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Volatility Implications for Asset Returns Correlation

Illia Ivanov

Illia Ivanov

Odesa National Economic University, Department of Financial Management and Stock MarketOdesa, Ukraine
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Ivanov, Illia
  
23 nov 2024
Volatility Implications for Asset Returns Correlation's Cover Image
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Pubblicato online: 23 nov 2024
Pagine: 424 - 446
DOI: https://doi.org/10.2478/ceej-2024-0027
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© 2024 Illia Ivanov, published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Figure 1.

VIX – volatility index, 1990–2024
VIX – volatility index, 1990–2024

Figure 2.

Distribution of correlation intervals by asset return periods
Distribution of correlation intervals by asset return periods

Figure 3.

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
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

Figure 4.

Average correlation of the rolling annual return of individual pairs of assets with a volatility index greater than 20 and less than 20
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
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
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 P-value 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 Shapiro-Wilk P-value Breusch-Pagan Stat Breusch-Pagan P-value Durbin-Watson Stat
1 TLT-XLU 0.26 0.81 −0.03 0.00 0.001 0.42 −0.19 −0.32 0.61 −41.56 −0.032 −0.029 0.960 0.000 364 0.000 0.0158
2 IEF-XLU 0.25 0.79 −0.03 0.00 0.001 0.41 −0.16 −0.33 0.57 −40.35 −0.031 −0.028 0.961 0.000 189 0.000 0.0150
3 DBO-XLU 0.20 −0.31 0.02 0.00 0.001 0.00 0.51 0.59 0.52 31.46 0.023 0.027 0.953 0.000 15 0.000 0.0124
4 CEMB-XLY 0.22 −0.29 0.03 0.00 0.001 0.15 0.65 0.72 0.50 26.74 0.030 0.035 0.966 0.000 41 0.000 0.0185
5 EMB-XLY 0.22 −0.23 0.03 0.00 0.001 0.15 0.63 0.73 0.48 32.36 0.026 0.030 0.962 0.000 78 0.000 0.0146
6 GBTC-^SP500-50 0.25 −0.10 0.03 0.00 0.001 0.28 0.75 0.78 0.48 24.52 0.026 0.031 0.899 0.000 36 0.000 0.0209
7 IEF-IYR 0.15 0.69 −0.03 0.00 0.001 0.33 −0.14 −0.39 0.47 −29.62 −0.028 −0.025 0.923 0.000 5 0.027 0.0082
8 IYR-TLT 0.15 0.66 −0.03 0.00 0.001 0.30 −0.16 −0.38 0.46 −29.76 −0.028 −0.025 0.942 0.000 39 0.000 0.0083
9 VEA-^SP500-50 0.19 −0.05 0.02 0.00 0.001 0.27 0.72 0.84 0.46 29.73 0.023 0.026 0.942 0.000 149 0.000 0.0112
