Volatility Implications for Asset Returns Correlation

Central European Economic Journal

Volume 11 (2024): Issue 58 (January 2024)

By:

Illia Ivanov

Open Access

|Nov 2024

Figures & Tables

Distribution of correlation intervals by asset return periods

Different responses to crisis of the range of holding/correlation periods of the price of silver and the broad US stock index during the period of the global financial crisis, 2007–2012

Average correlation of the rolling annual return of individual pairs of assets with a volatility index greater than 20 and less than 20

Rule of thumb for interpreting the size of a correlation coefficient

Size of correlation	Interpretation
.90 to 1.00 (−.90 to −1.00)	Very high positive (negative) correlation
.70 to .90 (−.70 to −.90)	High positive (negative) correlation
.50 to .70 (−.50 to −.70)	Moderate positive (negative) correlation
.30 to .50 (−.30 to −.50)	Low positive (negative) correlation
.00 to .30 (.00 to −.30)	Negligible correlation

Selected asset classes and data series and source description

Broad asset classes	Selected asset class	Representative ticker(s) or index	Sample period and frequency
U.S. equities	U.S. broad equity	Index: Wilshire 5000 Total Market Index, Close; Data series: WILL5000PR – FRED	1970-12-31 to 1979-11-30 – monthly, 1979-12-03 to 2024-03-28 – daily
	U.S. Large cap (S&P 500 index)	Ticker: SPY - SPDR S&P 500 ETF Trust, Close; Data series: SPY – Yahoo Finance	1980-01-02 to 2024-05-10 – daily
	U.S. sectoral equities	Tickers: XLE, XLU, XLK, XLB, XLP, XLY, XLI, XLV, XLF - Select Sectors SPDR Funds, all Close; Data series: all – Yahoo Finance; IYR - iShares U.S. Real Estate ETF, all Close; Data series: all – Yahoo Finance Index: S&P Communication Services Select Sector Index, Close; Data series: ^SP500-50 – Yahoo Finance	XLE, XLU, XLK, XLB, XLP, XLY, XLI, XLV, XLF - 1998-12-22 to 2024-04-05 – daily; IYR - 2000-06-19 to 2024-04-05 – daily; ^SP500-50 - 1993-05-04 to 2024-04-05 – daily.
	U.S. growth equities	Ticker: IUSG - iShares Core S&P U.S. Growth ETF, Close; Data series: IUSG - Yahoo Finance	2000-07-28 to 2024-04-08 – daily
	U.S. value equities	Ticker: IUSV - iShares Core S&P U.S. Value ETF, Close; Data series: IUSV – Yahoo Finance	2000-08-04 to 2024-04-05 – daily
International equities	Developed countries’ equities ex.-U.S.	Ticker: VEA - Vanguard FTSE Developed Markets Index Fund ETF Shares, Close; Data series: VEA – Yahoo Finance	2007-07-26 to 2024-04-05 – daily
	EU equities	Ticker: EZU - iShares MSCI Eurozone ETF, Close; Data series: EZU – Yahoo Finance	2000-07-31 to 2024-04-05 – daily
	Japan equities	Ticker: EWJ - iShares MSCI Japan ETF, Close; Data Series: EWJ – Yahoo Finance	1996-03-18 to 2024-04-05 – daily
