 6% equity returns. Slightly better than Bogle, but also worse than the 8% Random Walk assumption.

Big ERN Return Forecasts
Some equity expected return scenarios. Annualized return components, Real Total returns, nominal returns and P/E Ratio in 2027 implied by SPX/EPS expansion.

Talking about the 8% number, what would it take to maintain the 8% annual return assumption? Not that much! In the table, I also display the expected equity returns in a more optimistic and pessimistic and a very optimistic and very pessimistic scenario. Nobody is saying that the 8% (nominal) return assumption is impossible. It merely takes some optimism to jack up GDP growth to 2%, earnings outpacing GDP by 2%, no compression of earnings multiples and a continued 2% dividend yield. None one of those assumptions are crazy, but all three in conjunction seem a little bit too optimistic for my taste and considering today’s environment. In 1929 Irving Fisher claimed “Stock prices have reached what looks like a permanently high plateau” right before the crash so I would be cautious and not bet on a plateau in E/P!

On the flipside, if I make all inputs a bit more pessimistic than the baseline then I end up with a 3.5% (nominal) return number, just below Jack Bogle’s 4% estimate. Not the result of anything outrageous and unrealistic. In fact, the P/E still only slowly deflates to 19.02 but remains above its long-term average. GDP is a little bit weaker (but still better than in the 2000s) and earnings simply grow with in line with GDP.

Also noteworthy: Not even in a very optimistic scenario do we get to the 12% nominal returns floating around in certain circles (Dave Ramsey). Don’t get your hopes up too high about continued double-digit equity returns over the next decade!


My personal equity return forecast is just under 4% in real terms and just under 6% nominal. That’s the rate of return I use for my own projections. It’s also one of the reasons I’m skeptical about the 4% Rule: How can you withdraw 4% every year if equities return less than that (after inflation) and bonds hardly return more than inflation? But just like every forecast, it’s subject to uncertainty. Under pretty reasonable ranges of estimates, we cover the entire range from 3.5% to 8%.

One message from this research I want to stress again: This is not a reason to dump stocks. Holding bonds or keeping funds in a money market account is so much worse. The great irony is that since all expected returns (stocks, bonds, money market) are so low one probably has to increase the stock allocation to reach a real return target in the neighborhood of most people’s planned withdrawal rate!

We hope you enjoyed today’s post! Please leave your feedback below!


106 thoughts on “U.S. Equity Returns: History and Big ERN’s 10-Year Forecast

  1. What a nifty piece of analysis ERN. This expected forward return of just under 6% supports an SWR of 3.5% for those retiring today. Also, this normalization over the coming decade makes the whole market “healthier” in my view for the decade that follows it. I agree with you that remaining 100% equities is still the right way, especially as my portfolio has 3.8% Div yield that covers my SWR. I will continue to stick with my conservative 3.27% SWR that I covered in one of my articles on how I arrived at it. Keep up the great work!

    1. You rock (pardon the pun)! Thanks for stopping by. And you’re brave with 100% equities. But then again, that’s what might be required if all expected returns are so low. Hey, equity volatility is low, too, so maybe 100% stocks ain’t so bad?!

      1. Heard you on Choose FI podcast – it was awesome. During accumulation phase, what are your thoughts on a more aggressive position Ratio of 75% VTSAX (or S&P 500) and 25% small caps vs just 100% VTSAX??

        1. If you are comfortable, go for it. Over very long horizons, small cap stocks beat large cap stocks. But that return engine has sputtered a little bit, see our post from a few weeks ago.
          But if you’re young and believe that the small-cap premium will persist it’s definitely worth to take on more risk. Personally, I think that a more efficient/reliable way to jack up the risk is to use a little bit of leverage, say, 80% S&P500 plus 20% bond fund plus 40% equity futures. See the post from some time ago: Lower Risk Through Leverage

  2. Interesting read as always! I’m curious if you’ve considered the ratio of corporate earnings as a percentage of GDP in your forecast for EPS/GDP expansion. Short version is that corporate profits are at historic highs by this metric, and lead me to be more pessimistic about EPS/GDP expansion on a 10yr horizon. Here’s a reference:


    I’d be interested in hearing your thoughts on this.


    1. Very nice link! Thanks, Rob! This chart was very much on my mind! And I agree that corporate profits being a share of GDP cannot grow faster than GDP forever. But there is still room for a bit of expansion: currently at 9.5% we can definitely grow back to the old peak of 10% or so. Energy earnings are still recovering.

      Corporate earnings per share can also grow faster because of share buybacks. Corporate profits for the overall economy may grow in line with GDP, but through buybacks, the # of shares shrinks and thus the EPS can still grow a bit faster than GDP.

