Warning: The US Stock Market is an Anomaly

////Warning: The US Stock Market is an Anomaly

Warning: The US Stock Market is an Anomaly

U.S. stocks have delivered incredible stock market returns for a long time: the average compounded total return on the U.S. stock market has been nearly 10 percent per year from 1927 through 2016 (Using data from Ken French’s website on the market-capitalization weighted CRSP index).

Doesn’t sound impressive?

Consider the fact that a $100 invested for 90 years at 10 percent would compound to over $530,000. Perhaps this is why my two favorite investors of all time suggest that savers stash the bulk of their cash in the US stock market:

First, Warren Buffet’s advice:

Put 10% of the cash in short-term government bonds and 90% in a very low-cost S&P 500 index fund. (I suggest Vanguard’s.)

Next, Jack Bogle’s advice:

I wouldn’t invest outside the U.S. If someone wants to invest 20 percent or less of their portfolio outside the U.S., that’s fine. I wouldn’t do it, but if you want to, that’s fine.

When great minds speak, we should listen, but we should also ask a critical question: Are Warren and Jack making this recommendation based on evidence? Or are they basing this recommendation on their experience as long-time US equity market investors?

In this short essay, I explore the idea that Buffett and Bogle’s advice should be digested with a healthy dose of skepticism. To make this point, I highlight several recent research articles that suggest US stock returns are exceptional relative to all other stock markets across time. The US stock market is an anomaly and perhaps the ubiquitous disclaimer, “Past performance may not indicate future performance,” is an important consideration with respect to the expected performance of the US stock market over the next century.

What is the Equity Premium Puzzle?

The exceptional performance of the US stock market has been deemed the, “The equity premium puzzle,” by academic researchers and was first discussed in an influential academic paper by Rajnish Mehra and Edward Prescott in 1985.

Here is a quote from the original paper:

Restrictions that a class of general equilibrium models place upon the average returns of equity and Treasury bills are found to be strongly violated by the U.S. data in the 1889-1978 period…

The authors find that stocks beat bonds by an average of 6% a year, which is simply too high to be justified by any equilibrium model in existence at the time. Here is the key table that outlined the real risk premium for US stocks:

equity risk premium puzzle -- returns too high

The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.

How Academics Tackled the Equity Premium Puzzle

Academics struggled to build theoretical models that would predict such a high return for the U.S. stock market. Despite significant efforts, the research community never seemed to form a general consensus that the equity premium puzzle would be solved.

Nonetheless, one of two solutions was explored in an effort to answer the puzzle:

  • Approach #1: Build elaborate models that predict why the expected US equity premium is justifiably high.
  • Approach #2: Refute the premise that the historical US equity premium is a valid estimate: perhaps high past US stock market returns simply reflected a lucky run?

Researchers continue to explore solution #1, but there seems to be no clear answer in sight. Other academics have explored option #2, by collecting more data on various stock markets across different points in time. Philippe Jorion and William N. Goetzmann provide a good example of this research in their paper, “Global Stock Markets in the Twentieth Century.” The authors examine 39 global stock markets from 1921 through 1996 and, as before, saw evidence of the outperformance of the U.S. stock market, which provided a real return (i.e., adjusted for inflation) of 4.32% over the period, the highest of all countries (the median performance was 0.80% for the other countries). But the US stock market’s strong performance was old news and not the point of their story. Their key insight was identifying a clear survivor bias in the data: The longer a country’s stock market existed, the higher the annual return.

This relationship is best captured in Figure 1 from their original paper:

equity premiums across time

The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.

In short, the returns of the winners depend on their past survival. If investors can predict with perfect foresight which countries will survive and which countries will die, using the past results might be meaningful. However, is it realistic that investors have the ability to know future winners? Unlikely.

To make matters worse for those who have been conditioned to believe the US stock market experience is “normal,” a new paper by Notre Dame professor Benjamin Golez and Stanford professor Peter Koudijs, titled, “Four Centuries of Return Predictability,” performs a similar “out of sample” study as Jorion and Goetzmann. In their research the authors look at data from the Netherlands and the UK from 1629 to 1812, the UK market from 1813 to 1870, and US stock markets from 1871 to 2015. They estimate that the equity risk premium, or the spread in average returns between stocks and bonds, are around 2.3% to 3.5% for the Netherlands and the UK in the earlier time periods and around 6% for the US market.

summary stats on risk premium

The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.

