1. No category

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
Mean
Standard Deviation
0.014
0.025
0.012
0.02
0.01
0.008
0.015
0.006
0.01
0.004
0.005
0.002
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
0.16
0.12
Mean
0.1
Standard Deviation
0.14
0.12
0.08
0.1
0.06
0.08
0.04
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
0.009
0.012
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
0
Australia Australia
(10YR)
(3YR)
Canada
(10YR)
Germany Germany Germany
(10YR)
(2YR)
(5YR)
Italy
(10YR)
Japan
(10YR)
Spain
(10YR)
United
Kingdom
(10YR)
United
States
(10YR)
United
States
(2YR)
United
States
(30YR)
United
States
(5YR)
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
0.01
Mean
Standard Deviation
0.009
0.02
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
Mean Excess Return (in percent)
1
1 ‐ Low GRIX beta
0.8
0.6
0.4
3
2
4
0.2
5 ‐ High GRIX beta
0
0
0.2
0.4
0.6
Downside Risk CAPM Beta
0.8
1
1.2
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 ‐ Low GRIX beta
Mean Excess Return (in percent)
1
0.8
0.6
0.4 3
4
2
0.2
5 ‐ High GRIX beta
0
‐0.08
‐0.06
‐0.04
‐0.02
0
0.02
Kelly‐Jiang Tail Risk Beta
0.04
0.06
0.08
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 non‐
market‐based factors in multi‐factor models. Panel A: Monthly Portfolio Formation
Global CAPM
α
MSCI
Low RIX‐beta
0.703 1.138
(2.47) (15.24)
2
0.152 1.154
(0.53) (19.75)
3
0.057 1.157
(0.32) (19.45)
High RIX‐beta
‐0.051 1.107
(‐0.19) (17.22)
Low ‐ High
0.754 0.031
(2.38) (0.45)
FP 2 factor
α
BAB
0.627 0.275
(2.24) (2.29)
0.278 ‐0.332
(1.00) (‐2.01)
0.012 0.075
(0.06) (0.86)
‐0.050 ‐0.011
(‐0.19) (‐0.11)
0.677 0.286
(2.12) (2.25)
MOP 2 factor
AMP 3 factor
α
TSMOM
α
VAL
MOM
0.562 0.087
0.497 0.392 0.455
(2.25) (2.41)
(2.01) (2.96) (5.00)
0.193 ‐0.026
0.164 0.480 ‐0.109
(0.71) (‐0.83) (0.71) (3.90) (‐0.95)
0.037 0.012
‐0.079 0.447 0.268
(0.20) (0.47) (‐0.47) (4.99) (4.96)
‐0.053 0.001
‐0.175 0.537 0.224
(‐0.21) (0.04) (‐0.74) (5.04) (2.77)
0.615 0.086
0.672 ‐0.145 0.231
(2.12) (2.04)
(2.34) (‐0.89) (1.97)
Panel B: Quarterly Portfolio Formation
Global CAPM
FP 2 factor
α
MSCI
α
BAB
Low RIX‐beta
0.798 1.150
0.771 0.145
(3.03) (16.79) (2.93) (1.04)
2
0.372 1.205
0.426 ‐0.093
(1.67) (22.56) (1.90) (‐0.74)
3
0.095 1.171
‐0.002 0.201
(0.51) (21.87) (‐0.01) (2.15)
High RIX‐beta
‐0.064 1.164
‐0.015 ‐0.104
(‐0.25) (18.76) (‐0.06) (‐0.71)
Low ‐ High
0.861 ‐0.013
0.786 0.249
(2.52) (‐0.17) (2.13) (1.52)
MOP 2 factor
AMP 3 factor
α
TSMOM
α
VAL
MOM
0.668 0.081
0.613 0.443 0.399
(2.69) (2.16)
(2.60) (3.34) (2.92)
0.368 0.002
0.311 0.318 0.052
(1.64) (0.10)
(1.47) (2.99) (0.49)
0.040 0.035
‐0.039 0.355 0.274
(0.21) (1.51) (‐0.23) (4.08) (4.06)
‐0.070 0.004
‐0.201 0.679 0.136
(‐0.29) (0.13) (‐0.98) (6.88) (2.09)
0.738 0.077
0.814 ‐0.235 0.263
(2.28) (1.63)
(2.60) (‐1.38) (1.63)
α
0.452
(1.86)
0.003
(0.01)
‐0.129
(‐0.69)
‐0.206
(‐0.83)
0.658
(2.25)
FF 4 factor
SMB
HML
0.546 0.097
(5.13) (0.88)
0.258 0.165
(2.40) (1.85)
0.004 0.164
(0.04) (2.06)
0.278 0.205
(2.27) (2.21)
0.269 ‐0.108
(1.91) (‐0.62)
WML
0.076
(1.17)
‐0.057
(‐0.95)
0.060
(1.06)
‐0.074
(‐1.16)
0.150
(1.48)
HKK 3 factor
α
CP
SRET
0.442 0.157 0.234
(1.44) (1.79) (3.40)
‐0.004 0.166 0.027
(‐0.01) (1.92) (0.40)
‐0.276 0.204 0.149
(‐1.55) (3.82) (3.74)
‐0.331 0.256 0.044
(‐1.33) (3.14) (0.66)
0.773 ‐0.099 0.190
(2.26) (‐0.82) (1.95)
α
0.515
(2.32)
0.122
(0.53)
‐0.141
(‐0.74)
‐0.270
(‐1.16)
0.785
(2.51)
FF 4 factor
SMB
HML
0.598 ‐0.012
(4.79) (‐0.12)
0.214 0.208
(2.73) (2.03)
‐0.051 0.189
(‐0.53) (3.06)
0.246 0.197
(1.90) (2.00)
0.352 ‐0.209
(1.85) (‐1.21)
WML
0.056
(0.82)
‐0.018
(‐0.31)
0.088
(1.55)
‐0.087
(‐1.44)
0.143
(1.35)
HKK 3 factor
α
CP
SRET
0.588 0.054 0.220
(2.13) (0.59) (2.89)
0.074 0.263 0.116
(0.33) (3.21) (2.17)
‐0.293 0.215 0.139
(‐1.52) (4.51) (3.21)
‐0.313 0.188 0.008
(‐1.35) (2.39) (0.14)
0.901 ‐0.134 0.212
(2.41) (‐0.99) (2.14)
Panel C: Semi‐Annual Portfolio Formation
Global CAPM
FP 2 factor
α
MSCI
α
BAB
