Three Metrics

Market capitalization, debt-to-GDP ratio, and body mass index. What do these three metrics have in common? They all drive me crazy.

Take market capitalization. This is the price of one share of a company’s stock, multiplied by the number of shares held by investors. As of this writing Amazon has a market cap of around $1.6T, or $3300 per share times 498M shares. Radcom has a market cap of $135M, or $9.75 per share times 13.9M shares.

Comparing the market capitalization of two companies gives us an idea of their relative value. Amazon is a much more valuable company than Radcom in pretty much every dimension: It employs several hundred thousand people to Radcom’s few hundred people. It owns a lot more buildings. Jeff Bezos is much richer than whoever Radcom’s founder is.

People often call a company’s market cap its “total value,” but that’s wrong. You couldn’t buy all of Radcom’s shares for $135M; you’d find yourself paying a lot more if you tried. The current owners would charge you a premium if they knew you were set on buying every share.

What market cap means (beyond its literal definition) is hard to pin down. It’s sort of “how much money would be exchanged if every outstanding share changed hands in an orderly process that took place over the course of a few years?” But that’s another impossible situation.

Now take the debt-to-GDP ratio. This is how much money a country’s government has borrowed, divided by the total value of all the goods and services produced in that country for a year. In the U.S. the units are (dollars) / (dollars / year), i.e. “years.”

If you take this value literally, it’s “how many years would it take for a government to pay off its debt if it dedicated the entirety of its economic output to the task?” But this would be crazy: any government that tried to do that would implode.

“OK, so divide again by the fraction of GDP that the government can capture and dedicate to debt repayment,” you say. “You get a larger number of years, but it’s perfectly correlated with the original ratio.”

But that’s not right either: suppose I have $20,000 in debt and can pay $1,000 each month. How many months will it take me to get to $0 in debt? Not 20 months, unless the interest rate is 0%! If it’s 15%, it will take me 24 months.

Debt-to-GDP ratios are useful if you use them for comparisons. Suppose two countries both have $1T in debt. The first has an annual GDP of $1T (for a ratio of 1) and the second has an annual GDP of $10T (for a ratio of 0.1). The first country has much more of a debt burden than the second.

But there’s nothing special about any particular ratio. Sure, maybe in practice no country can actually have a ratio of 100. But let’s consider a ratio of 0.9: is it bad? Maybe! But to answer for real you’d want to know a lot more things, like: how much of the country’s debt is due over the course of the next 10 years? Is its economy growing or shrinking? Did it run up the debt winning a war? Losing one?

Body-mass index: this is the worst one. It’s a person’s weight (in kilograms) divided by the square of person’s height (in meters). The units are “kilograms per square meter.”

If you take this literally, it means something like “take a square sheet with sides equal to your height, then distribute weights that add up to your weight evenly over that sheet.” OK, and then what?

“Don’t think about it too much,” you say. “It’s not supposed to be physically meaningful in isolation. It’s constructed that way to allow us to compare people’s weights while taking into account the fact that taller people tend to weigh more.”

That’s right, but everybody goes ahead and uses it for individuals anyway. If you’re a bodybuilder in fantastic shape, you might get a lecture about weight loss from your doctor if your BMI is 25.1. Or you might get a clean bill of health at BMI 18.5 while suffering from crippling anorexia nervosa.

“It’s just a rule of thumb,” you counter. “It works pretty well for people who aren’t bodybuilders or suffering from eating disorders.”

That’s right too, but it still leaves a lot to be desired. Suppose a person’s BMI is 20, but last month it was 23. They should be concerned! Or suppose someone has a BMI of 27.2, but they just won a triathlon. They should be celebrating!

All of these metrics are useful. At extreme values they tell you a lot. A company with a trillion dollar market cap is very valuable, regardless of whatever else is going on with its equity. And they each correlate with something we care about. When we say we’re concerned about a company’s market cap, what we mean is “we’re concerned about whether this company’s equity is actually valuable.”

It’s interesting that they all have two components that are readily available, like weight and height. Body fat percentage is probably much more useful in determining whether someone is at a healthy weight for their build. But that is hard to measure - doing it well requires special equipment. Weight and height are easy for anybody to find out.

And it’s interesting that each of these metrics has a strange sort of literal meaning: A “number of years to pay off debt” that doesn’t take into account other expenses or the debt’s actual repayment schedule? That barely makes sense. But again, the idea is to use the numbers we have at hand to make an approximation.

What drives me crazy is this: specialists know that these metrics have value, but not rely solely on them for making decisions. Nonetheless, there are plenty of finance professionals, economists, and healthcare providers who are deeply confused about how to apply them.

This essay is really just an exploration of one of my pet peeves. But I think the misuse of these three metrics is connected to Slate Star Codex’s “pattern crystallization” concept (c.f. Can It Be Wrong To Crystallize Patterns? and Value Differences As Differently Crystallized Metaphysical Heuristics). For example:

EXPLICIT MODEL: People who weigh too much or too little for their height are unhealthy.

EMOTIONAL EXPERIENCE: Annoyance at having to take a bunch of measurements to determine health status.

REIFIED ESSENCE: Idea of BMI.

ENDORSED VALUE: Anyone outside the range of 18.5 to 25 is unhealthy.