So the US experienced an equity risk premium that was 2-3x that of other markets. Wow.

Will High US Equity Premium Continue into the Future?

On one hand, perhaps the US stock market will continue to defy market expectations and generate high realized returns in the future. However, on the other hand, investors may be wise to acknowledge the incredible amount of potential luck the US has experienced. Perhaps Jack Bogel, who ironically suggests a huge overweight position to US equities, makes the best case that we should think twice about this recommendation.

Consider a PBS interview with Jack Bogle where he states the following:

Good markets turn to bad markets, bad markets turn to good markets. So the system is almost rigged against human psychology that says if something has done well in the past, it will do well in the future. That is not true. And it’s categorically false. And the high likelihood is when you get to somebody at his peak, he’s about to go down to the valley. The last shall be first and the first shall be last.

As Bogle points out, it may be precisely the past winners who are about to fail.

Famed Wharton professor Jeremy Siegel has a related statement in his paper, “The Equity Premium: Stock and Bond Returns since 1802”:

Certainly investors in…1872…did not universally expect the United States to become the greatest economic power in the next century. This was not the case in many other countries. What if one had owned stock in Japanese or German firms before World War II? Or consider Argentina, which, at the turn of the century, was one of the great economic powers.

It’s probably likely that Argentinian investors predicted continued economic dominance at the turn of the century. They were wrong. Perhaps US investors are suffering from a similar level of hindsight bias? Can we determine with certainty that the U.S. will be a superpower 100 years from now? We should consider the fact that when we look at past U.S. returns, we are looking at a market that did not fail, but does it follow that it cannot fail in the future?

Conditioning on past returns can subject investors to form misguided expectations about the future (a reasonable premise since investors are often irrational). US investors should avoid their innate biases and take advantage of diversification — spread stock market bets around the globe — not just in US stocks. A concentrated bet on the US stock market is exactly that — a concentrated bet. And at current relative market valuations — the US stock market sells at a P/E of 21, developed markets sell at a P/E of 18, and emerging markets trade at a P/E of around 13 — hitting 10% annualized returns over the next 100 years via US stocks will be challenging and investors should plan accordingly.(1)

  • The views and opinions expressed herein are those of the author and do not necessarily reflect the views of Alpha Architect, its affiliates or its employees. Our full disclosures are available here. Definitions of common statistics used in our analysis are available here (towards the bottom).
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References   [ + ]

1. Lawrence Hamtil has an interesting piece here

About the Author:

After serving as a Captain in the United States Marine Corps, Dr. Gray earned a PhD, and worked as a finance professor at Drexel University. Dr. Gray’s interest in bridging the research gap between academia and industry led him to found Alpha Architect, an asset management that delivers affordable active exposures for tax-sensitive investors. Dr. Gray has published four books and a number of academic articles. Wes is a regular contributor to multiple industry outlets, to include the following: Wall Street Journal, Forbes, ETF.com, and the CFA Institute. Dr. Gray earned an MBA and a PhD in finance from the University of Chicago and graduated magna cum laude with a BS from The Wharton School of the University of Pennsylvania.


  1. gmacd18 March 21, 2017 at 12:00 pm

    Eric Falkenstein’s book “The Missing Risk Premium” goes in depth on the equity risk premium. He discusses how several markets went to zero during the two world wars, as well as other reasons why the returns seen in CRSP, etc. are too high to use for forecasting.