Low RIX‐beta
0.863 1.138
0.799 0.229
(3.28) (14.39) (2.85) (1.31)
2
0.199 1.177
0.256 ‐0.124
(0.93) (23.95) (1.22) (‐1.14)
3
0.252 1.228
0.184 0.112
(1.43) (24.48) (1.02) (1.27)
High RIX‐beta ‐0.107 1.149
‐0.090 ‐0.054
(‐0.42) (17.39) (‐0.35) (‐0.37)
Low ‐ High
0.970 ‐0.011
0.889 0.283
(2.79) (‐0.15) (2.30) (1.66)
MOP 2 factor
AMP 3 factor
α
TSMOM
α
VAL
MOM
0.720 0.089
0.660 0.453 0.460
(2.90) (2.02)
(2.71) (3.23) (3.03)
0.195 0.002
0.133 0.305 0.060
(0.90) (0.09)
(0.65) (2.51) (0.57)
0.213 0.024
0.140 0.310 0.203
(1.15) (1.15)
(0.85) (4.03) (2.67)
‐0.120 0.008
‐0.268 0.726 0.157
(‐0.51) (0.25) (‐1.39) (8.49) (2.43)
0.840 0.081
0.928 ‐0.273 0.303
(2.57) (1.50)
(2.84) (‐1.77) (1.73)
FF 4 factor
α
SMB
HML
WML
0.565 0.604 ‐0.003 0.078
(2.35) (4.86) (‐0.03) (0.96)
‐0.086 0.224 0.223 0.022
(‐0.39) (2.80) (2.42) (0.45)
0.101 ‐0.061 0.097 0.011
(0.53) (‐0.76) (1.54) (0.16)
‐0.354 0.241 0.253 ‐0.066
(‐1.55) (1.89) (2.66) (‐1.09)
0.919 0.363 ‐0.256 0.144
(2.68) (2.07) (‐1.31) (1.26)
HKK 3 factor
α
CP
SRET
0.580 0.072 0.263
(2.07) (0.67) (2.76)
‐0.106 0.255 0.138
(‐0.48) (3.27) (2.38)
‐0.050 0.187 0.068
(‐0.27) (3.94) (1.55)
‐0.389 0.192 0.020
(‐1.70) (2.61) (0.38)
0.969 ‐0.119 0.243
(2.50) (‐0.80) (2.05)
Panel D: Annual Portfolio Formation
Global CAPM
α
MSCI
Low RIX‐beta
0.791 1.192
(2.89) (12.28)
2
0.246 1.154
(1.15) (20.58)
3
0.141 1.188
(0.90) (26.43)
High RIX‐beta ‐0.130 1.143
(‐0.58) (22.40)
Low ‐ High
0.921 0.049
(2.95) (0.59)
MOP 2 factor
AMP 3 factor
α
TSMOM
α
VAL
MOM
0.697 0.059
0.570 0.537 0.475
(2.78) (1.25)
(2.35) (3.49) (3.26)
0.214 0.020
0.136 0.350 0.167
(1.05) (0.81)
(0.68) (3.17) (1.56)
0.155 ‐0.009
0.114 0.255 ‐0.048
(0.92) (‐0.43) (0.76) (3.02) (‐0.73)
‐0.178 0.030
‐0.290 0.664 0.188
(‐0.80) (1.19) (‐1.68) (8.79) (3.76)
0.876 0.028
0.860 ‐0.127 0.286
(2.89) (0.63)
(2.80) (‐0.75) (1.88)
FF 4 factor
α
SMB
HML
0.419 0.686 0.084
(1.77) (5.41) (0.79)
‐0.055 0.180 0.215
(‐0.24) (1.97) (2.34)
‐0.033 ‐0.076 0.244
(‐0.20) (‐0.83) (4.44)
‐0.306 0.235 0.132
(‐1.49) (2.02) (1.56)
0.725 0.451 ‐0.049
(2.47) (2.55) (‐0.30)
HKK 3 factor
α
CP
SRET
0.464 0.121 0.281
(1.70) (1.28) (3.33)
‐0.159 0.220 0.182
(‐0.71) (3.00) (3.39)
‐0.205 0.327 ‐0.029
(‐1.21) (6.28) (‐0.58)
‐0.260 0.093 0.015
(‐1.47) (1.38) (0.37)
0.724 0.028 0.266
(2.22) (0.23) (2.96)
FP 2 factor
α
BAB
0.691 0.311
(2.44) (1.83)
0.293 ‐0.116
(1.37) (‐1.01)
0.160 ‐0.078
(0.98) (‐1.00)
‐0.139 ‐0.006
(‐0.62) (‐0.05)
0.829 0.317
(2.50) (2.32)
WML
0.086
(1.17)
0.069
(1.22)
‐0.055
(‐0.95)
‐0.080
(‐1.79)
0.166
(1.88)
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
α
DOL
α
BAB
Low RIX‐beta
0.516 1.285
0.507 0.194
(3.30) (18.84) (3.29) (2.23)
2
‐0.101 1.028
‐0.090 ‐0.042
(‐1.24) (20.01) (‐1.07) (‐0.79)
3
0.077 1.031
0.069 0.060
(1.01) (22.73) (0.88) (1.42)
High RIX‐beta
0.174 1.154
0.160 0.135
(1.77) (19.20) (1.64) (2.74)
Low ‐ High
0.341 0.131
0.347 0.059
(1.81) (1.62)
(1.83) (0.53)
MOP 2 factor
AMP 3 factor
α
TSMOM
α
VAL
MOM
0.512 0.005
0.519 ‐0.048 0.043
(3.25) (0.17)
(3.38) (‐0.63) (0.58)
‐0.104 0.003
‐0.125 0.084 0.027
(‐1.20) (0.16) (‐1.57) (1.63) (0.65)
0.064 0.016
0.100 ‐0.075 ‐0.028
(0.83) (0.86)
(1.29) (‐2.08) (‐0.73)
0.180 ‐0.007
0.171 0.030 ‐0.017
(1.76) (‐0.30) (1.69) (0.44) (‐0.27)
0.332 0.012
0.348 ‐0.078 0.060
(1.72) (0.32)
(1.82) (‐0.87) (0.67)
LRV 2 factor
α
HML
0.495 0.031
(3.21) (0.51)
‐0.088 ‐0.021
(‐1.06) (‐0.43)
0.130 ‐0.078
(1.63) (‐2.33)
0.227 ‐0.080
(2.10) (‐1.56)
0.267 0.111
(1.39) (1.62)
Panel B: Quarterly Portfolio Formation
Currency Market
FP 2 factor
α
DOL
α
BAB
Low RIX‐beta
0.551 1.331
0.546 0.179
(3.14) (20.35) (3.17) (2.51)
2
0.001 1.013
‐0.002 ‐0.044
(0.01) (16.92) (‐0.02) (‐0.69)
3
0.070 1.026
0.086 0.035
(0.94) (20.38) (1.17) (1.02)
High RIX‐beta
0.077 1.136
0.049 0.169
(0.81) (18.09) (0.54) (4.33)
Low ‐ High
0.474 0.195
0.496 0.009
(2.46) (2.70)
(2.58) (0.11)
MOP 2 factor
AMP 3 factor
α
TSMOM
α
VAL
MOM
0.537 0.017
0.546 ‐0.030 0.060
(3.03) (0.63)
(3.20) (‐0.41) (0.87)