      1. Thanks for the reply ERN!
        Fair points on energy sector recovery and share buybacks – I wasn’t considering the later.

      2. Following up a few years (!) later:

        1. Now that corporate profits are above 10% of GDP – and even above 11% – might they revert back lower?

        2. And why assume a reversion to 10%? The average over that time series from FRED is 7% – why not assume a reversion to that mean?

        1. WIth the economic shifts post-pandemic, it’s likely that more and more of the economy will be dominated by corporations (as opposed to mom-and-pop proprietors). I don’t see that ratio trending down any time soon. Business cycle fluctuations will happen, but the trend is 10% and above.

          1. Interesting, I didn’t realize “Corporate Profits After Tax” excludes mom-and-pop proprietors – is it because they don’t file corporate tax returns? – maybe because mom-and-pop businesses file as part of the owners’ tax returns (say if their business is structured as an LLC)?

            The hypothesis that the pandemic secularly shifted this metric is interesting. It’s a significant hypothesis, because otherwise one could argue that there’s a lot of downside in equity valuations just from mean-reverting to the 7% level. What evidence has been marshaled to support this hypothesis?

            1. Not necessarily. If the mom-and-pop business is structures as a corporation, those profits would be included there. But LLC is a pass-through entity and should not show up there (despite the C in LLC)

              1. Thanks. And any thoughts about the question regarding what evidence supports the hypothesis that corporate profits won’t mean-revert to 7%?

  3. I think you have a typo in that math formula (wink). Wow, what a comprehensive analysis. I won’t pretend to understand your formula, but your conclusion of 4%/6% matches my (subjective) opinion. Interesting conclusion that a higher % to stocks is likely required given lower overall returns, I hadn’t thought of that but it’s a valid conclusion.

  4. Great analysis… I am not super up to date on the latest economic trends, but I am wondering what is your reasoning for the 2% inflation rate? I liked seeing the nominal column for comparison purposes because you can see how little inflation we have had since 2010, and maybe I’m answering my own question. But I did appreciate seeing it for the historical perspective.

    1. 2% inflation is the official target of the Federal Reserve. If we were to go much above that they will step on the breaks and cool the economy. And likewise, when inflation is low they will keep the stimulus.
      One caution: The Fed uses core-PCE, while I use CPI. They are related, but not exactly identical.

  5. Great Article! My personal analysis is similar in that 3-4% real returns on US stocks is my expectation for the next 10 years. In fact, I’ve shifted a lot to emerging markets from US stocks based on valuations and long-term mean reversion in profits. At the same time, I’m conservative with return expectations and will do just fine with even a 2% real return on stocks even though I don’t expect such poor returns. Also, a poor 10 year forecast will not be steady. There will most likely be a big drop (or a few) in that 10 year period that changes future expectations again. This is why some tactical allocation based on macro cycles can help. I’m currently 70% stocks at this stage but with a structured method of going back to 90% stocks if/when stocks drop different amounts. We’ll see if it ends up helping much.

    Thanks for adding more voice to this in the FIRE community. We need more discussion on investing beyond simple buy-and-hold if we want to manage our FI wealth optimally for 50 years!

    1. NiceQ!Thanks for sharing!
      International stocks, especially EM, can be the solution to expensive valuations. They have also benefited from a weaker dollar recently. And there is one concern I have: FX movements can undo any excess performance very quickly. If the Fed surprises with a more hawkish stance a lot of EM currencies will slide against the dollar. But then again, the Fed has been walking down their forecasts for rate hikes. Maybe it’s a risk worth taking to juice up returns.
      Love the macro asset allocation! It’s good to have some cash to use when/if the market drops!
      Best of luck!!!

  6. I think one can quibble over some of the finer details of the analysis but I think the general gestalt that near future returns will likely not be as high as recent past returns in the equity market is correct. I think it is also reasonable to be skeptical about the 4% withdrawal rate. If things go smoothly and we have a consistent 6% annual return for the next 20 years then all will be well with a 3-3.5% withdraw.
    However, if we have a poor sequence of returns (i.e. 1930s, 1970s) those nearing retirement or in retirement with 100% allocation to equities may not be able to recover. Hence, I would still keep some component of investments in bonds. Jack Bogle who was quoted in this ERN article (age 87) only has a 35% stock exposure ( from his book titled Enough). A 35% exposure to stocks is probably too low for most ( myself included) but I personally would not allocate 100% to stocks ,accept a lower rate of return, a lower draw down and sleep well at night.