    • Wesley Gray, PhD March 21, 2017 at 1:08 pm

      Yeah, Eric is great and he let us post his history of low volatility investing here:
      Thanks for pointing out his book

      • Adam Kearny March 28, 2017 at 1:25 am

        To some extent, this is an unanswerable question–the future is always uncertain, and it’s very possible that we have just had a great run for the past 150 years with dramatic technological change and demographics growth that will not necessarily occur ever again (though perhaps the tech change may come along at some point in the future). I do know that S&P EBITDA growth over the past 10 years is nearly zero, i.e. dramatically lower than it was over the previous couple of decades. It’s also clear that if you look at the long sweep of history, as in evolution, there are stock market “extinction events”–while the US hasn’t experienced a complete 100% wipe-out, for a retiree or endowment, both the 1930s and the 1970s were essentially the same thing–the early 1930s, an 89% drawdown and a 25-yr period of zero nominal returns (ex-divs). 1968-1982–the market flat in nominal terms, but down 87% in real terms. No retiree/endowment taking even a mere few percent out a year could have survived either of these events–they’re essentially giant macro-resets to deal with over-indebtedness and restore the possibility of future high growth. People are conditioned to assume the market always bounces back from a bear market–perhaps next time, it won’t. Japan had a nice run for a few decades post-WWII but never really bounced back since 1989, and we’re on the same trajectory in terms of demographics and over-indebtedness.

        • Hannibal Smith March 28, 2017 at 2:05 am

          It’s kinda doom porny to exclude dividends when they played a huge factor in the 1930’s in terms of the breakeven period, which was only about seven years. Even during the 70’s it was only about 12 years. At least in nominal terms. And retirees are very sensitive to dividends/total returns as well as inflation and sequence of returns (so they hold diversified portfolios). I do wonder, though, if assuming one can retire on their capital accumulation to be realistic anymore. The vast majority simply don’t have enough saved to retire on and I would think the upper classes will have such high incomes and/or high passive income sources during retirement that retirement planning is almost an afterthought.

          I really don’t see any good answer to this conundrum other than a Citizen’s Dividend. Social Security is going to have to expand. If Japan is a present model of the future sans full automation, it seems like it will work somewhat other than all the “save face” suicides and all the eldery “criminals” intent on becoming institutionalized.

          • Adam Kearny March 29, 2017 at 1:36 am

            News flash–you can’t eat nominal returns, only real returns. The Yale Endowment suffered so severely during the 1970s that the university’s financial independence was in doubt well into the 1980s (and don’t forget, they ultimately get bailed out by new contributions from alums). For the 1930s-1950s, I believe simulations show that an equities-heavy retirement portfolio would not survive (combination of horrendous drawdowns plus withdrawals during the lean years decimate its ability to benefit from the big rebound starting the 1950s).
            “Upper classes–only if you’re talking about those with tens of millions of dollars. You could have millions of dollars (in today’s terms) back in the late 1960s, and by 1982, you’re almost broke (in real terms).
            Expanded Social Security–yes, absolutely. Buffet and Munger know this–that’s why they say “I wouldn’t touch Social Security” and “Social Security will be expanded”–without going into details. They know the 1990s bull market notion of everyone retiring rich on their stock portfolio is a pipe dream going forward. Even the creator of the 401k is aghast that it’s been taken in recent decades as an excuse to abolish pensions.
            Not only are most not saving enough, but it’s IMPOSSIBLE for them to save/accumulate enough in a low-return world with zero interest rates and zero EBITDA growth (EBITDA growth equating to sustainable stock price growth, i.e. ex-bubble multiple expansion of the past 5 yrs). Only solution is dramatically down-sized cost of living and maintaining/boosting social security.

  2. Noel Dunivant March 21, 2017 at 12:49 pm


    An interesting piece and probably good caution for pensions and endowments that can bring a hundred-year perspective to their investments. (Most of them probably are already well diversified with global assets

    But I think the case for individual US investors to lose some of their home-country bias is stronger considering two other arguments: First, foreign stock markets have outperformed US stocks for multiyear periods in recent decades. Second, as you point out, US equities are greatly overvalued compared with developed-ex-US and EM stocks.

    To paraphrase Bogle, since the US market has outperformed foreign stocks for the past ~8 years, we should expect underperformance going forward. But repeated market booms and busts throughout history tell us that human psychology is unchanging. We know that most individual investors will not heed warnings of “what goes up, will come down.” The story will not end well, because investors are always momentum driven, while markets are mean reverting.

    In the grand sweep of human history, the American experience has been exceptional. History suggests that nothing endures forever, so it would be the exception if the US economy and stock market continues to outpace other countries for the next century or two. But that’s just too long a period to offer guidance to contemporary US investors in my opinion. There are good reasons to diversify that can be expected to play out over the next few years – some of which you describe and I’m sure concern you.

