Rare Disaster Concerns Everywhere George P. Gao and Zhaogang Song May 5, 2015 Internet Appendix: Additional Analyses and Robustness Checks Figure IA-1: Rare disaster concerns of 104 global assets (mean and standard deviation) Figure IA-2: Downside risk CAPM betas of GRIX-beta quintile portfolios Figure IA-3: Kelly-Jiang tail risk betas of GRIX-beta quintile portfolios Table IA-1: EQRIX-beta portfolio alphas and factor loadings Table IA-2: FXRIX-beta portfolio alphas and factor loadings Table IA-3: BDRIX-beta portfolio alphas and factor loadings Table IA-4: CMRIX-beta portfolio alphas and factor loadings Table IA-5: Asset-class RIX-beta COMBO portfolio alphas and factor loadings Table IA-6: GRIX-beta portfolio alphas and factor loadings Table IA-7: GRIX-beta portfolios within each of four asset classes Table IA-8: Correlations between rare disaster concerns and economic factors Table IA-9: Downside risk CAPM betas of asset-class RIX-beta portfolios Table IA-10: Kelly-Jiang tail risk betas of asset-class RIX-beta portfolios Table IA-11: Additional robustness checks on alternative return specifications and GRIX construction Table IA-12: Alternative measures of rare disaster concerns (within asset classes) Table IA-13: Alternative positions of average investors (within asset classes) Table IA-14: Prediction of GRIX on future economic fundamentals Table IA-15: Disaster concern innovation and returns of portfolios within and across asset classes Table IA-16: Kelly-Jiang tail risk and returns of portfolios within and across asset classes Table IA-17: U.S. exchange trade funds (ETFs) to track MSCI/FTSE international equity indices
Figure IA 1: Rare disaster concerns of individual assets in the global financial market This figure shows time series mean (left axis) and standard deviation (right axis) of monthly RIX for each of 30 international equity indices (Panel A), 32 foreign currencies (Panel B), 14 global government bonds (Panel C), and 28 commodities (Panel D). We also list option sample period below each panel. The full names of options are provided in the appendix of the paper. Panel A: International equity index 0.016 0.03 0.014 Mean Standard Deviation 0.025 0.012 0.01 0.02 0.008 0.015 0.006 0.01 0.004 0.002 0.005 0 0 Equity index option sample period: ASX200 (2001:02 2012:10), ATX (1996:01 2012:10), BEL20 (1996:01 2012:10), TSX60 (1999:09 2012:10), OMXC20 (2005:10 2012:01), ESTX50 (2001:07 2012:10), OMXH25 (2005:02 2012:10), CAC40 (2005:05 2012:10), DAX (2001:07 2012:10), ASE20 (2000:10 2012:10), HSI (1996:01 2012:10), NSEI (2001:07 2012:10), TA25 (1996:01 2012:10), MIB (2004:05 2012:10), N225 (1996:01 2012:10), IPC (2004:06 2012:10), AEX (1997:01 2012:10), VINX30 (2006:09 2012:10), OBX (1999:02 2012:10), WIG20 (2003:09 2012:10), RTS (2009:03 2012:10), SGX (2009:04 2012:10), KS200 (1997:07 2012:10), IBEX (2001:11 2012:10), OMXS30 (2004:11 2012:10), SMI (2001:07 2012:10), TAIEX (2001:06 2012:10), SET50 (2008:06 2012:10), FTSE100 (1996:01 2012:10), SPX (1996:01 2012:10).
Panel B: Foreign currency 0.12 0.1 Mean Standard Deviation 0.16 0.14 0.08 0.12 0.06 0.04 0.1 0.08 0.06 0.02 0.04 0 0.02 0.02 0 Currency option sample period: ARS (2004:03 2012:05), AUD (1996:01 2012:05), BRL (2004:03 2012:05), CAD (1996:02 2012:05), CLP (2004:03 2012:05), COP (2004:03 2012:05), CZK (2000:11 2012:05), DKK (1996:07 2012:05), EUR (1999:01 2012:05), HKD (1996:01 2012:05), HUF (2000:11 2012:05), ISK (2006:01 2012:05), INR (2004:03 2012:05), IDR (2001:03 2012:05), ILS (2004:03 2012:05), JPY (1996:02 2012:05), MYR (2000:11 2012:05), MXN (2000:11 2012:05), NZD (1996:12 2012:05), NOK (1996:02 2012:05), PEN (2004:03 2012:05), PHP (2003:02 2012:05), PLN (2000:11 2012:05), RUB (2006:01 2012:05), SGD (1997:03 2012:05), ZAR (1996:01 2012:05), KRW (2002:02 2012:05), SEK (1996:01 2012:05), CHF (1996:01 2012:05), TWD (2004:08 2012:05), THB (2000:11 2012:05), GBP (1996:01 2012:05). Note: The RIX mean and standard deviation of Icelandic Krona (ISK) are divided by 10.
Panel C: Glboal government bond 0.012 0.009 Mean Standard Deviation 0.008 0.01 0.007 0.008 0.006 0.005 0.006 0.004 0.004 0.003 0.002 0.002 0.001 0 Australia (10YR) Australia (3YR) Canada (10YR) Germany (10YR) Germany (2YR) Germany (5YR) Italy (10YR) Japan (10YR) Spain (10YR) United Kingdom (10YR) United States (10YR) United States (2YR) United States (30YR) United States (5YR) 0 Bond futures option sample period: AUS 10YR (1996:01 2012:12), AUS 3YR (1996:01 2012:12), CAN 10YR (1996:01 2003:05), DEU 10YR (1996:01 2012:12), DEU 2YR (1998:02 2012:12), DEU 5YR (1996:01 2012:12), ITA 10YR (1996:01 2000:06), JPN 10YR (1996:01 2012:12), ESP 10YR (1996:01 2000:08), GBR 10YR (1996:01 2012:12), USA 10YR (1996:01 2012:12), USA 2YR (2006:11 2012:12), USA 30YR (1996:01 2012:12), USA 5YR (1996:01 2012:12).
Panel D: Commodity 0.025 0.02 Mean Standard Deviation 0.01 0.009 0.008 0.007 0.015 0.006 0.005 0.01 0.004 0.003 0.005 0.002 0.001 0 0 Commodity futures option sample period 1996:01 2012:12 with the following exceptions: BA (2008:07 2012:12), HU (1996:01 2006:11), LH (1996:11 2012:12), PA (2010:11 2012:12), PB (1996:01 2010:05), QL (2009:07 2012:10), RB (2006:05 2012:12).
Figure IA 2: Downside risk of low minus high GRIX beta portfolios This figure presents mean excess returns of five GRIX beta quintiles against their downside risk CAPM (DR CAPM) betas. These quintile portfolios are monthly formed using 104 global assets of equity indices, currencies, government bonds, and commodities (see Table 4 in detail). To estimate each portfolio's DR CAPM beta, we regress its monthly excess returns on the MSCI world equity index excess returns using only downstates that are all months in which the market return is at least one standard deviation below its sample mean over the period from January 1998 through May 2012. The DR CAPM beta of low minus high GRIX beta hedge portfolio is 0.008 (with a t statistic of 0.03). 1.2 1 1 Low GRIX beta Mean (in percent) 0.8 0.6 0.4 3 2 0.2 4 5 High GRIX beta 0 0 0.2 0.4 0.6 0.8 1 1.2 Downside Risk CAPM Beta