    I’d rather lose a little to inflation than a massive amount to a poor sequence of returns . There is no correct answer, it comes down to your risk tolerance , how large your nest egg is relative to your retirement needs, your life expectancy and whether you want to leave anything to your heirs.

    1. Sorry, this comment was initially filtered out and went into the spam folder. I’m glad I found it! Very good and thoughtful comment.
      I didn’t mean that increasing the stock allocation necessarily means 100%. People who want to retire with 60/40 or even 50/50 Equity/Bond shares might want to multiply their weights with return expectations 5.75%/2.3%: that implies 4.37% for a 60/40 and 4.025% for 50/50. Subtract a 3.5%-4% SWR and 2% inflation and you’ll deplete that portfolio pretty badly after 10 years. No need to go to 100% stocks, but I think anything under 80/20 is asking for trouble.

  7. Good reading ERN. As always. I have two Q’s for you:

    1. What is/are the underlying assumption(s) in the dividend yield being fixed at 2% across all forecast scenarios? Especially in light of the time-weighted mean you calculated for dividend yield in the previous table.
    2. This question may be subject of a future post so feel free to pass on it. What do you see the expected returns of a global portfolio of, for example, 3:1 US: ex-US equities.

    All the best,

    Mr. PIE

    1. Great questions, Dr. PIE!
      Dividends have been quite stable at around 2% for quite some time now. It’s high enough to keep investors happy and low enough to ride through a garden-variety recession without having to cut dividends. I don’t see major shifts. And even if there were, say all companies now jack up their dividend yield by one percentage point, then I’d take 1% out of the profitability growth. If companies pay out more in dividends they do less in share buybakcs and other investments, so profits grow slower. So, I found it’s best to leave the 2% dividend yield untouched.
      About international stocks: for non-EM stocks (Europe, Japan) valuations may be good, but growth prospects are also not that great. I would easily take away 1% from GDP growth. EM stocks have their own challenges: Higher volality, political uncertainty, big FX risk
      I would never try to talk anyone out of international diversification. The CAPE does look better, but I’m concerned non-US stocks may be cheap for a reason…


  8. Great article! A question and a comment:

    Q: Have you done any such analysis for US stocks versus international? If you did, do you think you’d get a higher expected return for international (as some people believe based on the better valuation)?

    C: Unless I missed it, you didn’t actually say what return Bogle had predicted in the article, correct? A quick google search says 4% nominal, but I kept wondering what it was as I read the article.

    Appreciate the time you put into this, thanks.

    1. Brad:
      I like international stocks because they look cheaper (lower CAPE), but I am also afraid that they may be cheaper for a reason. Non-EM stocks are in countries with less GDP growth (Europe, Japan), and EM countries have some of their own challenges: politics (what’s going on in Brazil??????), FX volalility, etc. International diversification is no panacea.

      You didn’t miss it. I added the 4% figure in the text. Twice to be sure. Thanks for pointing that out!!!

      Big ERN

      1. Thanks for the reply. With respect to GDP growth of non-EM vs US, I’m certainly no economic expert and have little experience to fall back on in forming my own analysis on the matter. Of course, I’ve heard the consensus view that GDP growth is expected to be weaker in places like Europe. Perhaps that’s a good bet to take, but US GDP growth outperforming Europe is also no slam dunk (as we saw this year: https://www.ft.com/content/0bbc026a-ea12-11e6-967b-c88452263daf). I tend to be a little more “value-y” in my asset allocation, thinking that pessimism and optimism are both often overstated. As such, I’ve been tilting a bit more into international lately, but time will tell if that was a good thing to do.

      2. Loved the post and the analysis. To follow up on the international discussion – what occurred to me is that we have more global economic exposure even in US equities. For instance Boeing’s growth is dependent on global growth rather than solely US GDP growth. I’m curious if you think that is worth factoring in? For instance would it make sense to use a blended US/International GDP growth rate? I could easily see this adding 100bps to the overall expected returns Do you think this could explain the higher CAPE (e.g., is already priced in). Or do you think this has already been accounted for in the US GDP growth numbers due to some correlation between US and global growth?

        1. I agree: U.S. corporations sell more and more revenue outside the U.S. (I believe 40% of S&P500 revenue is from outside!).
          But I would think that the GDP for ex-US is weighed down by Europe and Japan but raised from EM countries. Might be a wash!
          I don’t think that the average GDP growth rate of our average export partners is materially different from the U.S. GDP estimates.

