Quantifying bitcoin patterns with PCA

We have seen a meaningful change in the common factors driving bitcoin performance in the short term, based on a principal component analysis (PCA) framework

May 10, 2023

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Key takeaways

  • In our view, bitcoin’s performance has been more sensitive to measures of endogenous supply and demand between January and April 2023, a shift from the preceding four months.
  • How this informs bitcoin behavior in the short-term is less clear considering the significant uncertainty around the credit situation in US banks and the standoff over the US debt ceiling.

Written by

  • David Duong, CFA, Head of Institutional Research


Our principal component analysis (PCA) framework looks at mutually orthogonal, linear combinations of bitcoin-related factors across four-month periods between early 2022 and 2023. Bitcoin performance year-to-date has been highly sensitive to the first principal component (PC1) represented by our results, which we interpret as a measure of the token’s endogenous supply and demand dynamics. Indeed, at the moment, PC1 is most positively associated with gold prices and average miner difficulty – a notable shift from the previous four months where PC1 was negatively associated with gold and most positively associated with US dollar movements. 

That prior inverse relationship may have been associated with the idiosyncratic deleveraging events that took place in the crypto space last year, while gold prices benefited from central bank demand. Consequently, the US regional banking turmoil in 1Q23 has helped realign gold and bitcoin as alternatives to the points of failure witnessed in the existing financial system. This has been evident in the rising correlation between the daily returns of these two assets.

But what this means for bitcoin’s performance in the next few months may not be clearcut. We see two key risks in the short-term – the credit situation in US regional banks and the impasse on the US debt ceiling. Although these issues should help reinforce bitcoin’s “store of value” fundamentals, we believe the high degree of uncertainty around potential outcomes complicates the outlook for digital assets and supports our preference for institutional investors to hedge their exposure via options.

PCA: Data sensitivities

We have seen a meaningful change in the common factors driving bitcoin performance in the short term, based on a principal component analysis (PCA) framework. Specifically, employing PCA provides an orthogonal representation of our standardized (mean-centered) dataset that includes US equities, gold, the (multilateral) US dollar index, bitcoin transaction volumes, bitcoin sentiment, average mining difficulty, miner fees, and bitcoin real volumes for the timespan between January and April 2023.

Over this period, daily bitcoin returns had a high 75.0% sensitivity to the first principal component (PC1). This is a noticeable change from the previous four months (September to December 2022) when a linear regression between bitcoin returns and PC1 reflected an r-squared of 59.7%. During the four months prior to that (May to August 2022), the relationship between bitcoin and PC1 reflected an r-squared of only 26.6%. (Note that PC1 currently explains 35.7% of the variance in our data, while the proportion of variance explained goes up to 75.2% if we include the first three principal components. The explained variance ratios in the previous periods were comparable.)

We partitioned the data into four-month increments not only for comparison purposes, but because the results suggest there were notable regime changes. A scatter plot of the first and second principal components compiled in 2022, for example (see chart 1), seems to show that the underlying structure of the data indicates three subgroupings of observations, divided by the periods January to April 2022, May to August 2022, and September to December 2022.

Chart 1. PCA results for factors driving bitcoin performance

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If bitcoin prices are sensitive to changes in the combination of variables that make up the first principal component, what then is being captured by the first principal component?

The loadings of the original variables on the first principal component suggests that between January and April 2023, it has been most strongly and positively associated with gold followed by bitcoin’s average mining difficulty. Comparatively, the highest absolute values of loadings on PC1 – from May to August 2022 and September to December 2022 – indicate it was most strongly associated with US dollar movements and gold. But during these periods, it was negatively associated with gold and positively associated with the US dollar. That’s an important shift. In our view, the first principal component’s current association with gold and mining difficulty suggests PC1 is a measure of the impact of endogenous supply and demand dynamics on bitcoin prices. 

There may be several reasons for that.

First, the inverse relationship between PC1 and gold between May and December 2022 may have had to do with the idiosyncratic deleveraging events taking place in the crypto space. These were concentrated in May, June, and November 2022. (Comparatively, gold was bid due to the unprecedented amount of central bank demand last year.) Those risk events may also explain why the second principal component (PC2) was most heavily (and positively) associated with bitcoin sentiment indicators like Tweet (Twitter) volumes during those 8 months in 2022. In contrast, between January and April 2023, PC2 was most highly and positively related to bitcoin transaction fees and volumes with an explained variance ratio of 25.7%.

