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Too big to scale: Long-term stock market returns

An inflatable globe of the Earth is an example of bringing big numbers down to size

Always be alert to the different ways in which large numbers can be (mis)interpreted when trying to make sense of the world.

Never forget: You’re an upgraded ape with delusions of grandeur, designed to hunt gazelles and run away from lions. You’re prone to fear and greed, you love being in with the crowd, and you’re afraid of heights and of the dark.

And all this equally well applies when investing – because what else have we got to go on?

We need to quieten the chimp within us to get unemotional about data, in order to invest through the cycles of boom and bust without getting giddy in the good times, or paranoid in the bad.

The view from the stock market’s summit

Let’s consider how a superficial read can mislead us by considering the long-term returns from the US stock market.

Below is a pretty typical graph, of the sort you see in the introduction to many investing books. It shows how the US stock market has risen from the 1930s until a year or two ago:


How do you feel when you look at this graph?

A pretty normal reaction might be: “Oh my goodness, we’re doomed!”

It looks as if the stock market only really got going in the Yuppie era of the mid-1980s. Until then, the City was asleep. How Warren Buffett made his billions seems a mystery, given the near flat line he had to trudge along for most of his career.

In short, we still appear to be in the midst of an enormous stock market bubble that is certain to burst! (Again!)

And indeed I have seen this graph used to make exactly that claim.

Now, this data is not wrong – the US stock market did indeed rise as indicated in the graph.

But if we consider its ascent in the light of various other factors, we may decide we look far less likely to be heading for a nasty fall.

Getting real about returns

The first thing to point out is that this graph shows the nominal price level. That means the data has not been adjusted for inflation.

Considering that inflation tends to run at 2-3% a year, this makes a big difference once compound interest has done its work over several decades.

The next graph is one of several I am going to use from Visualizing Economics.

Again it shows a huge spike in the past three decades for the equity market, compared to what has gone before – this time taking us back to 1880:

Click to enlarge

Click to enlarge

At first glance you might not see much different about this graph compared to my first graph.

However compare the two more carefully. This time you can clearly see several previous peaks, along with those double stalagmites of the recent highs (tested again, incidentally, since this graph was created in 2010).

By adjusting like this for inflation, we can more easily see the big run-up in stocks that occurred in the late 1960s. This graph also makes plain the 1920s bubble (which was already underway just as the first graph gets going – but even if it were fully shown, it would just look like a blip).

Displaying the market’s ascent in real terms like this helps us see that investors didn’t spend every day asleep at the office until the 1980s. There were plenty of roller-coaster rides on the way.

Tackling those twin peaks

The next and arguably the most crucial adjustment we need to make to the data is to change the scale we use.

Currently, we’re looking at it in a linear scale. This is misleading. Why?

Well, simply by eyeballing the graph above, we can see the US market went up about 50% between 1900 and 1906. That’s quite a move in just six years.

However on the graph as a whole this surge barely registers, compared to those Peaks of Doom to the far right of the graph.

This is because by the time we get to our era, the market is up at levels some 10-20x higher in absolute terms compared to the turn of the century, even after adjusting for inflation.

Again, the data is not wrong, but visually it exaggerates the recent past and tricks us into thinking we’re looking at an enormous and unusual bubble.

We can see this by using a logarithmic scale. With a logarithmic scale, percentage changes appear the same, even if the absolute changes are massively different. Using a log scale, a 50% rise between 1900 and 1906 would look the same as a 50% rise from 2003 to 2008.

Here’s how the long-term US stock market graph looks in log terms:

Click to enlarge

Click to enlarge

Now we’re getting somewhere!

When looked at in log terms, the stock market return over the last couple of decades – those big twin peaks of recent infamy – look positively ordinary. As indeed they should – due to the bear markets of 2000 and 2008 that wiped out most of the excesses of the late 1990s, stock market returns from 1990 to 2011 were actually below the long-run average!1

For the avoidance of doubt, I am not saying the market wasn’t grossly overvalued in the year 2000, or anything like that.