          1. What is going on in my country (Brazil)? Hum, this is a really difficult question.
            My written english is not good, but I want to say that your SWR articules are incredible. They are not that practical to us Brazilian (The Bonds here yield like 5-6% real, REITs yield like 8-9%, etc), but the way you construct your thoughts are amazing.
            We have in Brazil, a much smaller for sure than the US, a comumnity of personal finance blogs, and I was the first to discover your blog. Since then, I recommend your blog to people who can read english.
            Cheers and a big hug!

            1. Hi Soulsurfer,
              Thanks for stopping by! No worries, your English is excellent! You are right, translating this into other countries can be tricky, especially countries like Brazil with higher returns and growth rates, but at the same time higher inflation, higher inflation uncertainty and currently also pretty high political uncertainty.
              A big hug to you as well, and a big “obrigado” for stopping by!

          2. I agree that US is probably better than Europe/Japan on forward looking GDP growth. It’s a little tricky in the four component analysis looking at just US, though. I read this a year or two ago but just today it hit me that this is US only which presents a problem. In the aggregate, the real GDP growth of the world and of the US are what they are, but in the medium (but not long) term the EPS to GDP expansion for US stocks can be positive without reversion if US stock earnings increase overseas faster than domestically. And the constraint is less limited than it appears because the massive corporate earnings potential of, e.g., selling your product in India. Let’s just say everywhere grows at 2% (probably conservative for EM) but because the US is only ~25% of global GDP, even if it grows to 30% then for five years EPS to GDP expands by 1% without reversion. And I would argue that’s conservative given many of the large US companies are tech that sell to EM with faster growth (e.g. FB or GOOG earnings have a ton of potential in India and Pakistan as hundreds of millions of people come online).

            Not quite related to this article, but of a similar topic. I am curious to hear your thoughts on adjusting the CAPE (I know you’re a fan) by subtracting the 10Y rate. At minimum it seems like an important factor in opportunity cost. But really it’s a rough backdoor equity risk premium of sorts, which is really what we’d want to isolate to measure market sentiment and go-forward returns.

            1. Agree with all. The EPS/GDP can certainly grow due to non-US expansion of US business interests.
              I also agree that we should look at both the absolute CAPE and the 1/CAPE (=CAEY, earnings yield) relative to other assets, like the 10Y or 3M interest rates.
              Turns out, today’s CAPE is not that crazy overvalued relative to the 10Y and 3M rates.

                1. Very true. But real yields are also very low. Ideally, you want to use the 10Y yield minus the 10Y inflation expectation (essentially TIPS real yields). Both CAEY-nomYield and CAEY-realYield are not that crazy high in historical comparison.

  9. Big ERN – thanks for such a comprehensive analysis – but disappointed not to get a shout-out for the Equity Risk Premium! I’m a financial economist at heart so I like to use that as a gut-check. With the 10yr Treasury at about 2.5%, and 30yr at about 3% and an ERP of anything from 3-4% then you land on nominal equity returns of about 6% give or take. So I think your central assumption seems pretty good to me.
    Cheers! AOF

  10. Another excellent and thorough analysis from Big ERN. I’ve got your ChooseFI podcast downloaded and ready for listening on a drive tomorrow.

    Nearly 4% real is a number I can certainly live with. When I’ve made long-term projections for my 4 Physicians posts, I’ve done so using 2%, 4%, and 6% real returns. Not overly optimistic or pessimistic, and apparently right in line with the range we can reasonably expect to see based on your formula.


  11. Hi ERN-I’m confused by the “EPS/GDP”.

    A previous comment linked to earnings/GDP, not EPS/GDP https://earlyretirementnow.com/2017/08/09/us-equity-returns-history-and-10-year-forecast/#comment-3271.

    How are you calculating EPS(t)/GDP(t)?

    Also, the table has a “mean” line. Is it legit to take a average of averages? Most times, it’s not.

    What led me to ask these questions was the change how corporations decided to give money back to shareholders after buybacks became legal. I don’t think it’s coincidence that there’s a big drop in dividends in the ’90s.

    That also makes EPS pre-1990 a different thing that EPS post-1990 (along with all the other qualifications on changes in how earnings are reported through the years). It’s a little bold, but perhaps not reckless, to say that the only two numbers a shareholder can completely depend on are the price he paid and the dividends he received…

    Thanks for drilling down. Even if the future may not bow to the analysis, I feel like I understand the past a bit better !

    1. Regarding the EPS/GDP issue: Agree, share buybacks make this a bit of tricky calculation. Hence, I expect a positive EPS/GDP impact even after the strong growth we saw in the decade so far.
      I don’t share your pessimism about this sort of model. Just because dividend payout and buyback policies and accounting standards change over time, doesn’t mean we can’t look at historical data. We should be aware of those issues and factor in adjustments for our projections. For example, account for share buybacks in the EPS/GDP growth rate or different accounting standards in a higher “neutral” CAPE, likely above the historical mean of 15. A heck of a lot better than the buffoonish Random Walk hypothesis, that not even Burton Malkiel believes anymore.

