Bitcoin, VIX and expected inflation

Bitcoin has halved in value since its recent peak. Can this student be explained quantitatively? First look at the correlation with the most discussed factor in the most recent episode – risk.

figure 1: Coinbase Bitcoin (blue, left log scale) and VIX (brown, right scale). Source: Coinbase and CBOE via FRED.

There is some clear negative correlation between the risk represented by the VIX and the price of Bitcoin. However, Bitcoin has a large trend (even in recorded cases), so estimating first-order differences may be better suited to capture relationships. A finding from January 14, 2015 to January 21, 2022:

Δlog bitcoin_Ton = 0.0001 – 0.006ΔMuch Ado About Nothing_Ton – 7,310 ΔPI^e_Ton + you_Ton

adjust -R² = 0.04, SER = 0.048, DW = 2.45, N = 1371. black body Indicates significance at 10% msl using HAC robust standard error.

Where PI^e The projected 5-year inflation rate at the TIPS break-even point, expressed in decimal. Interestingly, neither expected inflation nor real interest rates (TIPS 5 years) are significant. However, even the established relationship with the VIX does not appear to be particularly strong. If the Bai-Perron Structural Fracture Test is used to look for a fracture, the fracture will be identified on March 12, 2020. Looking at Figure 1, it can be seen that this was before the VIX surged.

In Figure 2, I show data from March 1, 2020 to January 22, 2022.

figure 2: Coinbase Bitcoin (blue, left log scale) and VIX (brown, right scale). Red dotted line for March 12, 2020. Source: Coinbase and CBOE via FRED.

On the subsample determined by the Bai-Perron program (3/12/2020-1/21/2022), the regression yields:

Δlog bitcoin_Ton = 0.0001 – 0.010ΔMuch Ado About Nothing_Ton – 3,559 ΔPI^e_Ton + you_Ton

adjust -R² = 0.27, SER = 0.041, DW = 2.13, N = 365. black body Indicates significance at 10% msl using HAC robust standard error.

So yes, it looks like Bitcoin price changes – especially now – are driven by the risk appetite represented by the VIX: around 42% in the past month.

Estimates of sensitivity to inflation expectations rarely suggest that Bitcoin is not a good hedge against inflation; a statistically significant correlation with the S&P 500 indicates that it is not a good hedge for stocks.

For more speculation driving Bitcoin price, especially over longer periods, see here.