Correlations, The Long and Short Of It

July 2023 Commentary

With a spate of bitcoin spot ETF application announcements, a summary judgement that ruled that XRP is not an investment contract, a July US Fed decision that raised short term rates by only 25 bps to the 5.25% to 5.50% range, and a declining bitcoin to US equity correlation, the digital assets market is in a state of – uneasy nervousness? In what feels like a Wile E. Coyote moment when he finally catches the Road Runner, the industry got parts of what it wanted, but the prize is not what it appears to be.

Digging below the surface headlines reveal that each of these developments are quite nuanced. The Fed’s quarter point raise does not presage an end to the liquidity tightening. Inflation risks, oil price shocks, and supply chain uncertainties are not yet behind us. There is no clear indication as to what the approval timeline will be before one or a few of the institutional spot bitcoin ETFs start to trade or how much demand will actually follow. The XRP summary judgement is but one step in a long process towards proper digital assets legislation and regulatory clarity. Similarly, the declining correlation is but an artifact of how it is calculated and it’s worth diving into some of these details.

Which Correlation – Your Choices Matter

Within the financial markets, correlation measures the degree of co-movement between two disparate series around their respective means [1]. It’s a metric that ranges from +1.0 to -1.0. A value of +1 indicates a high degree of co-movement in the same direction; 0 indicates no co-movement; and a -1 indicates a high degree of co-movement but in the opposite direction. Correlation does not indicate causation. There are other metrics for that.

Correlation, if measured and used correctly, can be a useful tool. It may be able to indicate the degree of diversification from adding one new asset class to a portfolio. It may demonstrate how two assets may “normally” move in relation to each other, and any convergence or divergence of that movement may indicate the presence of a profitable trading opportunity.

Correlations are easy to calculate and perhaps because of this, it is also easy to misinterpret or bend the interpretation. Calculating the correlation between two return series of two assets requires simply inputting those two series into an Excel formula/python function and out comes your answer. This simple exercise belies the complex choices that one needs to implicitly or explicitly make.

Let’s say we want to examine how correlated cryptoassets are to traditional equities. The first question to answer is – what for? Finding the correlation for making long-term portfolio allocation decisions is different than using it to make a short-term hedging decision. For the sake of this discussion, let’s just say, we want to learn more about the shifts in correlations. In this simple use case, the next questions to ask are – which assets do I select to represent the cryptoassets and equities, and how much data do I need to grab?

Bitcoin represents less than half of the market capitalization of all the available tokens currently being traded, and is certainly not representative of the Layer 1s, DApps, and other projects. Yet it is ubiquitously known, so we’ll just proceed with BTC. As for equities, should we care about global equities or just the US? Many correlation analyses use the S&P 500, consisting of many of the largest companies in the US market. Given digital assets’ technological foundation and growth characteristics, we’ll choose to use the Nasdaq Composite for this exercise, dominated by more of the US listed technology stocks.

The question of how much data to grab is a bit thornier. Consider the chart below comparing the daily prices of the Nasdaq Composite Index to bitcoin prices over a 5-year period from August 2018 to July 2023. Prices are plotted on a log scale to allow for an easier visualization of the variations in the two series.

At the heart of our analysis, we are trying to maximize our information to noise ratio. That is, the data is noisy. Market price data is the combination of the efforts of several agents trading for their own respective utilities as well as the data provider aggregating the data using their proprietary methodology. Our analysis is to extract information from this data that is useful for us.

Source: CoinGecko, Yahoo Finance, Firinne Capital

Using the entire sample of data to calculate a correlation number is certainly feasible but we would miss out on the information that the variability is trying to tell us. To take advantage of this, we need to consider two parameters – the estimation window and the sampling frequency. With the estimation window, we are choosing a lens with which we want to view the data in a way that is the most pertinent to us. It is a tradeoff. A long window may provide insight into the long-term behaviour of the asset but may not be relevant as prices would’ve evolved over several boom-bust cycles and the blockchain developments would’ve iterated over several phases (e.g., rise of alt-L1s, DeFi, NFTs). Selecting a short estimation window will allow the estimated metrics to be more sensitive to recent developments but may introduce undesired variability into the estimation. For more complex analysis, if there are too many variables to estimate with too few data points, one cannot view the results with [statistical] confidence.

The choice of the sampling frequency is equally important. Cryptoasset prices trade constantly, 24/7, and prices are being updated across several venues every sub-second. By looking at daily data, we are implicitly opting to sample our data daily at a certain point in time. We very well could’ve looked at prices at an intraday day level, weekly, monthly or even quarterly. High frequency traders certainly would care to look at intraday prices and furthermore, would be specific as to what exchanges they are sourcing their data from. On the other end of the spectrum, consider comparing cryptoasset prices to a venture or private equity portfolio that offers little to no liquidity and is valued only quarterly or monthly at best. Comparing daily prices makes no sense, and even aggregating into monthly or quarterly returns is a dubious effort given the periodic valuation process for these alternative investments.