      Regarding means: With log-% growth rates you can take means over means. That’s the precise reason I use the log-%. You couldn’t do that with regular % growth rates, of course.

      1. Why not include buybacks in the analysis directly, rather than indirectly feeling their influence via EPS/GDP growth? That is, wherever the analysis considers “dividends”, use instead “distributions” which is the sum of dividends and buybacks?

        1. Roughly speaking, firms can spend their earnings on 1) dividends 2) buybacks and 3) investments through retained earnings. I lumped together 2+3. We can also further split everything into the 3 components. I don’t see how lumping together 1+2 and keeping 3 separate adds anything to the analysis.

  12. Fantastic article! I think this is my favourite so far! Simple and concise, yet very powerful.

    Very interesting decomposition indeed.

    Your 3.5%-8% nominal return range reminded me of and old lesson from Graham and Dodd’s Security Analysis about it being more an art than a science and using a range of estimates. It’s impossible to tell the actual outcome, but at least we can assert with a high degree of confidence that it should be within that range.

    Keep up the good work!

  13. Great analysis, Big ERN. But I’m afraid of your asset allocation suggestion. Is 60 / 40 a mistake for a 61 / 59 year old couple with no heirs? I’m thinking that a WR of 3 percent is probably safe in such a case (my case), without enduring the stomach-churning volatility of a higher-equity allocation. What do you think?

    1. Just eyeballing the numbers I’d say that 60/40 is not a bad allocation for older early retirees. Your horizon is shorter, so you don’t need the power of equity returns in the long-run.
      The WR can probably go up to 3.5-4%, too.
      And do you take into account Social Security? If you plan to lower your withdrawals when SS kicks in you can go even higher!

  14. Thank you, Biggie. I feel justified because today I trimmed back equity to 60 / 40.

    The 60 includes preferred funds, BTW. I’m not sure it really should, as their beta is about 50. Maybe only about 50 percent of preferred holdings should count as equity, eh? (Treatment of preferred in a portfolio would make a good column topic or two, considering the high yield and the on-going search for yield among older investors.)

    Yes, I saw your earlier post on how much SS can help, and no, it’s not in my numbers, and per your analysis I’m thinking it’s worth 25 to 50 bps or more in our WR — but I keep it in reserve in my emotional calculus. It’s my hedge for possibly insane health care costs. Peace of mind.

    I’m sure you’ve got a great encore career in personal finance if you want it. “After your 30 minutes a day of options trading, that is,” seclawyer remarked, enviously.

    1. Thanks, SecLawyer!
      I like Preferreds, too. But you have to have the strong belief that in the next recession they don’t act like in 2008/9. THey got hammered due to heavy financial sector exposure. But if under the assumption that the next recession will not take down financials as badly as before (and I think that’s a good assumption), you should be golden!
      See our post on Preferreds.
      Prudent move on Social Security: Keep that as a reserve to hedge potential surprise expenses!
      I have now streamlined my options trading to 5-10 minutes 3 times a week! More time for the fun stuff!

      1. Indeed. I give Dodd-Frank advice as part of my day job. I do believe and am betting that the big bank preferred stock issuers will not (be allowed to) self-destruct again as they did in the credit and trading orgy leading up to 2008-2009. So I hold PFF and PGX. Also BAC-L, one of only two individual stocks in my port. (The other is BRK.A.)

        My view of SS is that it’s a significant contingent asset, considering age (61 / 59), best accounted for and used as a hedge against our primary contingent liability (out-of-control health care costs). So you and I are in alignment on that also.

  15. I like this methodology. I look at it much the same way, although I tend to be a little less precise for my own use.

    But I think you basically guaranteed the result with your assumptions. If you assume there will be no significant PE compression then your analysis will generally hold. If you assume some mean revision of the PE then your return will be much worse.

    These two scenarios have been discussed in the recent GMO letters as the hell vs purgatory scenario.

    I’d also add that one of your favorite targets, John Hussman, has demonstrated quite a few different 10 to 12 year return projection models. I would not give him my money but his data analysis is pretty interesting. You probably are well aware of this material but your readers may not be.