But I am saying it’s been grossly overvalued and undervalued before.

The inflation-adjusted log graph shows us very clearly how the market has endured all kinds of booms and busts, and also how overall it has marched pretty steadily higher, provided you stand far enough back (and squint a bit!)

Real versus nominal, side by side

If you compare that inflation-adjusted log graph with the very first graph that showed nominal growth in linear terms, I think you’ll agree we’re now seeing a much less scary – and more informative – picture of stock market growth over the long-term.

The next graph illustrates the same point, via two log views of the US market.

The blue line has not been adjusted for inflation, whereas the black line has:


I wish I could show the blue line in linear terms, to ram the point home.

Perhaps that’s a project for a rainy day…

Dividends do it again

I’m not quite done yet. These graphs still don’t show the complete picture.

I mean, some of you may feel as deflated as the graphs by now. Why invest in equities, I hear someone cry, if over 120 years you just get a crummy line that limps higher from left to right?

To which a couple of points:

  • First, the linear graph still shows you how your money would grow – it’s just not as clear as the log graph at showing the rate of change. You still get rich!

Annual dividends are a huge part of the stock market’s total return, and the graphs we’ve seen so far assume you spent all your dividends partying with cads, flappers, hippies, punks, and ravers as the decades rolled by.

What if you sensibly reinvested your dividends for your long-term wealth?

Here’s what:

Click to enlarge

Click to enlarge

Who wants to be a millionaire? As you can see by the green line, reinvesting dividends makes an enormous difference to your return. Pumped up by dividends, the log graph now looks perky again.

Remember that the visual impact of this return is flattered by compound interest being applied over more than a century. Somebody reading this might have 100 years to live, but such precocious seven-year olds aside, that’s not a realistic investing time frame for most of us.

But by now you know to look twice at any data before reaching a conclusion, right?

Why equities grow over time

One more thing. There are some out there who think the whole stock market is a Ponzi scheme, built on suckers selling paper shares to other suckers, and so forth.

As such, these folk think even the steady growth we see in the later graphs is too good to be true.

I haven’t got much time for these people. Frankly I’m glad they tend to live in the caves and the backwoods of North America. (I get the impression that most of them don’t have much truck with fancy consumer goods such as soap and hot water.)

Nevertheless, it’s important to remind any doubters that there’s a good reason why equities can be worth more over time, even after inflation. And that’s that economies – or at least the one’s we’re concerned about – have tended to grow their GDP over time, too.

As GDP grows, listed companies benefit by expanding their share of business. So there’s a direct (if imperfect) relationship.

And here’s how US GDP grew during the last century and a bit:

Click to enlarge

Click to enlarge

Woo hoo! We’re going to the moon!

What’s that I hear you say? This is a linear scale, and you’d rather see it in log terms?

Absolutely right – well done young padawan. Double extra pudding for you for paying attention, plus your wish is my command:

Click to enlarge

Not so crazy now, is it?

The bottom line: Returns can be calculated and illustrated in many different ways, and whoever is doing so may well have an agenda. Meanwhile your first emotional reaction may well be your least reliable one.

Think first, and ask questions later.

  1. 20 year annualized real returns to the end of 2011 for US equities were 5.6%, versus 6.6% over the full 86 years for which data is available. Source: Barclays Equity-Gilt study 2012 []
{ 18 comments… add one }
  • 1 Neverland April 4, 2013, 12:27 pm

    In the 1880s the US was emerging into a group of world powers, including the UK, Germany, the Austro-Hungarian Empire, France and Imperial Russia

    By 1945 it was the pre-eminent power in the world

    Its not surprising its stock market gains look good

    Looking at the stock market histories of a couple of the other countries (e.g. Austria or Russia) on that list would look pretty different

  • 2 Ash G April 4, 2013, 12:28 pm

    Nice post, I especially like the last linear graph of US GDP, the exponential trend is uncanny.

    Now the real question is “will growth rates continue their exponential rise in the 21st century”

    Also it seems that while GDP has gone up by 2 orders of magnitude the stock market (without dividends) has only gone up by half an order of magnitude. Is there a known relationship between the two?

