Bitcoin: Profusion or Diffusion

As we approach year-end, the recent Bitcoin rally means that the main crypto-currencies have just about doubled  since January.   This takes them back to the valuations  last commanded in early 2022 -- prior to the UST depeg, collapse of LUNA and subsequent defaults of 3AC and FTX.  So did something get better or did the market simply roll a six? We’ve undertaken some timeseries analysis to explore this question.

The first interesting insight is that day-to-day Bitcoin price movements exhibit mean reversion.   In other words, when the price moves, it tends to move back in the opposite direction the next day and, to a lesser extent, for a few days after that.  This is also the case for fiat currencies (Chortareas  2009), and it’s assumed that this is because they are ultimately anchored to some notion of purchasing power parity.

Yet such an explanation doesn’t apply in crypto.  So it must be something else, like trader behaviour.  Market-makers push the currency one way and then, in a self-fulfilling way, expect it to swing back.  Not that you’d want to trade on this insight.  Presumably, the fiat effect hasn’t been corrected by the markets, because you could only make money for a few months, until some phase change event, like a Fed policy decision, wiped you out.

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Even after you allow for short-term mean reversion, though, Bitcoin can still roam widely.  The chart above tracks the actual price up to and through 2023 along with a fan chart showing a timeseries forecast from the start of the year.  The actual price is an 85th percentile outcome.   In other words, if Bitcoin’s price was the product of a flat trend with the observed historical volatility, the actual price we’ve seen is unlikely but possible.Another observation is that there’s a parallel short-term link between prices and market volumes.  This link is U-shaped.  Volumes go up whichever way prices move, as people seek to either cut losses or take profits:  The sharper the movement, the bigger the volume increase.  So the price hikes have generated more trading, with both effects increasing brokerage revenues and thereby reducing exchange risk.  This is what we’ve seen.So where will Bitcoin end 2024?  If you believe there’s no underlying trend with this diffusion, then there’s a 50% chance of it remaining between x0.6 to x1.6 of the starting price.  So that’s about  $27k and $68k - both  good numbers if your starting point is 2022.  And if you believe that this year’s performance is being driven by improving fundamentals that will continue into 2024, then prices could be higher still.

_{Chortareas, G. & Kapetanios, G. (2009). Getting PPP Right: Identifying-Mean Reverting Real Exchange Rates in Panels.  Journal of Banking and Finance 33(2), 390-404}