I'm going to make the following claim. The price of bitcoin is inherently
volatile. Even if bitcoin gets bigger, its core level of volatility is never
going to fall.
Bitcoin's hyperactive price movements prevent it from becoming a popular
medium of exchange. Merchants are too afraid to accept bitcoins. If they do,
they could experience large losses. Consumers who hold bitcoins are loath to
spend them. Many of these hodlers are trying to change their financial
lives by getting exposure to the very same roller-coaster ride that merchants
are trying to avoid. If they use their bitcoin to buy stuff, they risk losing
out on the opportunity for life-changing returns.
Why is bitcoin's high volatility intrinsic to its nature? Bitcoin is a rare
example of a pure Keynesian beauty contest. Players in a beauty
contest gamble on what John Maynard Keynes described as what "average
opinion expects the average opinion to be." No matter how big the game
gets, the best collective guess—bitcoin's current market price—will always by
hyper-volatile.
By contrast, other assets like stocks, gold, commodities, and banknotes have
a fundamental value that helps to anchor price. This ensures that their
prices can't travel very far as time passes.
But the standard deviation is falling!
In response to the claim I've just made, people have given me a version of
the following: as bitcoin gets bigger and more popular, its volatility will
inevitably fall. This eventual stabilization is one of the assumptions at the
core of Vijay Boyapati's bubble
theory of bitcoin. Bitcoin guru Andreas Antonopolous has also adopted this
viewpoint, noting that "volatility really is an expression of
size."
Manuel Polavieja provides evidence for this view by tweeting a chart of the
365-day standard deviation of bitcoin daily price changes.
— Manuel Polavieja (@ManuelPolavieja) June
9, 2019
The general slope of the curve in the chart seems to be declining, the
inevitable conclusion being that bitcoin's price isn't intrinsically
frenetic. As bitcoin has become more popular, its volatility has been
retreating.
Sure, but bitcoin's median absolute deviation isn't falling
Manuel has chosen to illustrate bitcoin's price dispersion with its standard
deviation. But the standard deviation of an asset's daily price change
isn't the only way to get a feel for its volatility. There are other measures
of dispersion that can flesh out the picture, particularly for
distributions that are characterized by extremely large outliers.
One problem with standard deviation is that it amplifies the influence of
extreme price changes. The calculation for standard deviation squares each
day's difference from the mean day's return. By their nature, outliers will
boast the largest differences. Squaring them has the effect of causing the
extremes to have a disproportionate influence on the final score. The
calculation further promotes outliers by taking the average of the squared
deviations from the mean. But in distributions such as bitcoin daily returns,
the average return will always be skewed by a few crazy daily fluctuations.
Median absolute deviation is one way to reduce the influence of
outliers. It calculates the differences from the median daily return, not the
mean. And rather than squaring the differences, and thus amplifying them, the
calculation simply takes their absolute value (i.e. it gets rid of all
negative amounts). It then locates the median of these absolute differences.
The advantage of using the median difference is that—unlike standard
deviation, which locates the average difference—the median can't be
influenced by insane values.
Below I've recreated Manuel's chart of bitcoin's 365-day standard deviation
of daily returns and overlaid it with bitcoin's 365-day median absolute
deviation of daily returns. The contrast is quite striking.
Standard deviation of bitcoin returns, the blue line, has been falling since
2011. But median absolute deviation of bitcoin returns, the green line, has
stayed constant. What I believe is happening here is that the craziness of
bitcoin's outlier days have been steadily falling over time, and thus the
standard deviation has been declining. But a typical day in the life of
bitcoin—i.e. the usual price volatility experienced by bitcoin holders, its
non-outliers—hasn't changed since bitcoin's inception. A regular day, as
captured by the median absolute deviation, is about as frenetic today as it
was back in when bitcoin was a fraction the size.
What is happening at the ends of the distribution?
We can get an even better feel for the dispersion of bitcoin's returns by
splitting them into quartiles and percentiles.
Let's look at the blue line first, the 25th percentile (or first quartile).
This measure gives us a feel for what a lethargic day is like in
bitcoin-land. Out of a sample of 365 days of bitcoin returns, 25% of them
will fall below the blue line. If bitcoin is indeed getting more stable, we'd
expect the 25% most lethargic bitcoin days to be getting even more lethargic.
But this isn't the case. Rather than falling, the blue trend line is flat
(and even slopes up ever so slightly). It seems that lethargic days are
getting a bit less lethargic as time passes.
The median (already discussed above) shows a similar pattern. The middle-most
day's return shows no sign of slackening, despite bitcoin's incredible growth
over the last decade.
