Mission Impossible: beating the market over long periods of time

/Mission Impossible: beating the market over long periods of time

Mission Impossible: beating the market over long periods of time

By | 2017-08-18T17:00:47+00:00 June 30th, 2011|Research Insights|50 Comments
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(Last Updated On: August 18, 2017)

I’ve been thinking about “extreme” returns recently. After all, who wouldn’t mind earning a few extra bucks in the stock market?

We all hear about quantitative strategies that are supposed to earn us 20%, 25%, or even 30%+ returns over long periods by simply “maintaining discipline to the strategy.”

Here are some examples we have discussed on our blog and have seen in the media:

This all sounds great, but it is intellectually dishonest to not highlight the logical conclusion of such high returns. And I definitely do not want this blog to convey the idea that earning 20%+ CAGR for many years is by any means easy, or possible. Perhaps this is possible on a very small capital base, but over time, the returns on pretty much ANY strategy will slowly revert to a fair rate of return (risk and return are in balance).

Summary Findings:

Before I even begin, here are some findings (I use the CRSP return database which starts January 1, 1926 and runs through December 31, 2010):

  • Earning 20%+ returns over very long horizons is for all intent and purposes virtually IMPOSSIBLE (assuming the market experience of the past ~90 years is representative of the future).
  • 31.5%+ returns over the 1926 to 2010 period imply that an investor will end up owning over half of the ENTIRE stock market.
  • 33%+ returns imply that an investor will end up owning the ENTIRE STOCK MARKET!
  • A 40% return will have you owning the entire stock market in ~60 years–not a bad retirement plan!
  • A “doable” 21.5% a year implies an investor will own .62241% of the market at the end of 2010. With a $16.4 trillion total market value as of December 31, 2010, this would imply a personal stock portfolio worth $102 billion!!!
  • Warren Buffett–and perhaps a very select handful of others–have been able to achieve 20%+ returns over very long time periods. These individuals represent some of the richest people on the planet because of this very phenomenon.
  • An investor might have an epic run of 20% returns for 5, 10, maybe even 15, or 20 years, but as an investor’s capital base grows exponentially, the capital base slowly becomes ALL capital, and all capital cannot outperform itself!


I am continually haunted by a note I received from one of my dissertation advisors at the University of Chicago–Gene Fama. He wrote the a response to an early draft of my paper on Valueinvestorsclub.com. In the document I sent, I stated proudly: “…this paper shows value investors outperform the market” (where outperforming the market is defined as earning average excess returns after controlling for a variety of market risks). Here was the 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 spot on…

I did not show that “value investors outperform the market”–far from it. I showed that “the small group of investors in Valueinvestorsclub.com outperformed the market,” but that did not imply value investors as a group outperform the market.

Regardless of the argument surrounding semantics, 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 (for every buyer there is a a seller and for every seller there is a buyer).

To this end, I decided to perform some analysis of extreme market returns over long periods.

My main inspiration for this exploratory study is the well known behavioral bias that humans (including me) have a hard time understanding the implications of compound growth.

Here is a quick video from Chris Martenson that captures the concept very well:

Click to get the video: The Power of Compounding.

Any discussion on compound growth and the profound implications it has on life would not be complete without referencing Al Bartlett http://www.albartlett.org/index.html.

Results and Analysis:

To perform this pilot study I grabbed a time series of the value-weighted return (including all distributions) for the entire CRSP universe from 1926 through 2010 (represents virtually all stocks on the NYSE/AMEX/NASDAQ). If you are unfamiliar with CRSP, you can think of it as the closest thing we have to the “Total US market.” The Wilshire 5000 is the best “practitioner” analogy.

Aside from depth, the great thing about CRSP is the long history of the database (goes all the way back to 1926, and the organization invests a painstaking amount of time in ensuring the database is free from survivor bias). For further information, see the documentation on CRSP indices here.

With a large amount of monthly return data extending back to 1926, I started my analysis (FYI, you can access this data and much more at Ken French’s website).

