Addressing Innumeracy in Reporting

Anyone involved in cybersecurity reporting needs a strong sense of numeracy, or mathematical literacy. I see two sorts of examples of innumeracy repeatedly in the media.

The first involves the time value of money. Recently CNN claimed Amazon CEO Jeff Bezos was the "richest person in history" and Recode said Bezos was "now worth more than Bill Gates ever was." Thankfully both Richard Steinnon and Noah Kirsch recognized the foolishness of these reports, correctly noting that Bezos would only rank number 17 on a list where wealth was adjusted for inflation.

This failure to recognize the time value of money is pervasive. Just today I heard the host of a podcast claim that the 1998 Jackie Chan movie Rush Hour was "the top grossing martial arts film of all time." According to Box Office Mojo, Rush Hour earned $244,386,864 worldwide. Adjusting for inflation, in 2017 dollars that's $367,509,865.67 -- impressive!

For comparison, I researched the box office returns for Bruce Lee's Enter the Dragon. Box Office Mojo lacked data, but I found a 2017 article stating his 1973 movie earned "$25 million in the U.S. and $90 million worldwide, excluding Hong Kong." If I adjust the worldwide figure of $90 million for inflation, in 2017 dollars that's $496,864,864.86 -- making Enter the Dragon easily more successful than Rush Hour.

If you're wondering about Crouching Tiger, Hidden Dragon, that 2000 movie earned $213,525,736 worldwide. That movie earned less than Rush Hour, and arrived two years later, so it's not worth doing the inflation math.

The take-away is that any time you are comparing dollars from different time periods, you must adjust for inflation to have your comparisons have any meaning whatsoever.

Chart by @CanadianFlags

The second sort of innumeracy I'd like to highlight today also involves money, but in a slightly different way. This involves changes in values over time.

For example, a company may grow revenue from 2015 to 2016, with 2015 revenue being $100,000 and 2016 being $200,000. That's a 100% gain.

If the company grows another $100,000 from 2016 to 2017, from $200,000 to $300,000, the growth rate has declined to 50%. To have maintained a 100% growth rate, the company needed to make $400,000 in 2016.

That same $100,000 dollar increase isn't so great when compared to the new base value.

We see the same dynamic at play when tracking the growth of individual stocks or market indices over time.

CNN wrote a story about the 1,000 point rise in the Dow Jones Industrial Average over a period of 7 days, from 25,000 to 26,000. One person Tweeted the chart at the above right, asking "is that healthy?" My answer -- you need a proper chart!

My second reaction was "that's a jump, but it's only (1-(25000/26000)) = 3.8%. Yes, 3.8% in 7 days is a lot, but that doesn't even rate in the top 20 one-day percentage gains or losses over the life of the index.

If the DJIA gained 1,000 points in 7 days 5 years ago, when the market was at 13,649, a rise to 14,649 would be a 6.8% gain. 20 years ago the market was roughly 3,310, so a 1,000 point rise to 4,310 would be a massive 23.2% gain.

A better way to depict the growth in the DJIA would be to use a logarithmic chart. The charts below show a linear version on the top and a logarithmic version below it.

Using barcharts.com, I drew the last 30 years of the DJIA at the top using a linear Y axis, meaning there is equal distance between 2,000 and 4,000, 4,000 and 6,000, and so on. The blue line shows the slope of the growth.

I then drew the same period using a logarithmic Y axis, meaning the percentage gains from one line to another are equal. For example, a 100% increase from 1,000 to 2,000 occupies the same distance as the 100% increase from 5,000 to 10,000. The green line shows the slope of the growth.

I put the blue and green lines on both charts to permit comparison of the slopes. As you can see, the growth, when properly indicated using a log chart and the green line, is less than the exaggerations introduced by the linear chart blue line.

There is indeed an upturn recently in the log chart, but the growth is probably on trend over time.

While we're talking about the market, let's take one minute to smack down the old trope that "what comes up, must come down." There is no "law of gravity" in investing, at least for the US market, as a whole.

The best example I have seen of the reality of the situation is this 2017 article titled The Dow’s tumultuous 120-year history, in one chart. Here is the chart:

Chart by Chris Kacher, managing director of MoKa Investors

What an amazing story. The title of the article should not be gloomy. It should be triumphant. Despite two World Wars, a Cold War, wars in Korea, Vietnam, the Middle East, and elsewhere, assassinations of world leaders, market depressions and recessions, and so on, the trend line is up, and up in a big way. While the DJIA doesn't represent the entire US market, it captures enough of it to be representative. This is why I do not bet against the US market over the long term. (And yes I recognize that the market and the economy are different.)

Individual companies may disappear, and the DJIA has indeed been changed many times over the years. However, those changes were made so that the index roughly reflected the makeup of the economy. Is it perfect? No. Does it capture the overall directional trend line since 1896? Yes.

Please keep in mind these two sorts of innumeracy -- the time value of money, and the importance of percentage changes over time -- when dealing with numbers and time.