10 CEMB-EWJ 0.15 −0.02 0.03 0.00 0.001 0.32 0.77 0.80 0.45 21.54 0.024 0.028 0.927 0.000 2 0.201 0.0121
11 DBO-XLP 0.21 −0.21 0.02 0.00 0.001 0.10 0.55 0.65 0.45 32.37 0.023 0.026 0.961 0.000 19 0.000 0.0130
12 GBTC-URA 0.27 −0.24 0.03 0.00 0.001 0.14 0.58 0.73 0.44 25.62 0.026 0.031 0.980 0.000 46 0.000 0.0232
13 BSV-XLU 0.10 0.57 −0.02 0.00 0.001 0.43 0.00 0.04 0.43 −21.10 −0.017 −0.014 0.976 0.000 709 0.000 0.0058
14 VCIT-XLU 0.16 0.82 −0.02 0.00 0.001 0.51 0.09 0.14 0.42 −24.45 −0.025 −0.021 0.963 0.000 976 0.000 0.0129
15 PCOPPUSDM-XLV 0.23 −0.22 0.03 0.00 0.001 0.12 0.54 0.66 0.42 42.07 0.025 0.027 0.955 0.000 176 0.000 0.0136
16 GBTC-silver 0.14 −0.03 0.02 0.00 0.001 0.16 0.57 0.61 0.41 14.61 0.014 0.019 0.911 0.000 4 0.048 0.0104
17 PCOPPUSDM-WILL5000PR 0.18 −0.26 0.03 0.00 0.001 0.14 0.55 0.70 0.41 41.07 0.027 0.030 0.930 0.000 232 0.000 0.0092
18 GBTC-PCOPPUSDM 0.18 0.01 0.02 0.00 0.001 0.30 0.70 0.76 0.40 19.53 0.021 0.025 0.919 0.000 31 0.000 0.0139
19 BND-XLU 0.07 0.58 −0.01 0.00 0.001 0.50 0.10 0.22 0.40 −16.83 −0.013 −0.011 0.971 0.000 852 0.000 0.0039
20 CEMB-EZU 0.10 0.10 0.02 0.00 0.001 0.38 0.78 0.86 0.40 17.27 0.020 0.025 0.912 0.000 126 0.000 0.0079
21 GBTC-XLY 0.28 0.08 0.02 0.00 0.001 0.37 0.75 0.79 0.39 26.36 0.021 0.024 0.917 0.000 44 0.000 0.0245
22 DBA-XLV 0.20 −0.23 0.02 0.00 0.001 0.04 0.43 0.53 0.38 30.87 0.019 0.022 0.982 0.000 39 0.000 0.0119
23 CEMB-IUSG 0.16 0.05 0.02 0.00 0.001 0.36 0.74 0.77 0.38 21.92 0.021 0.025 0.899 0.000 10 0.002 0.0125
24 DBA-XLP 0.18 −0.19 0.02 0.00 0.001 0.09 0.47 0.58 0.38 29.48 0.020 0.023 0.966 0.000 14 0.000 0.0109
25 URA-^SP500-50 0.22 −0.06 0.03 0.00 0.001 0.29 0.67 0.77 0.38 28.82 0.024 0.027 0.962 0.000 8 0.004 0.0190
26 EMB-EWJ 0.10 −0.01 0.02 0.00 0.001 0.24 0.61 0.64 0.38 20.57 0.017 0.021 0.931 0.000 65 0.000 0.0061
27 BND-IYR 0.07 0.68 −0.01 0.00 0.001 0.54 0.17 0.15 0.37 −16.58 −0.016 −0.012 0.913 0.000 361 0.000 0.0037
28 BSV-IYR 0.10 0.65 −0.02 0.00 0.001 0.49 0.12 0.00 0.37 −20.49 −0.017 −0.014 0.946 0.000 479 0.000 0.0055
29 IUSG-PCOPPUSDM 0.18 −0.04 0.02 0.00 0.001 0.28 0.65 0.75 0.37 34.90 0.022 0.024 0.912 0.000 140 0.000 0.0100
30 IYR-URA 0.18 0.08 0.02 0.00 0.001 0.36 0.72 0.79 0.36 25.31 0.020 0.023 0.948 0.000 0 0.892 0.0144
31 VCIT-XLY 0.08 −0.22 0.02 0.00 0.001 0.04 0.40 0.30 0.36 16.52 0.017 0.022 0.962 0.000 0 0.521 0.0061
32 EZU-PCOPPUSDM 0.16 0.08 0.02 0.00 0.001 0.35 0.71 0.80 0.36 31.80 0.019 0.022 0.909 0.000 154 0.000 0.0084