Here was my approach:

  • Start a “winner” portfolio on January 1, 1926 and invest at a given rate through December 31, 2010. For example, a 20% annual compound annual growth rate (CAGR) would imply a (1.2)^(1/12)-1 monthly return. Let’s pretend the “winner” portfolio invests in some objective quantitative value strategy that earns outsized returns.
  • The winner portfolio starts off owning 0.00001% of the entire market as of Jan 1926. This amounts to a very modest sum of $2,709, because the market cap of all securities at the time was around $27,090,070,400.
  • Start a “loser” portfolio that represents the ownership of the rest of the market: ~$27,090,067,691. The loser portfolio returns the overall value-weighted market return minus the return it ‘lost’ to the “winner” portfolio.
    • Quick example: The Jan 1926 overall VW CRSP market return (with distributions included) was .0724%. The “winner” portfolio–assuming a 30% CAGR–was 2.21%. The winner portfolio moves from 2,709 to 2,769, the entire market portfolio moves from 27,090,070,400 to 27,109,680,842, and the “loser” portfolio earns the ‘leftover’ after the “winner” portfolio takes their cut. Specifically, the “Loser” portfolio moves from 27,090,067,691 to 27,109,680,842 (27,109,680,842-2,769). In the end, the winner portfolio earns 2.21%, the loser portfolio earns .0723999%, and the entire market return earns .0724% (by construction, the value weighted returns of the “winner” and the “loser” portfolio must equal the actual value-weighted market return).
  • Next, I extend this analysis to the entire time period to determine the following:
    • When does the “winner” portfolio own over half the stock market?
    • What % of the stock market does the “winner” portfolio own at the end of 2010?
    • How do various assumptions about the “winner” portfolio CAGR affect the results?

Here is a table of results:

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.

What you should immediately notice is the implications of extreme CAGR and stock market ownership. Earning a high return eventually forces you to own a larger and larger percentage of the stock market.

And here is a chart showing how ownership changes over time when the winner portfolio earns 30% CAGR.

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.

What you see is that the underlying 30% CAGR portfolio is slowly turning a mole hill into a massive mountain that eventually becomes the entire market.


The point of this thought experiment seems to be quite clear:

Nobody–I repeat, NOBODY–can continuously outperform the market over long periods of time, because eventually this “genius” will own the market! And by definition, if you own the market, you can’t outperform the market.

  • 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:

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.
  • I would say that you are correct and wrong. What I read between the lines is that no person can beat the market systematically in the very long time. It doesn’t rule out that some strategy couldn’t systematically outperform in the long term.

    How’s this? Because of the limits that strategies have. For example we might be interested in a value investing strategy in small-cap universe that have historically given 20% p.a. profits. The profit will probably decline rapidly after some limit. F.ex. it can be that you can utilize this strategy to only X million dollars portfolio.

    So I would say that strategies can outperform market in the long term given the their limits.

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  • This blog has some interesting info. I am really impressed with your efforts and really pleased to visit this post. Keep up the Good work going!! Thanks

  • So to keep up my returns I just need to return capital to clients. Then win it back from them again and again. Pretty straightforward!

  • Excellent. Well stated. I often discuss with coaching clients the mathematical limits to growth with paper assets. This clearly illuminates one aspect to that issue. Thank you for making the point clear.

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  • Great post!

    I have made also the same analysis for the spanish market. You can see here, but it’s in spanish: http://valorcontable.com/2011/07/batir-el-mercado-continuamente/

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  • As always: very interesting stuff! How much ($) is the access to the “CRSP return database”?

  • Ramesh

    Not sure I understand Fama’s critique of your assertion. Since the value factor tends to earn a high risk premium, the average value investor may very well outperform the broad market, even if the superior value investors outperform at the excess of the inferior ones.

  • Paul Samuelson used to argue that Edward O. Thorp could not beat the market, either.

    Ed Thorp’s results – much of the while trading hundreds of millions of dollars – suggest otherwise. The website http://www.FortunesFormula.com highlights some of Thorp’s performance.

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  • Harry P

    A slightly different take …
    Interesting article, but ….

    The article assumes that one can find market beating opportunities for a long period of time. I fully agree with that.
    Yes, some people might be find market beating opportunities for a really long period of time.

