Bitcoin and Volatility, Part 3

Yesterday Russel Rhoads wrote an article comparing recent VIX and Bitcoin volatility. I am reposing a table that summarizes his findings:

But even though daily volatility of the two is at about the same level, it is a different type of volatility. While VIX moves quite a lot from day to day, over the long periods of time it stays in a relatively narrow range. Bitcoin on the other hand is volatility over the short term, and over the long term. 

To illustrate the difference I will create a plot of term structure of volatility - how historical volatility evolves as a function of interval. So the first point in the plot will be annualized volatility calculated from one day returns, the second point will be from 2 day returns, etc. 

The first chart pictures the term structure of VIX's historical volatility. What we see is that short-term volatility is high, and long-term volatility is low. This makes sense because this is what we actually observe from the time series, they appear to be mean-reverting (we're not saying necessarily that mean-reversion is the driving process), just that positive moves are likely to be followed by more negative moves, and negative moves are likely to be followed by more positive moves, keeping the index in a range.
The second chart is one for BTC USD rate I downloaded from Coindesk. What we see in the chart is just the opposite - volatility is increasing as function of time interval. Such behavior is common for trending time series, where positive moves are likely to be followed by more positive moves, and negative moves are likely to be followed by more negative moves.

So, if we were to extrapolate the historical behavior of these time series, and extend the charts beyond 100 trading days, we can make the following (and I'm sure quite imprecise) predictions: in a year from now 1 std move in VIX will be 30% ( 9.7-17.7 ), while 1 std move in BTC will be 190% ( 1,200-53,000 )

These forecasts are not serious forecasts, they just illustrate what some of the patterns we observe in the time series imply about future events. 

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