Figure IA 3: Tail risk of low minus high GRIX beta portfolios This figure presents mean excess returns of five GRIX beta quintiles against their tail risk betas based on the Kelly Jiang (2014) market tail risk factor. These quintile portfolios are monthly formed using 104 global assets of equity indices, currencies, government bonds, and commodities (see Table 4 in detail). In estimating each portfolio's tail risk beta, we control for its loading on the MSCI world equity market returns. The tail risk beta of low minus high GRIX beta portfolio is 0.035 (with a t statistic of 0.37). 1.2 1 1 Low GRIX beta Mean (in percent) 0.8 0.6 0.4 3 2 4 0.2 5 High GRIX beta 0 0.08 0.06 0.04 0.02 0 0.02 0.04 0.06 0.08 Kelly Jiang Tail Risk Beta
Table IA 1: EQRIX beta portfolio alphas and factor loadings This table reports detailed results of EQRIX beta portfolios. The benchmark factors include global CAPM (MSCI world equity market return), Frazzini Pedersen (FP) betting agains beta (BAB), Moskowitz Ooi Pedersen (MOP) time series momentum (TSMOM), Asness Moskowitz Pedersen (AMP) international equity index based value (VAL) and momentum (MOM), Fama French (FF) international size (SMB), value (HML), and momentum (WML), and Hou Karolyi Kho (HKK) cash flow to price (CP) and momentum (short term) return (SRET). For brevity, we present portfolios' loadings on only nonmarket based factors in multi factor models. Panel A: Monthly Portfolio Formation Global CAPM FP 2 factor MOP 2 factor AMP 3 factor FF 4 factor HKK 3 factor α MSCI α BAB α TSMOM α VAL MOM α SMB HML WML α CP SRET Low RIX beta 0.703 1.138 0.627 0.275 0.562 0.087 0.497 0.392 0.455 0.452 0.546 0.097 0.076 0.442 0.157 0.234 (2.47) (15.24) (2.24) (2.29) (2.25) (2.41) (2.01) (2.96) (5.00) (1.86) (5.13) (0.88) (1.17) (1.44) (1.79) (3.40) 2 0.152 1.154 0.278 0.332 0.193 0.026 0.164 0.480 0.109 0.003 0.258 0.165 0.057 0.004 0.166 0.027 (0.53) (19.75) (1.00) ( 2.01) (0.71) ( 0.83) (0.71) (3.90) ( 0.95) (0.01) (2.40) (1.85) ( 0.95) ( 0.01) (1.92) (0.40) 3 0.057 1.157 0.012 0.075 0.037 0.012 0.079 0.447 0.268 0.129 0.004 0.164 0.060 0.276 0.204 0.149 (0.32) (19.45) (0.06) (0.86) (0.20) (0.47) ( 0.47) (4.99) (4.96) ( 0.69) (0.04) (2.06) (1.06) ( 1.55) (3.82) (3.74) High RIX beta 0.051 1.107 0.050 0.011 0.053 0.001 0.175 0.537 0.224 0.206 0.278 0.205 0.074 0.331 0.256 0.044 ( 0.19) (17.22) ( 0.19) ( 0.11) ( 0.21) (0.04) ( 0.74) (5.04) (2.77) ( 0.83) (2.27) (2.21) ( 1.16) ( 1.33) (3.14) (0.66) Low High 0.754 0.031 0.677 0.286 0.615 0.086 0.672 0.145 0.231 0.658 0.269 0.108 0.150 0.773 0.099 0.190 (2.38) (0.45) (2.12) (2.25) (2.12) (2.04) (2.34) ( 0.89) (1.97) (2.25) (1.91) ( 0.62) (1.48) (2.26) ( 0.82) (1.95) Panel B: Quarterly Portfolio Formation Global CAPM FP 2 factor MOP 2 factor AMP 3 factor FF 4 factor HKK 3 factor α MSCI α BAB α TSMOM α VAL MOM α SMB HML WML α CP SRET Low RIX beta 0.798 1.150 0.771 0.145 0.668 0.081 0.613 0.443 0.399 0.515 0.598 0.012 0.056 0.588 0.054 0.220 (3.03) (16.79) (2.93) (1.04) (2.69) (2.16) (2.60) (3.34) (2.92) (2.32) (4.79) ( 0.12) (0.82) (2.13) (0.59) (2.89) 2 0.372 1.205 0.426 0.093 0.368 0.002 0.311 0.318 0.052 0.122 0.214 0.208 0.018 0.074 0.263 0.116 (1.67) (22.56) (1.90) ( 0.74) (1.64) (0.10) (1.47) (2.99) (0.49) (0.53) (2.73) (2.03) ( 0.31) (0.33) (3.21) (2.17) 3 0.095 1.171 0.002 0.201 0.040 0.035 0.039 0.355 0.274 0.141 0.051 0.189 0.088 0.293 0.215 0.139 (0.51) (21.87) ( 0.01) (2.15) (0.21) (1.51) ( 0.23) (4.08) (4.06) ( 0.74) ( 0.53) (3.06) (1.55) ( 1.52) (4.51) (3.21) High RIX beta 0.064 1.164 0.015 0.104 0.070 0.004 0.201 0.679 0.136 0.270 0.246 0.197 0.087 0.313 0.188 0.008 ( 0.25) (18.76) ( 0.06) ( 0.71) ( 0.29) (0.13) ( 0.98) (6.88) (2.09) ( 1.16) (1.90) (2.00) ( 1.44) ( 1.35) (2.39) (0.14) Low High 0.861 0.013 0.786 0.249 0.738 0.077 0.814 0.235 0.263 0.785 0.352 0.209 0.143 0.901 0.134 0.212 (2.52) ( 0.17) (2.13) (1.52) (2.28) (1.63) (2.60) ( 1.38) (1.63) (2.51) (1.85) ( 1.21) (1.35) (2.41) ( 0.99) (2.14)
Panel C: Semi Annual Portfolio Formation Global CAPM FP 2 factor MOP 2 factor AMP 3 factor FF 4 factor HKK 3 factor α MSCI α BAB α TSMOM α VAL MOM α SMB HML WML α CP SRET Low RIX beta 0.863 1.138 0.799 0.229 0.720 0.089 0.660 0.453 0.460 0.565 0.604 0.003 0.078 0.580 0.072 0.263 (3.28) (14.39) (2.85) (1.31) (2.90) (2.02) (2.71) (3.23) (3.03) (2.35) (4.86) ( 0.03) (0.96) (2.07) (0.67) (2.76) 2 0.199 1.177 0.256 0.124 0.195 0.002 0.133 0.305 0.060 0.086 0.224 0.223 0.022 0.106 0.255 0.138 (0.93) (23.95) (1.22) ( 1.14) (0.90) (0.09) (0.65) (2.51) (0.57) ( 0.39) (2.80) (2.42) (0.45) ( 0.48) (3.27) (2.38) 3 0.252 1.228 0.184 0.112 0.213 0.024 0.140 0.310 0.203 0.101 0.061 0.097 0.011 0.050 0.187 0.068 (1.43) (24.48) (1.02) (1.27) (1.15) (1.15) (0.85) (4.03) (2.67) (0.53) ( 0.76) (1.54) (0.16) ( 0.27) (3.94) (1.55) High RIX beta 0.107 1.149 0.090 0.054 0.120 0.008 0.268 0.726 0.157 0.354 0.241 0.253 0.066 0.389 0.192 0.020 ( 0.42) (17.39) ( 0.35) ( 0.37) ( 0.51) (0.25) ( 1.39) (8.49) (2.43) ( 1.55) (1.89) (2.66) ( 1.09) ( 1.70) (2.61) (0.38) Low High 0.970 0.011 0.889 0.283 0.840 0.081 0.928 0.273 0.303 0.919 0.363 0.256 0.144 0.969 0.119 0.243 (2.79) ( 0.15) (2.30) (1.66) (2.57) (1.50) (2.84) ( 1.77) (1.73) (2.68) (2.07) ( 1.31) (1.26) (2.50) ( 0.80) (2.05) Panel D: Annual Portfolio Formation Global CAPM FP 2 factor MOP 2 factor AMP 3 factor FF 4 factor HKK 3 factor α MSCI α BAB α TSMOM α VAL MOM α SMB HML WML α CP SRET Low RIX beta 0.791 1.192 0.691 0.311 0.697 0.059 0.570 0.537 0.475 0.419 0.686 0.084 0.086 0.464 0.121 0.281 (2.89) (12.28) (2.44) (1.83) (2.78) (1.25) (2.35) (3.49) (3.26) (1.77) (5.41) (0.79) (1.17) (1.70) (1.28) (3.33) 2 0.246 1.154 0.293 0.116 0.214 0.020 0.136 0.350 0.167 0.055 0.180 0.215 0.069 0.159 0.220 0.182 (1.15) (20.58) (1.37) ( 1.01) (1.05) (0.81) (0.68) (3.17) (1.56) ( 0.24) (1.97) (2.34) (1.22) ( 0.71) (3.00) (3.39) 3 0.141 1.188 0.160 0.078 0.155 0.009 0.114 0.255 0.048 0.033 0.076 0.244 0.055 0.205 0.327 0.029 (0.90) (26.43) (0.98) ( 1.00) (0.92) ( 0.43) (0.76) (3.02) ( 0.73) ( 0.20) ( 0.83) (4.44) ( 0.95) ( 1.21) (6.28) ( 0.58) High RIX beta 0.130 1.143 0.139 0.006 0.178 0.030 0.290 0.664 0.188 0.306 0.235 0.132 0.080 0.260 0.093 0.015 ( 0.58) (22.40) ( 0.62) ( 0.05) ( 0.80) (1.19) ( 1.68) (8.79) (3.76) ( 1.49) (2.02) (1.56) ( 1.79) ( 1.47) (1.38) (0.37) Low High 0.921 0.049 0.829 0.317 0.876 0.028 0.860 0.127 0.286 0.725 0.451 0.049 0.166 0.724 0.028 0.266 (2.95) (0.59) (2.50) (2.32) (2.89) (0.63) (2.80) ( 0.75) (1.88) (2.47) (2.55) ( 0.30) (1.88) (2.22) (0.23) (2.96)