    However, the article also assumes that you can find bigger and bigger market beating opportunities every year.
    This may not be true.

    While market may not behave like a true normal (bell) curve, let’s assume that it does, or is close enough.
    In general, you will have 50% of the “market investments” under-perform the market.
    This implies that you will have 10% market leaders who give unbelievable performance. And this is what we buy for our fancy portfolio.
    This also implies that you will have 10% laggards who lose out badly.
    While the 10% number is arbitrary, let’s assume it as a strict rule for further analysis. It an be changed to adjust the findings.

    So when your market portfolio has grown to 10.1% of the market size, how will you find the additional 0.1 % investment for this portfolio?
    Note that at this point we have exhausted all the opportunity to buy the value leaders, and anything else is going to yield inferior returns.

    And more pertinent to the point, why will the market let you buy this 10%?
    Are not there other buyers who will see what you are doing and change the dynamics?

    I bet the exponential growth of the portfolio using either value investing or day trading or stock picking does not go beyond 1% of the market size.
    If that.

  • Blabla

    It’s not possible to have have high returns forever. But as long as you are not a billionaire you can have high returns. It’s because when you have a lot of money, the stocks don’t have enough liquidity to easily buy and sell for large sums.

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  • “Nobody–I repeat, NOBODY–can continuously outperform the market over long periods of time, because eventually this ‘genius’ will own the market! And by definition, if you own the market, you can’t outperform the market.”

    This is correct if we are talking about compounding the capital base. But most/all managers who beat the market for long stretches of time eventually return capital to investors to keep the base from getting too high. These managers typically return investor funds while keeping their own capital compounding at high rates.

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  • Indrek

    This article is a nonsense because no real trader is dreaming about beating the market in the way described. If trading professionally, you do not grow your account forever but you systematically take money out from it. To trade for living you need approx USD 10,000 account and you keep it around this number all the time. You make 30-40 % of this sum per month, not grow your account from 10,000 to trillions.

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  • wes

    Hi Ramesh,
    The critique (I think) revolves around the idea that one could ‘index’ invest in the value factor, which may or may not be an ‘alpha’ factor depending on your stance (he would argue it is not alpha, I’d argue it is alpha). Regardless, assuming one can capture the general “value” premium by investing in a passive strategy taking on the lowest 10% P/E stocks, the winners and losers around that ‘value’ factor would wash out…

  • wes

    a lot if you need to access it for commercial purposes.

  • Derek

    30-40% a month???? and a $10k account? You must be joking.

    I’d happily stake you a mio if you could show me a 2-yr track record with that kind of return. I’d retire in 3 yrs with a billion dollars.

    Now seriously where do you get the impression that professional traders trade a few hundred thousand accounts and make 30% a month?

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  • Mishkafofer

    I am here strictly for Cash flow.
    Can you transfer this logic to Bond market? Junk Bonds?

  • Ezekiel Kruglick

    I think the Fama comment, at least as summarized, is tautological and appears 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).”

    The inherent assumption in this statement is that value investors buy and sell from and to other value investors. This seems to make sense until one considers that a stock does not stay a value stock from cradle to grave – value is a property that a stock acquires or loses by virtue of price. To say it another way: a typical value investment is bought as a value investment and sold when the price has increased such that it is no longer qualified as a value stock. Successful value investments are thus sold to momentum investors, growth investors, sector rotation investors, etc…

    This doesn’t establish that value investors ARE average outperformers, mind you, but it eliminates the argument presented.

  • wes

    I agree with you.

    I think his real point was that my specific claim was false based on the evidence I had–I was only looking at VIC members, who are definitely not ‘all value investors.’ So therefore, when I originally claimed that value investors outperform, he was technically correct–my statement was overreaching.

  • wes

    I think so.
    You can apply the logic pretty much anywhere. The key takeaway is that one should take their winnings each year and spend it on NFL tickets, charity, diamonds for their wife, a new surf board, a horse, etc etc etc–whatever floats your boat. In the end, trying to compound your kitty at high rates of returns will only make you mad–if your goal is to amass a large #. Buy hey, why not try? Sitting on Buffett’s stash would be pretty nice, eh?