  • 3 AJ April 4, 2013, 1:26 pm

    Very nicely put together!

  • 4 dearieme April 4, 2013, 1:59 pm

    “You’re an upgraded ape with delusions of grandeur, designed to hunt gazelles and run away from lions”: first designed to hunt fruit, nuts, fledgelings and the odd tree-lizard.

  • 5 Kurt @ Money Counselor April 4, 2013, 2:06 pm

    Whether nominal or real, logarithmic or linear, the S&P 500 crashed about 45% in 2007-2009, yes? To me, that’s scary, no matter how you dress it up. I’m sure the millions of retirees who saw half of their nest egg go “poof” feel the same way! 🙂

  • 6 rjack (Mr. Asset Allocation) April 4, 2013, 2:17 pm

    “There are three kinds of lies: lies, damned lies and statistics.” – Mark Twain.

    I guess we should add charts to the quote as well. Great post!

    If you want more of this kind of statistics stuff, read “The Signal and the Noise: Why So Many Predictions Fail — but Some Don’t” by Nate Silver. It’s a great book that describes how the best predictability can often come from a combination of statistics and human judgement.

  • 7 Greg April 4, 2013, 2:22 pm

    The CS Yearbook 2012 has a chapter (p37) on different countries. (I haven’t read the latest yearbook, so there might be more in that one.)

    There is huge variation between the countries! (The standout is Australia at 7.2% real return p.a. over 112 years: $1 becomes $2459 in real terms!) They do have a “globally diversified” portfolio mixing the countries according to annual capitalisation which gives +5.4% (£1 becomes £344) and an “ex-US” one which gives 4.8% (£1 becomes £200). Bonds and cash return 1.7% & 0.9% (£7 & £2.80) for Global & 1.3% & 0.9% (£4.10 & £2.80) Ex-US.

    Shares really are the only way to go for the ultra-long-term! I suppose if you don’t want the country-specific risk, then you should be globally diversified. However, seeing as we’re much more connected now, you already are even if by accident.

    I find it amusing when gold bugs claim “1 oz of gold could buy you a good suit in Roman times and still can! Blah blah fiat currency, blah blah Voltaire, blah blah Taleb, blah blah blah.” Wow. 0% return in 2000 years. £1 invested at 4.8% for 2k years is £5×10^40. That’s a lot of suits…

    As for the index only going up by a fraction of the GDP, there will have been an increase in the number of companies as well as the size of the largest X that are in the index. Hence they don’t need to keep pace.

    GDP is complex though and has all sorts of significant adjustments. e.g. People owning their own home are assumed to pay “rent” to themselves which counts as GDP…

  • 8 Greg April 4, 2013, 2:32 pm

    @ Kurt
    Why would the retirees be concerned that the stock market dropped 45%? They would be massively biased towards bonds, which IIRC, did rather well…

    Younger people who were mostly in stocks won’t be too distressed, seeing as they are back above where they were and they’ve had a chance to buy on the cheap.

    Oh an anyone retiring whinging about low bond yields can stop right now. Bond yields are low. The means that the bonds that make up the massive part of your portfolio have gone up in value hugely.
    100k yielding 2% gives the same as £50k yielding 4%. If you are moving from 100% stocks to 100% bonds, then something’s gone very wrong…

  • 9 William @ Bite the Bullet April 4, 2013, 3:48 pm

    I’ve seen several people point to the peaky thing and claiming we’re now due for the next crash. I like your analysis — well researched and well presented.

    There’s another perspective, admittedly a little simplistic, compared to yours. But it might be worth adding to the equation. And that’s the PE valuation of the market: http://bit.ly/willitcrash

    Think that thought has any merit?

  • 10 Greg April 4, 2013, 5:02 pm

    FTA: “You can clearly see how the PE ratio for the stock market spiked before each crash.”
    Rubbish. The US P/E ratio spiked in 2009. The crash happened before then. PE10 is a bit better but seeing as the last 10 years have been nuts, it is very hard to assess whether that’s a reasonable long term guide.

