One of the most-shown graphs in investing is the century-long story of the growth of the Dow Jones industrial Average. It looks something like this:
The graph is right.
But plotted this way it gives some seriously misleading insights.
For one, it appears that very little return was earned through investment in the market unless you started investing around 1982; at that point it seems to have an inflection point and suddenly started heading upwards.
A second takeaway is that volatility seems to have really increased starting around 1997. There are two booms and crashes, followed by the post-financial crisis boom. Is it sustainable? From just looking at the chart you might have doubts. And if you were to scour the internet you would can find many gloom-and-doom prognosticators calling for a 40%, 50% or even 60% drop in stocks lurking around the corner based on the shape of this graph (spoiler alert: they all want to sell you gold of some sort).
But looking at the facts this way gives some seriously misleading insights. And the reason has to do with the fact that returns – which is what we care about in investing – are measured in percent, not dollars. An investor who invested in the Dow index when it was 100 and then saw it grow to 200 got the same return as one who invested at 10,000 and saw it go to 20,000. In the chart above, both red arrows represent a 100% return at their respective starting levels. Because of the power of long-term compounding, a simple graph like this seems to pack most of its information into the last 30 years – precisely because compounding makes things bigger there, and even small amounts of percentage growth make the actual number grow fast.
Engineers, scientists, and economists have long-dealt with this is a very simple way. Back in the days of pen-and-paper, they used something called semi-log graph paper. Today, all spreadsheets let you do the same by asking for the Y-axis to be “logarithmic” rather than “linear”.
My goal is not a refresher in pre-calculus. It is to show why, over long periods of time, you really ought to look at graphs using the logarithmic choice for the Y-axis. Here for example, is the same DJIA graph with such a logarithmic Y-Axis:
The nice thing about a log axis (“log” is short for “logarithmic”) is that equal percentages of gains or losses are the same distance apart. In this graph, movement in value from one guide line up to the next represents a 272% gain, no matter what the current level. It allows us better to appreciate the size of moves relative to the level. And it let’s us see all the information that got compressed toward the bottom in the first 70 years simply because 20,000 had to be the top level.
Indeed, looking at this graph you can see that the prior chart gave almost all the wrong insights. Look back on Chart 1 and you can’t even see the Depression. This is because it happened when the DJIA was around perhaps 300, but if our chart goes to 20,000, that 300 – and big moves around it – are all pretty small. But now we can see that the Depression was by far the largest downward shock to the stock market in percentage terms.
You can also see that the post-1999 era is not quite the rocky road it appeared to be in Chart 1. Chart 1 would have you believe the market “took off” in the 1980s, but then suffered two major setbacks – and perhaps are an indicator of things to come. Yet, we can now see that in percentage terms both the 2000 Dot-com bust and even the 2008 financial crisis were small drops (in percent) compared to the Depression – and, indeed, compared to many ups-and-downs prior to the Depression and the 1940s.
Finally – and most important – you can see that the rate of growth of the markets has been amazingly steady, really, over the long-term. The reason the stock market seems like a straight line on a log chart is that, in general, what drives stock prices are corporate earnings. And what drives corporate earnings for the economy as a whole (as captured by index funds) are things that tend to grow by percentage: population, increased global trade, productivity, and even inflation. Yes, there are times when the great tug-of-war between buyers and sellers of stocks leads to departures from that line – as should happen in any good game of tug-of-war – and one could argue (retrospectively) that the market is at times both over-valued and under-valued compared to the long run. But most of us are going to invest over time, not at one exact moment, and capturing that upward drift for the long-run is really what matters.
A traditionally-scaled graph always gives the wrong impression when it is showing data about something that grows by percentages. Anything that grows by percentages looks like it has a “knee” and “takes off” on a normal graph, but will give a straight line with a log scale. These two charts show the same data, starting at 100 and growing 10% annually for 100 years, shown on both a traditional and a log chart:
I leave you with one final thought with real world data. I mentioned earlier that people are, right now, debating if the market is over- or under-valued: in other words, if you have cash should you wait for prices to drop, and if you own stock should you take profits and move to cash, or vice versa.
Given the large number of tools and data sources on the web, one might look at the recent activity of the SPDR, and ETF that captures the S&P 500 Index companies. If you look at the last 3 years in a regular graph you might come away worried or puzzled. Here is its price history over the last 5 or so years in linear format:
But now compare that – especially the jagged peaks on the right – to a 15 year history done using a log scale for the Y-Axis from the same online tool:
Given a longer view, and use of the log scale, makes those worrisome peaks of the last 18 months seem rather insignificant on the much larger progression upwards.
So do yourself a favor whenever looking at historical prices for securities. Always take a long view – and use a tool which will let you use a logarithmic scale for the Y-axis. We humans are terrible at intuitively understanding percentages and compounding. Taking a long view with a log scale will almost always give you a different – and better – picture of what matters most and what matters less.
And don’t worry about the math: just do it. I guarantee the computer will get it right.