  • wes

    indrek, I have a job for you if you can churn 10% a month, let alone 30% a month. Heck, 5% a month will do as well.

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  • Ezekiel Kruglick

    Ah, that would certainly be reasonable.

    Also I note that VIC has a lot of different “Value” investing types. Right now we seem pretty stable at about 50% reporting few value opportunities and about 50% reporting the usual number. I’d say with current market valuations the latter folk might be classed as “relative value” investors as opposed to “absolute value” 🙂

  • Ezekiel Kruglick

    This was directed at wes’ reply to mine way above, the “reply” connection was somehow lost.

  • Dan

    While an investor’s entire portfolio cannot grow for long periods of time at, say, 30% annualized, a portion of it could. Imagine a fund that produced 30% annualized returns for 30 years, but returned all profits every year to its investors. The fund would start each year at its original size, but the annualized return of that fund would be 30%. The invetors in that fund would not earn 30% compound on their entire portfolio, but the fund would indeed earn 30% a year.

  • wes

    definitely a possibility on a limited capital base.

  • CAGR wouldn’t remain independent of account size. At some point, there would be a negative correlation due lack of liquidity and new opportunities.

    The analysis should probably also look at marginal utility. At some point, as commenters have mentioned above, it makes more sense to take money out of the fund and spend it than to continue to trade the entire amount. With both CAGR and marginal utility negatively correlated to account size, it wouldn’t make sense for an investor to want to grow the account exponentially.

    I think the basic point is correct, though. Earning 30%+ returns isn’t possible over the long term because the market isn’t big enough to let you.

  • Jeff Cheesman

    Exactly on point that value investors do not buy from other value investors. Surprising that this is not obvious to Fama. The criteria that a value investor uses to select a stock to buy precisely would prohibit him from selling at that same price. More likely that Value investors buy from growth investors (or undercapitalized investors that are “forced” to sell); and conversely the value investor will be selling to growth or momentum investors once the price move out of the “value range.” Lastly, why the need to say that nobody can do something?

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  • So, it looks like the conclusion is that you can earn very high returns as an investor and get rich but after getting rich your returns decay back to the mean. Works for me! 🙂

  • TheShoeHorn

    I think what you’re showing is the logical extreme of CAGR as a measurement

    Now, a hedge fund or quant strategy can produce an ‘Average Annual Return’ of >20-30%, so long as it maintains an optimal AUM … Which is why the likes of Appaloosa (and presumably most top hedge funds) periodically return capital to investors

  • Eivitussaole

    In theory, the argument is sound, but perhaps indeed we shouldn’t be using the CAGR as metric of performance. What you are describing above is in a way actually happening in the world right now. Here is a quote from a year old article by The Guardian: “Billionaires and politicians gathering in Switzerland this week will
    come under pressure to tackle rising inequality after a study found that
    – on current trends – by next year, 1% of the world’s population will
    own more wealth than the other 99%.”

    How does this fit in to the context of the article? Of course it is impossible for that 1% to have double digit returns at that point, but couldn’t it be argued that they as a whole are still constantly outperforming everyone else if the gap keeps on increasing? Performance is always relative and at some point all you really can do is to just increase your wealth in the same proportion as the amount of money supply grows. Perhaps it might be a good idea to become a bank at that point and start issuing loans to people so you would still have someone to sell to and wait out until they have to start paying off interest so they are eventually forced to sell back in a manner where you end up outperforming them.

    In essence, you would become the unbeatable market itself, meaning that the assertion that it is an impossible idea to own 100% of the market is plausible, unless we count debt at which point it could be said that you might even own over 100% of the market at a given time point because your wealth exceeds the current money supply thanks to people owing you interest 🙂

    Just a hypothetical thought experiment. Also, if we take derivatives into consideration, everything becomes even more bizarre. We are essentially trading future potential as contracts with them in a way that is bigger than the current market capitalization so at least to me the line gets really blurry what consists of 100% market ownership or how to even define the market then.

    Anyway, thanks for another inspiring article.