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1/ I realized that my last article about #bitcoin's diminishing returns and volatility was a bit too long. I'll try to make it a bit shorter, in tweet form, here.
medium.com/coinmonks/bitc…
2/ Conclusions of the article:
- #btc grows slower and slower, long-term
- short-term volatility decreases over time
- these trends should continue in the future due to ever higher capital requirements
3/ Diminishing returns implies much lower future #btc prices compared to NON-diminishing returns.
Bitcoin's power-law corridor of growth used diminishing returns. We'll see more evidence for diminishing returns here.
medium.com/coinmonks/bitc…
4/ First, the long-term: What kind of returns can an investor in #bitcoin expect? How do the returns depend on:
1. his hodling time (how long he held his btc before selling them)
2. how early on he bought his bitcoin
?
5/ If #btc had NON-diminishing returns, the return curves for several hodling periods would look like this:
1. the longer the #hodl, the higher the return
2. it doesn't matter WHEN the investor bought. Only his hodling time would matter.
6/ If #bitcoin had DIMINISHING returns, the return curves for the same #hodling periods would look like this:
1. the longer the #hodl, the higher the return
2. the EARLIER the investor bought, the higher the return.
Returns depend on WHEN you buy.
7/ The realized return curves display diminishing returns. Actual bitcoin prices follow diminishing returns, not non-diminishing returns.
However, the data is very noisy (volatility is high).
8/ Conclusions regarding the long-term:
- returns are diminishing over time
- returns are noisy

@gsantostasi has observed this early on:
reddit.com/r/Bitcoin/comm…

#bitcointalk user Trolololo observed this already in 2014:
bitcointalk.org/index.php?topi…
9/ Short-term: Is the same mechanism which slows #bitcoin's price growth also making short-term price movements more difficult?
Let's divide #btc's price history based on the three #halving periods:
Short-term price swings appear to have been wilder in the early history.
10/ Let's be more thorough and look at statistics of the growth rates in the 3 #halving periods. The histograms of the growth rates for short-term #hodl periods have progressively less variance - confirming our hypothesis: the price swings less.
11/ The max #btc price growth rate over short terms have become smaller in successive halving periods. Min price growth rates have become tamer, too.
Same conclusion: Short-term price swings are becoming less crazy. Volatility decreases.
12/ Looking at more statistics keeps confirming the hypothesis. #bitcoin volatility decreases over time.
Here, each plot corresponds to one #halving period.
13/ We can plot the short-term statistics into the #bitcoin price graph for more context. The red cones shrinking over time means that volatility has become progressively less in each #halving period.
14/ What this all means:
Long-term: Predictions made by some individuals (@bitcointina, @fundstrat) seem to assume NON-diminishing returns, whereas we have observed DIMINISHING returns.
For these predictions to hold, #bitcoin needs to start to have NON-diminishing returns.
15/ #bitcoin "Cycle repeat predictions": Each new "cycle" (#halving period) should have less volatility than the previous one. This makes a repeat of the previous halving period unlikely. Each new cycle should become ever more tame.
16/ A naive forward projection with short-term growth rates that are attenuated compared to those in the 3rd #bitcoin #halving period could look like this:
17/ The #stocktoflow model put forward by @100trillionUSD has diminishing returns at first, but non-diminishing (~10x every 4 years) returns long-term.
So: for the #S2F model to hold, currently observed return curves need to change (transition to non-diminishing).
18/ Do diminishing returns imply a gloomy future for #bitcoin? Not at all: returns can still be way above traditional assets for a long time, leading to very high #btc valuations.
19/ Conclusions:
We have (so far?) seen no evidence for long-term:
- constant,
- accelerating, or
- S-curve type
growth.
#bitcoin price growth has been diminishing from the beginning of its history.
20/ Conclusions:
In the short-term, #btc price swings have become less wild. Bull markets take longer to develop. Extremely large swings upwards or downwards become less likely. #bitcoin volatility decreases with time.
21/ Why diminishing returns?
More and more capital is needed to move the #btc price. This is because order books are becoming deeper and deeper.
It becomes ever more difficult to attract ever bigger amounts of capital, making the #btc price ever more difficult to move.
22/ @davthewave came to similar conclusions already more than a year ago:

"As Bitcoin becomes more liquid, it becomes less volatile[...] These subsequent cycles also see the law of diminishing returns coming into effect [...]"

medium.com/max-exchange/b…
23/ @davthewave also noted in a second article:

"[...] the general principle being that with more liquidity, comes less volatility. Also predictable, [...] is volatility reducing on the over-all long-term macro chart of Bitcoin."

medium.com/max-exchange/m…
24/ Special thanks to @BitcoinEcon and @InTheLoopBTC for two interesting discussions which led me to the ideas of
- looking at short-term price changes
- seeing how far we can go without (almost) any model.
Thanks guys!
25/ This article

"Bitcoin’s increasing price resistance uphill, short- and long-term"

is also hosted on my personal website:
hcburger.com/blog/diminishi…

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