    1. The problem with mean reversion: You have to know what mean you revert to and how quickly you do so. I would trust neither GMO nor Hussman or the other perma-bears to educate me about those questions. These guys wanted me to get out of stocks when the S&P500 was at 1200 points. I’m glad I didn’t listen.
      I see reasons for the PE and CAPE to not drop all the way back to their all-time mean: less macro uncertainty, lower interest rates, lower inflation, lower inflation uncertainty, etc. So, create your own opinion. If you don’t like my mean prediction, go more into the pessimistic of disaster scenario.

      But I also don’t agree with the random walk buffoons who believe that the stock market will return an expected 8% or even 12% every year.

      1. I don’t disagree with you in general. My point was that if you want to assess the sequence of return risk you need to consider a reversion of the PE as a reasonable outcome. If the PE10 drops to 14 over the next couple years and then returns to a more typical 18 (or even your 21) that would be a lot scarier for a retire than a smooth glide.

        Even if you only give swing path a 10% probability it would affect your SWR.

        This uncertainty is exactly why your upcoming bond wedge article is interesting to me
        Putting a sufficient amount into a real bond or cd ladder for the first 5 to ten years seems like a good strategy to ameliorate that risk.
        Bond funds are good for ballast but seem less appropriate for this purpose.

        1. Let me ask you: What was the Shiller PE10 at the bottom of the 2009 crisis? 13.3. Do you expect a repeat of 2008/9? In 2002/3 the CAPE never even went below 20.
          I find a crash with the CAPE going to 14 and not recovering to more than 20 highly unlikely. But if it happens I think that a good stock/bond glidepath in retirement can handle that as well.

  16. Big ERN – I simply love your blog. New articles are clicked on with childlike Christmas morning enthusiasm!
    I don’t think anyone that has a basic comprehension of investing believes the 12% rule that Dave Ramsey touts. I believe his message is to inspire his target audience. These are folks carrying loads of high interest credit card debt (for perhaps decades), leasing cars and buying lottery tickets with religious fortitude. I view it as a tool he leverages to inspire folks very early in their “financial awakening” of wow – you can be a millionaire too with minimal consistent savings over a 30/40 year term. Is the debt snowball the most efficient way to eliminate the problem. Nope. Is the 12% nominal estimate return remotely accurate? Nope. But he does reach and help some folks of lesser means that all of us here. Be kind to old Dave, he does serve a purpose. Thanks again!

    1. True, he does serve a purpose. And an interesting idea: Maybe it’s all a bait-and-switch: motivate people to get out of debt waiving the 12% returns. Hmmm, who would have thought that good old Dave is so cunning! 🙂

  17. As I understand it, in your paper “Safe Withdrawal Rates: A Guide for Early Retirees” (SSRN-id2920322.pdf), the return assumption for stocks going forward from 2016 is “about 6.6% real p.a.”, i.e., roughly the same as long-term historic returns.

    Here you are proposing a long-term real return for stocks going forward of around 3.75%, which is markedly lower.

    It seems to me that if this is the case, then all the safe withdrawal analysis in the above paper is no longer applicable. Combining “real-world” market volatility with a long-term average return of 3.75% will surely result in substantially lower safe withdrawal rates.

    Am I missing something here?

    1. It would make a small difference at the backend of some of the tail events (1966). But remember, the last 10 years of a 60-year retirement horizon have very little impact on the SWR. Hint: go to the SWR Google Sheet (SWR series part 7). There you can play with the assumptions about forward-looking returns…

  18. I’m not talking about the last ten years of a 60-year retirement. I’m talking about the whole 60 years (beginning retirement after 2018) being run at an average long term return of say 3.75% instead of 6.6%. If you are going to assume that, going forward, long term returns will be much lower than in the past, then surely you need to re-analyze everything.

    The obvious first question is what will you assume about variations from the reduced long-term average. One approach might be to take the historic data and “tilt it downwards” (in the sense of changing the average slope of a log-linear plot) by subtracting 3-odd percent per year. That is probably too severe and would result in long runs of significant negative returns. Maybe there are some economic arguments that can be made about variability of returns, in the way you discussed average returns – certainly this is not my field!

    My basic point is this – you can do any amount of elaborate analysis based on historic data, but when it comes to predicting the future – which is surely what this is all about – that analysis is only valid to the extent that the historic data on which it is based is applicable to future behavior. Once you say that future returns will be different in some significant way, all bets are off, absent some new analysis.

    That’s why I asked if I was missing something in my previous post. For example, are you in fact proposing that long-term stock market returns going forward say 60 years from 2018 will likely average around 4% real?

