Note: I didn't write this essay, nor do I own the blog where it came from. I'm just sharing it to see what other people think about it. The essay text is displayed below this line.

In this essay, I will debunk the concept of market capitalization.

But first, let’s consider something else: the mass of a pile of bricks.

Suppose that I have a pile of identical bricks. I want to know the total mass of the bricks for some reason. So, I measure the mass of one brick on a scale. The mass of one brick is M. I then count the bricks. The number of bricks is N. I then caculate the total mass of the bricks as M × N.

M × N is meaningful. There are N units of size M, so N × M represents the total size of the units together..

The meaning of M × N is “the total mass of the bricks”. It is not just “M × N”. Note that I could use another method to get the same quantity. I could put each brick on a scale, measure its mass, and add up all of those numbers. If I had a really big scale, I could put all the bricks on the scale together, and measure the total mass directly. The meaning is not the method. The meaning is what the number represents.

Now, let’s consider market capitalization.

The market capitalization of a company is the current share price times the total number of shares. For simplicity, let’s assume that all shares are identical. So, if the current price of a share is P, and there are N shares, the market capitalization is P × N. This number supposedly represents the market value of the company (all the shares together).

This is very similar to the example of the bricks. You might never give it a second thought. But let’s give it a second thought.

The mass of a brick is a property of the brick. It is a stable property, and it does not depend on other things. Since the bricks are identical, it is semantically valid to multiply the mass of one brick by the number of bricks to get the total mass of all the bricks together.

Is this true for shares?

No. The current market price of a share is not a property of the share. It is a property of the last transaction: it is the price at which the last share was sold. We could also say that it is a property of the market in which the shares are traded. The market price could be defined simply as the price of the last transaction, or we could average over a few recent transactions. Either way, P is not a property of every share of the company, in the way that M is a property of every brick in the pile. P is not a property of any share.

There are not N units of size P, so P × N is not semantically valid. It doesn’t represent the total price of the shares. There is no such thing as the total price of the shares, because they are not traded as a unit.

If you tried to buy all the shares of the company (or a large number of them), the price would increase, due to increased demand. If you tried to sell a large number of shares, the price would decrease, due to increased supply. This shows that market capitalization is bogus, but it is not the reason why market capitalization is bogus. The reason is that market capitalization is semantically invalid.

For a mathematical function to be semantically valid, it is not enough that the inputs are meaningful. The mathematical operations must also be meaningful. P is a meaningful input: it is the price of the last transaction, and it is correlated with the price of the next transaction. It is informative. N is also a meaningful input. It represents the number of shares. But P × N is not a meaningful function of those inputs.

Let’s go back to the bricks for a moment, but now suppose that the bricks are not identical. Instead, they are various shapes and sizes, and thus have different masses. Suppose that M is the mass of the brick at the top of the pile. Is M × N a meaningful function? No, because it doesn’t represent anything. There are not N units of size M. Could M × N be used as a heuristic approximation to the total mass of the bricks? Well, it might be better than a random number, but it isn’t semantically valid.

In the case of market capitalization, it is not that the shares have different prices. They don’t have prices at all. The current market price is not a property of each share, or of any share, even the last one traded. Thus, it is meaningless to multiply P by N.

Market capitalization is based on a conceptual error. People think of the price metaphorically as a physical property, such as mass. This makes P × N seem valid, because it seems like there are N objects, each of which has a quantity P associated with it, and thus P × N is the total quantity associated with the objects together. But the market price is just information, not a physical property, and it is not a property of a share.

We are used to dealing with numbers that represent physical properties. So, we tend to think of quantities in that way. This metaphor makes it easier to think, but it can be misleading.

If you believe that market capitalization is meaningful, it is probably because of that conceptual error, combined with social validation. Since it is a common error, it seems correct. There are many other examples of common errors due to fallacies. People create language games that seem meaningful because people play them.