S&P Returns and the Remarkable Case of 2008

Ed. Note: Boing Boing's current guestblogger Clay Shirky is the author of Here Comes Everybody: The Power of Organizing Without Organizations. He teaches at the Interactive Telecommunications Program at NYU, where he works on the overlap of social and technological networks.


This is a graphic of the Standard and Poor's stock index's annual returns, placing every year since 1825 in a column of returns from -50% to +60%. As you can see, it is a rough bell curve, with 45 of those 185 years falling in the +0-10% column. There are only 5 years each in the 40-50% and 50-60% return columns, and, through 2007, there were only one year each in the -31-40% and -41-50% columns. You can see where 2008 to date falls.

(UPDATED: From DailyKos, via Greg Mankiw.)


  1. It should be noted that the S&P changes in it’s composition over time so while we can see volatility across the ages there is Survivorship bias at play. Still 2008 does suck.

  2. @4 Strawberryfrog:
    How can you possibly claim it’s not a bell curve? The data is right there, on a graph, reasonably matching a normal distribution.

  3. My own research on the Dow Jones is born out here… Every year ending in a “5” except one was a (+) year. Here only 3 years ending in a “5” are minuses.

  4. This is a bit premature, folks. 2008 isn’t over yet. A lot can happen in a month. Hell, a lot can happen in a DAY.

  5. @7 Patrick Dodds

    If I read you right, you’re saying that you plan to buy in 2010. That sounds to me like a strategy that’s destined to have you buy high and sell low. If you think that there are going to be great gains ~2010, the time to buy is ~now, when everything’s massively on sale. But of course, there’s no a priori reason to believe that the market will follow any previously followed pattern.

  6. Oh dear.
    It really isn’t a normal distribution.

    This could be a much less pleasant arrangement of affairs, a fat tailed distribution
    (http://en.wikipedia.org/wiki/Fat_tail) where a distribution that looks normal is actually prone to extreme events (like this year) more often than you would expect from a normal distribution. There are *far* too few points on this graph to tell exactly what sort of distribution this is.

    And I wouldn’t cite Makinw anyway. he’s influential, but not in the right way.

  7. @4 Strawberryfrog: It sounds like the bell curves described in your link is not the bell curve shown above. Your link was talking about the bell curve of returns on investment across the market, which is completely different from the bell curve of market changes year to year.

    Anyway, the fact that this is a bell curve isn’t really surprising — all it is says is that periods of wild expansion and wild contraction are rare, which is exactly what you’d expect from any mature market.

  8. Not to be a spoiler or anything but if you collect enough data points any distribution will look like normal distribution! Take a toss of a coin – it follows normal distribution.
    It is said that child population (=sample population ) became normal by the time it reaches 30 (not “years old”, bu “sample data points”)

  9. Maybe he should have referred to it as an approximation of the S&P Index. What we know as the S&P 500 has only been around since 1957. The index itself began in 1923 with 233 companies. Prior to that, I imagine this shows all stocks listed on the NYSE. And I’m not really sure how such info from over a century ago would apply to today’s conditions. FWIW.

  10. @#11 Isaac – since we’re quibbling here, if you think 2008 is like 1931 and 2010 is going to be like 1933, one could assume you think that 2009 is going to be like 1932. Which is a -10. Without further detail, I think you have to assume that means that anything bought (or held) at the start of 2009 would be worth 10% less at the end of 2009. So you’d want to buy end of 2009/beginning of 2010. Granted, this is not the same as “mid 2010” as #7 proposes. But if you think the situation is going to be closely analogous, this is not the time to buy.

  11. @19 BRIAN

    What exactly did you mean by that?

    @everyone else re: #5

    I think an important point here is that there is a danger of misinterpretation w/ the bell curve. Normal distribution is merely a graphic display of data, which will fluctuate constantly. You can’t safely infer that there is a pattern when considering this graph because there is no evidence to suggest that the future will follow the patterns of the past. And I think this is what Nassim Taleb is getting (from what I’ve seen of his talks).

    I think almost all of us saw 2008 and 1931 grouped together and immediately looked towards 1932, 33, 34, 35, etc to see if we could conceptualize how 2009-and-so-on would look.

    This can be grossly misleading, and it is really nothing more then a gamble. Statistically, there is nothing in this to suggest how the future will look.

    Make safe bets. Everything else is a gamble, always.