    1. As I have stated here and elsewhere, this is a limitation. But pick your poison: Not doing it the way I propose would limit how many 60-year simulations you can perform. You would miss the 1965/66 retirement cohort. Including those cohorts but making a reasonable assumption about the asset returns 2018-2025 (actually slightly less than 10Y) and then calculating the SWR for 1965 is more informative than ignoring the 1965 cohort completely. Hence my comment about “who cares about the final 10 years” because the first 50 or 52 or 53 year determine the SWR much more than the last 7 or 8.

      Also, you make the valid point that we should probably ignore the 2015 retirement cohort that relies almost exclusively on extrapolation of returns and ignores volatility. That’s fine, and I will not put much emphasis on that cohort. But I like to study the tail events of the Great Depression demand shock (that would not even rely on any extrapolated data) and the 1970s (a supply shock when bonds don’t offer diversification), which relies on a few years of extrapolation in the end.

      But just to be sure, you do understand that all of the SWR calculations are about tail events, right? You want a withdrawal strategy that is robust to those events. Whether the 2012 cohort has a SWR of 6% or 7% or 8% is not something that requires a lot of space here…

  19. Yes, I understand the basic math here, and the importance of tail events.in determining the SWR.

    But you didn’t answer my question: Are you in fact proposing that long-term stock market returns going forward say 60 years from 2018 will likely average around 4% real?

    If that is the case, then you can’t use a historic data set that clearly violates that assumption to simulate future behavior.

    1. No! What I am assuming right now in the GoogleSheet (Check part 7 https://earlyretirementnow.com/2017/01/25/the-ultimate-guide-to-safe-withdrawal-rates-part-7-toolbox/ then follow link) and in my other simulations is a 2-step extrapolation for returns:

      1: Years 1-10: trim real return expectations to 3.75% for stocks and 0.25% for 10Y U.S. Treasuries.
      2: for years 11 forward. Assume 5% real equity return and 1.5% real bond return.

      You are free to use your own assumptions, but keep in mind that raising all forward expected returns (medium-term and long-term) to their historic averages (6.7% stocks, 2% bonds) would only raise the 1965/66 failsafe WR from 3.43% to 3.46%. That’s how little of an impact the last few years of the simulations will have.

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  21. Thanks for the great article.

    To quote Warren Buffett: “Every decade or so, dark clouds will fill the economic skies, and they will briefly rain gold. When downpours of that sort occur, it’s imperative that we rush outdoors carrying washtubs, not teaspoons. And that we will do.”

    It occurs to me that if you’re very heavily invested in equities at the tail end of a 10 year bull market with CAPE ratios north of 30 then you’re not going to be able to find a washtub when the time comes.

    1. True. But if I had had that cash reserve for the last few years I would have also missed the rally of 1000+ points in the S&P500. So it’s always hard to time this. I’ve said here and elsewhere that low expected equity returns still make me bullish on stocks because expected bond returns look even worse! 🙂

      Also: Buffett has one amazing advantage over us: almost unlimited reserves of the BRK insurance business he can use for cheap leverage.
      Also, in my personal portfolio, I believe that the 10% in real estate and 35% in options trading will survive just fine through the next bear market. 🙂

  22. “I like international stocks because they look cheaper (lower CAPE), but I am also afraid that they may be cheaper for a reason. Non-EM stocks are in countries with less GDP growth (Europe, Japan), and EM countries have some of their own challenges: politics (what’s going on in Brazil??????), FX volalility, etc. International diversification is no panacea.”

    Hi ERN,
    Aren’t you a bit shifting the goalposts here? If we start with your observation that GDP growth and Dividends drive growth, taking data I could grab quickly from Wikipedia (the last 15 years): average Advanced GDP growth = 1.25%; average Developing = 4.9%.

    I get the difficulties, and of course Apple sells in China, but you have debunked that logic elsewhere. Developing is now > 40% of the world economy — at what point is it not foolish to ignore the faster GDP growth in your portfolio?

    1. Good point!
      I have to admit that EM vs. DM, there is a rationale to shift more into EM due to lower CAPE and better growth prospects.
      Independent of growth prospects, I will not invent in Commie-Fascist-China, though. But others look attractive.

      But within DM, a lot of the low-CAPE countries are also caught in a low-growth trap.

  23. Has your thoughts and forecast changed since Covid-19? It’s been a few years since this article was published and 2019 and 2020 were crazy years with valuations even higher now.

  24. Is there enough data to say anything not excessively speculative about real GDP growth as a function of population growth? Obviously, world population (and especially DM population) growth is falling…

    How should one understand the historical long-term negative trend in EPS/GDP? Has it been driven simply by an increased government share of GDP (e.g. medicare, defense)?

    Given mean reversion in equity valuation, couldn’t the displacement of dividends by share buybacks exacerbate a correction?