Table IA 2: FXRIX beta portfolio alphas and factor loadings This table reports detailed results of FXRIX beta portfolios. The benchmark factors include currency market (i.e., the dollar (DOL) factor in Lustig Roussanov Verdelhan 2 factor model using all countries), Frazzini Pedersen (FP) betting agains beta (BAB), Moskowitz Ooi Pedersen (MOP) time series momentum (TSMOM), Asness Moskowitz Pedersen (AMP) currency based value (VAL) and momentum (MOM), and Lustig Roussanov Verdelhan (LRV) carry (HML). Panel A: Monthly Portfolio Formation Currency Market FP 2 factor MOP 2 factor AMP 3 factor LRV 2 factor α DOL α BAB α TSMOM α VAL MOM α HML Low RIX beta 0.516 1.285 0.507 0.194 0.512 0.005 0.519 0.048 0.043 0.495 0.031 (3.30) (18.84) (3.29) (2.23) (3.25) (0.17) (3.38) ( 0.63) (0.58) (3.21) (0.51) 2 0.101 1.028 0.090 0.042 0.104 0.003 0.125 0.084 0.027 0.088 0.021 ( 1.24) (20.01) ( 1.07) ( 0.79) ( 1.20) (0.16) ( 1.57) (1.63) (0.65) ( 1.06) ( 0.43) 3 0.077 1.031 0.069 0.060 0.064 0.016 0.100 0.075 0.028 0.130 0.078 (1.01) (22.73) (0.88) (1.42) (0.83) (0.86) (1.29) ( 2.08) ( 0.73) (1.63) ( 2.33) High RIX beta 0.174 1.154 0.160 0.135 0.180 0.007 0.171 0.030 0.017 0.227 0.080 (1.77) (19.20) (1.64) (2.74) (1.76) ( 0.30) (1.69) (0.44) ( 0.27) (2.10) ( 1.56) Low High 0.341 0.131 0.347 0.059 0.332 0.012 0.348 0.078 0.060 0.267 0.111 (1.81) (1.62) (1.83) (0.53) (1.72) (0.32) (1.82) ( 0.87) (0.67) (1.39) (1.62) Panel B: Quarterly Portfolio Formation Currency Market FP 2 factor MOP 2 factor AMP 3 factor LRV 2 factor α DOL α BAB α TSMOM α VAL MOM α HML Low RIX beta 0.551 1.331 0.546 0.179 0.537 0.017 0.546 0.030 0.060 0.559 0.012 (3.14) (20.35) (3.17) (2.51) (3.03) (0.63) (3.20) ( 0.41) (0.87) (3.20) ( 0.18) 2 0.001 1.013 0.002 0.044 0.001 0.001 0.029 0.099 0.040 0.013 0.018 (0.01) (16.92) ( 0.02) ( 0.69) (0.02) ( 0.05) ( 0.35) (1.90) (0.84) (0.13) ( 0.33) 3 0.070 1.026 0.086 0.035 0.076 0.008 0.099 0.087 0.050 0.106 0.054 (0.94) (20.38) (1.17) (1.02) (1.02) ( 0.55) (1.32) ( 2.45) ( 1.37) (1.38) ( 1.46) High RIX beta 0.077 1.136 0.049 0.169 0.068 0.011 0.077 0.015 0.019 0.126 0.073 (0.81) (18.09) (0.54) (4.33) (0.72) (0.51) (0.78) (0.21) ( 0.30) (1.24) ( 1.65) Low High 0.474 0.195 0.496 0.009 0.469 0.006 0.469 0.045 0.078 0.433 0.061 (2.46) (2.70) (2.58) (0.11) (2.36) (0.19) (2.38) ( 0.53) (0.99) (2.21) (0.87)
Panel C: Semi Annual Portfolio Formation Currency Market FP 2 factor MOP 2 factor AMP 3 factor LRV 2 factor α DOL α BAB α TSMOM α VAL MOM α HML Low RIX beta 0.615 1.290 0.615 0.128 0.601 0.018 0.607 0.001 0.045 0.610 0.007 (3.41) (19.29) (3.42) (1.82) (3.28) (0.66) (3.43) ( 0.01) (0.62) (3.37) (0.11) 2 0.179 1.041 0.191 0.013 0.178 0.001 0.178 0.012 0.004 0.149 0.045 ( 2.05) (24.34) ( 2.16) (0.27) ( 2.09) ( 0.07) ( 2.02) ( 0.34) (0.11) ( 1.59) ( 0.93) 3 0.121 1.016 0.126 0.060 0.122 0.001 0.142 0.077 0.016 0.149 0.041 (1.54) (19.07) (1.57) (1.53) (1.51) ( 0.05) (1.75) ( 1.91) ( 0.43) (1.85) ( 0.96) High RIX beta 0.111 1.164 0.098 0.141 0.103 0.009 0.094 0.072 0.001 0.155 0.066 (1.22) (19.31) (1.13) (2.84) (1.12) (0.46) (1.00) (1.11) ( 0.01) (1.61) ( 1.53) Low High 0.505 0.126 0.516 0.012 0.497 0.009 0.512 0.073 0.046 0.456 0.073 (2.54) (1.71) (2.56) ( 0.14) (2.40) (0.28) (2.53) ( 0.90) (0.55) (2.26) (1.07) Panel D: Annual Portfolio Formation Currency Market FP 2 factor MOP 2 factor AMP 3 factor LRV 2 factor α DOL α BAB α TSMOM α VAL MOM α HML Low RIX beta 0.526 1.282 0.524 0.131 0.529 0.005 0.556 0.121 0.018 0.477 0.072 (3.29) (16.68) (3.28) (1.58) (3.24) ( 0.14) (3.61) ( 1.43) ( 0.22) (2.92) (1.06) 2 0.131 1.084 0.145 0.035 0.120 0.014 0.126 0.002 0.026 0.084 0.071 ( 1.60) (21.34) ( 1.76) (0.72) ( 1.49) ( 0.81) ( 1.53) (0.05) ( 0.70) ( 0.94) ( 1.56) 3 0.110 1.061 0.124 0.051 0.109 0.002 0.091 0.062 0.029 0.131 0.031 (1.32) (19.58) (1.47) ( 1.04) (1.26) (0.11) (1.07) (1.17) (0.62) (1.55) ( 0.69) High RIX beta 0.157 1.089 0.140 0.218 0.123 0.042 0.135 0.051 0.056 0.236 0.119 (1.56) (19.12) (1.46) (5.35) (1.21) (2.14) (1.29) (1.02) (1.13) (2.30) ( 2.86) Low High 0.369 0.193 0.384 0.087 0.407 0.047 0.422 0.172 0.074 0.241 0.191 (1.92) (2.06) (1.97) ( 0.97) (2.04) ( 1.18) (2.21) ( 1.89) ( 0.78) (1.22) (2.55)
Table IA 3: BDRIX beta portfolio alphas and factor loadings This table reports detailed results of BDRIX beta portfolios. The benchmark factors include global bond market (GBD), Frazzini Pedersen (FP) betting agains beta (BAB), Moskowitz Ooi Pedersen (MOP) time series momentum (TSMOM), Asness Moskowitz Pedersen (AMP) global government bond based value (VAL) and momentum (MOM). Panel A: Monthly Portfolio Formation Panel B: Quarterly Portfolio Formation Bond Market FP 2 factor MOP 2 factor AMP 3 factor Bond Market FP 2 factor MOP 2 factor AMP 3 factor α GBD α BAB α TSMOM α VAL MOM α GBD α BAB α TSMOM α VAL MOM Low RIX beta 0.364 1.361 0.357 0.201 0.289 0.048 0.361 0.021 0.214 Low RIX beta 0.272 1.263 0.260 0.167 0.205 0.041 0.274 0.055 0.099 (5.39) (11.99) (5.18) ( 1.81) (4.42) (3.40) (5.42) (0.13) (1.91) (4.13) (12.78) (3.91) ( 1.06) (3.24) (2.84) (4.14) ( 0.39) (1.04) 2 0.186 0.861 0.180 0.066 0.154 0.021 0.185 0.018 0.032 2 0.199 0.889 0.197 0.188 0.156 0.027 0.187 0.133 0.134 (4.54) (13.87) (4.45) ( 0.59) (3.87) (1.84) (4.41) (0.17) (0.37) (4.73) (11.78) (4.70) ( 2.35) (3.68) (2.51) (4.32) (1.60) (1.62) 3 0.157 0.768 0.165 0.187 0.135 0.014 0.161 0.087 0.061 3 0.161 0.743 0.167 0.167 0.131 0.018 0.164 0.064 0.075 (3.98) (12.88) (4.00) ( 2.78) (3.58) (1.54) (4.18) ( 1.27) (1.06) (3.35) (11.93) (3.34) ( 2.69) (2.95) (2.46) (3.62) ( 0.92) (1.19) High RIX beta 0.148 0.968 0.164 0.244 0.130 0.012 0.162 0.272 0.061 High RIX beta 0.188 1.016 0.205 0.215 0.162 0.016 0.201 0.202 0.074 (2.62) (9.58) (2.72) ( 2.16) (2.47) (0.94) (3.05) ( 3.29) (0.74) (3.40) (10.04) (3.53) ( 2.00) (3.12) (1.28) (3.73) ( 2.23) (0.88) Low High 0.216 0.393 0.193 0.043 0.159 0.036 0.199 0.292 0.153 Low High 0.084 0.247 0.055 0.048 0.043 0.026 0.073 0.146 0.025 (2.84) (2.38) (2.49) (0.30) (2.15) (2.22) (2.69) (1.65) (1.11) (1.08) (1.61) (0.70) (0.26) (0.56) (1.60) (0.94) (1.00) (0.21) Panel C: Semi Annual Portfolio Formation Panel D: Annual Portfolio Formation Bond Market FP 2 factor MOP 2 factor AMP 3 factor Bond Market FP 2 factor MOP 2 factor AMP 3 