	Developing countries’ equities ex.-China	Ticker: EMXC - iShares MSCI Emerging Markets ex China ETF, Close; Data Series: EMXC – Yahoo Finance	2017-07-26 to 2024-04-05 – daily
Metals such as gold, silver, platinum and copper	Gold	Index: LBMA Gold Price PM ($/ozt); Data Series: Global Gold price - Historical Data (1979-Present) – Kaggle	1985-01-01 to 2023-10-06 - daily
	Silver	Index: LBMA Silver Price ($/ozt); Data Series: Daily Silver prices (1968 – 2022) – Kaggle	1968-01-02 to 2022-04-21 - daily
	Platinum	Index: Platinum London PM Fix ($/ozt); Data Series: Daily London Fix Prices 1990 – 2024 – Kaggle	1990-04-02 to 2023-10-09 – daily
	Copper	Index: FRED Global price of Copper ($/ton); Data Series: PCOPPUSDM – FRED	1991-01-01 to 2024-02-01 – monthly
Oil, Energy, and Agriculture commodities – exposure	Oil	Ticker: DBO - Invesco DB Oil Fund, Close; Data Series: DBO – Yahoo Finance	2007-01-05 to 2024-04-05 – daily
	Uranium	Ticker: URA - Global X Uranium ETF, Close; Data Series: URA – Yahoo Finance	2010-11-05 to 2024-04-05 – daily
	Agriculture commodities	Ticker: DBA - Invesco DB Agriculture Fund, Close; Data Series: DBA – Yahoo Finance	2007-01-05 to 2024-04-05 – daily
Alternative investment – exposure	Cryptocurrency – Bitcoin	Ticker: GBTC - Grayscale Bitcoin Trust ETF (BTC), Close; Data Series: GBTC – Yahoo Finance	2015-05-11 to 2024-04-08 – daily
Government bonds – exposure	U.S. Long-term bonds	Ticker: TLT - iShares 20+ Year Treasury Bond ETF), Close; Data Series: TLT – Yahoo Finance	2002-07-30 to 2024-04-19 – daily
	U.S. Mid-term bonds	Ticker: IEF - iShares 7–10 Year Treasury Bond ETF, Close; Data Series: IEF – Yahoo Finance	2002-07-30 to 2024-04-19 – daily
	U.S. Inflation-linked bonds	Ticker: TIP - iShares TIPS Bond ETF, Close; Data Series: TIP – Yahoo Finance	2003-12-05 to 2024-04-19 – daily
	Developing countries’ government bonds	Ticker: EMB - iShares J.P. Morgan USD Emerging Markets Bond ETF, Close; Data Series: EMB – Yahoo Finance	2007-12-19 to 2024-04-19 – daily
Corporate bonds - exposure	U.S. Corporate bonds	Ticker: VCIT - Vanguard Intermediate-Term Corporate Bond Index Fund ETF Shares, Close; Data Series: VCIT – Yahoo Finance	2009-11-23 to 2024-04-19 – daily
Corporate bonds - exposure	International corporate bonds	Ticker: CEMB - iShares J.P. Morgan EM Corporate Bond ETF, Close; Data Series: CEMB – Yahoo Finance	2012-04-19 to 2024-04-19 – daily
Mixed bonds – exposure	T-Bills, Corporate, MBS and Agency Bonds	Ticker: BND - Vanguard Total Bond Market Index Fund, Close; Data Series: BND – Yahoo Finance	2007-04-10 to 2024-04-19 – daily
Mixed bonds – exposure	Broad-based short-term investment grade	Ticker: BSV - Vanguard Short-Term Bond Index Fund ETF Shares, Close; Data Series: BSV – Yahoo Finance	2007-04-10 to 2024-04-19 – daily