0.001 ‐0.001 ‐0.029 0.099 0.040
(0.02) (‐0.05) (‐0.35) (1.90) (0.84)
0.076 ‐0.008
0.099 ‐0.087 ‐0.050
(1.02) (‐0.55) (1.32) (‐2.45) (‐1.37)
0.068 0.011
0.077 0.015 ‐0.019
(0.72) (0.51)
(0.78) (0.21) (‐0.30)
0.469 0.006
0.469 ‐0.045 0.078
(2.36) (0.19)
(2.38) (‐0.53) (0.99)
LRV 2 factor
α
HML
0.559 ‐0.012
(3.20) (‐0.18)
0.013 ‐0.018
(0.13) (‐0.33)
0.106 ‐0.054
(1.38) (‐1.46)
0.126 ‐0.073
(1.24) (‐1.65)
0.433 0.061
(2.21) (0.87)
Panel C: Semi‐Annual Portfolio Formation
Currency Market
FP 2 factor
α
DOL
α
BAB
Low RIX‐beta
0.615 1.290
0.615 0.128
(3.41) (19.29) (3.42) (1.82)
2
‐0.179 1.041
‐0.191 0.013
(‐2.05) (24.34) (‐2.16) (0.27)
3
0.121 1.016
0.126 0.060
(1.54) (19.07) (1.57) (1.53)
High RIX‐beta
0.111 1.164
0.098 0.141
(1.22) (19.31) (1.13) (2.84)
Low ‐ High
0.505 0.126
0.516 ‐0.012
(2.54) (1.71)
(2.56) (‐0.14)
MOP 2 factor
α
TSMOM
0.601 0.018
(3.28) (0.66)
‐0.178 ‐0.001
(‐2.09) (‐0.07)
0.122 ‐0.001
(1.51) (‐0.05)
0.103 0.009
(1.12) (0.46)
0.497 0.009
(2.40) (0.28)
AMP 3 factor
α
VAL
MOM
0.607 ‐0.001 0.045
(3.43) (‐0.01) (0.62)
‐0.178 ‐0.012 0.004
(‐2.02) (‐0.34) (0.11)
0.142 ‐0.077 ‐0.016
(1.75) (‐1.91) (‐0.43)
0.094 0.072 ‐0.001
(1.00) (1.11) (‐0.01)
0.512 ‐0.073 0.046
(2.53) (‐0.90) (0.55)
LRV 2 factor
α
HML
0.610 0.007
(3.37) (0.11)
‐0.149 ‐0.045
(‐1.59) (‐0.93)
0.149 ‐0.041
(1.85) (‐0.96)
0.155 ‐0.066
(1.61) (‐1.53)
0.456 0.073
(2.26) (1.07)
Panel D: Annual Portfolio Formation
Currency Market
α
DOL
Low RIX‐beta
0.526 1.282
(3.29) (16.68)
2
‐0.131 1.084
(‐1.60) (21.34)
3
0.110 1.061
(1.32) (19.58)
High RIX‐beta
0.157 1.089
(1.56) (19.12)
Low ‐ High
0.369 0.193
(1.92) (2.06)
MOP 2 factor
α
TSMOM
0.529 ‐0.005
(3.24) (‐0.14)
‐0.120 ‐0.014
(‐1.49) (‐0.81)
0.109 0.002
(1.26) (0.11)
0.123 0.042
(1.21) (2.14)
0.407 ‐0.047
(2.04) (‐1.18)
AMP 3 factor
α
VAL
MOM
0.556 ‐0.121 ‐0.018
(3.61) (‐1.43) (‐0.22)
‐0.126 0.002 ‐0.026
(‐1.53) (0.05) (‐0.70)
0.091 0.062 0.029
(1.07) (1.17) (0.62)
0.135 0.051 0.056
(1.29) (1.02) (1.13)
0.422 ‐0.172 ‐0.074
(2.21) (‐1.89) (‐0.78)
LRV 2 factor
α
HML
0.477 0.072
(2.92) (1.06)
‐0.084 ‐0.071
(‐0.94) (‐1.56)
0.131 ‐0.031
(1.55) (‐0.69)
0.236 ‐0.119
(2.30) (‐2.86)
0.241 0.191
(1.22) (2.55)
FP 2 factor
α
BAB
0.524 0.131
(3.28) (1.58)
‐0.145 0.035
(‐1.76) (0.72)
0.124 ‐0.051
(1.47) (‐1.04)
0.140 0.218
(1.46) (5.35)
0.384 ‐0.087
(1.97) (‐0.97)
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
Bond Market
FP 2 factor
α
GBD
α
BAB
Low RIX‐beta 0.364 1.361
0.357 ‐0.201
(5.39) (11.99) (5.18) (‐1.81)
2
0.186 0.861
0.180 ‐0.066
(4.54) (13.87) (4.45) (‐0.59)
3
0.157 0.768
0.165 ‐0.187
(3.98) (12.88) (4.00) (‐2.78)
High RIX‐beta 0.148 0.968
0.164 ‐0.244
(2.62) (9.58)
(2.72) (‐2.16)
Low ‐ High
0.216 0.393
0.193 0.043
(2.84) (2.38)
(2.49) (0.30)
MOP 2 factor
α
TSMOM
0.289 0.048
(4.42) (3.40)
0.154 0.021
(3.87) (1.84)
0.135 0.014
(3.58) (1.54)
0.130 0.012
(2.47) (0.94)
0.159 0.036
(2.15) (2.22)
AMP 3 factor
α
VAL
MOM
0.361 0.021 0.214
(5.42) (0.13) (1.91)
0.185 0.018 0.032
(4.41) (0.17) (0.37)
0.161 ‐0.087 0.061
(4.18) (‐1.27) (1.06)
0.162 ‐0.272 0.061
(3.05) (‐3.29) (0.74)
0.199 0.292 0.153
(2.69) (1.65) (1.11)
Panel B: Quarterly Portfolio Formation
Bond Market
FP 2 factor
α
GBD
α
BAB
Low RIX‐beta 0.272 1.263
0.260 ‐0.167
(4.13) (12.78) (3.91) (‐1.06)
2
0.199 0.889
0.197 ‐0.188
(4.73) (11.78) (4.70) (‐2.35)
3
0.161 0.743
0.167 ‐0.167
(3.35) (11.93) (3.34) (‐2.69)
High RIX‐beta 0.188 1.016
0.205 ‐0.215
(3.40) (10.04) (3.53) (‐2.00)
Low ‐ High
0.084 0.247
0.055 0.048
(1.08) (1.61)
(0.70) (0.26)
MOP 2 factor
α
TSMOM
0.205 0.041
(3.24) (2.84)
0.156 0.027
(3.68) (2.51)
0.131 0.018
(2.95) (2.46)
0.162 0.016
(3.12) (1.28)
0.043 0.026
(0.56) (1.60)
AMP 3 factor
α
VAL
MOM
0.274 ‐0.055 0.099
(4.14) (‐0.39) (1.04)
0.187 0.133 0.134
(4.32) (1.60) (1.62)
0.164 ‐0.064 0.075
(3.62) (‐0.92) (1.19)
0.201 ‐0.202 0.074
(3.73) (‐2.23) (0.88)
0.073 0.146 0.025
(0.94) (1.00) (0.21)
Panel C: Semi‐Annual Portfolio Formation
Bond Market
FP 2 factor
α
GBD
α
BAB
