Bitcoin and covariance

by on February 6, 2018 at 11:19 am in Uncategorized | Permalink

Bitcoin and stocks bottomed at almost exactly the same moment.  This is bad for Bitcoin.  Part of Bitcoin’s appeal is that it is weird, and perhaps does not covary with  standard financial assets in traditional ways.  But at least yesterday it did, and that should be a force pushing Bitcoin lower.

Addendum from DB in the comments:

Matt Levine from yesterday: “Bloomberg tells me that Bitcoin’s daily correlation with the S&P 500 Index was 0.047 in 2017, -0.049 in 2016, 0.07 in 2015 and -0.081 in 2014. That is about as uncorrelated an asset as you could ask for — and a lot of Bitcoin buyers were asking for uncorrelated assets. So far in 2018 the correlation is 0.286. Still pretty uncorrelated! But … less so. When Bitcoin was a weird alternate-currency dream of anarchists, there was no reason for it to be correlated with stocks. When it is just an asset class that regular people trade, buying when they feel confident and selling when they feel nervous, that correlation ticks up.”

1 Anonymous February 6, 2018 at 11:28 am

More evidence, if we needed it, that we live in a simulation.


2 DB February 6, 2018 at 11:40 am

Matt Levine from yesterday:
“Bloomberg tells me that Bitcoin’s daily correlation with the S&P 500 Index was 0.047 in 2017, -0.049 in 2016, 0.07 in 2015 and -0.081 in 2014. That is about as uncorrelated an asset as you could ask for — and a lot of Bitcoin buyers were asking for uncorrelated assets. So far in 2018 the correlation is 0.286. Still pretty uncorrelated! But … less so. When Bitcoin was a weird alternate-currency dream of anarchists, there was no reason for it to be correlated with stocks. When it is just an asset class that regular people trade, buying when they feel confident and selling when they feel nervous, that correlation ticks up.”


3 Brian Donohue February 6, 2018 at 11:45 am

Correlations are not constant over time, as your data suggest. There is a lot of evidence from the 2008 financial crisis that, during a crisis, correlations among diverse risky assets (not strictly hedging assets) move towards 1. This is of course unsettling given the whole point of diversification.


4 Anon. February 6, 2018 at 12:05 pm

This is actually an artifact of increased volatility. Here’s a good primer on the math:


5 Brian Donohue February 6, 2018 at 12:32 pm

Artifact or not, it’s a problem.


6 Ray Lopez February 6, 2018 at 1:04 pm

@Anon – nice cite, thanks, note the ignorant BD still is fighting the facts. Another way of looking at this is to note here: and how the standard deviations of sx and sy form a asymptotic limit. At first glance it seems that as sx, sy -> infinity, the correlation should go to zero, not one, but the E (the expected value operator) makes it so in fact, via the inverse, the limit is one rather than zero (I trust the math, from your cite, even though my eyes tell me at first glance that it’s zero).

Another example of people being fooled by math (and randomness) though my intuition tells me that perhaps the correlations jumps up due to people treating all things except cash as ‘risky’, which is probably also a factor above and beyond the math.


7 WC Varones February 6, 2018 at 11:42 am

One observation does not a correlation make.


8 Ray Lopez February 6, 2018 at 11:46 am

Still,correlation of 0.286 is pretty good (pretty uncorrelated).


9 Fred C February 6, 2018 at 11:46 am

An interesting note, a Bitcoin now costs less to buy than to mine in the United States. If the market is in a correction phase, might the same be happening with BTC? I expect, in the best case, that Bitcoin will bottom out somewhere near its average mining costs. If it falls significantly lower than mining costs, will we see an exodus from Bitcoin to other, potentially more secure, cryptocurrencies?


10 Ray Lopez February 6, 2018 at 11:52 am

I think this is a fallacy, because the same thing has been said about oil, gold, silver, diamonds, etc: that the floor to their price is average mining costs. The reason this is not true is that miners go out of business, and new ones come into business, depending on the expected future cost of the product being mined, not the average sunk costs.


