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Bitcoin: its correlations with other assets

Bitcoin: 2013-2020As I write the markets are crashing.  The Dow Jones is down, gold and silver are down, and Bitcoin has been smashed.  I suppose that was something to do with the Full Moon at the beginning of the week, which coincided with a Venus-Saturn opposition.  That makes sense.  Venus is the planet of money, and a hard aspect with Saturn is going to lead to financial losses.

However, I don’t want to get too hung up with astrology.  There are other ways of looking at the world.  And with reference to Bitcoin, we need to consider how it relates to other financial assets.  One way of doing this is with correlation.  When two assets go up one-for-one with each other, they have a perfect correlation, of 1.  But when one goes up and the other goes down, in inverse lock-step, the correlation is -1.  Looking at Bitcoin since April 2013, we can see the following correlations:

Asset correlations

Over the last seven and a half years Bitcoin has a correlation of .87 with the Standand and Poor, which is the most important measure of the US stock market.  As the stock market goes up, so does Bitcoin.  There is also a positive correlation with GLD, the gold ETF, of .56.  The correlation with the Dollar Index is weaker, at .30, and with SLV, the silver ETF, it is slightly negative, at -.18.

I should say that in an ideal world I should have taken the spot prices for silver and gold, rather than their ETF surrogates.  However, they are a pretty good match, even counting for the small shrinkages caused by managment fees.

If we take these correlations at face value, we might argue that Bitcoin is a risk-on asset.  It goes up as the markets go up, and it is not averse to a strong dollar.  Yet correlations can be treacherous, and they can quickly break down.  You can see this in the graph of the 100-day correlation between Bitcoin and the Standard & Poor:

Bitcoin S&P correlation

At the end of 2019 the 100-day correlation was almost -.75, with Bitcoin and the S & P moving in opposite directions.  By early September 2020, the correlation was sky-high, at .86.  This correlation may hold, as it did through 2017, but it might break down.  This is possibly what many Bitcoin bulls are hoping for.  They want Bitcoin to be regarded as a safe-haven asset, that investors will run to in times of crisis.  The broad correlation since 2013 suggests this is not the case, but in the markets correlations can change very quickly.

Another asset that apparently has a big influence on the price of Bitcoin is the Dollar.  Over the last few months Bitcoin has been seen as an anti-Dollar asset, along with gold and silver.  So many investors have been buying Bitcoin out of fear rather than greed.  They see it as a safe-haven asset, that can protect them from inflation and a collapsing dollar.   This has been reflected in a developing negative 100-day correlation between Bitcoin and the Dollar Index:

BTC_DXY 100 day correlation

The 100-day correlation between Bitcoin and the Dollar Index started 2020 at .28, and peaked at the beginning of March at .58.  Then the markets crashed, including Bitcoin.  Everyone took refuge in the dollar, and the inverse correlation was established.  Then as Bitcoin recovered from its lows the Dollar started falling.  The fall continued, with investors worrying that the Federal Reserve was going to print the Dollar into oblivion.

And here’s Bitcoin’s correlation with the gold ETF:

BTC-GLD correlation

Since the beginning of 2019 the correlation has been increasing, perhaps as people started seeing Bitcoin as digital gold.  With the silver ETF, it is only in 2020 that the two assets have really connected, and by September 2 the correlation was .88:

BTC-SLV 100-day correlation

We now move to a more complex analysis, namely multiple regression.  This involves looking at how a range of assets impact Bitcoin.  The predictor assets are the Standard and Poor, the Dollar Index and the gold and silver ETFs.  Here’s the standardized regression table:

BTC regression (standardized)

All four predictor variables have a significant impact on Bitcoin, though the absolute betas (see the estimate column) are particularly high for the Standard and Poor and the Dollar Index.  The overall model accounts for 81% of the variance in the Bitcoin price.  It all seems straighforward, doesn’t it?

It is true that regressions and correlations are part of the standard fare of financial analysis.  They are a good way of proving a point, and they are difficult to argue with.  Unfortuntely, there is a problem.  One of the assumptions of regression and correlation is that every data point is independent, and doesn’t influence other data points.  If I randomly select 20 American school children, and correlate their math and English scores, I can be reasonably confident that the scores of one child are not influencing another child’s.  However, when you are dealing with asset prices there is a high level of dependence.  The price of Bitcoin today is going to have an influence on what it is tomorrow.  And if you use regression to predict the price of bitcoin, the difference between the predicted price and the actual price can be similar for days and weeks at a time.

I can take the regression model of Bitcoin, using the four predictors, and compare the predicted price with the error.  If the data points are independent, rather than feeding on each other, one would expect the graph to be an unpatterned mess.  Instead we get this:

BTC residuals

It looks rather like a witch’s hat.  Patterns all over the place, and a clear sign that there is something wrong with the regression. We can visualize these residuals in another way, using time on the x axis:

BTC residuals, time on the x axis.

For a linear regression the residuals, or the errors, should not be behaving like this, and we therefore need to make an adustment, to deal with the autocorrelation of the errors.  So we’ll use the Cochrane-Orcutt adjustment.  This gives us the following standardized regression table:

BTC, Cochrane-Orcutt regression

In the unadjusted regression 81% of the variance is explained by the Standard and Poor, the Dollar, gold and silver.  After we adjust for autocorrelation, it crashes to 3%.  Yes, the Standard and Poor and gold have a statistically signficant impact on the price of Bitcoin, but the effect is tiny.  Probably not even worth bothering with.  Yes, there will be times when particular assets move with or against Bitcoin, but that doesn’t help when it comes to understanding what actually moves it.

Having said that, correlations come and go, and I have been looking at the time period from 2013 onwards.  If we narrow down the  data, to this year, 2020, we get a stronger set of relationships.  Here is the Cochrane-Orcutt table for 2020:

BTC Cochrane-Orcutt, 2020

For this model, over 37% of the variance is explained, and again we see that the Standard and Poor and gold are the factors with the influence.  The Dollar Index and silver play no signficant role.  You might nonetheless think that in 2020 the Dollar Index affected the Standard and Poor, but once you have adjusted for autocorrelation there is no statistically signficant relationship.

So what does this exercise tell us?  The Standard and Poor and gold have a small but signficant impact on Bitcoin.  The Dollar Index has no impact.  And even if you see a correlation between two assets, it can disappear in the blink of an eye.  In terms of forecasting the Bitcoin price, you might as well use astrology, and I am confident that the Jupiter-Saturn conjunct on December 21 2020  will propel Bitcoin to new, six-figure highs in the years to come.

{ 3 comments… add one }
  • John Mansfield September 6, 2020, 11:19 am

    Archie, can I take it you have a healthy and profitable portfolio of shares?
    You certainly seem very thorough in your analysis.
    Thanks for the posting.

    • Archie Dunlop September 6, 2020, 5:40 pm


      Thanks for reading my article. I didn’t think anyone would! I was wondering about what correlated with Bitcoin, and this blog was the only place to write down my thoughts. Unfortunately I have the Sun in the Second House – I am too concerned about money to think rationally about it, a trait which has undermined my investment performance.

  • Alex September 7, 2020, 12:02 pm

    Yes, you might make an historical correlation analysis between Saturn-Jupiter angular separation and the 2 key components of SP500=EPS x P/E
    Sometimes the SP500 is driven by EPS growth, other times by multiple expansion/contraction (P/E) or by both. Can ask raw data at Yardeni.com for free, I guess. They are very nice.

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