Let's look at the top two lines. 25% of all bitcoin daily price changes are
in excess of the red line, the 75th-percentile. Unlike the median, this line
has been steadily falling. This means that the 25% most frenetic bitcoin days
have been getting a little less frenetic. The purple line, the 90th percentile,
shows an even steeper decline. The 10% most frenetic bitcoin days are quickly
becoming less frenetic.
The interpretation of this chart seem pretty clear. The typical bitcoin
trading day is not getting any less crazy. It's the outliers, those outside
of the 90th percentile, that have mellowed. The softening of bitcoin's
extreme price fluctuations, the purple line, explains why bitcoin's standard
deviation has been trending downwards. But if we only focus on standard
deviation, we'll fail to see that the typical day—i.e. the median day—is just
as hyperactive as before.
What about Netflix?
It's always nice to get some context by looking at how a similar data series
behaves. I've chosen Netflix. Like bitcoin, Netflix has gone from nothing to
billions of dollars in market capitalization and millions of users in the
space of a few short years.
As Netflix has grown, its median absolute deviation and its standard
deviation have softened. So both Netflix's outliers and its regular days have
been tempered over time. Compare this to bitcoin, where the typical day
continues to be just as frenetic as before.
I believe that the contrast between the two assets can be explained by the
fact that at its core, bitcoin is a Keynesian beauty contest. Netflix isn't.
As Netflix has grown and its earnings have become more certain, Netflix's
typical day-to-day price fluctuations (as captured by its median absolute
deviation) have softened. But the failure of a prototypical bitcoin day to
stabilize, even as the asset grows, can be explained by bitcoin's basic lack
of fundamentals. Its price is permanently anchorless.
Intrinsic vs extrinsic price fluctuations
So why has bitcoin's typical volatility stayed constant while its extremes
have softened? If bitcoin is a Keynesian beauty contest, shouldn't both
typical volatility and extreme volatility have stayed high and constant?
Let's assume that there are two types of bitcoin price fluctuations. Intrinsic
price changes are due to the nature of bitcoin itself. Extrinsic changes
occur because of malfunctions in the unregulated third-parties (wallets,
exchanges, investment products) that have been built around bitcoin. Mature
assets like stocks and bonds that trade on well-developed and regulated
market infrastructure tend not to suffer from extrinsic volatility.
Over the years, third-party catastrophes have accounted for some of the
largest shocks to the bitcoin price. When Mt. Gox failed in 2014 it caused
massive fluctuations in the price of bitcoin. But this was extrinsic to
bitcoin, not intrinsic. It had nothing to do with bitcoin itself, but a
security breach at Mt. Gox.
If you've been around as long as I have, you'll remember Pirate's Bitcoin
Savings & Trust—a ponzi scheme that caught up many in the bitcoin
community. When BST collapsed in 2012, it dragged the price of bitcoin down
with it. Again, this was an extrinsic price fluctuation, not an intrinsic
one.
The infrastructure surrounding bitcoin has grown up since those early days.
Mt. Gox blow ups and BST scams just aren't as prevalent as they used to be.
There are enough robust exchanges now that the collapse of any single one
won't do significant damage to bitcoin's price. And so bitcoin's price
outliers have gotten less extreme. The declining influence of third-party
infrastructure on bitcoin's price is reflected in bitcoin's falling standard
deviation. Once the infrastructure surrounding bitcoin reaches the same
calibre as the infrastructure that serves more traditional assets, bitcoin's
extrinsic price fluctuations will cease to occur. At that point the steady
decline in bitcoin's standard deviation will have petered out.
Median absolute volatility screens out the Mt. Goxes and BSTs. And so it is
the best measure for capturing bitcoin's intrinsic volatility. Think of this
as the base level of volatility that emerges as people try to guess what
average opinion expects average opinion to be. And as I pointed out earlier,
this sort of volatility has stayed constant over many years. A Keynesian
beauty contest is manic by nature, it isn't going to mellow out with time.
In sum, on a typical day bitcoin is about as volatile in 2019 (at a market
cap of +$100 billion) as it was in 2013 (when its market cap was at $1
billion back in 2013). Which would seem to indicate that if and when it
becomes "huge" (i.e. $10 trillion), it will continue to be just as
volatile as it is now.
New recruits are being introduced to bitcoin on the premise that they are
buying into tomorrow's global money at a bargain price. But shouldn't they be
warned that they are playing a new sort of financial contest? Sure, bitcoin
can be used for payments. But the underlying beauty contest nature of bitcoin
will always interfere with its payments functionality. Which means that usage
of bitcoin for payments is likely to be confined to a small niche of
enthusiasts who are willing to put up with these nuisances, and the
de-banked, who have no choice. Bitcoin is risky, play responsible.
