Because of the quality of data that can be derived from cryptocurrency markets, Spearman’s rank correlation coefficient or Spearman’s ρ (rho) is used as a non-parametric measure of rank correlation (statistical dependence between the ranking of two variables) because it assesses how well the relationship between two variables can be described using a monotonic function.
The selection of Spearman’s ρ is deliberate because much of the volatility data that can be gleaned from Bitcoin’s price movements in the bulk of markets is tied to two opaque datasets. First, the bulk of Bitcoin is traded in Tether (USDT), the dollar-based stablecoin, for which allegations of Bitcoin price manipulation have been made. Second, as trade volumes from a variety of cryptocurrency exchanges are also alleged to be heavily manipulated, filtering the data for the purposes of calculating correlation is challenging at best and impossible at worst.
Hence, instead of trying to layer an opaque variable – volatility – to correlations between gold and Bitcoin, it would be more helpful to assess the monotonic relationship (whether linear or not) between the two asset classes.
If there are no repeated data values, a perfect Spearman correlation of +1 or -1 occurs when each of the variables is a perfect monotone function of the other.
Intuitively, Spearman’s ρ will be high when observations have a similar (or identical for a correlation of 1) rank between the two variables and low rank when observations have a dissimilar (or fully opposed for a correlation of -1) rank between the two variables.
Spearman’s ρ was also selected because it is appropriate for use for both continuous and discrete ordinal variables. And given that Bitcoin is traded 24/7, whereas gold is not, Spearman’s ρ, represents an acceptable compromise for the formulation of a general correlation coefficient between the two asset classes.
For brevity, Spearman’s ρ or the Spearman correlation coefficient can be represented as follows for a sample size of n, the n raw scores Xi, Yi are converted to ranks rgXi, rgYi and rs, computed as follows:
where,
In this analysis, I have included the data set of the time series covering the period from October 3, 2013 to as late data as is available for the purposes of analysis, February 18, 2020. The selected time series covers several market fluctuations, including the sharp fall in Bitcoin’s price after the hack of the world’s first Bitcoin exchange, Mt.Gox as well as other periods of economic stress.
The assets utilised for this analysis are gold prices in USD per oz, S&P500 Index and Bitcoin. For conventional assets, the closing price or index points of each trading day is used from Datastream with a GMT timestamp. For Bitcoin, the data is an average of data from both Coindesk.com and CoinMarketCap.com, which themselves use weighted averages of Bitcoin price data from various sources, also with a GMT timestamp.
Unlike conventional assets, Bitcoin is traded non-stop and in order to synchronise the datasets, the hours for which gold and the S&P500 are not trading, the last done price of the asset is taken as a datapoint.
Applying the Spearman Correlation Coefficient to the data produces the chart in Figure 1, which demonstrates a weak correlation between Bitcoin and Gold. Events in time did however make the two assets seem synchronous, but specific events do not make a trend and the general price patterns of both gold and Bitcoin offer little by way of correlation.
Historical correlation data between gold and Bitcoin has vacillated between -0.15 and +0.25 which is at the weaker end of the spectrum for correlation, with -1 being zero correlation and +1 representing perfect correlation.
Figure 1: Spearman Correlation Coefficient for Bitcoin vs Gold for the period 3 October 2013 to 18 February 2020
And while recent trends in gold and Bitcoin prices have suggested a short-term correlation between the two asset classes, the immediacy of the data does not make a long-term trend.
Using a 60-day correlation coefficient, data from Bloomberg suggests that beginning this year, the two 60-day correlation coefficient of the two assets had flipped from negative to positive above the trailing one-year daily average (Figure 2).
Figure 2: Rolling 60-day correlation coefficient between Bitcoin and Gold. (Source: Bloomberg)
Using a rolling 60-day correlation coefficient, what is observed is that while there is a positive correlation between gold and Bitcoin, that correlation is moderate at best.
Over a longer data series, Spearman’s ρ demonstrates that Bitcoin’s correlation with gold has been minimal, often trending towards 0 at regular intervals.
One observation is that while there may at times be short-term correlations between Bitcoin and gold, over the long run, such correlations are statistically insignificant.
To see what a short-term correlation between Bitcoin and gold looks like, consider this graph provided by Bloomberg after Iran’s missile strike on U.S. assets in Iraq, in retaliation for a U.S. drone strike on Iran’s General Qassem Soleimani, in Figure 3.
Figure 3: Bitcoin and Gold prices after the Iran missile strike (Source: Bloomberg)
Whilst not quite moving in lockstep, the 24-hour tracing of the price of Bitcoin and gold were certainly more than inspired.
