Ecoinometrics - Diminishing Returns

August 04, 2021

Bitcoin is getting big. Right now it’s market cap is around $700 billion but it peaked just above $1 trillion earlier this year.

That has people worried about diminishing returns.

The bigger the market, the harder it is to grow right? Or is it?

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Diminishing returns

If you look at the growth from the past halving cycles and project it forward you can estimate where Bitcoin will be if the growth falls in the same range.

This is basically what this chart does.

Some people are in disbelief when they see those numbers. It just seems too big.

However if you place them in context of the market size of other financial assets they do fall within a reasonable, albeit wide, range:

  • Low 6 figures per coin would put Bitcoin at the market cap of Apple.

  • Mid 6 figures per coin would put Bitcoin at the market size of physical gold.

All that is big, but not unrealistically big.

Still, talking about growth when it comes to a market cap of hundreds of billion or even more than one trillion of US$ makes people nervous. 

And one of the most common  things that I hear is that surely the law of diminishing returns is already starting to kick in.

One way of formulating the law of diminishing returns is the following:

The larger the market cap of an asset, the slower its growth.

Or to frame it in a more quantitative way:

The larger the market cap of an asset, the longer it will take for its market cap to double.

I’ve chosen this specific formulation because it makes it pretty easy to visualize the supposed law when stated that way.

You’ll see why in a second. 

Alright, question: can we see any effect of the law of diminishing returns on Bitcoin?

To answer the question we can plot the evolution of Bitcoin’s market cap using a base 2 logarithmic scale as our vertical axis. What that means is that on the chart below every tick on the vertical axis corresponds to a doubling in the market cap. 

The axis spans the full range from a $1 billion market cap to the top around $1 trillion.

Take a look.

First thing to observe is that the rise of the market cap is pretty volatile. During a bull market Bitcoin can double its market cap a few times within a few months to 2 years. But during a bear market everything runs in slow motion relatively speaking.

Second thing to notice is that as the market cap is getting larger, the doubling period isn’t necessarily increasing by much.

Example, it took about the same time for Bitcoin to jump from a $64 billion to a $128 billion market than it took to jump from $512 billion to $1 trillion.

What that means is that, at first sight, a larger market cap doesn’t significantly affect the growth rate when it comes to the doubling periods.

Said differently: Bitcoin’s growth rate doesn’t look to be significantly affected by the size of its market cap, i.e. no clear diminishing returns.

Is that kind of behaviour in line with what we see for other assets?

Let’s take a look at Apple using the same method. After all Apple is the largest stock by market cap so if there are diminishing returns it should show up there.

Check it out.

Okay… so interestingly it took longer for Apple to jump from a $500 billion market cap to $1 trillion than it did to go from $1 trillion to $2 trillion.

And actually it took Apple the same amount of time to see its market cap double from $32 billion to $64 billion as it did to go from $1 trillion to $2 trillion…

This is not an anomaly, you can keep adding more of the mega cap stocks to this chart and observe a similar behaviour.  

For the mega caps at least, it seems that it doesn’t take longer to double your market cap as your market cap grows larger. 

To make sure, let's look at it in a different way. 

Take the current mega cap / growth / tech stocks (Amazon, Apple, Facebook, Google, Microsoft, Tesla) and Bitcoin.

How long did it take for each of those assets to go from $1 billion to $2 billion, then from $2 billion to $4 billion… and so on until $1 trillion to $2 trillion (which only Apple and Microsoft have achieved)?

Let’s plot that:

  • The vertical axis represents market cap levels. Each level is double the previous one.

  • The horizontal axis is the number of years it took to go from one market cap level to double that.

  • Different assets are coded with different colours.

  • Each point represents the first time an asset reached a given market cap level from the previous level.

E.g. if you look at the points on the $2.048 trillion market cap row, the x coordinates tells you how long it took to get there for the first time after they had reached $1.024 trillion.

If there is an effect of diminishing returns we should see that as the market cap gets higher the points are shifting to the right (taking longer to double).

See for yourself.

If you focus on a stock like Facebook, you might think there are indeed diminishing returns.

But looking at everything else there is actually a lot of noise. It is quite typical to see doubling periods larger at smaller market caps than they are at larger market caps.

There is no clear effect of diminishing returns and maybe there is nothing to worry about when it comes to Bitcoin.

Now if you look at the growth trajectories of the mega cap stocks since 2008 you can observe that they seem to be converging to the same growth rate.

That tells me some external factor is probably pushing everything higher… cough cough… Federal Reserve… cough cough… money printing …

Is Bitcoin going to continue growing at the same pace to add the next $1 trillion to its market cap? Or are we going to see some convergence with the mega cap stocks once enough institutional investors get into the game?

These are questions for another day, but at least I don’t think we should worry too much about growth slowing down significantly before Bitcoin manages to flip Apple.

That’s it for today. If you have learned something please subscribe and share to help the newsletter grow.




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