Low RIX‐beta 0.404 1.362
0.401 ‐0.385
(6.17) (10.95) (6.02) (‐3.14)
2
0.171 0.779
0.164 ‐0.044
(4.91) (13.26) (4.75) (‐0.42)
3
0.149 0.711
0.156 ‐0.138
(3.76) (11.42) (3.73) (‐2.31)
0.141 ‐0.254
High RIX‐beta 0.126 1.089
(2.08) (9.97)
(2.22) (‐2.33)
Low ‐ High
0.278 0.273
0.260 ‐0.131
(3.46) (1.70)
(3.18) (‐0.81)
MOP 2 factor
α
TSMOM
0.340 0.039
(5.62) (2.62)
0.127 0.027
(3.32) (2.50)
0.126 0.014
(3.31) (2.19)
0.094 0.020
(1.59) (1.51)
0.246 0.019
(3.08) (1.08)
AMP 3 factor
α
VAL
MOM
0.386 0.170 0.302
(5.73) (1.31) (2.30)
0.170 0.005 0.016
(4.86) (0.07) (0.22)
0.156 ‐0.101 0.020
(3.90) (‐1.45) (0.36)
0.139 ‐0.210 0.089
(2.37) (‐2.20) (1.05)
0.247 0.380 0.212
(3.11) (2.81) (1.47)
Panel D: Annual Portfolio Formation
Bond Market
FP 2 factor
α
GBD
α
BAB
Low RIX‐beta 0.377 1.434
0.372 ‐0.417
(5.36) (10.92) (5.15) (‐2.22)
2
0.162 0.749
0.158 ‐0.087
(4.51) (10.71) (4.49) (‐1.23)
3
0.132 0.728
0.134 ‐0.010
(3.21) (9.89)
(3.09) (‐0.14)
High RIX‐beta 0.181 1.065
0.199 ‐0.231
(2.99) (10.45) (3.19) (‐2.32)
Low ‐ High
0.196 0.369
0.174 ‐0.185
(2.55) (2.01)
(2.23) (‐0.87)
MOP 2 factor
α
TSMOM
0.282 0.061
(4.45) (3.40)
0.128 0.022
(3.34) (2.07)
0.123 0.006
(3.11) (0.79)
0.168 0.008
(2.74) (0.63)
0.114 0.053
(1.43) (2.51)
AMP 3 factor
α
VAL
MOM
0.378 ‐0.062 0.308
(5.38) (‐0.33) (1.83)
0.162 0.009 0.066
(4.48) (0.13) (0.95)
0.140 ‐0.154 0.036
(3.55) (‐2.25) (0.65)
0.188 ‐0.148 ‐0.002
(3.15) (‐1.60) (‐0.02)
0.189 0.086 0.309
(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
α
SPGSCI
α
BAB
Low RIX‐beta
0.543 0.524
0.582 0.274
(1.92) (11.98) (2.10) (3.66)
2
0.334 0.509
0.295 0.235
(1.19) (11.50) (1.05) (3.01)
3
0.133 0.488
0.127 0.348
(0.44) (8.08)
(0.44) (4.91)
High RIX‐beta ‐0.280 0.373
‐0.373 0.318
(‐0.89) (6.83) (‐1.22) (4.35)
Low ‐ High
0.823 0.151
0.955 ‐0.044
(1.96) (2.00)
(2.19) (‐0.35)
MOP 2 factor
AMP 3 factor
α
TSMOM
α
VAL
MOM
0.559 ‐0.020
0.575 0.075 ‐0.039
(1.90) (‐0.29) (1.98) (1.05) (‐0.60)
0.237 0.115
0.287 0.045 0.068
(0.82) (1.40)
(0.97) (0.58) (0.87)
0.156 ‐0.028
0.143 0.206 0.000
(0.53) (‐0.35) (0.50) (2.99) (0.01)
‐0.355 0.089
‐0.326 0.211 0.080
(‐1.13) (1.04) (‐1.06) (2.90) (1.08)
0.914 ‐0.109
0.901 ‐0.136 ‐0.120
(2.18) (‐1.10) (2.12) (‐1.30) (‐1.32)
BK 2 factor
α
FTB
0.738 ‐0.072
(2.37) (‐1.13)
0.263 0.036
(0.82) (0.46)
0.225 ‐0.048
(0.74) (‐0.56)
‐0.364 0.019
(‐1.07) (0.22)
1.102 ‐0.091
(2.49) (‐1.00)
Yang 2 factor
α
HML
0.521
0.012
(1.78)
(0.19)
0.134
0.059
(0.49)
(0.89)
0.287
‐0.052
(0.94)
(‐1.04)
‐0.186
‐0.032
(‐0.51)
(‐0.49)
0.707
0.044
(1.51)
(0.53)
Panel B: Quarterly Portfolio Formation
Comm. Market
FP 2 factor
α
SPGSCI
α
BAB
Low RIX‐beta
0.487 0.634
0.553 0.253
(1.58) (11.93) (1.79) (3.09)
2
0.132 0.419
0.152 0.402
(0.46) (7.59)
(0.57) (6.75)
3
0.200 0.392
0.210 0.380
(0.73) (7.05)
(0.81) (5.81)
High RIX‐beta ‐0.444 0.334
‐0.462 0.332
(‐1.55) (6.30) (‐1.71) (5.74)
Low ‐ High
0.930 0.300
1.015 ‐0.080
(2.10) (3.79)
(2.23) (‐0.78)
MOP 2 factor
AMP 3 factor
α
TSMOM
α
VAL
MOM
0.558 ‐0.081
0.511 0.087 ‐0.038
(1.69) (‐1.04) (1.56) (1.03) (‐0.48)
0.102 0.034
0.141 0.126 ‐0.020
(0.36) (0.37)
(0.49) (1.76) (‐0.31)
0.211 ‐0.013
0.220 0.164 ‐0.037
(0.77) (‐0.15) (0.79) (2.79) (‐0.60)
‐0.477 0.038
‐0.470 0.161 0.028
(‐1.66) (0.55) (‐1.64) (2.52) (0.43)
1.035 ‐0.119
0.981 ‐0.074 ‐0.066
(2.32) (‐1.27) (2.15) (‐0.73) (‐0.71)
BK 2 factor
α
FTB
0.669 ‐0.074
(1.84) (‐0.91)
0.256 ‐0.088
(0.84) (‐1.02)
0.201 ‐0.008
(0.72) (‐0.11)
‐0.542 0.035
(‐1.86) (0.48)
1.211 ‐0.109
(2.48) (‐1.18)
Yang 2 factor
α
HML
0.604
0.021
(2.26)
(0.32)
0.389
0.020
(1.37)
(0.37)
‐0.109
‐0.000
(‐0.38)
(‐0.00)
‐0.173
‐0.060
(‐0.57)
(‐1.24)
0.777
0.081
(1.86)
(1.00)
Panel C: Semi‐Annual Portfolio Formation
Comm. Market
FP 2 factor
α
SPGSCI
α
BAB
Low RIX‐beta
0.754 0.557
0.833 0.254
(2.53) (10.10) (2.80) (3.19)
2
‐0.248 0.490
‐0.220 0.396
(‐0.99) (12.33) (‐0.95) (5.77)
3
0.556 0.416
0.526 0.372
(1.97) (8.31)
(2.03) (5.77)
High RIX‐beta ‐0.582 0.341
‐0.584 0.319
(‐2.13) (5.97)
(‐2.26) (5.80)
