Bitcoin vs Equity Realised Volatility
The widespread evidence that the volatility of returns tends to cluster over time and across asset classes has crucial implications for portfolio decision making. Any evidence of increasing integration and correlation of volatility could potentially affect not only asset selection and allocation, but also regulators’ policies aimed at mitigating contagion effects between traditional equity markets and the new and still developing class of cryptoasset investments.
Thus far, there is little consensus on the relationship between cryptoassets, and Bitcoin in particular, and conventional equity markets. Perhaps more importantly, there is even less understanding of how volatility interacts across these two markets (see, e.g., Kyriazis 2019 for an extensive literature review). It follows that there is an increasing need to investigate the relationship between risk, in the form of realised volatility, across equity and cryptoasset markets. This is particularly relevant given the staggering levels of volatility within the context of Bitcoin, and cryptoasset investments at large.
In this report, we try to expand the existing literature on the correlation between Bitcoin and the volatility of equity returns by looking at a large cross section of 153 characteristic-managed portfolios as proposed by Jensen et al. (2022), as well as five conventional equity risk factors as originally proposed by Fama and French (2015). We restrict our analysis to value-weighted strategies that can be constructed using the Centre for Research in Security Prices (CRSP) monthly and daily stock files, the Compustat Fundamental annual and quarterly files, and the Institutional Broker Estimate (IBES) database. The ability to investigate the correlation of a wide array of investment strategies based on firm fundamentals, from momentum to liquidity and profitability, allows us to shed further light on the volatility spillover between Bitcoin and equity markets in a more comprehensive way.
A first look at the volatility dynamics
The importance of volatility dynamics for investment decisions is rooted in the standard mean-variance portfolio allocation rule. That is, the optimal portfolio – in a risk-adjusted sense – is proportional to the attractiveness of the risk return trade-off. Put differently, it is really the return “per unit of risk” that matters, rather than the realised return itself. Motivated by extensive empirical evidence that volatility is highly time-varying, persistent and does not predict returns, we approximate the conditional risk each month by a simple realised volatility estimate,
Where d is the number of days within a given month for a given asset. An appealing feature of this approach is that it can be easily implemented by an investor in real time and does not rely on any parameter estimation (see Andersen et al. 2003). In addition, by using a non-parametric, model-free approximation of volatility we can abstract from potential unobserved heterogeneity across asset classes. This is particularly convenient when comparing two class of investments which, a priori, could not necessarily share the same economic fundamentals, such as equity and Bitcoin.
Figure 1 compares the average realised volatility RVt for the characteristic-managed equity portfolios vs Bitcoin (left panel) and the aggregate equity market portfolio vs Bitcoin (right panel). The monthly realised volatility is expressed in decimals, so that 0.1=10% monthly realised volatility. Two main facts emerge: first, perhaps not surprisingly, the realised volatility of Bitcoin is substantially larger than both the average equity strategy and the equity market portfolio. For instance, the spike in monthly realised volatility around the Covid-19 outbreak is about 20% for the equity market, versus more than 50% for Bitcoin over the same month. The gap between Bitcoin and equity realised volatility is even larger during the 2017/2019 period, where the realised volatility of Bitcoin is essentially an order of magnitude higher than the average characteristic-managed portfolio or the aggregate equity market portfolio.
Figure 1: Realised volatility of characteristic-managed equity portfolios vs Bitcoin
Perhaps more interestingly, Figure 1 suggests that there could be some correlation between the realised volatility of equity and Bitcoin. However, this seems to hold primarily for the aggregate market portfolio. For instance, except for the Covid-19 outbreak in early 2020, the correlation between the RVt of Bitcoin and characteristic-managed portfolios is low (0.18) and not significant from zero at conventional significance levels (p-value: 0.091). On the other hand, the correlation between the realised volatility of Bitcoin vs the market portfolio is moderate (0.33) and highly statistically significant (p-value: 0.010). This suggests that any risk spillover between equity and Bitcoin is primarily concentrated at the aggregate market portfolio level.
Bitcoin vs equity realised volatility
Figure 1 focuses on the time series dynamics of Bitcoin vs equity realised volatility. When looking at the average RVt across characteristic-managed portfolios the correlation with Bitcoin RVt seems rather dismal. We now delve further into such relationship by reporting the cross-sectional distribution of the realised volatility correlations between each equity portfolio and Bitcoin. Notice that in addition to the Jensen et al. (2022) strategies, we also consider the monthly realised volatility for the Fama and French (2015) (henceforth FF). These include the returns on a value-weighted equity market portfolio in excess of the risk-free rate, in addition to conventional size (SMB), value (HML), profitability (RMW) and investment (CMA) portfolios. This gives almost a full year into the so-called post-COVID period, while the sample from Jensen et al. (2022) ends in 2021, the Fama-French factors are reported until the end of 2022.
