Mission Impossible: Beating the Market Forever

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Mission Impossible: Beating the Market Forever

By |2017-08-18T17:00:48+00:00November 18th, 2014|Research Insights, Key Research, Value Investing Research|10 Comments

Mission Impossible: Beating the Market Forever

The remarkable fact is that nobody can beat the market forever — not even Warren Buffett.

A quick glance at the most recent Berkshire Hathaway annual report (PDF) highlights an amazing data point: Warren Buffett has compounded at 19.7% a year from 1965 through 2013; the S&P 500 Total Return Index has compounded at 9.8% a year from 1965 through 2013. The immediate reaction to these figures is predictable: “Warren Buffett is an investing god, so we should buy Berkshire Hathaway and throw away the keys.” The gut reaction is that Buffett can continue to beat the market forever. Unfortunately, as this post highlights, this is an impossible feat.

Market-Beating Strategies Are Everywhere

Active fund managers like Buffett are not the only ones showing they can outperform the market over the long term. Academic research is littered with investment strategies that purport to generate anomalous returns that almost double the market’s return each year. A few examples follow:

But Markets Are Efficient . . . Right?

I am continually haunted by a note I received from Eugene Fama, one of my dissertation advisers while I was finishing my PhD at the University of Chicago. Professor Fama went on to win the Nobel Prize in Economic Sciences for his work on market efficiency, so when Fama speaks, you listen. Fama wrote a response on an early draft of my paper on the performance of stock picks submitted to Value Investors Club. In the early manuscript I sent him, I stated proudly:  “. . . this paper shows value investors outperform the market.”

Here was his response:

Your conclusion must be false. Passive value managers hold value-weight portfolios of value stocks. Thus, if some active value managers win, it has to be at the expense of other active value managers. Active value management has to be a zero-sum game (before costs).

To my chagrin, Fama’s comments were technically correct. I did not show that “value investors outperform the market” — far from it. I showed that a “select group of investors participating in Value Investors Club outperformed the market.” My evidence did not support the notion that value investors as a group outperform the market. I was broken from a fresh whipping by a market efficiency expert, but I learned a great lesson in arithmetic: Value-weight market returns have to be representative of the collective investor experience because the value-weight market return represents the return to all investors in the stock market. And for every active winner who outperforms the market, there necessarily must be a loser somewhere along the line.

How Long Can We Beat the Market?

If value-weight market returns reflect a binding constraint on the collective investor experience, how long can an individual investor “beat the market” before he actually becomes the market? As it turns out, compound growth prevents skilled investors from beating the market forever. This result is counterintuitive but follows the established behavioral bias that humans have a hard time understanding the implications of compound growth. Al Bartlett, professor emeritus in nuclear physics at the University of Colorado at Boulder, states this bias succinctly: “The greatest shortcoming of the human race is our inability to understand the exponential function.”

To identify just how long a skilled investor can beat the market, I perform a study on the time series of value-weighted return (including all distributions) for the entire CRSP universe from 1926 through 2013 (representing all stocks traded on the NYSE, AMEX, and NASDAQ). If you are unfamiliar with CRSP, think of the database as the closest thing researchers have to the “total US market.” The Wilshire 5000 Index is the best “practitioner” analogy.

With a large amount of monthly return data extending back to 1926, I conduct the following experiment:

  • Start a guaranteed “winner” portfolio on 1 January 1926 and invest at an above-market rate through 31 December 2013. This portfolio represents the experience of a highly skilled investor.
  • Start a “loser” portfolio that represents the ownership of the rest of the market, approximately $28 billion. The loser portfolio returns the overall value-weighted market return minus the return it “lost” to the “winner” portfolio. This portfolio represents the experience of a passive investor who simply holds the market.

An example highlights how my experiment works. The winner portfolio starts off owning 0.00001% of the entire market as of January 1926 and grows consistently at a market-beating rate of return. This initial ownership percentage amounts to a very modest sum of $2,804 billion because that is the market cap of all securities as of January 1926; the loser portfolio starts off owning the remaining 99.99999%. Consider the January 1926 CRSP value-weight market return (with distributions included), which was 0.7405%. This 0.7405% gain grows the total market value of all securities from $2,804 billion to $2,824 billion. The “winner” portfolio — assuming a 30% compound annual growth rate — was 2.5% (30%/12). The winner portfolio grows from $2,804 billion to $2,866 billion. The “loser” portfolio, which represents the return remaining after the winner portfolio takes its outsized returns out of the market, decreases to $2,824 billion. In the end, the winner portfolio earns 2.50%, the loser portfolio earns 0.7404999%, and the entire market return earns 0.7405% (by construction, the value-weighted returns of the “winner” and the “loser” portfolios must equal the actual value-weighted market return).

With this in mind, I decided to investigate answers to the following questions:

  • When does the “winner” portfolio own over half of the stock market?
  • What percentage of the stock market does the “winner” portfolio own at the end of 2013?

The following graph examines ownership percentage for various annual compounding rate assumptions and highlights why amazing compound annual growth rates must mean revert over time. With high levels of compounding, an investor quickly becomes the entire stock market. For example, at a 30% compound annual return, an investor owns 29.48% of the entire stock market at the end of 2013 — approximately $7.5 trillion of the $25.6 trillion in total market wealth as of 31 December 2013.

Mission Impossible_Beating the Market Forever 1

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.

At even higher rates of compounding, say 32% and higher, an investor would eventually own the entire stock market. This result is impossible on many levels. The harsh mathematical reality is that all great investors eventually manage a portfolio with massive scale. Earning a high return eventually forces a skilled investor to own a larger and larger percentage of the stock market.