11 Judah Benjamin Hur February 6, 2018 at 3:57 pm

Yes, but mining costs, even average costs, are pretty important in determining value. For example, if fracking costs hadn’t come down so much, the Saudi strategy would have worked and we could have confidently predicted a durable increase in oil prices. Likewise, the ability to drill massive quantities at a higher prices can serve as somewhat of a ceiling.

Of course, unlike the other examples, Bitcoin has no intrinsic value and could easily fall to zero, regardless of mining costs. Imagine you had an option. You could have 1 million dollars worth of gold or 10 million in Bitcoin. The only condition is that you can’t sell for 50 years. Would anyone take Bitcoin? Without a doubt, I’d want to leave my kids the gold. I’d probably take 1M in gold over 1 billion in Bitcoin. The odds of it being a long-term store of value are ridiculously small (though perhaps more than 1/1000 so I’d have to think about it).


12 Ray Lopez February 7, 2018 at 3:20 am

Good points made, but your average cost goes to the supply side, not the demand. Just because there’s lots of supply doesn’t mean that demand will increase unless there’s intrinsic value to the stuff supplied. As you say, demand for Bitcoin does not depend on intrinsic value (nor for that matter for gold that much, though it does have jewelry and dental value). I too would chose AU over BTC, BTW.


13 Bjartur February 6, 2018 at 11:47 am

That’s when you look at a non-randomly selected moment. How’s the correlation when you look at the last year, or the last 5 years? If you just look at a moment they are also highly (inversely) correlated with traffic at the MSP airport, but I wouldn’t count on that correlation holding up for too long.


14 Bryan Willman February 6, 2018 at 11:57 am

In world in which very many trades involve somehow shorting A to go long B, where A and B may have nothing else to do with each other, what does it mean to be uncorrelated? If some large pool of money goes long shoe string futures and funds that bet by shorting tickets on Lady Gaga concerts, then shoe strings and Lady Gaga concerts will become correlated in the markets, even if they are utterly uncorrelated in real life.

So people short S&P 500 index and use the funds to go long bitcoin. They are now correlated, at least in the market.


15 Pshrnk February 6, 2018 at 1:38 pm
16 Axa February 6, 2018 at 11:58 am

This ia could be reat natural experiment for bitcoin. CCanit become a safe currency or behave like an emerging economy currency in the next financial crisis ?


17 clockwork_prior February 6, 2018 at 12:06 pm


And how is that eurogeddon fascination doing these days, by the way?


18 Ray Lopez February 6, 2018 at 12:34 pm

Fellow European c_p, I don’t think Eurogeddon is over, just delayed. My relatives keep telling me to pull the money we have in Greek banks even though I tell them the crisis is over, for now. They may be right…

Bonus trivia: my going senile Greek uncle, even before he went senile, did not trust Swiss banks over Greek ones. And he was rich. Talk about ‘home bias’. He ended up putting his Greek bank money under his mattress and the servants got a good portion of it before I rescued it.


19 Stéphane February 6, 2018 at 12:24 pm

For perspective, at the same time as stock markets went down, China declared to ban all advertisements concerning Crypto and blocking all (foreign, domestic were already banned) exchanges using it’s firewall. There is thus for once a reasonably immediate cause for the tanking price; a cause that is not related to a bottoming stock market.

The apparent correlation in 2018 might thus just be a coincidence. We’ll see 🙂

But many thanks for this short post @Tyler, I was wondering the exact same thing this morning (“Damn, shouldn’t BTC go up with such a stock market!”) and it’s great to hear your perspective.


20 Doug February 6, 2018 at 12:33 pm

The positive correlation is very likely a spurious statistical artifact.

There’s only been about 30 trading days in 2018. The standard error of correlation measured on i.i.d. samples is (1-corr^2) / sqrt(N-2).

0.28 correlation is only 1.5 standard errors away from the null hypothesis of zero correlation. We can’t even reject for p<0.05, let alone anything more serious.


21 Potato February 6, 2018 at 6:19 pm

There’s an argument to be made that with rising interest rates, the risk adjusted difference in expected returns is rising between bonds and riskier assets (decreasing equity premium and bitcoin premium?).