Figure 2: Cross-sectional distribution of realized volatility correlations
The left panel of Figure 2 reports the cross-sectional distribution of realised volatility correlation between Bitcoin and the 153 equity portfolios outlined above. Interestingly, there is a substantial cross-sectional heterogeneity in the pairwise correlation of equity realised volatilities with respect to Bitcoin’s. While the average correlation is around 0.2 (in line with Figure 1), the correlation with Bitcoin realised volatility is as high as 0.5 for a non-trivial fraction of equity portfolios. Perhaps this is not unexpected, but Figure 2 suggests that by aggregating equity strategies, as in Figure 1, might underrepresent the risk of spillover between Bitcoin and equity markets.
The right panel of Figure 2 offers a less granular picture by focusing on the five FF risk factors. A quite interesting result emerges; except for the realised volatility on market risk, none of the FF factors seem to have a substantial correlation in terms of realised volatility with respect to Bitcoin. For instance, the correlation of RVt from Bitcoin and RVt from the RMW or CMA is a mere 0.078 and 0.118, respectively. This is less than half of the one between Bitcoin and the equity market returns. This validates the point made in Figure 1, whereby there is indeed a non-trivial, contemporaneous, spillover between equity and Bitcoin returns volatility.
The dynamics of option implied volatilities
Figure 1 and 2 seem to suggest there is a potential interaction between Bitcoin and broader equity market realised volatilities. We now expand this analysis by looking at the option market. More specifically, we compare the traditional equity VIX index from the Chicago Board Options Exchange (CBOE) with the Bitcoin option implied volatility, as proposed by Alexander and Imeraj (2020). Similar to the VIX index for equity, the Bitcoin implied volatility index generates a 30-day forward projection of Bitcoin volatility, which can be thought of as a measure of market sentiment, and in particular a potential measure of “fear” among market participants.
Figure 3: Bitcoin and Equity option implied volatility
Figure 3 compares the time series of the Bitcoin implied volatility vs equity VIX (left panel) and reports their correlation in the form of a scatter plot (right panel). Two interesting facts emerge. First, perhaps not unexpectedly, the implied volatility from Bitcoin options is substantially higher than the one on equity markets as measure by the VIX. This is quite natural considering the option implied volatility should reflect the underlying asset volatility dynamics; the right panel of Figure 1 already pointed out the massive differences in realised volatility between Bitcoin and the aggregate equity market.
Second, and perhaps more interestingly, Figure 3 seems to suggest there is a slightly negative correlation between the implied volatility of Bitcoin vs equity market. Such negative correlation is small in magnitude (-0.12) but statistically significant at conventional levels (p-value: 0.001). This suggests there is a slight divergence in the expected volatility across markets, or at least there is no substantial cross contamination. By looking carefully at the scatter plot though, it seems quite clear that such a disconnect is primarily focused on the period between late 2020, early 2021, when the Bitcoin volatility index was substantially high in the face of a relatively low and stable equity option implied volatility. As a matter of fact, when focusing only on the period post 2021, the correlation between the Bitcoin and equity implied volatility becomes essentially zero in statistical terms. Nevertheless, from Figure 1 and 3 there seems to be a disconnect between realised and implied volatility correlations.
The idea that equity risk spill over into cryptoasset markets has been increasingly discussed by commentators and market participants. On the one hand, comovements in volatility across asset classes potentially hamper diversification benefits within the context of a conventional mean-variance portfolio allocation, especially in the presence of positive correlations across assets. On the other hand, the presence of positive correlations in volatility may suggest some form of market integration that has more to do with risks, and goes beyond expected returns.
In this report, we implement an extended correlation analysis on a comprehensive set of equity risk factors and show some interesting evidence as far as volatility spillovers are concerned. We show that there is indeed a non-zero correlation between the realised volatility on the market portfolio and Bitcoin. Such correlation is positive and significant and seems to be particularly evidence during volatility spikes in the equity market. The empirical analysis also points towards a substantial heterogeneity in the realised volatility correlations across different equity, characteristic-managed, portfolios, with such correlations as high as 0.5 for a small subset of equity portfolios.
This result possibly has important implications in our understanding of the potentially increasing “integration” between Bitcoin and equity markets. The bottom-line is that risk in equity markets, as captured by a simple realised volatility measure, potentially show an increasing correlation with the risk dynamics in Bitcoin. It is worth noticing though that if this correlation is simply the result of correlated trading, or there are some shared economic fundamentals, then it is a different question which cannot be fully answered based on simple correlation analysis.
Alexander, Carol, and Arben Imeraj. "BVIN: The Bitcoin Volatility Index." (2020).
Andersen, Torben G., et al. "Modeling and forecasting realized volatility." Econometrica 71.2 (2003): 579-625.
Fama, Eugene F., and Kenneth R. French. "A five-factor asset pricing model." Journal of financial economics 116.1 (2015): 1-22.
T. I. Jensen, B. T. Kelly, and L. H. Pedersen. “Is there a replication crisis in Finance?” Journal of Finance, (Forthcoming), 2022
Kyriazis, Nikolaos A. "A survey on empirical findings about spillovers in cryptocurrency markets." Journal of Risk and Financial Management 12.4 (2019): 170.