factor α GBD α BAB α TSMOM α VAL MOM α GBD α BAB α TSMOM α VAL MOM Low RIX beta 0.404 1.362 0.401 0.385 0.340 0.039 0.386 0.170 0.302 Low RIX beta 0.377 1.434 0.372 0.417 0.282 0.061 0.378 0.062 0.308 (6.17) (10.95) (6.02) ( 3.14) (5.62) (2.62) (5.73) (1.31) (2.30) (5.36) (10.92) (5.15) ( 2.22) (4.45) (3.40) (5.38) ( 0.33) (1.83) 2 0.171 0.779 0.164 0.044 0.127 0.027 0.170 0.005 0.016 2 0.162 0.749 0.158 0.087 0.128 0.022 0.162 0.009 0.066 (4.91) (13.26) (4.75) ( 0.42) (3.32) (2.50) (4.86) (0.07) (0.22) (4.51) (10.71) (4.49) ( 1.23) (3.34) (2.07) (4.48) (0.13) (0.95) 3 0.149 0.711 0.156 0.138 0.126 0.014 0.156 0.101 0.020 3 0.132 0.728 0.134 0.010 0.123 0.006 0.140 0.154 0.036 (3.76) (11.42) (3.73) ( 2.31) (3.31) (2.19) (3.90) ( 1.45) (0.36) (3.21) (9.89) (3.09) ( 0.14) (3.11) (0.79) (3.55) ( 2.25) (0.65) High RIX beta 0.126 1.089 0.141 0.254 0.094 0.020 0.139 0.210 0.089 High RIX beta 0.181 1.065 0.199 0.231 0.168 0.008 0.188 0.148 0.002 (2.08) (9.97) (2.22) ( 2.33) (1.59) (1.51) (2.37) ( 2.20) (1.05) (2.99) (10.45) (3.19) ( 2.32) (2.74) (0.63) (3.15) ( 1.60) ( 0.02) Low High 0.278 0.273 0.260 0.131 0.246 0.019 0.247 0.380 0.212 Low High 0.196 0.369 0.174 0.185 0.114 0.053 0.189 0.086 0.309 (3.46) (1.70) (3.18) ( 0.81) (3.08) (1.08) (3.11) (2.81) (1.47) (2.55) (2.01) (2.23) ( 0.87) (1.43) (2.51) (2.52) (0.42) (1.66)
Table IA 4: CMRIX beta portfolio alphas and factor loadings This table reports detailed results of CMRIX beta portfolios. The benchmark factors include commodity market (SPGSCI), Frazzini Pedersen (FP) betting agains beta (BAB), Moskowitz Ooi Pedersen (MOP) time series momentum (TSMOM), Asness Moskowitz Pedersen (AMP) commodity based value (VAL) and momentum (MOM), Baltas and Kosowski (BK) trend following time series momentum at monthly frequency domain (FTB), and Yang basis (HML). Note: the time series of commodity basis factor provided in Yang (2014) is only up to December 2008. Panel A: Monthly Portfolio Formation Comm. Market FP 2 factor MOP 2 factor AMP 3 factor BK 2 factor Yang 2 factor α SPGSCI α BAB α TSMOM α VAL MOM α FTB α HML Low RIX beta 0.543 0.524 0.582 0.274 0.559 0.020 0.575 0.075 0.039 0.738 0.072 0.521 0.012 (1.92) (11.98) (2.10) (3.66) (1.90) ( 0.29) (1.98) (1.05) ( 0.60) (2.37) ( 1.13) (1.78) (0.19) 2 0.334 0.509 0.295 0.235 0.237 0.115 0.287 0.045 0.068 0.263 0.036 0.134 0.059 (1.19) (11.50) (1.05) (3.01) (0.82) (1.40) (0.97) (0.58) (0.87) (0.82) (0.46) (0.49) (0.89) 3 0.133 0.488 0.127 0.348 0.156 0.028 0.143 0.206 0.000 0.225 0.048 0.287 0.052 (0.44) (8.08) (0.44) (4.91) (0.53) ( 0.35) (0.50) (2.99) (0.01) (0.74) ( 0.56) (0.94) ( 1.04) High RIX beta 0.280 0.373 0.373 0.318 0.355 0.089 0.326 0.211 0.080 0.364 0.019 0.186 0.032 ( 0.89) (6.83) ( 1.22) (4.35) ( 1.13) (1.04) ( 1.06) (2.90) (1.08) ( 1.07) (0.22) ( 0.51) ( 0.49) Low High 0.823 0.151 0.955 0.044 0.914 0.109 0.901 0.136 0.120 1.102 0.091 0.707 0.044 (1.96) (2.00) (2.19) ( 0.35) (2.18) ( 1.10) (2.12) ( 1.30) ( 1.32) (2.49) ( 1.00) (1.51) (0.53) Panel B: Quarterly Portfolio Formation Comm. Market FP 2 factor MOP 2 factor AMP 3 factor BK 2 factor Yang 2 factor α SPGSCI α BAB α TSMOM α VAL MOM α FTB α HML Low RIX beta 0.487 0.634 0.553 0.253 0.558 0.081 0.511 0.087 0.038 0.669 0.074 0.604 0.021 (1.58) (11.93) (1.79) (3.09) (1.69) ( 1.04) (1.56) (1.03) ( 0.48) (1.84) ( 0.91) (2.26) (0.32) 2 0.132 0.419 0.152 0.402 0.102 0.034 0.141 0.126 0.020 0.256 0.088 0.389 0.020 (0.46) (7.59) (0.57) (6.75) (0.36) (0.37) (0.49) (1.76) ( 0.31) (0.84) ( 1.02) (1.37) (0.37) 3 0.200 0.392 0.210 0.380 0.211 0.013 0.220 0.164 0.037 0.201 0.008 0.109 0.000 (0.73) (7.05) (0.81) (5.81) (0.77) ( 0.15) (0.79) (2.79) ( 0.60) (0.72) ( 0.11) ( 0.38) ( 0.00) High RIX beta 0.444 0.334 0.462 0.332 0.477 0.038 0.470 0.161 0.028 0.542 0.035 0.173 0.060 ( 1.55) (6.30) ( 1.71) (5.74) ( 1.66) (0.55) ( 1.64) (2.52) (0.43) ( 1.86) (0.48) ( 0.57) ( 1.24) Low High 0.930 0.300 1.015 0.080 1.035 0.119 0.981 0.074 0.066 1.211 0.109 0.777 0.081 (2.10) (3.79) (2.23) ( 0.78) (2.32) ( 1.27) (2.15) ( 0.73) ( 0.71) (2.48) ( 1.18) (1.86) (1.00)
Panel C: Semi Annual Portfolio Formation Comm. Market FP 2 factor MOP 2 factor AMP 3 factor BK 2 factor Yang 2 factor α SPGSCI α BAB α TSMOM α VAL MOM α FTB α HML Low RIX beta 0.754 0.557 0.833 0.254 0.753 0.001 0.740 0.099 0.014 0.893 0.033 0.827 0.025 (2.53) (10.10) (2.80) (3.19) (2.34) (0.01) (2.34) (1.19) (0.17) (2.51) ( 0.37) (2.52) ( 0.34) 2 0.248 0.490 0.220 0.396 0.278 0.034 0.266 0.146 0.017 0.284 0.035 0.395 0.049 ( 0.99) (12.33) ( 0.95) (5.77) ( 1.08) (0.50) ( 1.04) (2.13) (0.26) ( 1.08) (0.60) ( 1.42) (0.86) 3 0.556 0.416 0.526 0.372 0.524 0.037 0.563 0.165 0.018 0.476 0.001 0.331 0.034 (1.97) (8.31) (2.03) (5.77) (1.85) (0.40) (1.95) (2.36) ( 0.29) (1.65) (0.01) (1.02) ( 0.62) High RIX beta 0.582 0.341 0.584 0.319 0.546 0.041 0.564 0.148 0.032 0.473 0.083 0.500 0.051 ( 2.13) (5.97) ( 2.26) (5.80) ( 1.99) ( 0.63) ( 2.03) (2.48) ( 0.49) ( 1.61) ( 1.20) ( 1.58) ( 0.92) Low High 1.336 0.216 1.417 0.066 1.299 0.042 1.304 0.048 0.046 1.365 0.050 1.327 0.026 (3.39) (2.92) (3.51) ( 0.65) (3.19) (0.45) (3.21) ( 0.50) (0.46) (3.03) (0.50) (2.84) (0.32) Panel D: Annual Portfolio Formation Comm. Market FP 2 factor MOP 2 factor AMP 3 factor BK 2 factor Yang 2 factor α SPGSCI α BAB α TSMOM α VAL MOM α FTB α HML Low RIX beta 0.488 0.515 0.551 0.308 0.469 0.021 0.450 0.147 0.043 0.521 0.022 0.539 0.001 (1.59) (8.07) (1.81) (3.80) (1.43) (0.25) (1.36) (1.81) (0.51) (1.46) (0.25) (1.53) (0.02) 2 0.060 0.452 0.049 0.434 0.071 0.012 0.026 0.150 0.055 0.039 0.016 0.243 0.008 ( 0.21) (10.13) ( 0.18) (5.80) ( 0.24) (0.15) ( 0.09) (1.92) ( 0.82) ( 0.13) ( 0.23) ( 0.84) (0.14) 3 0.646 0.433 0.634 0.321 0.626 0.022 0.616 0.173 0.032 0.728 0.092 0.529 0.007 (2.24) (7.38) (2.39) (5.20) (2.12) (0.28) (2.08) (2.75) (0.57) (2.43) ( 1.27) (1.51) ( 0.16) High RIX beta 0.601 0.400 0.587 0.287 0.568 0.038 0.575 0.099 0.041 0.562 0.023 0.541 0.071 ( 2.26) (8.91) ( 2.29) (5.29) ( 2.12) ( 0.60) ( 2.13) (1.75) ( 0.60) ( 2.06) ( 0.30) ( 1.68) ( 1.17) Low High 1.089 0.116 1.138 0.021 1.036 0.060 1.025 0.048 0.084 1.083 0.044 1.081 0.072 (2.74) (1.47) (2.77) (0.20) (2.52) (0.68) (2.45) (0.52) (0.82) (2.38) (0.44) (2.26) (0.81)