Low ‐ High
1.336 0.216
1.417 ‐0.066
(3.39) (2.92)
(3.51) (‐0.65)
MOP 2 factor
α
TSMOM
0.753 0.001
(2.34) (0.01)
‐0.278 0.034
(‐1.08) (0.50)
0.524 0.037
(1.85) (0.40)
‐0.546 ‐0.041
(‐1.99) (‐0.63)
1.299 0.042
(3.19) (0.45)
AMP 3 factor
α
VAL
MOM
0.740 0.099 0.014
(2.34) (1.19) (0.17)
‐0.266 0.146 0.017
(‐1.04) (2.13) (0.26)
0.563 0.165 ‐0.018
(1.95) (2.36) (‐0.29)
‐0.564 0.148 ‐0.032
(‐2.03) (2.48) (‐0.49)
1.304 ‐0.048 0.046
(3.21) (‐0.50) (0.46)
BK 2 factor
α
FTB
0.893 ‐0.033
(2.51) (‐0.37)
‐0.284 0.035
(‐1.08) (0.60)
0.476 0.001
(1.65) (0.01)
‐0.473 ‐0.083
(‐1.61) (‐1.20)
1.365 0.050
(3.03) (0.50)
Yang 2 factor
α
HML
0.827
‐0.025
(2.52)
(‐0.34)
‐0.395
0.049
(‐1.42)
(0.86)
0.331
‐0.034
(1.02)
(‐0.62)
‐0.500
‐0.051
(‐1.58)
(‐0.92)
1.327
0.026
(2.84)
(0.32)
Panel D: Annual Portfolio Formation
Comm. Market
α
SPGSCI
Low RIX‐beta
0.488 0.515
(1.59) (8.07)
2
‐0.060 0.452
(‐0.21) (10.13)
3
0.646 0.433
(2.24) (7.38)
High RIX‐beta ‐0.601 0.400
(‐2.26) (8.91)
Low ‐ High
1.089 0.116
(2.74) (1.47)
MOP 2 factor
α
TSMOM
0.469 0.021
(1.43) (0.25)
‐0.071 0.012
(‐0.24) (0.15)
0.626 0.022
(2.12) (0.28)
‐0.568 ‐0.038
(‐2.12) (‐0.60)
1.036 0.060
(2.52) (0.68)
AMP 3 factor
α
VAL
MOM
0.450 0.147 0.043
(1.36) (1.81) (0.51)
‐0.026 0.150 ‐0.055
(‐0.09) (1.92) (‐0.82)
0.616 0.173 0.032
(2.08) (2.75) (0.57)
‐0.575 0.099 ‐0.041
(‐2.13) (1.75) (‐0.60)
1.025 0.048 0.084
(2.45) (0.52) (0.82)
BK 2 factor
α
FTB
0.521 0.022
(1.46) (0.25)
‐0.039 ‐0.016
(‐0.13) (‐0.23)
0.728 ‐0.092
(2.43) (‐1.27)
‐0.562 ‐0.023
(‐2.06) (‐0.30)
1.083 0.044
(2.38) (0.44)
Yang 2 factor
α
HML
0.539
0.001
(1.53)
(0.02)
‐0.243
0.008
(‐0.84)
(0.14)
0.529
‐0.007
(1.51)
(‐0.16)
‐0.541
‐0.071
(‐1.68)
(‐1.17)
1.081
0.072
(2.26)
(0.81)
FP 2 factor
α
BAB
0.551 0.308
(1.81) (3.80)
‐0.049 0.434
(‐0.18) (5.80)
0.634 0.321
(2.39) (5.20)
‐0.587 0.287
(‐2.29) (5.29)
1.138 0.021
(2.77) (0.20)
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
α
MSCI
α
BAB
Low RIX‐beta
0.641 0.434
0.327 0.704
(3.78) (9.46)
(2.13) (5.44)
2
0.222 0.444
0.071 0.337
(1.42) (12.30) (0.43) (2.98)
3
0.181 0.438
‐0.098 0.619
(1.30) (8.12) (‐0.76) (5.51)
High RIX‐beta
0.053 0.395
‐0.287 0.754
(0.31) (7.88) (‐1.97) (5.53)
Low ‐ High
0.588 0.039
0.614 ‐0.050
(3.53) (1.28)
(3.53) (‐0.30)
MOP 2 factor
AMP 3 factor
α
TSMOM
α
VAL
MOM
0.500 0.113
0.603 ‐0.073 0.133
(3.19) (2.15)
(3.94) (‐0.70) (1.35)
0.121 0.080
0.226 ‐0.076 0.022
(0.76) (1.75)
(1.43) (‐0.63) (0.25)
0.118 0.050
0.119 0.090 0.121
(0.89) (1.14)
(0.84) (0.90) (1.60)
‐0.063 0.093
‐0.055 0.217 0.186
(‐0.39) (1.87) (‐0.34) (2.18) (2.38)
0.563 0.020
0.659 ‐0.290 ‐0.054
(3.26) (0.53)
(4.17) (‐2.32) (‐0.57)
BK 2 factor
α
FTB
0.591 0.065
(3.55) (1.43)
0.224 0.015
(1.32) (0.30)
0.187 0.012
(1.44) (0.29)
0.036 0.034
(0.22) (0.76)
0.555 0.031
(3.22) (0.87)
Panel B: Quarterly Portfolio Formation
Global CAPM
FP 2 factor
α
MSCI
α
BAB
Low RIX‐beta
0.615 0.455
0.282 0.731
(3.31) (7.85)
(1.81) (5.07)
2
0.187 0.453
‐0.024 0.441
(1.22) (12.17) (‐0.14) (3.98)
3
0.160 0.417
‐0.108 0.575
(1.09) (8.87) (‐0.87) (5.28)
High RIX‐beta
0.012 0.406
‐0.292 0.645
(0.08) (8.70) (‐2.19) (5.38)
Low ‐ High
0.604 0.049
0.574 0.087
(3.48) (1.60)
(3.35) (0.51)
MOP 2 factor
AMP 3 factor
α
TSMOM
α
VAL
MOM
0.520 0.079
0.582 ‐0.074 0.125
(3.21) (1.37)
(3.52) (‐0.65) (1.18)
0.132 0.046
0.155 0.068 0.052
(0.83) (1.02)
(0.96) (0.50) (0.53)
0.089 0.059
0.102 0.068 0.122
(0.65) (1.30)
(0.71) (0.88) (1.96)
‐0.082 0.077
‐0.068 0.172 0.131
(‐0.59) (1.60) (‐0.48) (1.68) (1.84)
0.602 0.001
0.650 ‐0.245 ‐0.007
(3.69) (0.03)
(4.02) (‐1.80) (‐0.07)
BK 2 factor
α
FTB
0.582 0.048
(3.47) (0.92)
0.216 ‐0.010
(1.25) (‐0.20)
0.136 0.027
(0.98) (0.71)
‐0.017 0.028
(‐0.12) (0.66)
0.599 0.020
(3.57) (0.52)
Panel C: Semi‐Annual Portfolio Formation
Global CAPM
FP 2 factor
α
MSCI
α
BAB
Low RIX‐beta
0.703 0.425
0.395 0.683
(3.78) (7.37)
(2.26) (4.48)
2
0.051 0.447
‐0.229 0.584
(0.34) (12.35) (‐1.65) (6.06)
3
0.299 0.435
0.072 0.454
(2.09) (10.18) (0.49) (3.99)