Second, we think the current strength and positive direction between PC1 and gold reflects an alignment of assets that exist as alternatives to the points of failure witnessed among US regional banks. The scarcity value that informs bitcoin’s fundamental properties may also be evident in the relationship between PC1 and average mining difficulty, which is adjusted every 2016 blocks (around 2 weeks) based on the total computing power on the network. Rising difficulty levels this year have led to a decrease in the rate of new bitcoin supply entering the market, coupled with more bitcoin locked up in government and self-custody. This reinforces bitcoin’s “store of value” properties by constraining supply versus available demand.

Bitcoin’s “store of value” properties may also be evident by looking at the correlation between daily gold and bitcoin prices. The positive relationship between these two variables has increased year-to-date, rising from a coefficient of 0.18 at the start of the year to 0.40 as of end-April based on a 40-day rolling window. See chart 2.

Chart 2: Rolling correlation between daily bitcoin vs gold returns

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Outlook amid an uneasy background

How this informs bitcoin’s performance in the next few months may be trickier. We see two key sources of macroeconomic risk in the short-term: (1) the credit situation in US regional banks and (2) the standoff on the US debt ceiling.

Regarding the former, it’s difficult to assess the current situation with US regional banks and the potential risk of further contagion. After the failures of Silicon Valley Bank (SVB) and Signature Bank in March, First Republic Bank was sold to JP Morgan Chase on May 1 while PacWest Bancorp has said it is exploring strategic options. Many of these banks were sitting on big commercial and real estate lending portfolios, and it’s not clear how making those part of the assets at larger banks will affect risk appetite. Regardless, we believe a credit crunch is already underway. Since early March, around US$416B has moved into money market funds, accelerating a trend that has been ongoing since 4Q22 and acting as a constraint on lending.

Chart 3. Increasing constraints on bank lending

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Meanwhile, a prolonged stalemate on the US debt ceiling could create a disorderly situation for all assets. The US Treasury Department believes the “X date” to raise the debt limit is sometime in early June, and previous showdowns have come down to the final hours of the deadline. Complicating matters is that in the unlikely event of a default, it’s possible the Federal Reserve could stop its quantitative tightening program and enact policies that increase liquidity in the market - potentially benefiting cryptocurrencies. In the case of a resolution, we also need to think about the impact that replenishing the Treasury General Account (TGA) balance could have on drawing liquidity from the market.

Bitcoin’s behavior after the collapse of SVB suggests it served its function well as a hedge against financial instability, so we think many market players see bullish short-term prospects for bitcoin in light of these two risks. As an analogue, gold rallied by 29% between early January 2011 and end-August 2011 during the 2011 US debt ceiling crisis, when ratings agency S&P downgraded US Treasury bonds from AAA to AA+. At that time, bitcoin was not as ubiquitous as it is today, so it’s possible bitcoin could pick up some market share in the current standoff. On the other hand, gold weakened by 24% during the debt ceiling crisis in 2013, so there’s no guarantee. It’s also difficult to disentangle gold’s 2013 performance from the Fed’s tapering of quantitative easing around the same time.

Ultimately, how digital assets perform amid the current backdrop is anyone’s guess, as we expect countervailing factors may offset some of the positives. First, we have already seen a healthy amount of bitcoin appreciation post-SVB, absorbing the flows from a disenchanted depositor base. Second, we think that we could see more tactical rather than fundamental positioning into these event risks. Still, even if the extent of upside potential is unclear, we think the downside may be limited. Given the extent of the uncertainty, we believe bitcoin options may be the better way for institutional investors to hedge themselves as implied volatility levels have come down in recent weeks.

Technicals and on-chain data

In April, a moderation in on-chain activity factored into bitcoin’s 1.3% price decline, as evidenced by the slower pace of transaction fee growth. Fees ended the month at 1.5 standard deviations above the 12m average compared to a sigma of 2.5 at the end of March. That said, the minting of fungible BRC-20 tokens has recently driven fees on the network in early May to a whopping 5.6 standard deviations over the 12m average. See chart 4.

Chart 4. Transaction fees on Bitcoin and Ethereum networks (rolling z-score)

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Transaction fees on Ethereum also picked up in the second half of April (and into May) due to a memecoin phenomenon after hewing close to the 12m average in March. That said, the magnitude of the fees increase in standard deviation terms (see table 1) was more muted than what was observed on the bitcoin network. The higher fees on Ethereum (which are burned as part of the EIP-1559 burn mechanism) were however reflected in a higher deflation rate in April of 1.67% MoM compared to an average deflation rate of 0.01% over the previous five months. If we annualized the rate of supply growth over the last six months, that would amount to a 3.47% YoY decline in available ETH. On the other hand, the number of transactions per active unique addresses actually declined by 4.2% last month.

Table 1. On-chain indicators for networks by market cap (April 2023)

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