The number of transition pairs with a change in the sign of correlation and the strength of correlation for each rolling period

	3-month	6-month	1 year	2 years	5 years
x=pos, y=pos	341	356	364	308	242
x=pos, y=neg	11	15	21	17	67
x=neg, y=pos	64	33	39	53	2
x=neg, y=neg	51	63	43	89	92
Share of asset pairs which do not change the sign of the correlation	16%	10%	13%	15%	17%
x<0.3; x>−0.3; y>−0.3; y<0.3 – weak correlation during both periods	238	196	126	114	140
x<0.3; x>−0.3; y<−0.3; y>0.3 – weak correlation during VIX<20, stronger correlation during VIX>20	82	90	104	75	42
x>0.3; x<−0.3; y>−0.3; y<0.3 – stronger correlation during VIX<20, weak correlation during VIX>20	12	19	31	40	56
x>0.3; x<−0.3; y<−0.3; y>0.3 – stronger correlation during both periods	135	162	206	238	165
Share of asset pairs which changed correlation both from weak to stronger and from stronger to weak	20%	23%	29%	25%	24%

Summary statistics of asset yearly rolling returns

	Count	Mean	Std	Min	Max
BND	4,036	0.028	0.050	−0.168	0.180
BSV	4,034	0.020	0.029	−0.077	0.135
CEMB	2,770	0.026	0.070	−0.187	0.294
DBA	4,091	0.002	0.185	−0.470	0.642
DBO	4,091	0.027	0.363	−0.646	1.374
EMB	3,859	0.046	0.102	−0.257	0.644
EMXC	1,433	0.041	0.199	−0.319	0.875
EWJ	6,809	0.036	0.204	−0.434	0.854
EZU	5,707	0.062	0.227	−0.591	0.814
GBTC	1,990	1.835	3.404	−0.891	33.085
gold	9,854	0.059	0.150	−0.292	0.709
IEF	5,218	0.033	0.066	−0.181	0.205
IUSG	5,709	0.092	0.192	−0.513	0.825
IUSV	5,703	0.090	0.167	−0.508	0.797
IYR	5,736	0.101	0.211	−0.592	1.250
PCOPPUSDM	8,373	0.081	0.312	−0.581	1.486
platinum	8,147	0.047	0.219	−0.543	0.978
silver	10,438	0.045	0.303	−0.700	1.712
SPY	10,932	0.103	0.163	−0.486	0.750
TIP	4,877	0.034	0.057	−0.134	0.206
TLT	5,218	0.045	0.130	−0.358	0.434
URA	3,122	−0.035	0.381	−0.600	1.776
VCIT	3,373	0.037	0.062	−0.182	0.211
VEA	3,951	0.049	0.191	−0.525	0.787
WILL5000PR	11,282	0.101	0.168	−0.488	0.817
XLB	6,111	0.093	0.191	−0.545	1.017
XLE	6,111	0.108	0.264	−0.595	1.166
XLF	6,111	0.073	0.235	−0.721	1.507
XLI	6,111	0.095	0.191	−0.555	0.995
XLK	6,111	0.111	0.253	−0.638	0.878
XLP	6,111	0.074	0.112	−0.299	0.452
XLU	6,111	0.081	0.153	−0.463	0.504
XLV	6,111	0.090	0.129	−0.337	0.557
XLY	6,111	0.106	0.193	−0.495	1.003
^SP500-50	7,532	0.052	0.228	−0.58	0.755

Average absolute difference of average correlation during VIX>20 and VIX<20 per different periods

Asset class pair	3-month	6-month	1-year	2-year	5-year
International equities-Alternative investment	0.301	0.269	0.125	0.160	n/a
International equities-Government bonds	0.140	0.109	0.168	0.202	0.125
International equities-Mixed bonds	0.243	0.058	0.147	0.247	0.066
International equities-Corporate bonds	0.268	0.155	0.265	0.213	0.096
International equities-Metals such as gold, silver, platinum and copper	0.119	0.094	0.220	0.167	0.105
U.S. equities-International equities	0.112	0.150	0.123	0.120	0.078
U.S. equities-Oil. Energy. and Agriculture commodities	0.157	0.137	0.215	0.112	0.181
U.S. equities-Alternative investment	0.229	0.186	0.229	0.165	n/a
U.S. equities-Government bonds	0.143	0.153	0.216	0.169	0.195
U.S. equities-Mixed bonds	0.173	0.119	0.144	0.203	0.138
U.S. equities-Corporate bonds	0.203	0.198	0.218	0.169	0.075
U.S. equities-Metals such as gold, silver, platinum and copper	0.071	0.111	0.177	0.203	0.323
Oil, Energy, and Agriculture commodities - International equities	0.110	0.137	0.207	0.118	0.103
Oil, Energy, and Agriculture commodities - Alternative investment	0.257	0.35	0.224	0.374	n/a
Oil, Energy, and Agriculture commodities - Government bonds	0.149	0.086	0.123	0.123	0.110
Oil, Energy, and Agriculture commodities - Mixed bonds	0.135	0.04	0.130	0.087	0.164
Oil, Energy, and Agriculture commodities - Corporate bonds	0.167	0.059	0.129	0.193	0.168
Oil, Energy, and Agriculture commodities - Metals such as gold, silver, platinum and copper	0.129	0.146	0.122	0.164	0.057
Alternative investment - Government bonds	0.181	0.227	0.149	0.227	n/a
Alternative investment - Mixed bonds	0.042	0.272	0.062	0.353	n/a
Alternative investment - Corporate bonds	0.158	0.087	0.167	0.168	n/a
Alternative investment - Metals such as gold, silver, platinum and copper	0.183	0.180	0.234	0.174	n/a
Government bonds-Mixed bonds	0.072	0.058	0.128	0.125	0.034
Government bonds-Corporate bonds	0.084	0.066	0.113	0.119	0.043
Government bonds-Metals such as gold, silver, platinum and copper	0.095	0.116	0.16	0.093	0.261
Mixed bonds-Corporate bonds	0.084	0.051	0.072	0.154	0.030
Mixed bonds-Metals such as gold, silver, platinum and copper	0.084	0.067	0.095	0.173	0.050
Corporate bonds-Metals such as gold, silver, platinum and copper	0.170	0.085	0.106	0.090	0.187
The absolute value of the correlation difference at VIX >20 and at VIX <= 20, the average value of the difference across all asset pairs	0.139	0.132	0.173	0.160	0.160