    I was unaware of the anomalous historic US equity premium, and appreciate the education. Thanks for another thought-provoking post.


    • Hannibal Smith March 21, 2017 at 4:47 pm

      Noel, are you’re aware that pension funds are not addressing the long-term at all? They’re still stuck in a fantasy land expecting a high equity risk premium which is why they’re starting to go bankrupt. The first one just happened in New York recently and now all the retirees are suffering with $12K/yearly pensions from the PBC. You can’t live on that amount in high priced, high taxed New York or New Jersey. Get ready for the tsunami. It is Swiss cheese everywhere at the local and state level.

      The only point of going outside your own country is for higher growth and/or a weaker currency. Even though I think he’s a narrow-minded feeble old man past his prime, I do understand where Bogle is coming from on this topic. He would not go outside the USA unless expected future returns were so low that the headwinds of a stronger dollar were muted. That may be the case in emerging markets at present. But do this smartly — use currency hedged funds and net it out.

    • Wesley Gray, PhD March 21, 2017 at 4:53 pm

      To reiterate, I don’t know the answer on how one tactically positions their portfolio to consider 100 year expectation forecasts. ha. That’s why I recommend staying diversified and to trend-follow. Perhaps that is the only practical takeaway from this piece. Who knows

  3. paul rossi March 21, 2017 at 4:29 pm

    Good article…although I like to try and understand the fundamentals behind some of the data and why things in the past may persist and why some things may not persist going forward.

    Example: I would argue no country has what the US has: enormous amount of natural resources, large geographic area, large population (while aging, isn’t aging as many European countries and Japan), positive immigration (at least historically), first rate higher education system, stable government governed by a rule of law, a people who still believe they have an opportunity for a better way of life, and the list goes on and on. I guess to frame the question: What county do you think has better qualities than the US? I can’t think of one. While I freely admit we have major issues that we need to address and resolve, we are still the one place where people from all over the world want to come for the opportunity for a better life for themselves and their families. This can not be over stated.

    Having said that, I do not assume the incredible returns the US has enjoyed will continue at the same clip into the future forever. While I do believe we have such a strong tailwind that it will be sometime before we hand the baton off.

    So many additional points to address but I’m typing on my phone so…

    • Wesley Gray, PhD March 21, 2017 at 4:51 pm

      Hey Paul,

      Great comment. And I am in agreement with you: I think America is totally bada$$ and I’d die for the place if asked (signed up for that gig while I was a US Marine for nearly 4 years). So I’m a buyer of the country.

      But buying quality isn’t necessarily a good investment strategy — one needs to consider the price paid. So the US can end up being the best country over the next 100 years (which I expect), but simultaneously end up being the worst investment. How is this possible? This would happen if the prices paid don’t embed expectations that are too high relative to the realization.

      Here is some empirical evidence on this subject: http://blog.alphaarchitect.com/2014/01/31/finance-mythbuster-economic-growth-doesnt-help-investors/

      Amazingly, strong economic growth has no connection to realized returns. Crazy, but true.

      • paul rossi March 21, 2017 at 5:04 pm


        Totally agree with you regarding valuation, et al. Typing on my phone just isn’t ideal for being able to fully convey my thoughts.

        Thanks for the reply and more importantly for your service. Several members of my family served in the US Marine Corps.

        From one proud American to another.

  4. Hannibal Smith March 21, 2017 at 4:39 pm

    I hope there’s more substantial studies than this kind of superficial analysis so far. The USA has numerous proprietary structural advantages that no other country had or has (or likely will ever again, not counting interplanetary colonization). It may have been “luck” to have been “born” into these advantages, but it’s not “luck” to have them translated into superior economic growth. So aside from valuations which are mean reverting in the long run, if one was really concerned about the “luck” running out, just pay attention to what was the downfall of the failed countries. Threat of or actual Communist takeover (Germany, China), the terrible economic drag of Socialism and its offshoots (Argentina, Venezuela), Orwellian strangling of free minds and free markets (North Korea, Cuba), etc.. It’s all about the “quality” of the government and whether it goes off the rails.

