The recent turn of events in the crypto market left a lot of people who entered the market as of late withstanding substantial losses. The ones who entered the market some time ago tend to remind the newcomers how stuff like this has happened already and things tend to bounce back. As the oldest crypto currency out there Bitcoin (BTC) is evoked as having displayed resilience in the past, mostly in hopes of it displaying this same resilience in the future. This may turn out to be far fetched since the market now is not what it was a month ago, let alone some years ago. Nevertheless, market dynamics may be similar and to provide some insight on the recent behaviour of BTC price I present a rather simple, but in my opinion interesting observation on the current crash. First I take a look into the BTC price crash of 2013 and put it into perspective with the recent crash. I do not dwell on describing the causes, but instead focus on quantitative aspects and look at the dynamical behaviour of BTC price. Given that the media are flooded with all sorts of reasons for the crash I feel the lack of quantitative data in the public space has to be increased and awareness on dynamical behaviour of BTC augmented.
I start off by displaying the price of BTC in 2013 in Figure 1. As can be seen prior to the rise the price is hovering around 100 USD and then a sharp rise gets initiated towards late 2013 with a peak at 1 155 USD on 4th December 2013. After the peak prices start declining with oscillations through most of the following year with the price finally settling around 250 USD mid 2015. The whole transient period after the rise lasted over a whole year. This sort of response is characteristic of a dynamical system responding to a perturbation, the perturbation here being a sudden rise in price at the end of 2013. Looking backwards we can view 2014 as a transitional period, ending with a change of the steady state price from roughly 100 USD in 2013, to 250 USD per BTC in 2015, via a perturbation that took place in 2013. The settling down of the BTC price implies BTC is a stable system in this case, because it withstood a large perturbation, on the order of 12 magnitudes the price at the start (peak price divided by the initial price).
Figure 1. Bitcoin price prior to and after the 2013 crash.
To explore the transition in more detail, by analogy with physical systems we can calculate the second derivative of the BTC price to explore its acceleration. The analogy is with Newtons second law, according to which a force acting on an object causes it to change its momentum, and acceleration is a measure of the change in velocity due to the applied force. In our scenario, BTC price is equivalent to the position of a physical object and rate of change of price is equivalent to the velocity. The second derivative of BTC price therefore measures the rate of change of the rate of change in BTC price. A somewhat wordy expression but the analogy is clear. In the real world acceleration is the thing you feel when a car speeds up or slows down, or what a child feels when on a swing in the playground.
In Figure 2 I displayed acceleration of the BTC price during the same time interval as in Figure 1. Acceleration is calculated from daily velocity but the weekly moving averages are plotted to remove higher frequency oscillations with the goal of highlighting the relevant dynamics. From the figure we can see the initial positive acceleration (during the initial rise in price) followed by more or less periodic oscillations with decreasing amplitude. This sort of response is characteristic of a damped system going towards equilibrium and verifies quantitatively that BTC is stable in this period. In the figure I have also plotted two exponentially decreasing functions (grey lines) to highlight the decrease in the amplitude of acceleration. A real world analogy would be a swing moved from the bottom stable position to a higher one and left to its own to settle at the bottom once again. On the way to the bottom the swing oscillates and finally settles. The situation with BTC is not quite analogous, however the acceleration shown in Figure 2 bears a quite strong resemblance to what is seen in real world physical oscillators.
Figure 2. Acceleration of Bitcoin price prior to and after the 2013 crash. Weekly moving averages are plotted to smooth out the noise. The grey curves represent the decline in the amplitude of acceleration (not fitted, only plotted for illustrative reasons).
Coming now to the more recent events with the BTC price during 2017 displayed in Figure 3. Here we can immediately spot the slower rise in price in comparison to 2013. The price starts off roughly around a 1 000 USD and builds up all the way to 19 895 on 17th December 2017. We all know what happens afterwards. A rise in price of around 20 times build over a year starts to melt over a month. The characteristic of this rise in comparison to the one in 2013 is that the price slowly started building up prior to the peak, taking almost a year to reach the peak, whereas in 2013 it was far more rapid.
Figure 3. Bitcoin price during 2017.
To observe the dynamical behaviour prior to the rise in price I calculate acceleration during 2017 and display it in Figure 4. As can be seen from the figure initiation of the oscillations can be observed early in 2017. Although small in amplitude the amplitude itself grows and with it price of BTC begins to surge. Finally at the point of the peak a sudden shift in the sign of acceleration occurs. Afterwards the oscillations continue with another change in sign. Coming back now to the analogy of the swing. The situation in 2017 is somewhat different from the one in 2013. Here we can imagine the swing as stationary at the beginning (price of BTC in early 2017) and then we start pushing it in periodic sequences every time it comes back to us. Like this we achieve resonance and the amplitude of the displacement from the bottom position increases over time as it keeps swinging. The analogy is of course not totally correct, but is a good visualisation tool.
Figure 4. Acceleration of Bitcoin price prior to and after the 2018 crash. Weekly moving averages are plotted to smooth out the noise. The grey curves represent the increase in the amplitude of acceleration (not fitted, only plotted for illustrative reasons).
What will follow as a result of this "swinging'' is still early to say. Will the price continue to oscillate or will it settle once more, proving BTC is stable? Time will show. One thing is certain, with this much volatility and the recent drop, the ever watchful eye of professional traders turns to the crypto market. With more professional traders entering the, somewhat speculative crypto market, the game may slightly change. The biggest asset most professional traders bring to the table is discipline and the natural corollary of discipline is of course increased predictability of market behaviour. Whereas normal people use emotions, most professional trades use technical analysis and reason to guide them in their decisions. Will this make BTC price more resilient or not, we can't say.
In conclusion, the crash of 2013 is not very similar to the one in 2017. In 2013 there were no oscillations prior to the rise in price and the oscillations followed after the crash, i.e. they were caused by it. In 2017 oscillations were evident before the crash and we can ask whether the crash itself is caused by them? Is this just an oscillation that will continue to increase its amplitude even further and drive the price even higher during the next phase with positive acceleration?