Regression results for 1-year rolling correlation of 1-year rolling returns, asset pairs with difference >0_30 of average correlation between different volatility regimes

No.	Ticker Pair	R^2	Intcpt.	Slope	Stand. Err.	Avg Corr VIX <=20	Avg Corr VIX > 20	Avg Corr VIX > 30	Abs. difference at VIX > 20 and VIX <=20	T-val.	Conf Int Lower	Conf Int Upper	Shapiro-Wilk Stat	Breusch-Pagan Stat	Breusch-Pagan P-value	Durbin-Watson Stat
1	TLT-XLU	0.26	0.81	−0.03	0.001	0.42	−0.19	−0.32	0.61	−41.56	−0.032	−0.029	0.960	364	0.000	0.0158
2	IEF-XLU	0.25	0.79	−0.03	0.001	0.41	−0.16	−0.33	0.57	−40.35	−0.031	−0.028	0.961	189	0.000	0.0150
3	DBO-XLU	0.20	−0.31	0.02	0.001	0.00	0.51	0.59	0.52	31.46	0.023	0.027	0.953	15	0.000	0.0124
4	CEMB-XLY	0.22	−0.29	0.03	0.001	0.15	0.65	0.72	0.50	26.74	0.030	0.035	0.966	41	0.000	0.0185
5	EMB-XLY	0.22	−0.23	0.03	0.001	0.15	0.63	0.73	0.48	32.36	0.026	0.030	0.962	78	0.000	0.0146
6	GBTC-^SP500-50	0.25	−0.10	0.03	0.001	0.28	0.75	0.78	0.48	24.52	0.026	0.031	0.899	36	0.000	0.0209
7	IEF-IYR	0.15	0.69	−0.03	0.001	0.33	−0.14	−0.39	0.47	−29.62	−0.028	−0.025	0.923	5	0.027	0.0082
8	IYR-TLT	0.15	0.66	−0.03	0.001	0.30	−0.16	−0.38	0.46	−29.76	−0.028	−0.025	0.942	39	0.000	0.0083
9	VEA-^SP500-50	0.19	−0.05	0.02	0.001	0.27	0.72	0.84	0.46	29.73	0.023	0.026	0.942	149	0.000	0.0112
10	CEMB-EWJ	0.15	−0.02	0.03	0.001	0.32	0.77	0.80	0.45	21.54	0.024	0.028	0.927	2	0.201	0.0121
11	DBO-XLP	0.21	−0.21	0.02	0.001	0.10	0.55	0.65	0.45	32.37	0.023	0.026	0.961	19	0.000	0.0130
12	GBTC-URA	0.27	−0.24	0.03	0.001	0.14	0.58	0.73	0.44	25.62	0.026	0.031	0.980	46	0.000	0.0232
13	BSV-XLU	0.10	0.57	−0.02	0.001	0.43	0.00	0.04	0.43	−21.10	−0.017	−0.014	0.976	709	0.000	0.0058
14	VCIT-XLU	0.16	0.82	−0.02	0.001	0.51	0.09	0.14	0.42	−24.45	−0.025	−0.021	0.963	976	0.000	0.0129
15	PCOPPUSDM-XLV	0.23	−0.22	0.03	0.001	0.12	0.54	0.66	0.42	42.07	0.025	0.027	0.955	176	0.000	0.0136
16	GBTC-silver	0.14	−0.03	0.02	0.001	0.16	0.57	0.61	0.41	14.61	0.014	0.019	0.911	4	0.048	0.0104
17	PCOPPUSDM-WILL5000PR	0.18	−0.26	0.03	0.001	0.14	0.55	0.70	0.41	41.07	0.027	0.030	0.930	232	0.000	0.0092
18	GBTC-PCOPPUSDM	0.18	0.01	0.02	0.001	0.30	0.70	0.76	0.40	19.53	0.021	0.025	0.919	31	0.000	0.0139
19	BND-XLU	0.07	0.58	−0.01	0.001	0.50	0.10	0.22	0.40	−16.83	−0.013	−0.011	0.971	852	0.000	0.0039
20	CEMB-EZU	0.10	0.10	0.02	0.001	0.38	0.78	0.86	0.40	17.27	0.020	0.025	0.912	126	0.000	0.0079
21	GBTC-XLY	0.28	0.08	0.02	0.001	0.37	0.75	0.79	0.39	26.36	0.021	0.024	0.917	44	0.000	0.0245
22	DBA-XLV	0.20	−0.23	0.02	0.001	0.04	0.43	0.53	0.38	30.87	0.019	0.022	0.982	39	0.000	0.0119