Table IA 5: Asset class RIX beta COMBO portfolio alphas and factor loadings This table reports detailed results of four asset class RIX beta combination portfolios. The benchmark factors include global equity market (MSCI world equity market return), Frazzini Pedersen (FP) betting agains beta (BAB), Moskowitz Ooi Pedersen (MOP) time series momentum (TSMOM), Asness Moskowitz Pedersen (AMP) all asset based value (VAL) and momentum (MOM), and Baltas and Kosowski (BK) trend following time series momentum at monthly frequency domain (FTB). Panel A: Monthly Portfolio Formation Global CAPM FP 2 factor MOP 2 factor AMP 3 factor BK 2 factor α MSCI α BAB α TSMOM α VAL MOM α FTB Low RIX beta 0.641 0.434 0.327 0.704 0.500 0.113 0.603 0.073 0.133 0.591 0.065 (3.78) (9.46) (2.13) (5.44) (3.19) (2.15) (3.94) ( 0.70) (1.35) (3.55) (1.43) 2 0.222 0.444 0.071 0.337 0.121 0.080 0.226 0.076 0.022 0.224 0.015 (1.42) (12.30) (0.43) (2.98) (0.76) (1.75) (1.43) ( 0.63) (0.25) (1.32) (0.30) 3 0.181 0.438 0.098 0.619 0.118 0.050 0.119 0.090 0.121 0.187 0.012 (1.30) (8.12) ( 0.76) (5.51) (0.89) (1.14) (0.84) (0.90) (1.60) (1.44) (0.29) High RIX beta 0.053 0.395 0.287 0.754 0.063 0.093 0.055 0.217 0.186 0.036 0.034 (0.31) (7.88) ( 1.97) (5.53) ( 0.39) (1.87) ( 0.34) (2.18) (2.38) (0.22) (0.76) Low High 0.588 0.039 0.614 0.050 0.563 0.020 0.659 0.290 0.054 0.555 0.031 (3.53) (1.28) (3.53) ( 0.30) (3.26) (0.53) (4.17) ( 2.32) ( 0.57) (3.22) (0.87) Panel B: Quarterly Portfolio Formation Global CAPM FP 2 factor MOP 2 factor AMP 3 factor BK 2 factor α MSCI α BAB α TSMOM α VAL MOM α FTB Low RIX beta 0.615 0.455 0.282 0.731 0.520 0.079 0.582 0.074 0.125 0.582 0.048 (3.31) (7.85) (1.81) (5.07) (3.21) (1.37) (3.52) ( 0.65) (1.18) (3.47) (0.92) 2 0.187 0.453 0.024 0.441 0.132 0.046 0.155 0.068 0.052 0.216 0.010 (1.22) (12.17) ( 0.14) (3.98) (0.83) (1.02) (0.96) (0.50) (0.53) (1.25) ( 0.20) 3 0.160 0.417 0.108 0.575 0.089 0.059 0.102 0.068 0.122 0.136 0.027 (1.09) (8.87) ( 0.87) (5.28) (0.65) (1.30) (0.71) (0.88) (1.96) (0.98) (0.71) High RIX beta 0.012 0.406 0.292 0.645 0.082 0.077 0.068 0.172 0.131 0.017 0.028 (0.08) (8.70) ( 2.19) (5.38) ( 0.59) (1.60) ( 0.48) (1.68) (1.84) ( 0.12) (0.66) Low High 0.604 0.049 0.574 0.087 0.602 0.001 0.650 0.245 0.007 0.599 0.020 (3.48) (1.60) (3.35) (0.51) (3.69) (0.03) (4.02) ( 1.80) ( 0.07) (3.57) (0.52)
Panel C: Semi Annual Portfolio Formation Global CAPM FP 2 factor MOP 2 factor AMP 3 factor BK 2 factor α MSCI α BAB α TSMOM α VAL MOM α FTB Low RIX beta 0.703 0.425 0.395 0.683 0.609 0.077 0.652 0.035 0.151 0.678 0.044 (3.78) (7.37) (2.26) (4.48) (3.43) (1.34) (3.70) ( 0.28) (1.55) (3.78) (0.81) 2 0.051 0.447 0.229 0.584 0.057 0.089 0.008 0.088 0.116 0.021 0.033 (0.34) (12.35) ( 1.65) (6.06) ( 0.40) (2.09) ( 0.06) (0.88) (1.37) (0.14) (0.75) 3 0.299 0.435 0.072 0.454 0.237 0.051 0.288 0.017 0.038 0.253 0.025 (2.09) (10.18) (0.49) (3.99) (1.60) (1.01) (1.90) ( 0.24) (0.53) (1.75) (0.62) High RIX beta 0.066 0.426 0.363 0.649 0.133 0.055 0.158 0.219 0.141 0.047 0.004 ( 0.46) (9.07) ( 3.04) (5.96) ( 1.03) (1.22) ( 1.21) (2.07) (2.05) ( 0.36) (0.10) Low High 0.769 0.001 0.758 0.034 0.742 0.022 0.810 0.254 0.011 0.725 0.040 (4.58) ( 0.04) (4.20) (0.21) (4.36) (0.44) (4.97) ( 1.89) (0.14) (4.19) (0.85) Panel D: Annual Portfolio Formation Global CAPM FP 2 factor MOP 2 factor AMP 3 factor BK 2 factor α MSCI α BAB α TSMOM α VAL MOM α FTB Low RIX beta 0.590 0.446 0.292 0.693 0.487 0.089 0.511 0.030 0.202 0.586 0.040 (3.09) (6.97) (1.54) (4.11) (2.69) (1.60) (2.75) (0.25) (1.92) (3.26) (0.76) 2 0.106 0.432 0.194 0.604 0.014 0.079 0.069 0.038 0.082 0.079 0.023 (0.69) (10.89) ( 1.33) (6.15) (0.10) (1.87) (0.45) (0.36) (1.00) (0.51) (0.53) 3 0.280 0.431 0.046 0.485 0.250 0.026 0.249 0.085 0.040 0.300 0.015 (2.06) (11.11) (0.35) (4.36) (1.73) (0.55) (1.88) (0.88) (0.55) (2.15) ( 0.36) High RIX beta 0.028 0.421 0.288 0.563 0.097 0.060 0.081 0.081 0.105 0.055 0.033 ( 0.21) (9.99) ( 2.66) (6.73) ( 0.80) (1.31) ( 0.64) (0.89) (1.52) ( 0.45) (0.80) Low High 0.618 0.025 0.581 0.130 0.584 0.029 0.592 0.051 0.097 0.641 0.008 (3.87) (0.68) (3.14) (0.82) (3.54) (0.73) (3.45) ( 0.36) (1.15) (3.99) (0.20)
Table IA 6: GRIX beta portfolio alphas and factor loadings This table reports detailed results of GRIX beta portfolios. The benchmark factors include global equity market (MSCI world equity market return), Frazzini Pedersen (FP) betting agains beta (BAB), Moskowitz Ooi Pedersen (MOP) time series momentum (TSMOM), Asness Moskowitz Pedersen (AMP) all asset based value (VAL) and momentum (MOM), and Baltas and Kosowski (BK) trend following time series momentum at monthly frequency domain (FTB). Panel A: Monthly Portfolio Formation Global CAPM FP 2 factor MOP 2 factor AMP 3 factor BK 2 factor α MSCI α BAB α TSMOM α VAL MOM α FTB Low GRIX beta 0.944 0.531 0.675 0.679 0.672 0.217 0.914 0.144 0.142 0.884 0.091 (3.98) (8.41) (2.80) (3.56) (2.75) (2.15) (3.75) ( 0.77) (0.97) (3.47) (1.16) 2 0.300 0.358 0.081 0.517 0.159 0.113 0.246 0.061 0.114 0.271 0.048 (1.90) (7.89) (0.53) (5.55) (0.98) (2.03) (1.47) (0.58) (1.15) (1.60) (0.98) 3 0.302 0.346 0.048 0.527 0.160 0.113 0.191 0.174 0.211 0.217 0.066 (2.31) (7.97) (0.37) (5.19) (1.29) (3.21) (1.54) (1.80) (2.96) (1.72) (1.78) 4 0.119 0.544 0.233 0.760 0.111 0.007 0.023 0.363 0.207 0.199 0.036 (0.56) (6.73) ( 1.03) (3.65) (0.51) (0.11) ( 0.10) (2.72) (1.70) (0.88) ( 0.54) High GRIX beta 0.060 0.543 0.534 1.076 0.033 0.022 0.080 0.028 0.065 0.025 0.024 ( 0.22) (6.23) ( 2.05) (5.43) ( 0.13) ( 0.25) ( 0.27) ( 0.18) (0.45) (0.10) ( 0.30) Low High 1.004 0.012 1.208 0.396 0.704 0.238 0.994 0.115 0.077 0.860 0.116 (3.61) ( 0.20) (4.07) ( 1.70) (2.55) (2.50) (3.32) ( 0.55) (0.46) (2.89) (1.47) Panel B: Quarterly Portfolio Formation Global CAPM FP 2 factor MOP 2 factor AMP 3 factor BK 2 factor α MSCI α BAB α TSMOM α VAL MOM α FTB Low GRIX beta 0.772 0.502 0.548 0.619 0.585 0.147 0.752 0.129 0.099 0.780 0.041 (3.29) (7.50) (2.30) (3.01) (2.52) (1.63) (3.13) ( 0.70) (0.70) (3.28) (0.57) 2 0.329 0.337 0.117 0.530 0.241 0.069 0.273 0.077 0.108 0.341 0.024 (1.98) (7.31) (0.74) (5.53) (1.40) (1.14) (1.59) (0.57) (1.21) (2.02) (0.49) 3 0.212 0.357 0.026 0.537 0.103 0.086 0.141 0.079 0.142 0.154 0.051 (1.48) (7.19) ( 0.18) (5.00) (0.75) (1.95) (0.97) (0.93) (1.83) (1.14) (1.14) 4 0.189 0.528 0.189 0.843 0.113 0.060 0.037 0.305 0.255 0.207 0.002 (0.89) (6.77) ( 0.87) (4.16) (0.53) (0.88) (0.17) (2.19) (1.97) (0.96) ( 0.03) High GRIX beta 0.040 0.537 0.384 1.032 0.110 0.055 0.022 0.072 0.016 0.175 0.060 (0.15) (6.90) ( 1.51) (5.93) (0.40) ( 0.64) (0.08) (0.47) (0.11) (0.61) ( 0.73) Low High 0.731 0.035 0.932 0.413 0.475 0.201 0.730 0.200 0.082 0.605 0.102 (2.55) ( 0.61) (3.00) ( 1.72) (1.62) (2.39) (2.32) ( 0.91) (0.47) (1.87) (1.30)
