Table A1 Variables used in this study...

Table A1

Variables used in this study

Symbol	Name	Definition	Source
P_it	Price	Cryptocurrency price	coindesk.com
LPRICE	Natural log of price
RET_it	Daily return	Daily return, ln[p(t)/p(t-1)] of i th cryptocurrency on day t; also called ΔLPRICE
ΔLPRICE	Difference in log price of cryptos, daily return	ln[p(t+1)/p(t)] = ln[p(t+1)] – ln[p(t)] = RET
R_stock	Daily change in index	Three indices are used: 1) S&P 500; 2) MSCI emerging markets; 3) MSCI World	yahoo.com; msci.com
Δ_yield	Daily change in treasury yields	Three U.S. treasury yields: 1) 3-month T-Bill; 2) 10-year T-Note; 3) 30-year T-Bond	fred.stlouisfed.org
R_Gold	Daily gold return	Gold daily return, ln(pt/pt−1) of i th currency on day t	gold.org
ΔVolm	Daily volume	Daily volume of crypto transactions in $ billions	coindesk.com
ΔVolt	Volatility of crypto	Volatility (standard deviation of last five days' daily return)	cboe.com
ΔVIX	Implied option volatility	Daily VIX	cboe.com
$α$	(a) Excess return (constant term); (b) ARCH coeff	Used in 2 places; (a) five-factor Fama-French factor analysis; (b) GARCH	(a) French website
$β$	(a) Five Fama-French factros; (b) GARCH coeff	Used in 2 places: (a) β_M:market, β_S:size, β_H:value, β_R:profitability, β_C:style; (b) GARCH	(a) French website
R_Ft	Daily risk-free rate	One-month treasury bill rate (from Ibbotson associates)	French website
R_Mt	Daily market return	Value-weight return of all CRSP firms incorporated in the US	French website
$β_{0}$ or C	Constant term in regression
$β_{1}$	Regression coefficient	Regression coefficient of daily return on S&P 500
$β_{2}$	Regression coefficient	Regression coefficient of daily return on MSCI EM
$β_{3}$	Regression coefficient	Regression coefficient of daily return on MSCI World
$β_{4}$	Regression coefficient	Regression coefficient of 3-month T-Bill yield daily change
$β_{5}$	Regression coefficient	Regression coefficient of 10-year T-Note yield daily change
$β_{6}$	Regression coefficient	Regression coefficient of 30-year T-Bond yield daily change
$β_{7}$	Regression coefficient	Regression coefficient of daily gold return
$β_{8}$	Regression coefficient	Regression coefficient of cryptocurrency change in daily volume
$β_{9}$	Regression coefficient	Regression coefficient of cryptocurrency change in volatility of past 5 day returns
$β_{10}$	Regression coefficient	Regression coefficient of change in daily VIX
$μ_{t}$	Regression residual term in pooled OLS, FEM	$E (μ_{i t}) \sim N (0, σ^{2})$
$w_{t}$	Regression residual term in REM	w_it = μ_it + ε_i, ε_i is a random error term with mean 0 and variance $σ_{ε}^{2}$
$ε_{i}$	Random error term	ε_i is a random error term with mean 0 and variance $σ_{ε}^{2}$
$σ_{ε}^{2}$	Variance of the random error term	Used in w_t
$ε_{t}, η_{t}$	Two uncorrelated white-noise	$E [ε_{t} ε_{s}] = 0 = E [η_{t} η_{s}], s \neq t, and E [ε_{t} ε_{s}] = 0 for all s and t$
X_t and Y_t	Two stationary time series	X_t and Y_t are two stationary time series with zero mean
$f (x_{t})$	A positive term in GARCH	X_t exogenous variable(s) are presumed to effect
$σ_{Ret (t)}^{2}$	Conditional variance of daily returns	Used in GARCH volatility model

Symbol	Name	Definition	Source
P_it	Price	Cryptocurrency price	coindesk.com
LPRICE	Natural log of price
RET_it	Daily return	Daily return, ln[p(t)/p(t-1)] of i th cryptocurrency on day t; also called ΔLPRICE
ΔLPRICE	Difference in log price of cryptos, daily return	ln[p(t+1)/p(t)] = ln[p(t+1)] – ln[p(t)] = RET
R_stock	Daily change in index	Three indices are used: 1) S&P 500; 2) MSCI emerging markets; 3) MSCI World	yahoo.com; msci.com
Δ_yield	Daily change in treasury yields	Three U.S. treasury yields: 1) 3-month T-Bill; 2) 10-year T-Note; 3) 30-year T-Bond	fred.stlouisfed.org
R_Gold	Daily gold return	Gold daily return, ln(pt/pt−1) of i th currency on day t	gold.org
ΔVolm	Daily volume	Daily volume of crypto transactions in $ billions	coindesk.com
ΔVolt	Volatility of crypto	Volatility (standard deviation of last five days' daily return)	cboe.com
ΔVIX	Implied option volatility	Daily VIX	cboe.com
$α$	(a) Excess return (constant term); (b) ARCH coeff	Used in 2 places; (a) five-factor Fama-French factor analysis; (b) GARCH	(a) French website
$β$	(a) Five Fama-French factros; (b) GARCH coeff	Used in 2 places: (a) β_M:market, β_S:size, β_H:value, β_R:profitability, β_C:style; (b) GARCH	(a) French website
R_Ft	Daily risk-free rate	One-month treasury bill rate (from Ibbotson associates)	French website
R_Mt	Daily market return	Value-weight return of all CRSP firms incorporated in the US	French website
$β_{0}$ or C	Constant term in regression
$β_{1}$	Regression coefficient	Regression coefficient of daily return on S&P 500
$β_{2}$	Regression coefficient	Regression coefficient of daily return on MSCI EM
$β_{3}$	Regression coefficient	Regression coefficient of daily return on MSCI World
$β_{4}$	Regression coefficient	Regression coefficient of 3-month T-Bill yield daily change
$β_{5}$	Regression coefficient	Regression coefficient of 10-year T-Note yield daily change
$β_{6}$	Regression coefficient	Regression coefficient of 30-year T-Bond yield daily change
$β_{7}$	Regression coefficient	Regression coefficient of daily gold return
$β_{8}$	Regression coefficient	Regression coefficient of cryptocurrency change in daily volume
$β_{9}$	Regression coefficient	Regression coefficient of cryptocurrency change in volatility of past 5 day returns
$β_{10}$	Regression coefficient	Regression coefficient of change in daily VIX
$μ_{t}$	Regression residual term in pooled OLS, FEM	$E (μ_{i t}) \sim N (0, σ^{2})$
$w_{t}$	Regression residual term in REM	w_it = μ_it + ε_i, ε_i is a random error term with mean 0 and variance $σ_{ε}^{2}$
$ε_{i}$	Random error term	ε_i is a random error term with mean 0 and variance $σ_{ε}^{2}$
$σ_{ε}^{2}$	Variance of the random error term	Used in w_t
$ε_{t}, η_{t}$	Two uncorrelated white-noise	$E [ε_{t} ε_{s}] = 0 = E [η_{t} η_{s}], s \neq t, and E [ε_{t} ε_{s}] = 0 for all s and t$
X_t and Y_t	Two stationary time series	X_t and Y_t are two stationary time series with zero mean
$f (x_{t})$	A positive term in GARCH	X_t exogenous variable(s) are presumed to effect
$σ_{Ret (t)}^{2}$	Conditional variance of daily returns	Used in GARCH volatility model

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