High RIX‐beta
‐0.066 0.426
‐0.363 0.649
(‐0.46) (9.07)
(‐3.04) (5.96)
Low ‐ High
0.769 ‐0.001
0.758 0.034
(4.58) (‐0.04)
(4.20) (0.21)
MOP 2 factor
α
TSMOM
0.609 0.077
(3.43) (1.34)
‐0.057 0.089
(‐0.40) (2.09)
0.237 0.051
(1.60) (1.01)
‐0.133 0.055
(‐1.03) (1.22)
0.742 0.022
(4.36) (0.44)
AMP 3 factor
α
VAL
MOM
0.652 ‐0.035 0.151
(3.70) (‐0.28) (1.55)
‐0.008 0.088 0.116
(‐0.06) (0.88) (1.37)
0.288 ‐0.017 0.038
(1.90) (‐0.24) (0.53)
‐0.158 0.219 0.141
(‐1.21) (2.07) (2.05)
0.810 ‐0.254 0.011
(4.97) (‐1.89) (0.14)
BK 2 factor
α
FTB
0.678 0.044
(3.78) (0.81)
0.021 0.033
(0.14) (0.75)
0.253 0.025
(1.75) (0.62)
‐0.047 0.004
(‐0.36) (0.10)
0.725 0.040
(4.19) (0.85)
Panel D: Annual Portfolio Formation
Global CAPM
α
MSCI
Low RIX‐beta
0.590 0.446
(3.09) (6.97)
2
0.106 0.432
(0.69) (10.89)
3
0.280 0.431
(2.06) (11.11)
High RIX‐beta
‐0.028 0.421
(‐0.21) (9.99)
Low ‐ High
0.618 0.025
(3.87) (0.68)
MOP 2 factor
α
TSMOM
0.487 0.089
(2.69) (1.60)
0.014 0.079
(0.10) (1.87)
0.250 0.026
(1.73) (0.55)
‐0.097 0.060
(‐0.80) (1.31)
0.584 0.029
(3.54) (0.73)
AMP 3 factor
α
VAL
MOM
0.511 0.030 0.202
(2.75) (0.25) (1.92)
0.069 0.038 0.082
(0.45) (0.36) (1.00)
0.249 0.085 0.040
(1.88) (0.88) (0.55)
‐0.081 0.081 0.105
(‐0.64) (0.89) (1.52)
0.592 ‐0.051 0.097
(3.45) (‐0.36) (1.15)
BK 2 factor
α
FTB
0.586 0.040
(3.26) (0.76)
0.079 0.023
(0.51) (0.53)
0.300 ‐0.015
(2.15) (‐0.36)
‐0.055 0.033
(‐0.45) (0.80)
0.641 0.008
(3.99) (0.20)
FP 2 factor
α
BAB
0.292 0.693
(1.54) (4.11)
‐0.194 0.604
(‐1.33) (6.15)
0.046 0.485
(0.35) (4.36)
‐0.288 0.563
(‐2.66) (6.73)
0.581 0.130
(3.14) (0.82)
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
α
MSCI
Low GRIX‐beta
0.944 0.531
(3.98) (8.41)
2
0.300 0.358
(1.90) (7.89)
3
0.302 0.346
(2.31) (7.97)
4
0.119 0.544
(0.56) (6.73)
High GRIX‐beta
‐0.060 0.543
(‐0.22) (6.23)
Low ‐ High
1.004 ‐0.012
(3.61) (‐0.20)
FP 2 factor
α
BAB
0.675 0.679
(2.80) (3.56)
0.081 0.517
(0.53) (5.55)
0.048 0.527
(0.37) (5.19)
‐0.233 0.760
(‐1.03) (3.65)
‐0.534 1.076
(‐2.05) (5.43)
1.208 ‐0.396
(4.07) (‐1.70)
MOP 2 factor
α
TSMOM
0.672 0.217
(2.75) (2.15)
0.159 0.113
(0.98) (2.03)
0.160 0.113
(1.29) (3.21)
0.111 0.007
(0.51) (0.11)
‐0.033 ‐0.022
(‐0.13) (‐0.25)
0.704 0.238
(2.55) (2.50)
AMP 3 factor
α
VAL
MOM
0.914 ‐0.144 0.142
(3.75) (‐0.77) (0.97)
0.246 0.061 0.114
(1.47) (0.58) (1.15)
0.191 0.174 0.211
(1.54) (1.80) (2.96)
‐0.023 0.363 0.207
(‐0.10) (2.72) (1.70)
‐0.080 ‐0.028 0.065
(‐0.27) (‐0.18) (0.45)
0.994 ‐0.115 0.077
(3.32) (‐0.55) (0.46)
BK 2 factor
α
FTB
0.884 0.091
(3.47) (1.16)
0.271 0.048
(1.60) (0.98)
0.217 0.066
(1.72) (1.78)
0.199 ‐0.036
(0.88) (‐0.54)
0.025 ‐0.024
(0.10) (‐0.30)
0.860 0.116
(2.89) (1.47)
Panel B: Quarterly Portfolio Formation
Global CAPM
α
MSCI
Low GRIX‐beta
0.772 0.502
(3.29) (7.50)
2
0.329 0.337
(1.98) (7.31)
3
0.212 0.357
(1.48) (7.19)
4
0.189 0.528
(0.89) (6.77)
High GRIX‐beta
0.040 0.537
(0.15) (6.90)
Low ‐ High
0.731 ‐0.035
(2.55) (‐0.61)
FP 2 factor
α
BAB
0.548 0.619
(2.30) (3.01)
0.117 0.530
(0.74) (5.53)
‐0.026 0.537
(‐0.18) (5.00)
‐0.189 0.843
(‐0.87) (4.16)
‐0.384 1.032
(‐1.51) (5.93)
0.932 ‐0.413
(3.00) (‐1.72)
MOP 2 factor
α
TSMOM
0.585 0.147
(2.52) (1.63)
0.241 0.069
(1.40) (1.14)
0.103 0.086
(0.75) (1.95)
0.113 0.060
(0.53) (0.88)
0.110 ‐0.055
(0.40) (‐0.64)
0.475 0.201
(1.62) (2.39)
AMP 3 factor
α
VAL
MOM
0.752 ‐0.129 0.099
(3.13) (‐0.70) (0.70)
0.273 0.077 0.108
(1.59) (0.57) (1.21)
0.141 0.079 0.142
(0.97) (0.93) (1.83)
0.037 0.305 0.255
(0.17) (2.19) (1.97)
0.022 0.072 0.016
(0.08) (0.47) (0.11)
0.730 ‐0.200 0.082
(2.32) (‐0.91) (0.47)
BK 2 factor
α
FTB
0.780 0.041
(3.28) (0.57)
0.341 0.024
(2.02) (0.49)
0.154 0.051
(1.14) (1.14)
0.207 ‐0.002
(0.96) (‐0.03)
0.175 ‐0.060
(0.61) (‐0.73)
0.605 0.102
(1.87) (1.30)
Panel C: Semi‐Annual Portfolio Formation
Global CAPM
FP 2 factor
α
MSCI
α
BAB
Low GRIX‐beta
0.608 0.485
0.306 0.775
(2.59) (6.36)
(1.23) (3.43)
2
0.467 0.352
0.256 0.506
(2.58) (6.58)
(1.33) (3.55)
3