Panel C: Semi Annual Portfolio Formation Global CAPM FP 2 factor MOP 2 factor AMP 3 factor BK 2 factor α MSCI α BAB α TSMOM α VAL MOM α FTB Low GRIX beta 0.608 0.485 0.306 0.775 0.449 0.125 0.543 0.080 0.189 0.585 0.056 (2.59) (6.36) (1.23) (3.43) (1.92) (1.26) (2.14) ( 0.42) (1.16) (2.41) (0.70) 2 0.467 0.352 0.256 0.506 0.414 0.042 0.486 0.099 0.009 0.515 0.006 (2.58) (6.58) (1.33) (3.55) (2.16) (0.65) (2.45) ( 0.60) ( 0.07) (2.72) ( 0.10) 3 0.214 0.372 0.001 0.520 0.101 0.089 0.132 0.127 0.154 0.177 0.049 (1.51) (6.85) (0.01) (3.77) (0.73) (2.12) (0.91) (1.61) (2.11) (1.29) (1.18) 4 0.001 0.512 0.328 0.775 0.096 0.075 0.173 0.385 0.272 0.012 0.013 ( 0.00) (8.25) ( 1.79) (5.56) ( 0.54) (1.25) ( 0.90) (2.92) (2.63) (0.07) (0.22) High GRIX beta 0.179 0.526 0.258 1.018 0.210 0.024 0.178 0.035 0.012 0.290 0.056 (0.65) (6.71) ( 1.01) (6.08) (0.76) ( 0.28) (0.64) (0.22) ( 0.08) (1.02) ( 0.67) Low High 0.429 0.041 0.564 0.243 0.239 0.149 0.365 0.115 0.201 0.295 0.112 (1.68) ( 0.73) (1.89) ( 1.07) (0.89) (1.75) (1.25) ( 0.50) (1.11) (1.00) (1.47) Panel D: Annual Portfolio Formation Global CAPM FP 2 factor MOP 2 factor AMP 3 factor BK 2 factor α MSCI α BAB α TSMOM α VAL MOM α FTB Low GRIX beta 0.561 0.545 0.175 0.904 0.395 0.133 0.484 0.062 0.231 0.535 0.058 (2.20) (6.11) (0.63) (3.55) (1.54) (1.44) (1.77) ( 0.35) (1.36) (2.05) (0.75) 2 0.219 0.436 0.129 0.750 0.098 0.096 0.197 0.029 0.072 0.264 0.008 (0.86) (4.47) ( 0.40) (2.64) (0.39) (1.46) (0.71) ( 0.15) (0.49) (1.11) ( 0.13) 3 0.205 0.324 0.022 0.435 0.056 0.119 0.143 0.103 0.117 0.149 0.063 (1.48) (7.05) (0.16) (3.57) (0.45) (2.89) (1.06) (1.29) (1.70) (1.13) (1.53) 4 0.002 0.473 0.284 0.644 0.088 0.069 0.147 0.376 0.212 0.012 0.015 ( 0.01) (8.80) ( 1.42) (3.89) ( 0.45) (1.06) ( 0.79) (2.22) (1.86) (0.06) (0.23) High GRIX beta 0.553 0.514 0.166 0.869 0.550 0.002 0.528 0.001 0.064 0.584 0.006 (1.94) (6.77) (0.61) (4.83) (1.97) (0.02) (1.84) (0.01) (0.42) (2.05) (0.06) Low High 0.009 0.032 0.009 0.035 0.155 0.130 0.044 0.064 0.167 0.049 0.052 (0.03) (0.42) (0.03) (0.12) ( 0.50) (1.44) ( 0.14) ( 0.28) (0.89) ( 0.15) (0.66)
Table IA 7: GRIX beta portfolios within each of four asset classes We monthly form four GRIX beta portfolios within each asset class. This table reports excess returns, five factor alphas and loadings. Panel A: GRIX beta portfolios formed using only international equity indices MSCI MOP FP BAB Market TSMOM AMP Value AMP Momentum Low GRIX beta 1.209 0.719 1.233 0.061 0.034 0.368 0.343 (1.90) (2.50) (19.22) ( 0.43) (1.03) (2.48) (2.67) 2 0.084 0.202 0.989 0.220 0.030 0.536 0.018 (0.16) ( 0.91) (17.71) ( 1.74) (1.10) (4.67) (0.16) 3 0.322 0.003 1.016 0.033 0.024 0.460 0.181 (0.67) (0.02) (25.92) ( 0.40) ( 1.20) (5.50) (2.39) High GRIX beta 0.514 0.134 1.171 0.113 0.048 0.635 0.406 (0.92) (0.65) (28.35) ( 1.13) ( 1.51) (5.33) (3.74) Low High 0.695 0.585 0.062 0.052 0.082 0.267 0.064 (2.22) (1.84) (0.86) (0.30) (2.01) ( 1.43) ( 0.45) Panel B: GRIX beta portfolios formed using only currencies Dollar MOP FP BAB Market TSMOM AMP Value AMP Momentum Low GRIX beta 0.679 0.397 1.196 0.085 0.019 0.076 0.048 (2.63) (2.85) (14.26) (1.30) (0.45) ( 0.88) (0.42) 2 0.326 0.109 0.986 0.102 0.018 0.006 0.045 (1.63) (1.10) (18.15) (2.18) ( 0.70) (0.14) ( 0.76) 3 0.283 0.017 1.134 0.082 0.012 0.029 0.002 (1.50) ( 0.21) (22.25) (1.92) (0.46) (0.85) ( 0.04) High GRIX beta 0.497 0.152 1.177 0.103 0.017 0.085 0.034 (2.32) (1.47) (18.88) (1.82) (0.48) (1.54) (0.44) Low High 0.182 0.245 0.019 0.018 0.002 0.161 0.014 (1.09) (1.64) (0.18) ( 0.22) (0.04) ( 1.55) (0.10) Panel C: GRIX beta portfolios formed using only global government bonds Global MOP Bond FP BAB TSMOM AMP Value AMP Momentum Market Low GRIX beta 0.296 0.235 0.898 0.136 0.038 0.028 0.074 (2.66) (3.25) (5.51) (0.87) (2.67) ( 0.14) ( 0.53) 2 0.281 0.258 0.775 0.086 0.012 0.056 0.005 (3.67) (5.25) (9.89) ( 0.96) (1.18) (0.53) ( 0.07) 3 0.136 0.113 0.644 0.213 0.017 0.082 0.015 (2.32) (2.63) (7.64) ( 3.14) (1.77) (1.01) (0.22) High GRIX beta 0.114 0.135 0.912 0.319 0.009 0.341 0.098 (1.27) (2.18) (7.74) ( 3.47) (0.71) ( 2.88) (1.03) Low High 0.183 0.100 0.013 0.455 0.029 0.314 0.172 (1.66) (0.91) ( 0.05) (2.32) (1.28) (1.17) ( 0.87)
Panel D: GRIX beta portfolios formed using only commodities SPGSCI MOP FP BAB Market TSMOM AMP Value AMP Momentum Low GRIX beta 1.126 0.734 0.524 0.234 0.188 0.075 0.053 (2.87) (2.68) (10.76) (3.21) (1.80) ( 0.92) ( 0.61) 2 0.174 0.305 0.662 0.299 0.207 0.126 0.008 (0.44) ( 1.43) (13.80) (3.62) (1.79) (1.49) (0.08) 3 0.168 0.110 0.521 0.315 0.108 0.019 0.055 (0.42) ( 0.42) (11.05) (5.29) (1.33) (0.31) ( 0.87) High GRIX beta 0.368 0.311 0.595 0.271 0.030 0.003 0.198 (0.90) (1.11) (10.08) (3.43) ( 0.31) ( 0.03) ( 2.37) Low High 0.758 0.423 0.071 0.038 0.218 0.073 0.145 (1.78) (0.98) ( 0.94) ( 0.33) (1.44) ( 0.63) (1.00)
Table IA 8: Correlations between rare disaster concerns and economic factors The macroeconomic variables include quarterly real GDP growth per capita, inflation based on the change of CPI, recession dummy based on NBER recession dates, default risk based on the change of default spread (the spread between investment grade and non investmentgrade corporate bonds), and term risk based on the change of term spread (the spread between long term and short term government bonds). The variables of finanical market risk include market excess return, the Pastor Stambaugh innovation measure, the spread between on the run and off the run 10 year Treasury notes, market volatility risk based on the innovation of implied volatility, and risk neutral (RN) moment risks of variance, skewness, and kurtosis. In calculating correlations between asset class RIX and market return/volatility risk/moment risks, we use asset class specific measures of return, volatility, and moments. In calculating correlations between