Can ETFs affect U.S. financial stability? A quantile cointegration analysis

Financial Innovation

Table 4 Quantile cointegration estimates for VIX

\({\varvec{\tau}}\)	0.05	0.1	0.15	0.2	0.25	0.3	0.35	0.4	0.45
\({\beta }_{d}\)	0.95	0.46	0.38	− 0.60	− 0.81	− 2.14	− 1.25	-1.27	0.13
p-value	0.80	0.89	0.92	0.88	0.87	0.67	0.84	0.85	0.98
\({\beta }_{EPS}\)	2.02	1.78	− 0.55	0.21	0.78	1.77	1.19	1.21	0.81
p-value	0.60	0.63	0.89	0.96	0.87	0.70	0.84	0.84	0.89
\({\beta }_{FED}\)	− 1.56	− 1.57	− 1.49	− 1.52	− 1.55	− 1.57	− 1.51	− 1.47	− 1.28
p-value	0.00	0.00	0.00	0.01	0.01	0.01	0.02	0.03	0.05
\({\beta }_{Lev}\)	21.89	19.86	15.03	15.97	17.37	17.82	14.52	16.41	16.72
p-value	0.02	0.04	0.08	0.09	0.07	0.08	0.21	0.19	0.21
\({\beta }_{ETF FOF}\)	− 3.29	− 2.95	− 2.31	− 2.12	− 2.42	− 2.49	− 3.08	− 3.51	− 4.27
p-value	0.13	0.11	0.20	0.20	0.21	0.22	0.13	0.09	0.04

\({\varvec{\tau}}\)	0.5	0.55	0.60	0.65	0.70	0.80	0.85	0.90	0.95	OLS
\({\beta }_{d}\)	− 0.11	− 1.81	− 0.27	− 0.71	− 2.52	− 9.17	− 9.94	− 7.61	− 9.86	− 0.86
p-value	0.99	0.77	0.97	0.91	0.71	0.16	0.15	0.31	0.27	0.79
\({\beta }_{EPS}\)	1.42	3.25	2.53	2.71	2.99	6.11	6.17	6.29	5.48	1.12
p-value	0.80	0.55	0.67	0.66	0.64	0.33	0.36	0.36	0.48	0.64
\({\beta }_{FED}\)	− 1.19	− 1.32	− 1.23	− 1.21	− 1.20	− 1.39	− 1.25	− 1.27	− 1.30	− 1.23
p-value	0.08	0.05	0.07	0.08	0.09	0.07	0.12	0.07	0.02	0.00
\({\beta }_{Lev}\)	17.52	23.53	22.45	20.92	19.68	7.76	4.97	8.55	12.26	12.89
p-value	0.21	0.08	0.11	0.16	0.24	0.66	0.81	0.69	0.62	0.09
\({\beta }_{ETF FOF}\)	− 4.13	− 2.98	− 3.85	− 4.06	− 3.02	− 3.38	− 3.39	− 4.79	− 1.69	− 3.21
p-value	0.05	0.06	0.07	0.09	0.24	0.21	0.21	0.16	0.61	0.14

The Table 4 shows the OLS and quantile regression estimates of the cointegrating coefficients and the respective p-values using a lag of order 2 (K = 2) applied to the VIX data, variables related to index fundamentals and fund flows to ETFs. The model estimated is \({Q}_{VIX\left(\tau |{\mathcal{F}}_{t}\right)}=\mathrm{\alpha }\left(\tau \right)+{\beta }_{d}\left(\tau \right){d}_{t}+{\beta }_{EPS}\left(\tau \right){EPS}_{t}+{\beta }_{FED}\left(\tau \right){FED}_{t}+{\beta }_{Leverage}\left(\tau \right){Leverage}_{t}+{\beta }_{ETF FOF}\left(\tau \right){ETF FOF}_{t}+\sum_{j=-K}^{K}{\pi }_{d,j}\left(\tau \right)\Delta {d}_{t-j}+\sum_{j=-K}^{K}{\pi }_{EPS,jt}\Delta {EPS}_{t-j}+\sum_{j=-K}^{K}{\pi }_{FED,j}\left(\tau \right)\Delta {FED}_{t-j}+\sum_{j=-K}^{K}{\pi }_{Leverage,j}\left(\tau \right)\Delta {Leverage}_{t-j}+\sum_{j=-K}^{K}{\pi }_{ETF FOF,j}\left(\tau \right)\Delta {ETF FOF}_{t-j}+{F}_{\varepsilon }^{-1}\left(\tau \right)\), where \({\text{d}}\), is the logarithm over the last twelve months in dividend per share, EPS is the logarithm over the last twelve months in earning per share, FED is the U.S. Federal Funds Effective Rate, Lev, is the natural logarithm of the debt-to-equity ratio of the S&P 500, and ETF FOF is the ratio of net FoF to equity ETFs to nominal GDP. Quarterly data for the period 1994–2020 is used, resulting in a time series with 108 data points. Most data is retrieved from Compustat