We Can’t Beat the Market Forever

The point of this thought experiment is clear: No investor can continuously outperform the market over long periods of time. Eventually, this “genius” would own all wealth in the economy. And by definition, if you own the market, you can’t outperform the market. Accordingly, we are left with the following:

  • Earning 25% — or more — compound annual returns over long horizons is virtually impossible.
  • Investors earning 32% or higher returns end up owning the entire stock market.
  • A “doable” 20% a year implies that an investor will own 0.026% of the market at the end of 2013. With a $25.6 trillion total market value as of 31 December 2013, this implies a personal stock portfolio worth $6.6 billion — not a bad retirement plan.
  • Warren Buffett — and perhaps a select handful of others — has been able to achieve 20%+ returns over very long time periods. These individuals represent some of the richest people on the planet because of the phenomenon described in this experiment.
  • Great investors might have an epic run of 20%+ returns for five, 10, maybe even 15 or 20 years, but as an investor’s capital base grows exponentially, the capital base slowly becomes the market, and the market cannot outperform itself.


  • 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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About the Author:

Wesley Gray, PhD
Wes Gray has published multiple academic papers and four books, including Quantitative Value (Wiley, 2012), DIY Financial Advisor (Wiley, 2015), and Quantitative Momentum (Wiley, 2016).After serving as a Captain in the United States Marine Corps, Dr. Gray earned an MBA and a PhD in finance from the University of Chicago where he studied under Nobel Prize Winner Eugene Fama. Next, Wes took an academic job in his wife’s hometown of Philadelphia 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 firm that delivers affordable active exposures for tax-sensitive investors. He is a contributor to multiple industry publications and regularly speaks to professional investor groups across the country. Wes currently resides in the suburbs of Philadelphia with his wife and three children.


  1. Bob Marlin November 18, 2014 at 10:10 pm

    I’m not interested in becoming a bajillionaire, I just want it to be able to retire 15 years earlier…

    • Wesley Gray, PhD
      Wesley Gray, PhD November 18, 2014 at 10:21 pm

      I hear that. Go for it on niche focused high octane strategies. If you can compound tax-deferred at 20-25% you’ll get rich pretty fast…

      • bubba123 August 5, 2017 at 12:09 pm

        That’s what I’m doing, my CAGR is 90% last 3.5 years. lol. I only just started though. But i’m ok trying to become a billionaire. Shame my capital base is low.

  2. Alexander Angerer
    AA November 18, 2014 at 10:57 pm

    Hi Dr Gray,

    As usual, an absolutely terrific post.

    My question is more on semantics than anything else. You mentioned that ‘I was broken from a fresh whipping by a market efficiency expert, but I learned a great lesson in
    arithmetic: Value-weight market returns have to be representative of the
    collective investor experience because the value-weight market return
    represents the return to all investors in the stock market. And for every
    active winner who outperforms the market, there necessarily must be a loser
    somewhere along the line.’

    My confusion lies more on ‘value-weight market return
    represents the return to all investors in the stock market’. It seems to me the
    missing part is to define the market as a value-weighted index e.g. indices
    that are continually rebalanced to weight most heavily those stocks
    that are priced at the largest discount to various measures of value, instead
    of the current market cap weighted indices (e.g. S&P Russell), that we
    commonly refer to as the market. Once we define the investable universe a
    value-weighted index that contains all securities within the investable universe,
    then the comments on passive and active managers by both you and Dr Fama make
    more sense as we’re no longer referring to a market that is market -cap weighted

    Is this the right way of thinking?

  3. Michael Milburn November 19, 2014 at 4:23 am

    Good post. When that one superior investor owns 100% percent of the market, could we then say the market has become efficiently priced (assuming a market still exists)? Just thinking what that might mean.

  4. PaulGoldt November 20, 2014 at 1:19 am

    Ok, your thesis assumes a long only strategy and not take into account the fact that more money goes through the stock market than its market cap. Also it looks like it does not take into account an ability buy winners low and sell high several times. So it is possible to make 30% compounded returns for longer. In addition if you distribute your profits as dividends you can continue compounding at 30% for longer. In my impression your paper shows how powerful compounding is not impossibility of sustained 30% returns.

    Also stock market is not a zero sum game, that is a terrible misconception. If it was US GDP would still be at 1776 levels today.

    P.S. call me a nihilist but I dont trust Nobel laureates when it comes to investing money, we all know how that ended last time. Efficient market hypothesis is the nonsense. It assumes perfect knowledge of future events and equal distribution of information which will never be the case due to human nature.

    • Wesley Gray, PhD
      Wesley Gray, PhD November 20, 2014 at 10:48 am

      Hey Paul,

      Thanks for the comments. There are certainly opportunities for smart investors to win and dumb investors to lose. The point of this article is that smart investors own a bigger and bigger portion of the market, and if you are a bigger and bigger portion of the market, by definition you can’t outperform the market.

      With limited capital and distributions, one could theoretically maintain an edge on a small base of capital.

      The stock market is a zero sum game after taking out the general market returns. That is made clear in Sharpe’s piece: http://www.cfapubs.org/doi/abs/10.2469/faj.v47.n1.7

      • PaulGoldt November 21, 2014 at 5:53 am

        Appreciate your reply. I strongly disagree with many thesis in Sharpe’s paper, it has many misconception which are distant from practicsl aspects of trading. e.g. active money managers trade more often, I would say it is not always the case at all. More importantly here is a simple disproof of his concept. A 2 stock market, passive managers buy stocks A and B, active managers buy B only. A stays flat B doubles, as a result all active managers outperform, fees would be negligible. This proves active management done right will always outperform. Also Sharpes arguement would only be valid if the weighted average of active portfolio combinations is equal to the market. I.e. for every active investor done right there is an active investor who did the opposite.

        Moreover in my simple example everyone is a winner unlike a casino for instance.

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