GRIX and market return/volatility risk/moment risks, we use the MSCI world equity index return and across asset class global measures of implied volatility and risk neutral moments. Global volatility and RN moments are estimated on the set of equity indices, currencies, bond futures, and commodity futures options (the aggregation procedures within and across asset classes are similar to those of constructing asset class RIXs and GRIX). The variables of funding and liquidity constraints of financial intermediaries include the Adrian Etula Muir broker dealer leverage shock, the Hu Pan Wang noise measure, the Treasury Eurodollar (TED) spread, the spread between interest rate swap and T bill, the spread between LIBOR and repo, and the aggregated funding liquidity risk based on the principal component analysis (PCA) of the last three types of spreads. Correlations that are statistically significant at the 5% level are in bold. EQRIX FXRIX BDRIX CMRIX GRIX Panel A: Macroeconomic Fundamental Risk Real GDP Growth 0.34 0.24 0.20 0.18 0.29 Inflation 0.10 0.25 0.05 0.22 0.14 Recession 0.39 0.42 0.36 0.41 0.49 Default Risk 0.38 0.07 0.01 0.06 0.07 Term Risk 0.18 0.20 0.20 0.17 0.23 Panel B: Financial Market Risk Market 0.19 0.01 0.04 0.11 0.09 Pastor Stambaugh Liquidity 0.09 0.06 0.10 0.06 0.10 On Off Run Spread 0.32 0.09 0.09 0.02 0.13 Market Volatility Risk 0.27 0.06 0.10 0.15 0.10 RN Moment Risk (Variance) 0.26 0.07 0.13 0.09 0.08 RN Moment Risk (Skewness) 0.07 0.05 0.05 0.12 0.12 RN Moment Risk (Kurtosis) 0.01 0.04 0.05 0.07 0.01 Panel C: Funding and Liquidity Constraints of Financial Intermediaries Hu Pan Wang Noise 0.33 0.01 0.06 0.07 0.07 Broker Dealer Leverage Shock 0.49 0.60 0.48 0.49 0.61 TED Spread 0.10 0.12 0.08 0.18 0.10 Swap T bill 0.13 0.19 0.11 0.16 0.19 Libor Repo 0.11 0.09 0.06 0.16 0.07 Funding Liquidity Risk (PCA) 0.16 0.07 0.05 0.16 0.05
Table IA 9: Downside risk CAPM betas of asset class RIX beta portfolios To estimate each portfolio's downside risk CAPM beta, we regress its monthly excess returns on the (asset class specific) market excess returns using only downsates that are all months in which the market return is at least one standard deviation below its sample mean. Panel A: monthly portfolio formation EQRIX beta Portfolios FXRIX beta Portfolios BDRIX beta Portfolios CMRIX beta Portfolios β t(β) Adj. R 2 β t(β) Adj. R 2 β t(β) Adj. R 2 β t(β) Adj. R 2 Low RIX beta 1.257 4.59 46.6% 1.334 5.61 61.6% 0.505 0.95 0.4% 0.544 3.78 34.7% 2 1.353 6.61 65.0% 0.859 4.22 46.9% 0.664 1.93 8.9% 0.506 3.32 28.6% 3 1.415 7.13 68.5% 1.111 5.46 60.3% 1.008 2.87 20.5% 0.771 4.06 38.3% High RIX beta 1.086 4.56 46.2% 1.230 4.34 48.4% 1.074 1.90 8.6% 0.565 2.74 20.7% Low High 0.171 0.56 3.1% 0.103 0.32 5.0% 0.569 0.75 1.6% 0.021 0.08 4.1% Panel B: quarterly portfolio formation EQRIX beta Portfolios FXRIX beta Portfolios BDRIX beta Portfolios CMRIX beta Portfolios β t(β) Adj. R 2 β t(β) Adj. R 2 β t(β) Adj. R 2 β t(β) Adj. R 2 Low RIX beta 1.304 4.42 45.8% 1.143 5.31 58.9% 0.546 1.06 0.4% 0.820 4.85 47.4% 2 1.521 7.28 70.3% 0.928 3.90 42.8% 0.769 1.99 9.6% 0.582 3.44 30.2% 3 1.541 10.33 82.8% 1.222 5.46 60.2% 1.168 3.20 24.8% 0.456 2.64 19.3% High RIX beta 1.209 4.46 46.2% 1.248 4.54 50.8% 0.881 1.62 5.5% 0.584 3.22 27.2% Low High 0.095 0.26 4.4% 0.105 0.35 4.8% 0.336 0.45 3.0% 0.236 0.84 1.2% Panel C: semi annual portfolio formation EQRIX beta Portfolios FXRIX beta Portfolios BDRIX beta Portfolios CMRIX beta Portfolios β t(β) Adj. R 2 β t(β) Adj. R 2 β t(β) Adj. R 2 β t(β) Adj. R 2 Low RIX beta 1.431 5.27 54.9% 1.274 4.31 48.1% 1.372 2.34 13.8% 0.536 2.63 19.1% 2 1.348 6.20 63.0% 0.829 3.32 34.5% 0.475 1.43 3.6% 0.676 5.40 53.0% 3 1.498 11.25 85.1% 1.305 4.89 54.7% 0.859 2.87 20.6% 0.661 3.75 34.3% High RIX beta 1.284 4.76 49.7% 1.092 4.04 44.6% 0.823 1.52 4.5% 0.545 3.54 31.6% Low High 0.148 0.46 3.7% 0.183 0.52 4.0% 0.548 0.70 1.9% 0.009 0.04 4.2% Panel D: annual portfolio formation EQRIX beta Portfolios FXRIX beta Portfolios BDRIX beta Portfolios CMRIX beta Portfolios β t(β) Adj. R 2 β t(β) Adj. R 2 β t(β) Adj. R 2 β t(β) Adj. R 2 Low RIX beta 1.655 5.57 57.8% 1.468 4.12 45.6% 2.206 2.62 17.3% 0.573 2.33 15.1% 2 1.526 7.56 71.8% 0.733 2.93 28.5% 0.615 1.66 5.9% 0.417 2.61 18.9% 3 1.273 9.37 79.8% 1.415 5.98 64.7% 0.775 2.66 17.8% 0.844 5.53 54.2% High RIX beta 1.098 4.44 45.9% 0.885 3.36 35.2% 0.177 0.36 3.2% 0.569 4.35 41.7% Low High 0.558 1.75 8.5% 0.582 1.24 2.8% 2.028 2.01 9.8% 0.004 0.01 4.2%
Table IA 10: Kelly Jiang tail risk betas of asset class RIX beta portfolios To estimate each portfolio's market tail risk beta, we regress its monthly excess returns on the (asset class specific) market excess returns and the market tail risk in Kelly and Jiang (2014). For brevity, we only report tail risk beta estimates, t statistics, and adjusted R squared. Panel A: monthly portfolio formation EQRIX beta Portfolios FXRIX beta Portfolios BDRIX beta Portfolios CMRIX beta Portfolios β t(β) Adj. R 2 β t(β) Adj. R 2 β t(β) Adj. R 2 β t(β) Adj. R 2 Low RIX beta 0.153 1.70 67.7% 0.100 2.11 58.7% 0.004 0.18 54.2% 0.078 0.95 46.2% 2 0.101 1.30 74.4% 0.006 0.21 73.8% 0.017 1.18 52.3% 0.044 0.54 45.2% 3 0.066 1.21 85.5% 0.005 0.22 78.6% 0.021 1.64 52.0% 0.108 1.27 40.8% High RIX beta 0.086 1.18 75.4% 0.015 0.52 74.6% 0.002 0.11 50.5% 0.065 0.72 26.2% Low High 0.068 0.67 0.8% 0.085 1.52 1.2% 0.002 0.08 6.2% 0.142 1.18 2.9% Panel B: quarterly portfolio formation EQRIX beta Portfolios FXRIX beta Portfolios BDRIX beta Portfolios CMRIX beta Portfolios β t(β) Adj. R 2 β t(β) Adj. R 2 β t(β) Adj. R 2 β t(β) Adj. R 2 Low RIX beta 0.122 1.37 69.4% 0.093 2.08 63.0% 0.003 0.16 56.8% 0.065 0.69 50.3% 2 0.006 0.10 82.6% 0.004 0.13 71.9% 0.013 0.88 53.7% 0.059 0.68 32.2% 3 0.047 0.84 85.9% 0.004 0.18 81.5% 0.019 1.37 47.6% 0.134 1.50 29.4% High RIX beta 0.051 0.73 78.6% 0.037 1.26 74.2% 0.004 0.22 52.6% 0.063 0.66 19.3% Low High 0.070 0.67 0.9% 0.056 1.08 2.1% 0.007 0.30 2.5% 0.002 0.01 9.7% Panel C: semi annual portfolio formation EQRIX beta Portfolios FXRIX beta Portfolios BDRIX beta Portfolios CMRIX beta Portfolios β t(β) Adj. R 2 β t(β) Adj. R 2 β t(β) Adj. R 2 β t(β) Adj. R 2 Low RIX beta 0.042 0.46 67.5% 0.090 1.99 61.4% 0.002 0.10 53.8% 0.053 0.56 44.0% 2 0.091 1.44 82.3% 0.005 0.20 76.7% 0.011 0.86 53.8% 0.080 1.02 44.5% 3 0.015 0.28 87.4% 0.002 0.10 76.9% 0.009 0.71 48.5% 0.012 0.13 29.1% High RIX beta 0.057 0.82 78.5% 0.026 0.89 74.9% 0.011 0.61 54.2% 0.122 1.32 22.2% Low High 0.015 0.14 1.2% 0.063 1.20 0.8% 0.008 0.35 2.9% 0.174 1.36 6.7% Panel D: annual portfolio formation EQRIX beta Portfolios FXRIX beta Portfolios BDRIX beta Portfolios CMRIX beta Portfolios β t(β) Adj. R 2 β t(β) Adj. R 2 β t(β) Adj. R 2 β t(β) Adj. R 2 Low RIX beta 0.043 0.49 70.9% 0.066 1.39 57.8% 0.000 0.00 51.5% 0.027 0.28 39.2% 2 0.094 1.46 81.2% 0.016 0.62 77.7% 0.009 0.68 51.6% 0.059 0.64 32.5% 3 0.029 0.59 88.3% 0.016 0.63 76.8% 0.004 0.34 49.6% 0.027 0.31 34.3% High RIX beta 0.098 1.52 81.1% 0.036 1.18 71.2% 0.024 1.40 54.3% 0.161 1.89 31.3% Low High 0.054 0.58 0.6% 0.030 0.55 1.3% 0.024 0.91 5.0% 0.188 1.50 2.9%