23	CEMB-IUSG	0.16	0.05	0.02	0.001	0.36	0.74	0.77	0.38	21.92	0.021	0.025	0.899	10	0.002	0.0125
24	DBA-XLP	0.18	−0.19	0.02	0.001	0.09	0.47	0.58	0.38	29.48	0.020	0.023	0.966	14	0.000	0.0109
25	URA-^SP500-50	0.22	−0.06	0.03	0.001	0.29	0.67	0.77	0.38	28.82	0.024	0.027	0.962	8	0.004	0.0190
26	EMB-EWJ	0.10	−0.01	0.02	0.001	0.24	0.61	0.64	0.38	20.57	0.017	0.021	0.931	65	0.000	0.0061
27	BND-IYR	0.07	0.68	−0.01	0.001	0.54	0.17	0.15	0.37	−16.58	−0.016	−0.012	0.913	361	0.000	0.0037
28	BSV-IYR	0.10	0.65	−0.02	0.001	0.49	0.12	0.00	0.37	−20.49	−0.017	−0.014	0.946	479	0.000	0.0055
29	IUSG-PCOPPUSDM	0.18	−0.04	0.02	0.001	0.28	0.65	0.75	0.37	34.90	0.022	0.024	0.912	140	0.000	0.0100
30	IYR-URA	0.18	0.08	0.02	0.001	0.36	0.72	0.79	0.36	25.31	0.020	0.023	0.948	0	0.892	0.0144
31	VCIT-XLY	0.08	−0.22	0.02	0.001	0.04	0.40	0.30	0.36	16.52	0.017	0.022	0.962	0	0.521	0.0061
32	EZU-PCOPPUSDM	0.16	0.08	0.02	0.001	0.35	0.71	0.80	0.36	31.80	0.019	0.022	0.909	154	0.000	0.0084
33	DBO-IYR	0.14	−0.09	0.02	0.001	0.18	0.54	0.63	0.36	25.49	0.019	0.022	0.930	35	0.000	0.0083
34	EZU-^SP500-50	0.13	0.00	0.02	0.001	0.29	0.65	0.77	0.36	29.13	0.020	0.023	0.937	251	0.000	0.0069
35	TLT-XLE	0.12	0.04	−0.02	0.001	−0.19	−0.55	−0.65	0.36	−26.26	−0.019	−0.016	0.956	1	0.299	0.0065
36	DBA-EWJ	0.13	−0.23	0.02	0.001	0.06	0.42	0.55	0.36	24.49	0.020	0.023	0.930	110	0.000	0.0075
37	PCOPPUSDM-XLY	0.17	−0.25	0.03	0.001	0.12	0.47	0.67	0.35	35.23	0.024	0.027	0.938	33	0.000	0.0096
38	EWJ-TIP	0.09	−0.40	0.02	0.001	−0.16	0.20	0.25	0.35	21.03	0.017	0.021	0.937	67	0.000	0.0045
39	silver-XLV	0.20	−0.40	0.02	0.001	−0.10	0.26	0.41	0.35	36.31	0.021	0.023	0.967	43	0.000	0.0107
40	DBA-XLY	0.16	−0.27	0.02	0.001	0.04	0.40	0.53	0.35	27.12	0.020	0.024	0.949	47	0.000	0.0092
41	PCOPPUSDM-SPY	0.15	−0.20	0.03	0.001	0.17	0.52	0.66	0.35	37.52	0.024	0.027	0.922	168	0.000	0.0077
42	CEMB-VEA	0.11	0.22	0.02	0.001	0.47	0.82	0.86	0.35	17.80	0.017	0.022	0.888	97	0.000	0.0084
43	EWJ-URA	0.19	−0.13	0.03	0.001	0.25	0.59	0.73	0.35	26.14	0.025	0.029	0.950	4	0.047	0.0157
44	EMB-EZU	0.09	0.09	0.02	0.001	0.32	0.67	0.70	0.35	19.36	0.016	0.020	0.914	122	0.000	0.0054
45	TLT-XLP	0.12	0.35	−0.02	0.001	0.05	−0.29	−0.45	0.35	−26.44	−0.023	−0.020	0.926	9	0.003	0.0065
46	EZU-silver	0.17	−0.07	0.02	0.001	0.19	0.53	0.61	0.34	31.46	0.018	0.020	0.949	38	0.000	0.0088
47	DBA-VCIT	0.10	0.62	−0.02	0.001	0.34	0.00	−0.27	0.34	−18.95	−0.023	−0.018	0.938	57	0.000	0.0081
48	EWJ-IYR	0.17	−0.10	0.02	0.001	0.19	0.53	0.62	0.34	33.59	0.020	0.022	0.955	8	0.004	0.0091
49	silver-VEA	0.20	−0.03	0.02	0.001	0.21	0.55	0.69	0.34	28.22	0.017	0.019	0.952	146	0.000	0.0114