33 DBO-IYR 0.14 −0.09 0.02 0.00 0.001 0.18 0.54 0.63 0.36 25.49 0.019 0.022 0.930 0.000 35 0.000 0.0083
34 EZU-^SP500-50 0.13 0.00 0.02 0.00 0.001 0.29 0.65 0.77 0.36 29.13 0.020 0.023 0.937 0.000 251 0.000 0.0069
35 TLT-XLE 0.12 0.04 −0.02 0.00 0.001 −0.19 −0.55 −0.65 0.36 −26.26 −0.019 −0.016 0.956 0.000 1 0.299 0.0065
36 DBA-EWJ 0.13 −0.23 0.02 0.00 0.001 0.06 0.42 0.55 0.36 24.49 0.020 0.023 0.930 0.000 110 0.000 0.0075
37 PCOPPUSDM-XLY 0.17 −0.25 0.03 0.00 0.001 0.12 0.47 0.67 0.35 35.23 0.024 0.027 0.938 0.000 33 0.000 0.0096
38 EWJ-TIP 0.09 −0.40 0.02 0.00 0.001 −0.16 0.20 0.25 0.35 21.03 0.017 0.021 0.937 0.000 67 0.000 0.0045
39 silver-XLV 0.20 −0.40 0.02 0.00 0.001 −0.10 0.26 0.41 0.35 36.31 0.021 0.023 0.967 0.000 43 0.000 0.0107
40 DBA-XLY 0.16 −0.27 0.02 0.00 0.001 0.04 0.40 0.53 0.35 27.12 0.020 0.024 0.949 0.000 47 0.000 0.0092
41 PCOPPUSDM-SPY 0.15 −0.20 0.03 0.00 0.001 0.17 0.52 0.66 0.35 37.52 0.024 0.027 0.922 0.000 168 0.000 0.0077
42 CEMB-VEA 0.11 0.22 0.02 0.00 0.001 0.47 0.82 0.86 0.35 17.80 0.017 0.022 0.888 0.000 97 0.000 0.0084
43 EWJ-URA 0.19 −0.13 0.03 0.00 0.001 0.25 0.59 0.73 0.35 26.14 0.025 0.029 0.950 0.000 4 0.047 0.0157
44 EMB-EZU 0.09 0.09 0.02 0.00 0.001 0.32 0.67 0.70 0.35 19.36 0.016 0.020 0.914 0.000 122 0.000 0.0054
45 TLT-XLP 0.12 0.35 −0.02 0.00 0.001 0.05 −0.29 −0.45 0.35 −26.44 −0.023 −0.020 0.926 0.000 9 0.003 0.0065
46 EZU-silver 0.17 −0.07 0.02 0.00 0.001 0.19 0.53 0.61 0.34 31.46 0.018 0.020 0.949 0.000 38 0.000 0.0088
47 DBA-VCIT 0.10 0.62 −0.02 0.00 0.001 0.34 0.00 −0.27 0.34 −18.95 −0.023 −0.018 0.938 0.000 57 0.000 0.0081
48 EWJ-IYR 0.17 −0.10 0.02 0.00 0.001 0.19 0.53 0.62 0.34 33.59 0.020 0.022 0.955 0.000 8 0.004 0.0091
49 silver-VEA 0.20 −0.03 0.02 0.00 0.001 0.21 0.55 0.69 0.34 28.22 0.017 0.019 0.952 0.000 146 0.000 0.0114
50 EMB-IUSG 0.13 0.06 0.02 0.00 0.001 0.31 0.65 0.70 0.34 23.00 0.017 0.020 0.908 0.000 54 0.000 0.0075
51 TIP-XLY 0.09 −0.33 0.02 0.00 0.001 −0.10 0.24 0.32 0.34 21.67 0.017 0.020 0.964 0.000 65 0.000 0.0048
52 silver-TLT 0.11 0.32 −0.02 0.00 0.001 0.06 −0.28 −0.52 0.33 −23.31 −0.021 −0.018 0.971 0.000 195 0.000 0.0055
53 IEF-XLP 0.13 0.39 −0.02 0.00 0.001 0.09 −0.24 −0.44 0.33 −26.77 −0.023 −0.020 0.948 0.000 18 0.000 0.0067
54 IUSG-silver 0.15 −0.18 0.02 0.00 0.001 0.08 0.41 0.50 0.33 29.90 0.018 0.021 0.971 0.000 2 0.169 0.0078