0.214 0.372
0.001 0.520
(1.51) (6.85)
(0.01) (3.77)
4
‐0.001 0.512
‐0.328 0.775
(‐0.00) (8.25)
(‐1.79) (5.56)
High GRIX‐beta
0.179 0.526
‐0.258 1.018
(0.65) (6.71)
(‐1.01) (6.08)
Low ‐ High
0.429 ‐0.041
0.564 ‐0.243
(1.68) (‐0.73)
(1.89) (‐1.07)
MOP 2 factor
α
TSMOM
0.449 0.125
(1.92) (1.26)
0.414 0.042
(2.16) (0.65)
0.101 0.089
(0.73) (2.12)
‐0.096 0.075
(‐0.54) (1.25)
0.210 ‐0.024
(0.76) (‐0.28)
0.239 0.149
(0.89) (1.75)
AMP 3 factor
α
VAL
MOM
0.543 ‐0.080 0.189
(2.14) (‐0.42) (1.16)
0.486 ‐0.099 ‐0.009
(2.45) (‐0.60) (‐0.07)
0.132 0.127 0.154
(0.91) (1.61) (2.11)
‐0.173 0.385 0.272
(‐0.90) (2.92) (2.63)
0.178 0.035 ‐0.012
(0.64) (0.22) (‐0.08)
0.365 ‐0.115 0.201
(1.25) (‐0.50) (1.11)
BK 2 factor
α
FTB
0.585 0.056
(2.41) (0.70)
0.515 ‐0.006
(2.72) (‐0.10)
0.177 0.049
(1.29) (1.18)
0.012 0.013
(0.07) (0.22)
0.290 ‐0.056
(1.02) (‐0.67)
0.295 0.112
(1.00) (1.47)
Panel D: Annual Portfolio Formation
Global CAPM
α
MSCI
Low GRIX‐beta
0.561 0.545
(2.20) (6.11)
2
0.219 0.436
(0.86) (4.47)
3
0.205 0.324
(1.48) (7.05)
4
‐0.002 0.473
(‐0.01) (8.80)
High GRIX‐beta
0.553 0.514
(1.94) (6.77)
Low ‐ High
0.009 0.032
(0.03) (0.42)
MOP 2 factor
α
TSMOM
0.395 0.133
(1.54) (1.44)
0.098 0.096
(0.39) (1.46)
0.056 0.119
(0.45) (2.89)
‐0.088 0.069
(‐0.45) (1.06)
0.550 0.002
(1.97) (0.02)
‐0.155 0.130
(‐0.50) (1.44)
AMP 3 factor
α
VAL
MOM
0.484 ‐0.062 0.231
(1.77) (‐0.35) (1.36)
0.197 ‐0.029 0.072
(0.71) (‐0.15) (0.49)
0.143 0.103 0.117
(1.06) (1.29) (1.70)
‐0.147 0.376 0.212
(‐0.79) (2.22) (1.86)
0.528 0.001 0.064
(1.84) (0.01) (0.42)
‐0.044 ‐0.064 0.167
(‐0.14) (‐0.28) (0.89)
BK 2 factor
α
FTB
0.535 0.058
(2.05) (0.75)
0.264 ‐0.008
(1.11) (‐0.13)
0.149 0.063
(1.13) (1.53)
0.012 0.015
(0.06) (0.23)
0.584 0.006
(2.05) (0.06)
‐0.049 0.052
(‐0.15) (0.66)
FP 2 factor
α
BAB
0.175 0.904
(0.63) (3.55)
‐0.129 0.750
(‐0.40) (2.64)
0.022 0.435
(0.16) (3.57)
‐0.284 0.644
(‐1.42) (3.89)
0.166 0.869
(0.61) (4.83)
0.009 0.035
(0.03) (0.12)
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
Excess MSCI MOP Alpha
FP BAB
Return
Market
TSMOM
Low GRIX‐beta
1.209
0.719
1.233
‐0.061
0.034
(1.90)
(2.50)
(19.22)
(‐0.43)
(1.03)
2
0.084
‐0.202
0.989
‐0.220
0.030
(0.16)
(‐0.91)
(17.71)
(‐1.74)
(1.10)
3
0.322
0.003
1.016
‐0.033
‐0.024
(0.67)
(0.02)
(25.92)
(‐0.40)
(‐1.20)
High GRIX‐beta
0.514
0.134
1.171
‐0.113
‐0.048
(0.92)
(0.65)
(28.35)
(‐1.13)
(‐1.51)
Low ‐ High
0.695
0.585
0.062
0.052
0.082
(2.22)
(1.84)
(0.86)
(0.30)
(2.01)
Panel B: GRIX‐beta portfolios formed using only currencies
Excess Dollar Alpha
Return
Market
Low GRIX‐beta
0.679
0.397
1.196
(2.63)
(2.85)
(14.26)
2
0.326
0.109
0.986
(1.63)
(1.10)
(18.15)
3
0.283
‐0.017
1.134
(1.50)
(‐0.21)
(22.25)
High GRIX‐beta
0.497
0.152
1.177
(2.32)
(1.47)
(18.88)
Low ‐ High
0.182
0.245
0.019
(1.09)
(1.64)
(0.18)
FP BAB
0.085
(1.30)
0.102
(2.18)
0.082
(1.92)
0.103
(1.82)
‐0.018
(‐0.22)
MOP TSMOM
0.019
(0.45)
‐0.018
(‐0.70)
0.012
(0.46)
0.017
(0.48)
0.002
(0.04)
Panel C: GRIX‐beta portfolios formed using only global government bonds
Global Excess MOP Alpha
Bond FP BAB
Return
TSMOM
Market
Low GRIX‐beta
0.296
0.235
0.898
0.136
0.038
(2.66)
(3.25)
(5.51)
(0.87)
(2.67)
2
0.281
0.258
0.775
‐0.086
0.012
(3.67)
(5.25)
(9.89)
(‐0.96)
(1.18)
3
0.136
0.113
0.644
‐0.213
0.017
(2.32)
(2.63)
(7.64)
(‐3.14)
(1.77)
High GRIX‐beta
0.114
0.135
0.912
‐0.319
0.009
(1.27)
(2.18)
(7.74)
(‐3.47)
(0.71)
Low ‐ High
0.183
0.100
‐0.013
0.455
0.029
(1.66)
(0.91)
(‐0.05)
(2.32)
(1.28)
AMP Value
0.368
(2.48)
0.536
(4.67)
0.460
(5.50)
0.635
(5.33)
‐0.267
(‐1.43)
AMP Value
‐0.076
(‐0.88)
0.006
(0.14)
0.029
(0.85)
0.085
(1.54)
‐0.161
(‐1.55)
AMP Momentum
0.343
(2.67)
0.018
(0.16)
0.181
(2.39)
0.406
(3.74)
‐0.064
(‐0.45)
AMP Momentum
0.048
(0.42)
‐0.045
(‐0.76)
‐0.002
(‐0.04)
0.034
(0.44)
0.014
(0.10)
AMP Value
AMP Momentum
‐0.028
(‐0.14)
0.056
(0.53)
0.082
(1.01)
‐0.341
(‐2.88)
0.314
(1.17)
‐0.074
(‐0.53)
‐0.005
(‐0.07)
0.015
(0.22)
0.098
(1.03)
‐0.172
(‐0.87)
