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?
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:
- Earnings Growth,
- Multiples expansion (i.e., excess returns of the price index over an on top of earnings), and
- Dividend income (i.e., excess returns of the total return over and on top of the price index),
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.
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!
And for the math geeks, here’s the derivation of the Big ERN Equity return formula:
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:
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.
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!
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