  12. #20, What’s a safe bet now? Treasuries? How about holding treasuries three years? That’s dicey. Gold? Holding physical in the thirties meant losing your shirt once confiscation and dollar devaluation were legislated. Could happen again. Anything will be done to protect the dollar if threatened.

    There really aren’t safe investments right now. “Bets” are never safe, that’s why they’re bets. Until markets and economies bottom (don’t hold your breath…that long) safe investments are a guessing game, hence, no safe havens.

    In other words, Everything else isn’t a gamble, always, but everything IS a gamble, right now.

  13. Ya #7, I’m looking at 1933 too, a mere 2 years after the 1931 parallel to 2008. I was imagining a much longer lag before a rebound…

  14. @21 Have to hold your gold overseas. The international markets are making it safer. You can also hold stock in mining companies that have rights to large physical assets. There’s an ETF that tracks those (GDX).

    @16 Everything’s not a normal distribution. In fact, a lot of errors in judgment arise from that poor assumption.

    @7, 23 I wouldn’t count on a 1933.

  15. Not to be a spoiler or anything but if you collect enough data points any distribution will look like normal distribution! Take a toss of a coin – it follows normal distribution.

    This sounds like a misunderstanding of the Central Limit Theorem (http://en.wikipedia.org/wiki/Central_limit_theorem), which is a wonderful result, but is a little more nuanced than that and depends on a couple of assumptions. Read the Wikipedia article if you want to know more; it’s not the same as “everything is normal if you take enough samples.”

  16. There is the “half-full” manner of seeing this chart and focusing, as some have, on 1933’s astounding rebound. But it’s important to note as well that 2008 has been the year in which most economists see the current “recession” as having its beginning.
    So while the quick comparison people are making between 2008 and 1931 (based on visual chart proximity) is understandable, the more appropriate year would be 1929 or possibly 1930. Which would suggest our corollary 1931 is next year or even 2010.
    Not to be a downer or anything.

  17. Looking at the past, especially back to 1933 is pretty much as useless as Astrology. The market is totally different, bigger, more interconnected, etc. Things can break faster, opportunities are exploited faster and we quite different technology multiplying the efforts of a larger population.

    Uncommonsense (#17) is correct and finishes off with “FWIW”. Totally correcy. In my opinion this sort of simplistic graph is worth nothing at all.

    BTW Matt(#24) When you say “hold your gold overseas” I think you’re being a bit extreme until I realise you might be posting from the USA or somewhere like that.

  18. Oh boy, people, a coin toss is a normal distribution. There is an inherent assumption in the game that causes it to follow a normal distribution and that is that the value of getting a heads or a tails is some constant. So for example if the value of getting either is a 1 then the likelihood of getting some value is 1 * the likelihood of seeing either a heads or a tails, which is 1/2. So 1 * 1/2 taken over the set of all flips made, produces a graph that should look very similar to a normal distribution with a high peek on the x-axis centered around 0.5 between 0 and 1 with the peak approaching 0.5 as you have more flips (y-axis). This is pretty much the text book definition of a normal distribution. For more information go here: http://www.ccs.fau.edu/~liebovitch/complexity-20.html

    In fact many things are a normal distribution, or tend to follow one. It is why there is a whole set of probabilistic formulas surrounding this assumption. For more information go here: http://www.duncanwil.co.uk/norm.html

    Now, this data shown above is a normal distribution. But it’s a pointless one. I can move data around until it looks like a normal distribution and call it a normal distribution, but the important aspect is whether that information is useful. I think someone else said it above, all this tells us is that this is a mature market with typical market fluctuations being small except in some rare cases like this horrible year, 2008. For more pointless information go here: http://www.maths.tcd.ie/~bratkek/facts.html

  19. What index is this? The S&P500 didn’t start until 1957. 1820’s Were there even indexes back then? I question the accuracy of this.

  20. But the S&P is not down over 40% yet this year. It was 1447.25 on 1/2/08, and is about 908 right now. That is “only” about 37%, so 2008 is in the wrong column.

  21. There’s TONS of research that point to market returns being more log-normal than anything else, no?

    See, because of the fact that returns can NEVER be worse than -100%, the distribution is bound on the left side, which is not the case for the right side of the histogram, which theoretically is limitless. This fact alone precludes (one period) returns being normal.

  22. “the fact that returns can NEVER be worse than -100%”

    This statement is simply untrue. If one borrowed to invest and that investment becomes worthless, then they have lost more than 100% of their principal…just ask the people who were at firms that bought CDO equity (and other assets that are now worthless) and borrowed money to do so. They lost more than their shirt.

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