    • Kevin March 22, 2017 at 8:39 am

      I don’t disagree with you, but it strikes me that other countries at different time periods could also have correctly said, “_insert country_ has numerous proprietary structural advantages that no other country had or has”. Most strikingly England. You wouldn’t have known in 1750 or 1800 that the previous couple centuries of structural advantages wouldn’t carry over for the next couple centuries. Similiary, its hard to say with certainty ours will either. That said, I’m not investing a hundred years out, only 30-40, so I’m not sure that it affects me. Still interesting to ponder.

      • Hannibal Smith March 22, 2017 at 11:15 am

        It’s little known that the USA is directly responsible for killing the British Pound over the Suez Canal crisis thusly getting the USD installed as the world’s reserve currency. So it all comes down to hegemony. Changes to that is what you need to watch out for if you’re concerned the USA’s “luck” will run out. China doesn’t seem legally or culturally ready to take up the mantle anytime soon (India could be a surprise sleeper hit), so I’m going to speculate that technological decentralization is so powerful now that the glory days of the patriotic nation-state will be over after the next global monetary crisis. I’m not shedding any tears. Give me some terrorist-proof body armor and a mini-nuke and I’ll be fine. 🙂

    • Wheelz57 March 23, 2017 at 7:59 am

      Absolutely. Also, readers should keep in mind that most of the DOW and S&P 500 are GLOBAL companies. Just because they are domiciled in the USA doesn’t mean their futures are solely bound by economics in the USA. When you own KO or MCD you own properties and productive capacity in most developed countries in the world.

    • Hannibal Smith March 23, 2017 at 9:35 pm

      And to follow up on “quality”, Dalio recently released a 50+ page report on populism and the political and financial effects of such 14-past leaders:


    • Michael Milburn June 6, 2017 at 11:03 pm

      My takeaway instead was: Don’t lose a world war and have your country devastated.

  5. Outcast_Searcher March 23, 2017 at 8:46 pm

    While I’m a big fan of Bogle overall, I never agreed with his advice for US investors not to invest in stocks outside the US. It’s not like a place run by Capitol Hill is something I want to invest 100% of my marbles in.

    So for me, looking at the relative return of US vs. ex-US stocks since the 2008-2009 fiasco, when I wanted to lighten up on my stock holdings to rebalance (given the, ahem, potential lack of stability and thoughtfulness of our new POTUS and the possibility of sudden very negative financial fallout from his statements and actions), I decided to do all my selling in my US stocks.

    So now my global stocks exceed Mr. Bogle’s 20% allocation recommendation. Looking at the relative valuations of US vs. well diversified international (ex-US), I’ll sleep better taking my chances.

    To me, “winning” financially is about having enough to be secure, and diversifying helps do that. It’s not about having absolutely the maximum number of dollars (as if there were any reliable way to do that via investing anyway).

    • Hannibal Smith March 23, 2017 at 9:50 pm

      What is Bogle’s rationale for a 20% allocation? Was he just curmudgeonly hedging or is there actually a quantitative basis for that percentage? In my backtesting, I do not find that non-U.S. stocks work as a USD hedge except during the stagflation era. Gold is vastly superior for that hedging purpose. I’m on board for the relative valuation, though — is Bogle?

      • Michael Milburn March 23, 2017 at 11:46 pm

        I think there’s a study on Vanguard’s site suggesting 20-40% intl might be optimal from some type of portfolio construction standpoint. Not sure where to find the link.

  6. Irondoor March 24, 2017 at 8:38 am

    Appears to me the just as important question is, why own bonds? Sure, they offer some buffer against extreme fluctuations, but today you don’t even get your money back after taxes and inflation considering that stocks yield about the same. Where’s the capital growth in fixed income? In other words, would you buy a 100 year bond today?

  7. Travis Tremayne March 28, 2017 at 3:08 am

    Sounds to me that USA is the Big Casino, with the biggest house edge then?
    We know it has the biggest edge but you can’t really ‘win’ anywhere else. So, play on!
    When you get a ‘tailwind’ like this, you put up your spinnaker, hey!
    Not sure what is going to ‘lull’ that wind.
    I am fascinated how the US killed the £ to be the reserve currency?
    What would it take now for another country/region to do that to the USA?

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