Abstract:

We document a highly significant, strongly nonlinear dependence of Bitcoin, stock, and bond returns on past equity market volatility as measured by the VIX. We propose a new estimator for the shape of the nonlinear forecasting relationship that exploits variation in the cross-section of returns. We find that the nonlinear relationship between Bitcoin and bonds are very similar to the nonlinear relationship between stocks and bond. The nonlinearity are mirror images for stocks and bonds, as well as for Bitcoin and bonds, revealing flight-to-safety: expected returns increase for Bitcoin and stocks when volatility increases from low to moderate while they decline for Bitcoin and Treasuries. Expected returns decrease for stocks when volatility increases from moderate to high while they increase for Bitcoin and Treasuries. These findings provide support that Bitcoin price is highly correlated with the stock market and treasuries. The price of risk is a nonlinear function of market volatility.