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You’re Warren Buffett’s second coming. You’re almost 6 (kids don’t tell you how old they are—only how old they’re about to be), and you’ve just helped a neighbor clean out his garage. Now you have a shiny $10 bill in your pocket.
Good start, but you’re WB2 and aiming for the stars. New neighbor, new mark: another $10, and you’ve doubled your fractional shares in VOO at Fidelity! Soon you’re covering multiple neighborhoods and employing a crew of kids to multiply your profits.
You’re almost 7, and you’re rocking $2,500 in VOO. That old neighbor offers you $10 to help with his garage again. You do it out of kindness; he pays, but that $10 just doesn’t stir the blood like before.
It also barely shows up on the graph paper you’re using to chart your progress. Then you learn about percentages—10%, 20%, 100%—and they make more sense. You convert your graph paper’s y-axis to show both dollars and percentages.
And then, when you’re almost 8, you discover that logarithms give the same result on the y-axis using just dollar amounts! Joy fills you. Doubling the vertical distance means doubling the value. One vertical inch that got you from $10 to $20 also gets you from $1,000 to $2,000.
Moral of the story: Look for the “log” button on the y-axis of every financial chart you see. Compare linear and log scales. Learn how accurate data can deceive when displayed poorly.
I downloaded Shiller’s amazing dataset for the S&P 500 today—he synthesized it back to 1871. I plotted it in both linear and log formats.
I have no idea what you said, but the graph is nice, what is it telling me?
Most people, myself included are not wired to easily perform non-linear math in their heads. Nevertheless, it is valuable if we at least grasp the concepts. There are of course a myriad of sources to tap, but for you and our fellow investors, a great resource is Bill Bernstein’s first, (and my favorite) finance book, “The Intelligent Asset Allocator”. He was chided after its release by family and friends for his math-heavy discussions. So in response, he wrote “The Four Pillars of Investing” targeted to a broader audience. The updated second edition is especially good, and I have gifted several copies. First, he explained in detail how and why some of his ideas have evolved since publication of the first edition. Secondly, the math is still there for those of us who like to read it and work through the calculations for ourselves, but it is sequestered into “math boxes” so others can skim or skip over it. He explains things lucidly enough so that reasonably intelligent people with little math training can understand or at least grasp the main ideas. Time very well spent. I personally prefer accurate and well designed charts and graphs to dense prose with lots of equations.
It tells you the power of compound growth. That is the rate of growth of your investments are proportional to your current investments, which ultimately means that the growth of your investments are not linear with time but exponential.
Anything you want it to tell you. 🙂
I want it to go up and down in a way that makes sense to my rate-of-return mindset as if I were a long-term investor anywhere along its date range.
The log plot makes big numbers and little numbers comparable over time, much like present value makes different future income streams comparable.
Linear plots are appropriate when the data is already in percentages or you’re trying to sell something.
The fun/evil thing is that you can say anything you want with graphs using the same data simply by scaling it differently. The great depression didn’t happen on the linear plot for example. Leave it linear and zoom in the date range and it’s the apocalypse (yet we’re still here, aren’t we?).
That’s what I’m trying to communicate (OK, mostly I just love graphs).
The Apocalypse Graph!
Well said.
Interesting to see the log plot. Certainly adds a neat perspective that the rate of compounding has been broadly pretty similar over time, which the linear plot doesn’t show.
Thanks!
Two pretty clear regions: Pre WW2/Post WW2
Yes! I noticed that a while ago and I think I’m gonna do a post on it someday. Money is a historical proxy for human culture.
WW2 Vertex Graph
WWII spurred technological innovation. Perhaps another break came in at the end of 2022, and if you wait long enough you may see it on your chart? 🙂
Another excellent post. Thanks!