Finally, after all this data collection and calculation, we need to judge how useful this metric is. What can we infer about the future and how good is that inference for? Intuitively, it doesn’t make sense to look at three months of data and infer an outcome for the next 12 months. Similarly, it also doesn’t make sense to focus on the last 5 years of data to foretell the next week. We need to be reasonable about our inference window.

Our exercise here is far easier. We are looking to analyze the correlation between bitcoin and the Nasdaq composite using a 5-year data set of daily returns. We’ll look at how different estimation windows and sampling frequencies provide us with different results, and what those results may mean over the next three to 12 months.

Correlations – There’s Not Just One Number

For our exercise, we calculate correlations of the daily price returns of the Nasdaq Composite and bitcoin, using only the business days for which there is a price for the two series. That is, our sampling frequency is one business day. We use estimation windows of 63, 125, and 250 business days, roughly equivalent to 3-, 6-, and 12-month windows. We then roll the estimation window forward to show how the correlations evolve over time as old return data fall out and new return data come into the estimation window. To further demonstrate the impact of the choice of parameters on the calculated outcomes, we also ran correlations using calendar month returns (i.e., monthly sampling) with a 12-month estimation window.

The diagram below stacks two charts on top of each other - the price movement of these two series, followed by several rolling correlation calculations using different parameters. Changes to just a couple of parameters provide very different outcomes and can lead to vastly different conclusions.

Source: CoinGecko, Yahoo Finance, Firinne Capital

One of the first takeaways is the variability of the correlation results, even for the same set of parameters. Over this five-year period, rolling correlations vary from a low of -0.4 to a high of +0.7. Nothing suggests that this range is tightening or expanding. Furthermore, trends can easily reverse, due to shocks to the market.

Correlations measured with shorter estimation windows and higher sampling frequencies (the purple and tan lines above) are going to be much more responsive to market shocks and changes than those measured with longer windows and sampled at a lower frequency (the green and grey lines above). For example, when the markets dropped in March-2020 at the onset of Covid, it’s the purple line, the correlation series calculated with a three-month estimation window, that was the first to pick up on the co-movement of bitcoin and the Nasdaq Composite. After three months, with that pair of returns dropping out of its estimation window, it is the purple line that signaled that the correlation was no longer nearly as strong by the summer of 2020.

More recently at the end of 2022, the various correlation measures all seemed to agree that the bitcoin-Nasdaq correlation was around 0.60. That began to break in 2023 and that trend has continued such that the shorter-term metrics are suggesting that bitcoin and Nasdaq returns are no longer correlated. Many have jumped on this to suggest that bitcoin, and digital assets more broadly, are no longer driven by macro concerns and have returned to more “normalized” behaviour compared to other assets.

Pick Your Metric Wisely

We think statements like these can be misleading or at least, need to be placed in the proper context. This drop in correlation may indeed be beneficial for short-term traders who are looking for diversification in their trading strategies. For long-term allocators, these different metrics of correlations need to be taken together with a fundamental understanding of the difference between pricing and intrinsic value. (Refer to our June 2022 commentary, Where Did All That Value Go? — Firinne Capital.) Digital assets are growth assets with unclear streams of cashflow. When macro conditions capture the center of the investor’s attention, they are going to behave like other growth assets, e.g., tech stocks. Macro conditions that suck out liquidity – Central Bank tightening, a surprise pandemic, the breakout of war – will punish all growth assets alike. Correlations will rise. Once this is no longer new information, i.e., it is priced into the markets, its ability to drive investor behaviour diminishes. New, unexpected information will come to the fore. And this is what we have experienced thus far in 2023. Macro events have receded, and the actual outcomes have not been as dark as the shadows were foretelling. In the US, we have not witnessed massive unemployment and recession, as indicated by the inversion of the US 2y – 10 y Treasury yields. Food and energy prices have risen substantially since the Russian invasion of Ukraine, but inflation is moderating globally. Meanwhile, issues specific to the digital assets industry have become more important. That was already the case in 2022. We continue to feel the effects of that fallout in early 2023 with the flurry of legislative proposals and regulatory enforcements. We’ve also had our share of good news from the XRP summary judgement to TradFi institutions submitting their spot bitcoin ETF applications.

It's not surprising that shorter term measures of correlations are picking up this shift in investor attention. Absent macro shocks and continuing to receive news specific to digital assets, we should expect to see all the correlation metrics trend lower, in due course. Which metric(s) do you want to manage to?

Endnote

[1] Correlation says something about movements around the mean but not the long-term direction. You can have two series with a correlation of +1 but if their long-term mean returns have opposing signs, one will be appreciating, while the other depreciating in absolute terms. Conversely, two series may have a correlation of -1 but if they have similar long-term means, they will be moving in tandem in the long-term.