Table IA 11: Additional robustness checks on return specifications and GRIX construction This table presents portfolio mean excess returns at various formation frequencies. For currency class (Panel A), we use log returns in estimating currencies' FXRIX beta and calculating portfolio returns. For bond class (Panel B), we use interpolated futures returns of 30 day constant maturity in estimating bonds' BDRIX beta and calculating portfolio returns. For commodity class (Panel C), we use far/back futures contract returns in estimating commodities' CMRIX beta and calculating portfolio returns. In Panel D, we use a simple average of four asset class RIX to construct GRIX and estimate each asset's GRIX beta (the return specifications are the same as those of the baseline analysis in the paper). Panel A: Currency log returns FXRIX beta Portfolios Monthly Portfolio Formation Quarterly Portfolio Formation Semi Annual Portfolio Formation Annual Portfolio Formation Low RIX beta 0.734 0.795 0.802 0.723 (3.06) (3.26) (3.41) (2.97) 2 0.074 0.163 0.061 0.093 (0.42) (0.96) (0.35) (0.51) 3 0.319 0.276 0.301 0.318 (1.94) (1.71) (1.84) (1.88) High RIX beta 0.374 0.296 0.342 0.366 (1.93) (1.56) (1.76) (1.97) Low High 0.360 0.499 0.46 0.357 (2.00) (2.86) (2.72) (1.92) Panel B: Bond futures interpolated returns of 30 day constant maturity BDRIX beta Portfolios Monthly Portfolio Formation Quarterly Portfolio Formation Semi Annual Portfolio Formation Annual Portfolio Formation Low RIX beta 0.320 0.252 0.353 0.325 (2.82) (2.37) (3.17) (2.65) 2 0.149 0.153 0.125 0.095 (2.10) (2.17) (1.91) (1.34) 3 0.116 0.097 0.085 0.070 (1.83) (1.52) (1.33) (1.06) High RIX beta 0.102 0.155 0.124 0.158 (1.38) (2.07) (1.58) (2.16) Low High 0.219 0.097 0.229 0.167 (2.38) (1.17) (2.62) (1.72) Panel C: Commodity futures returns of far/back contracts CMRIX beta Portfolios Monthly Portfolio Formation Quarterly Portfolio Formation Semi Annual Portfolio Formation Annual Portfolio Formation Low RIX beta 0.431 0.652 0.841 0.645 (1.05) (1.42) (1.94) (1.49) 2 0.085 0.113 0.107 0.001 (0.23) (0.29) ( 0.28) (0.00) 3 0.433 0.203 0.514 0.561 (1.20) (0.54) (1.35) (1.44) High RIX beta 0.291 0.409 0.562 0.553 ( 0.80) ( 1.18) ( 1.59) ( 1.51) Low High 0.722 1.061 1.402 1.198 (1.66) (2.22) (3.20) (2.75)
Panel D: All assets (GRIX estimated as the simple average of four asset class RIXs) GRIX beta Portfolios Monthly Portfolio Formation Quarterly Portfolio Formation Semi Annual Portfolio Formation Annual Portfolio Formation Low RIX beta 0.844 0.750 0.670 0.589 (2.68) (2.40) (2.02) (1.49) 2 0.612 0.507 0.512 0.345 (2.51) (2.08) (2.17) (1.24) 3 0.368 0.368 0.258 0.335 (1.91) (1.93) (1.13) (1.53) 4 0.029 0.031 0.100 0.040 ( 0.09) ( 0.10) (0.35) (0.15) High RIX beta 0.189 0.401 0.391 0.735 (0.51) (1.04) (1.02) (2.03) Low High 0.655 0.349 0.279 0.146 (2.36) (1.12) (0.79) ( 0.39)
Table IA 12: Alternative measures of rare disaster concerns (within asset classes) This table presents mean excess returns and five factor alphas of monthly formed portfolios within each asset class. We estimate each asset's beta with respect to asset class implied volatility (Panel A) and volatility skew (Panel B) in a similar manner to the asset's RIX beta. Panel A: option based implied volatility within each asset class (asset class VIX) Equity Indices Currencies Govt. Bonds Commodities Low beta 0.971 0.596 0.611 0.305 0.323 0.232 0.512 0.322 (1.60) (2.14) (2.37) (2.28) (2.56) (2.88) (1.25) (1.11) 2 0.401 0.076 0.222 0.009 0.205 0.174 0.839 0.505 (0.70) (0.32) (1.07) ( 0.09) (2.81) (3.91) (2.18) (1.85) 3 0.496 0.161 0.284 0.016 0.140 0.146 0.709 0.336 (0.97) (0.87) (1.48) ( 0.19) (2.40) (3.94) (1.77) (1.48) High beta 0.289 0.040 0.607 0.289 0.157 0.195 0.192 0.560 (0.55) ( 0.22) (2.93) (2.65) (2.26) (3.96) ( 0.50) ( 1.95) Low High 0.682 0.635 0.005 0.016 0.165 0.037 0.705 0.883 (2.03) (1.80) (0.02) (0.09) (1.75) (0.44) (1.64) (2.06) Panel B: option based implied volatility skew within each asset class Equity Indices Currencies Govt. Bonds Commodities Low beta 0.715 0.403 0.766 0.420 0.297 0.252 0.439 0.221 (1.29) (2.05) (2.63) (2.68) (2.59) (3.45) (1.13) (0.83) 2 0.187 0.204 0.257 0.044 0.143 0.145 0.502 0.243 (0.35) ( 1.17) (1.33) (0.56) (2.08) (3.03) (1.32) (1.07) 3 0.825 0.525 0.337 0.102 0.163 0.133 0.662 0.205 (1.61) (2.65) (1.90) (1.34) (2.29) (3.32) (1.69) (0.83) High beta 0.446 0.063 0.380 0.025 0.202 0.207 0.247 0.075 (0.76) (0.29) (1.79) (0.22) (2.66) (3.58) (0.65) ( 0.31) Low High 0.269 0.339 0.386 0.395 0.096 0.045 0.192 0.296 (1.04) (1.22) (1.73) (2.09) (0.98) (0.46) (0.52) (0.85)
Table IA 13: Alternative positions of average investors (within asset classes) This table presents mean excess returns and five factor alphas of monthly formed asset class RIXbeta portfolios. In estimating an asset's RIX beta, we consider alternative long/short positions of average investors to construct BDRIX, FXRIX, and CMRIX. Bond (Short) Foreign Currency Commodity (Long or (Long or Short) Short) Low RIX beta 0.337 0.267 0.892 0.545 0.746 0.442 (2.65) (3.71) (2.83) (2.94) (1.80) (1.40) 2 0.151 0.111 0.241 0.005 0.869 0.569 (2.26) (2.64) (1.07) ( 0.06) (2.17) (2.35) 3 0.191 0.193 0.280 0.046 0.325 0.028 (3.12) (5.05) (1.63) (0.53) (0.78) ( 0.12) High RIX beta 0.155 0.190 0.356 0.030 0.087 0.371 (2.23) (3.77) (1.68) (0.29) ( 0.24) ( 1.24) Low High 0.182 0.077 0.536 0.515 0.833 0.813 (1.95) (0.97) (2.31) (2.48) (1.84) (1.79)