This would explain a correlation, if not a covariance.

Another pointless just so explanation: rising interest rates causes uncertainty about the future path of risk adjusted difference in expected returns. Also, increasing volatility in equity causes people to increase their demand for less risky assets across the board, for behavioral finance reasons.

Just throwing possibilities out there.


22 John February 6, 2018 at 12:49 pm

What interest me is where does all the money being knocked off stock quotations and cryptocurrency quotations actually go?

Surely if people sell stocks and thereby drive the price down, they must put the money somewhere. In 2000 I seem to recall that it was to pay capital gains tax on trades in the previous year’s booming markets. This time President Trump cut taxes, maybe with this in mind.

Or are most people sitting tight and ignoring the prices being quoted?


23 Borjigid February 6, 2018 at 3:15 pm

For the most part, nowhere.

If there are 100 shares of stock A outstanding, and there is only one trade at a price of $10 today, we say the market cap for stock A is $1000.

If tomorrow one share of stock A trades for $8, we say the market cap for stock A has dropped $200 to $800, even though only $8 has changed hands.


24 Potato February 6, 2018 at 7:57 pm

Perhaps unintentionally, you’ve made a great point about illiquid assets and poorly functioning financial markets.

In well functioning financial markets with liquid assets, your point is not only moot but incredibly misleading.


25 liberalarts February 7, 2018 at 5:25 am

So instead suppose that there are many trades at $8 instead of $10, because today people don’t feel that stock A is worth $10 like they did yesterday. Lots of people trade their stock A for cash and an equal number of people trade their cash for stock A. There is no more cash and no less stock, so the money in stock A hasn’t gone anywhere at all. If there is an asset that people suddenly feel better about, then its price price will be bid up, but that is not required for stock A to go down.


26 Lumifer February 6, 2018 at 1:42 pm

No one cares about assets that are merely uncorrelated with the stock market. Buying lottery tickets produces returns entirely uncorrelated with the market, but so what?

What everyone wants is an asset with positive drift (= significant positive expected returns) that is uncorrelated with the stock market.


27 Borjigid February 6, 2018 at 3:26 pm

If you take a portfolio perspective, merely uncorrelated is still valuable.


28 A B February 6, 2018 at 5:29 pm

Suppose I had two variables and I knew that they would never bottom at the same time. Doesn’t that suggest a non-zero correlation?


29 John Pinkerton February 6, 2018 at 7:14 pm

By what measure is .286 “pretty uncorrelated”? Given the much higher standard deviation of bitcoin compared to the S&P 500, by my calculations at that correlation you’d be getting more stock market exposure with bitcoin than with an index fund. Bitcoin would provide no diversification and the minimum variance portfolio would have zero bitcoin. Accordingly, I tend to go with Doug’s conclusion that the correlation is not that high.


30 David Barker February 6, 2018 at 11:21 pm

Maybe noise traders take over multiple markets at once when something gets them going. In normal times markets A and B would be uncorrelated, but when noise traders move in A and B become correlated. Prosperity and political euphoria might have driven noise traders into both stocks and bitcoin, with self-reinforcing panic hitting last week.


31 IVV February 7, 2018 at 10:17 am

Is there any asset class that isn’t actually covariant? It has seemed to be for the past couple decades (see dotcom bust, commodity pump and dump during the financial meltdown) that all asset categories are far more subject to large players getting nervous and desperately seeking returns than any underlying profitability fundamentals.

Those fundamentals are more important when there isn’t panic, but in bubble/panic times, the effect of profitability fundamentals is swamped by emotion and return-chasing.


32 Johan Ryos February 7, 2018 at 9:57 pm

I think with Bitcoin or even Cryptos in general, it got to be taken that it will move on these lines only. You will either see people in panic mode or in over-confidence mode. There is just no middle ground for it, so that’s why it is not exactly for faint-hearted people. We must keep our options open; it’s why I go for dividing my investment across carefully. Bace is amongst the hottest deal right now with the dual-service. They are an upcoming Exchange with their token as well. The Pre-ICO is to begin from 26th February with 20% bonus; it’s a highly worthy deal!


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