50	EMB-IUSG	0.13	0.06	0.02	0.001	0.31	0.65	0.70	0.34	23.00	0.017	0.020	0.908	54	0.000	0.0075
51	TIP-XLY	0.09	−0.33	0.02	0.001	−0.10	0.24	0.32	0.34	21.67	0.017	0.020	0.964	65	0.000	0.0048
52	silver-TLT	0.11	0.32	−0.02	0.001	0.06	−0.28	−0.52	0.33	−23.31	−0.021	−0.018	0.971	195	0.000	0.0055
53	IEF-XLP	0.13	0.39	−0.02	0.001	0.09	−0.24	−0.44	0.33	−26.77	−0.023	−0.020	0.948	18	0.000	0.0067
54	IUSG-silver	0.15	−0.18	0.02	0.001	0.08	0.41	0.50	0.33	29.90	0.018	0.021	0.971	2	0.169	0.0078
55	DBA-TLT	0.10	0.23	−0.02	0.001	−0.01	−0.34	−0.53	0.33	−20.89	−0.020	−0.017	0.967	0	0.784	0.0056
56	DBA-IUSG	0.17	−0.07	0.02	0.001	0.19	0.52	0.62	0.33	28.49	0.018	0.020	0.957	1	0.351	0.0102
57	TLT-XLV	0.12	0.25	−0.02	0.001	−0.04	−0.36	−0.49	0.33	−26.59	−0.022	−0.019	0.929	39	0.000	0.0067
58	URA-XLY	0.18	−0.03	0.03	0.001	0.34	0.67	0.78	0.32	25.42	0.024	0.028	0.923	22	0.000	0.0149
59	GBTC-WILL5000PR	0.23	0.18	0.02	0.001	0.43	0.75	0.80	0.32	23.25	0.018	0.021	0.890	5	0.021	0.0189
60	platinum-XLV	0.15	−0.22	0.02	0.001	0.07	0.39	0.46	0.32	32.13	0.019	0.022	0.951	272	0.000	0.0082
61	EMB-XLF	0.12	0.04	0.02	0.001	0.30	0.62	0.70	0.32	22.75	0.017	0.021	0.944	234	0.000	0.0075
62	IUSV-PCOPPUSDM	0.14	0.04	0.02	0.001	0.32	0.63	0.72	0.31	30.19	0.019	0.021	0.906	18	0.000	0.0077
63	IYR-VCIT	0.14	0.94	−0.02	0.001	0.73	0.42	0.37	0.31	−22.93	−0.018	−0.015	0.897	289	0.000	0.0114
64	GBTC-IUSV	0.17	0.06	0.02	0.001	0.34	0.65	0.71	0.31	19.18	0.019	0.023	0.862	46	0.000	0.0128
65	TLT-^SP500-50	0.09	0.40	−0.02	0.001	0.11	−0.19	−0.46	0.31	−22.15	−0.022	−0.018	0.960	14	0.000	0.0047
66	EWJ-XLU	0.13	−0.40	0.02	0.001	−0.09	0.22	0.41	0.30	29.87	0.020	0.023	0.978	192	0.000	0.0069
67	EMB-XLI	0.08	0.18	0.02	0.001	0.39	0.69	0.73	0.30	18.23	0.014	0.018	0.882	196	0.000	0.0048
68	CEMB-WILL5000PR	0.11	0.24	0.02	0.001	0.47	0.78	0.81	0.30	18.15	0.016	0.020	0.889	46	0.000	0.0087
69	EMB-VEA	0.08	0.20	0.02	0.001	0.40	0.70	0.72	0.30	18.21	0.014	0.017	0.905	79	0.000	0.0049
70	EMB-XLV	0.14	−0.05	0.02	0.001	0.21	0.51	0.67	0.30	24.53	0.017	0.020	0.962	198	0.000	0.0086
71	EZU-TIP	0.08	−0.28	0.02	0.001	−0.07	0.23	0.31	0.30	19.54	0.015	0.018	0.958	60	0.000	0.0040
72	IUSG-TIP	0.06	−0.19	0.02	0.001	0.00	0.30	0.33	0.30	17.90	0.014	0.017	0.953	97	0.000	0.0034
73	DBA-SPY	0.14	0.03	0.02	0.001	0.26	0.56	0.63	0.30	24.94	0.016	0.018	0.928	31	0.000	0.0080
74	IYR-PCOPPUSDM	0.16	−0.14	0.02	0.001	0.18	0.47	0.64	0.30	32.04	0.020	0.023	0.955	4	0.058	0.0085
75	CEMB-XLI	0.09	0.28	0.02	0.001	0.50	0.80	0.84	0.30	16.33	0.015	0.019	0.845	64	0.000	0.0071
76	URA-XLF	0.19	0.12	0.02	0.001	0.43	0.72	0.82	0.30	26.02	0.020	0.024	0.936	3	0.070	0.0156