    1. All good questions!

      I don’t quite agree with the premise here. The correlation over the decade average RGDP vs. EPS/GDP is -0.21. I wouldn’t read too much into that.

      I view the lower dividend yields positively. Gives companies more leeway in recessions to restructure.

      1. Thanks for the reply. I should have numbered my three different questions. Let’s call them Q1, Q2, and Q3.

        Re: Q1: I don’t think you replied to this one.

        Re: Q2: I’m not sure I follow your reply. I meant to refer to the fact that EPS/GDP has been shrinking over time – on average -1.41% per year, according to your helpful table. I was just wondering why that is – and speculating that over time, government has increased in size (through spending on defense and other expenditures), and so less GDP is flowing through corporate EPS…? I would have thought that if the corporate sector represented a stable fraction of GDP, then EPS/GDP would stay more or less the same…

        Re: Q3: “lower dividend yields… [give] companies more leeway in recessions to restructure” – is your idea basically that by retaining cash, companies are delevering and thus less likely to enter chapter 11 (and thereby wipe out equity holders) in a downturn? But I’m asking specifically about companies buying back stock instead of paying dividends. If companies buy back shares with the same cash they would have spent on dividends, then they don’t retain cash. (Now it’s true that companies have been hoarding cash, but that is arguably a separate matter from the fact that they’ve been switching from dividends to buybacks.) The worry I’m raising is that if companies buy back stock at high prices, then that’s bad for shareholders, simply because the prices are high. Put differently: if hypothetically the CAPE popped up to 300, wouldn’t you want the S&P 500 CEOs to pay out cash instead of buy back shares? Buying back shares in this case would be tantamount to setting their cash on fire. And setting cash on fire would exacerbate a stock market collapse (which would presumably be inevitable with a CAPE at 300! – but it would make the crash even worse).

        Note that CEOs are financially incentivized to cause their stock’s total return to manifest as much as possible as an increase in stock price, rather than dividends, in order to maximize the value of their stock options – so they might always push for buybacks over dividends…

        1. Q1: long-term growth forecasts certainly factor in population growth. Productivity matters, too. Can’t venture too much into predicting productivity, but it looks like population growth will be lower in the future.

          Q2: There is no negative trend in EPS/GDP. It used to be mostly negative early on (due to high dividend payouts) and over the last 4 decades the average EPS/GDP growth was positive.

          Q3: It’s not just about avoiding bankruptcy. It’s also about retainting talent, buying takeover targets at bargain prices, etc.

          I’m not a big fan of buybacks either. I’d prefer that companies use their cash to invest more in the most productive ventures. With buybacks, they just buy the “average” of their business.
          That said, buybacks are still more tax-efficient for us investors than dividends.

  25. A question on how you constructed your 4-component table: how did you derive EPS/GDP Expansion?

    My guess is this: almost all of the raw data can be obtained from Shiller’s website; you just need to add nominal GDP to the spreadsheet, and then you can calculate your Real GDP growth; then SPX/EPS Expansion, Dividends, and Total Return can be derived from Shiller’s data; and then you back into EPS/GDP Expansion since by design the sum of the 4 components equals the Total Return. Did I get it right?

    1. Correct. I have data for Nominal GDP (not from Shiller) and include that in the EPS data (from Shiller). One small, quirky thing I do is to assume that real GDP is nominal over CPI (while you’d normally do the nominal GDP over GDP deflator). I simply like to deflate both nominal numbers, GDP and EPS by the same inflation measure, CPI in this case.

      1. May I please ask where one can find the GDP dataset you used? (Not many go all the way back to 1871!)

  26. Could you please clarify why the term “log (TR_t/P_t)/(TR_0/P_0)” is described qualitatively as “dividends”? How exactly are TR_t and P_t defined in terms of prices and dividends?

    1. The different in growth rates can be expressed that way. The difference in total vs. price return is the dividend yield.
      One caveat: this is subject to a small approximation error when using logs instead of the standard calculation.

      1. It sounds like that in your spreadsheet, the “Dividends” component is the *actual* realized dividend yield during the period – and so the “GDP/EPS Expansion” component by design picks up any “approximation error”, since it equals (by definition) the total return minus the other 3 components (Real GDP Growth, SPX/EPS Expansion, and Dividends). Is that correct?

        I guess that would mean that the formula showing the derivation is not exactly the formula used in the spreadsheet…

        1. I’m trying to disect actual realized returns into the different components. Hence, I’m using actual realized dividends. (what else?)
          Not sure what you mean by ” the formula showing the derivation is not exactly the formula used in the spreadsheet…” because I use the exact formula to derive the values in the tables displayed here.

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