    In addition, as mentioned in earlier articles, (I forget whether they were Monevator ones,) with a crude exponential fit, it makes a huge difference where you start and stop the line. e.g. imagine starting in 1921 and looking at it at the mid ’50s. The ’20s look like a odd blip against a normal of weak returns. The bump up for the Korean war would look like a significant bubble and there’s no inkling of the explosion up for the next decade. Similarly, starting in the ’80s and looking at 2007, everything looks massively undervalued!

    As for a crash? No idea. I suppose investing wise, I hope there is one as I will be a net buyer for some time. However, seeing as crashes make people miserable and there’s more to life than making money, I’d really rather everything settled down and we had stability!

  • 11 Dylantherabbit April 4, 2013, 7:43 pm

    Great post. Longterm it shows the benefits of just buying the index and reinvesting the income, accumulation units FTW, at least until retirement.

  • 12 Grumpy Old Paul April 5, 2013, 3:26 pm

    This is how I parody certain people who, mercifully, don’t post very often on here:
    “Pieces of eight. Fiat currency.”
    “Pieces of eight. Von Mises.”
    “Pieces of eight. EUSSR.”
    “Pieces of eight. Zanulabour.”

    I suppose that it’s easier than thinking.

    Apropos nothing, something which irritates me is references to “pensioners on fixed incomes”. Of course, the State Pension increases are governed by the “triple lock” and occupational pensions increase annually in line with either CPI or RPI subject to a cap. So, in general, pensioners are better protected against the rise in the cost of living than folk at work who are subject, in many cases, to wage freezes, or 1% increases. So who precisely is on a fixed income?

    Like you, I have no idea what and when the next crash will be but I rather hope that it will be crude oil!

  • 13 Greg April 5, 2013, 5:09 pm

    You forgot “Sheeple”!

  • 14 Grumpy Old Paul April 5, 2013, 5:51 pm

    So I did!

  • 15 The Accumulator April 5, 2013, 6:53 pm

    @ Grumpy – I wouldn’t fancy living on the State Pension myself. And one of my nearest and dearest doesn’t have an occupational pension, does have a fixed income and is being flayed alive by the combination of naff-all interest and escalating inflation.

    @ Neverland – I guess that’s where the globally diversified portfolio comes in.

    @ Ash G – the Gordon Equation traces a link between stock market growth and GDP growth. But countering that, here’s a quote from a Larry Swedroe piece citing evidence that high rates of economic growth and stock market returns are unrelated:

    While most people believe that economic growth is good for equity investors, for the period 1900-2002, the correlation of per capita GDP growth and stock returns for 16 countries was actually negative (-0.37) — countries with above-average growth rates provided below average returns. Another study, covering the period 1970-97, found that the correlation between stock returns and GDP growth was -0.32 for seventeen developed countries and -0.03 for eighteen emerging markets.

  • 16 K April 6, 2013, 2:18 am

    Good analysis from a good blog!

    As I’ve done before allow me to play the devil’s advocate though.

    Re the GDP and stock returns correlation, you have to account that while a company is listed in a country, lets say the USA, it may not operate only in that country and therefore its global earnings ( or losses ) are not fully accounted in that country’s GDP – but they are accounted for the stock valuation . Also the market is affected by investor mood to be in the market, which can be quantified by looking under what PE ratios people are willing to invest, and mood probably (?) is uncorrelated to GDP – though this would be an interesting thing to check (PE to GDP growth correl).

    But … the reason I don’t believe in the predictive power of most of these things (PEs, correlations to GDP)? look at 2008, PE was looking okish, forward PEs were looking okish – all was looking okish. Then … earnings collapsed for banks and other sectors followed. People may argue that the quality of earnings was not good, but this is said in retrospect, who could know then how Lehman’s derivatives books are marked and even if they did, who’d know the effect this would have on the global economy?