55 DBA-TLT 0.10 0.23 −0.02 0.00 0.001 −0.01 −0.34 −0.53 0.33 −20.89 −0.020 −0.017 0.967 0.000 0 0.784 0.0056
56 DBA-IUSG 0.17 −0.07 0.02 0.00 0.001 0.19 0.52 0.62 0.33 28.49 0.018 0.020 0.957 0.000 1 0.351 0.0102
57 TLT-XLV 0.12 0.25 −0.02 0.00 0.001 −0.04 −0.36 −0.49 0.33 −26.59 −0.022 −0.019 0.929 0.000 39 0.000 0.0067
58 URA-XLY 0.18 −0.03 0.03 0.00 0.001 0.34 0.67 0.78 0.32 25.42 0.024 0.028 0.923 0.000 22 0.000 0.0149
59 GBTC-WILL5000PR 0.23 0.18 0.02 0.00 0.001 0.43 0.75 0.80 0.32 23.25 0.018 0.021 0.890 0.000 5 0.021 0.0189
60 platinum-XLV 0.15 −0.22 0.02 0.00 0.001 0.07 0.39 0.46 0.32 32.13 0.019 0.022 0.951 0.000 272 0.000 0.0082
61 EMB-XLF 0.12 0.04 0.02 0.00 0.001 0.30 0.62 0.70 0.32 22.75 0.017 0.021 0.944 0.000 234 0.000 0.0075
62 IUSV-PCOPPUSDM 0.14 0.04 0.02 0.00 0.001 0.32 0.63 0.72 0.31 30.19 0.019 0.021 0.906 0.000 18 0.000 0.0077
63 IYR-VCIT 0.14 0.94 −0.02 0.00 0.001 0.73 0.42 0.37 0.31 −22.93 −0.018 −0.015 0.897 0.000 289 0.000 0.0114
64 GBTC-IUSV 0.17 0.06 0.02 0.00 0.001 0.34 0.65 0.71 0.31 19.18 0.019 0.023 0.862 0.000 46 0.000 0.0128
65 TLT-^SP500-50 0.09 0.40 −0.02 0.00 0.001 0.11 −0.19 −0.46 0.31 −22.15 −0.022 −0.018 0.960 0.000 14 0.000 0.0047
66 EWJ-XLU 0.13 −0.40 0.02 0.00 0.001 −0.09 0.22 0.41 0.30 29.87 0.020 0.023 0.978 0.000 192 0.000 0.0069
67 EMB-XLI 0.08 0.18 0.02 0.00 0.001 0.39 0.69 0.73 0.30 18.23 0.014 0.018 0.882 0.000 196 0.000 0.0048
68 CEMB-WILL5000PR 0.11 0.24 0.02 0.00 0.001 0.47 0.78 0.81 0.30 18.15 0.016 0.020 0.889 0.000 46 0.000 0.0087
69 EMB-VEA 0.08 0.20 0.02 0.00 0.001 0.40 0.70 0.72 0.30 18.21 0.014 0.017 0.905 0.000 79 0.000 0.0049
70 EMB-XLV 0.14 −0.05 0.02 0.00 0.001 0.21 0.51 0.67 0.30 24.53 0.017 0.020 0.962 0.000 198 0.000 0.0086
71 EZU-TIP 0.08 −0.28 0.02 0.00 0.001 −0.07 0.23 0.31 0.30 19.54 0.015 0.018 0.958 0.000 60 0.000 0.0040
72 IUSG-TIP 0.06 −0.19 0.02 0.00 0.001 0.00 0.30 0.33 0.30 17.90 0.014 0.017 0.953 0.000 97 0.000 0.0034
73 DBA-SPY 0.14 0.03 0.02 0.00 0.001 0.26 0.56 0.63 0.30 24.94 0.016 0.018 0.928 0.000 31 0.000 0.0080
74 IYR-PCOPPUSDM 0.16 −0.14 0.02 0.00 0.001 0.18 0.47 0.64 0.30 32.04 0.020 0.023 0.955 0.000 4 0.058 0.0085
75 CEMB-XLI 0.09 0.28 0.02 0.00 0.001 0.50 0.80 0.84 0.30 16.33 0.015 0.019 0.845 0.000 64 0.000 0.0071
76 URA-XLF 0.19 0.12 0.02 0.00 0.001 0.43 0.72 0.82 0.30 26.02 0.020 0.024 0.936 0.000 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
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