1-year rolling volatility implications on annual rolling asset returns correlation, sample table of regression results_

Ticker Pair	TLT-XLU	IEF-XLU	DBO-XLU	CEMB-XLY	EMB-XLY	GBTC-^SP500-50	IEF-IYR	IYR-TLT	VEA-^SP500-50
R^2	0.26	0.25	0.20	0.22	0.22	0.25	0.15	0.15	0.19
Intercept	0.81	0.79	−0.31	−0.29	−0.23	−0.10	0.69	0.66	−0.05
Slope	−0.03	−0.03	0.02	0.03	0.03	0.03	−0.03	−0.03	0.02
P-value	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
Standard Error	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001
Avg Corr VIX <= 20	0.42	0.41	0.00	0.15	0.15	0.28	0.33	0.30	0.27
Avg Corr VIX > 20	−0.19	−0.16	0.51	0.65	0.63	0.75	−0.14	−0.16	0.72
Avg Corr VIX > 30	−0.32	−0.33	0.59	0.72	0.73	0.78	−0.39	−0.38	0.84
Absolute difference at VIX > 20 and VIX <= 20	0.61	0.57	0.52	0.50	0.48	0.48	0.47	0.46	0.46
T-value	−41.56	−40.35	31.46	26.74	32.36	24.52	−29.62	−29.76	29.73
Conf Int Lower	−0.032	−0.031	0.023	0.030	0.026	0.026	−0.028	−0.028	0.023
Conf Int Upper	−0.029	−0.028	0.027	0.035	0.030	0.031	−0.025	−0.025	0.026
Shapiro-Wilk Stat	0.960	0.961	0.953	0.966	0.962	0.899	0.923	0.942	0.942
Shapiro-Wilk P-value	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
Breusch-Pagan Stat	364	189	15	41	78	36	5	39	149
Breusch-Pagan P-value	0.000	0.000	0.000	0.000	0.000	0.000	0.027	0.000	0.000
Durbin-Watson Stat	0.0158	0.0150	0.0124	0.0185	0.0146	0.0209	0.0082	0.0083	0.0112