    Then sometimes comes an argument in the lines of “banks are a singular case because of how they account their assets” but who isn’t? any S&P large company has such a complex structure that assessing it’s earnings quality is totally beyond me.

    Then assuming we don’t know where the market goes and we go ahead and build e.g. a 60-40 portfolio. Applying this to Japan would have been a disaster for 20 whole years! we’d be adding equity to a market that was stale for an eternity.

    returns from the US market have been good in the long term, both in real and nominal terms, will they continue to be so ? who knows? I certainly don’t. Maybe they will, maybe they won’t.

    In my personal portfolio I own stocks, I own bonds too ( even long term ones ! ) – I could be sorry for doing that one day though.

    For me the main reason to be invested for the (very) long run is one, where there is a central bank put(*)(**) it makes sense. Why ? well if the put turns out to be a bad gamble for any of those major world economies, I’ll have more serious problems to worry about than what happened to my investments, so in this scenario I probably won’t care. If, on the other hand, the puts prove to work while I’m alive – so much for the better.

    (*) which is different to a healthy growing economy, or great companies that will keep producing earnings, it just means that the central bank will use a monetary policy that favours those invested, they may eg push up the nominal earnings of companies by inflating. If central banks can keep writing puts forever is something I’m not sure about but again if it comes to this, stock performance will probably be the last thing I’ll be worried about.

    (**) Japan didn’t apply a put soon enough after their crash 20+ yrs ago, that’s why common wisdom extracted from US markets doesn’t apply to 90s-2000s there

  • 17 Moonbreakzor October 8, 2020, 1:31 pm

    First, I’d like to say it’s an awesome blog with great illustrations!

    I’d just like to point out, that the graph with/without dividends give roughly annual interest rates of ~1.5% and ~6.3% (1).

    That is quite a big difference. Investing $1000 for 20 years will result in respectively $1350 or $3400, excluding inflation (2). More than 3 fold your money back in just 20 years, which is less than a average mortgage term! I doubt most housings yield a 3 fold return in just 20 years. Not to mention the loans you may have to pay!

    Saving $100 every month for 20 years would give $24,000, which is a pretty nice savings, but would only take you so far (3).

    Investing $100 every month for 20 years would yield ~$47,000 (4). That’s almost doubling your savings! I wish my parents had done that. However, investing all $24,000 immediately would’ve given you ~$81,000 (5)!

    Thereby, dollar cost averaging approximately halves your interest rate (6), but makes it way more attainable (it’s not that often that people can just put $24,000 in stocks immediately) and also reduces your risk slightly! So I’m in and I wish this was taught better in school for everyone! Just try to put 10% of your salary in stocks and see how it’ll turn out in 5 years or 20. And do the same for your kids!

    1) 1,000/100*(1/150)-1 and 1,000,000/100*(1/150)-1
    2) 1000*1.015^20 and 1000*1.063^20
    3) 100*20*12
    4) 100*sum(1.063^(i/12),i=0..20*12-1)
    5) 24000*1.063^20
    6) “r” interest rate in “n” years // root(n,sum((1+r)^(i/12),i=0..12*n-1)/(12*n))

    6.3% in 20 years // root(20,sum((1.063)^(i/12),i=0..12*20-1)/(12*20)) ~ 1.034 // 3.4% or a factor of 1.9 less than the original

    10% in 20 years ~ 5.6% // factor 1.8
    10% in 5 years ~ 5% // factor 2
    10% in 1 year ~ 4.5% // factor 2.2
    5% in 20 years ~ 2.7% // factor 1.9
    5% in 100 years ~ 3.3% // factor 1.5
    5% in 999 years ~ 4.6% // factor 1.1
    20% in 20 years ~ 12.3% // factor 1.6

    The longer the period and the higher the interest rate, the lower the factor. But it’s approximately a factor of 2.

  • 18 Clara Tan May 22, 2021, 2:43 pm

    I don’t yet understand the promise that the market/GDP will always increase in the long term. What about climate change and finite resources? Note: Am in process of learning more about this question, so if anyone has inputs please share.

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