Panel D: GRIX‐beta portfolios formed using only commodities
Excess SPGSCI Alpha
FP BAB
Return
Market
Low GRIX‐beta
1.126
0.734
0.524
0.234
(2.87)
(2.68)
(10.76)
(3.21)
2
0.174
‐0.305
0.662
0.299
(0.44)
(‐1.43)
(13.80)
(3.62)
3
0.168
‐0.110
0.521
0.315
(0.42)
(‐0.42)
(11.05)
(5.29)
High GRIX‐beta
0.368
0.311
0.595
0.271
(0.90)
(1.11)
(10.08)
(3.43)
Low ‐ High
0.758
0.423
‐0.071
‐0.038
(1.78)
(0.98)
(‐0.94)
(‐0.33)
MOP TSMOM
0.188
(1.80)
0.207
(1.79)
0.108
(1.33)
‐0.030
(‐0.31)
0.218
(1.44)
AMP Value
‐0.075
(‐0.92)
0.126
(1.49)
0.019
(0.31)
‐0.003
(‐0.03)
‐0.073
(‐0.63)
AMP Momentum
‐0.053
(‐0.61)
0.008
(0.08)
‐0.055
(‐0.87)
‐0.198
(‐2.37)
0.145
(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‐investment‐
grade 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
Panel A: Macroeconomic Fundamental Risk
Real GDP Growth
‐0.34
Inflation
0.10
Recession
0.39
Default Risk
0.38
Term Risk
0.18
Panel B: Financial Market Risk
Market Excess Return
Pastor‐Stambaugh Liquidity
On‐Off Run Spread
Market Volatility Risk
RN Moment Risk (Variance)
RN Moment Risk (Skewness)
RN Moment Risk (Kurtosis)
‐0.19
‐0.09
0.32
0.27
0.26
‐0.07
0.01
FXRIX
BDRIX
CMRIX
GRIX
‐0.24
‐0.25
0.42
0.07
0.20
‐0.20
‐0.05
0.36
‐0.01
0.20
‐0.18
‐0.22
0.41
‐0.06
0.17
‐0.29
‐0.14
0.49
0.07
0.23
‐0.01
‐0.06
0.09
0.06
0.07
0.05
‐0.04
0.04
‐0.10
0.09
0.10
0.13
‐0.05
‐0.05
‐0.11
‐0.06
‐0.02
0.15
0.09
0.12
‐0.07
‐0.09
‐0.10
0.13
0.10
0.08
0.12
‐0.01
‐0.07
‐0.49
‐0.18
0.16
‐0.16
‐0.16
0.07
‐0.61
‐0.10
0.19
‐0.07
‐0.05
Panel C: Funding and Liquidity Constraints of Financial Intermediaries
Hu‐Pan‐Wang Noise
0.33
‐0.01
0.06
Broker‐Dealer Leverage Shock
‐0.49
‐0.60
‐0.48
TED Spread
0.10
‐0.12
‐0.08
Swap ‐ T‐bill
0.13
0.19
0.11
Libor ‐ Repo
0.11
‐0.09
‐0.06
Funding Liquidity Risk (PCA)
0.16
‐0.07
‐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
β
t(β)
Adj. R2
Low RIX‐beta
4.59
1.257
46.6%
6.61
2
1.353
65.0%
7.13
3
1.415
68.5%
High RIX‐beta
4.56
1.086
46.2%
0.56
Low ‐ High
0.171
‐3.1%
FXRIX‐beta Portfolios
β
t(β)
Adj. R2
5.61
1.334
61.6%
4.22
0.859
46.9%
5.46
1.111
60.3%
4.34
1.230
48.4%
0.32
0.103
‐5.0%
BDRIX‐beta Portfolios
β
t(β)
Adj. R2
0.95
0.505
‐0.4%
1.93
0.664
8.9%
2.87
1.008
20.5%
1.90
1.074
8.6%
‐0.75
‐0.569
‐1.6%
CMRIX‐beta Portfolios
β
t(β)
Adj. R2
3.78
0.544
34.7%
3.32
0.506
28.6%
4.06
0.771
38.3%
2.74
0.565
20.7%
‐0.08
‐0.021
‐4.1%
Panel B: quarterly portfolio formation
EQRIX‐beta Portfolios
β
t(β)
Adj. R2
Low RIX‐beta
4.42
1.304
45.8%
7.28
2
1.521
70.3%
10.33
3
1.541
82.8%
High RIX‐beta
4.46
1.209
46.2%
0.26
Low ‐ High
0.095
‐4.4%
FXRIX‐beta Portfolios
β
t(β)
Adj. R2
5.31
1.143
58.9%
3.90
0.928
42.8%
5.46
1.222
60.2%
4.54
1.248
50.8%
‐0.35
‐0.105
‐4.8%
BDRIX‐beta Portfolios
β
t(β)
Adj. R2
1.06
0.546
0.4%
1.99
0.769
9.6%
3.20
1.168
24.8%
1.62
0.881
5.5%
‐0.45
‐0.336
‐3.0%
CMRIX‐beta Portfolios
β
t(β)
Adj. R2
4.85
0.820
47.4%
3.44
0.582
30.2%
2.64
0.456
19.3%
3.22
0.584
27.2%
0.84
0.236
‐1.2%
Panel C: semi‐annual portfolio formation
EQRIX‐beta Portfolios
β
t(β)
Adj. R2
Low RIX‐beta
5.27
1.431
54.9%
6.20
2
1.348
63.0%
11.25
3
1.498
85.1%
High RIX‐beta
4.76
1.284
49.7%
0.46
Low ‐ High
0.148
‐3.7%
FXRIX‐beta Portfolios
β
t(β)
Adj. R2
4.31
1.274
48.1%
3.32
0.829
34.5%
4.89
1.305
54.7%
4.04
1.092
44.6%
0.52
0.183
‐4.0%
BDRIX‐beta Portfolios
β
t(β)
Adj. R2
2.34
1.372
13.8%
1.43
0.475
3.6%
2.87
0.859
20.6%
1.52
0.823
4.5%
0.70
0.548
‐1.9%
CMRIX‐beta Portfolios
β
t(β)
Adj. R2
2.63
0.536
19.1%
5.40
0.676
53.0%
3.75
0.661
34.3%
3.54
0.545
31.6%
‐0.04
‐0.009
‐4.2%
Panel D: annual portfolio formation
EQRIX‐beta Portfolios
β
t(β)
Adj. R2
Low RIX‐beta
5.57
1.655
57.8%
7.56
2
1.526
71.8%
9.37
3
1.273
79.8%
High RIX‐beta
4.44
1.098
45.9%
1.75
Low ‐ High
0.558
8.5%
FXRIX‐beta Portfolios
β
t(β)
Adj. R2
4.12
1.468
45.6%
2.93
0.733
28.5%
5.98
1.415
64.7%
3.36
0.885
35.2%
1.24
0.582
2.8%
BDRIX‐beta Portfolios
β
t(β)
Adj. R2
2.62
2.206
17.3%
1.66
0.615
5.9%
2.66
0.775
17.8%
0.36
0.177
‐3.2%
2.01
2.028
9.8%
CMRIX‐beta Portfolios
β
t(β)
Adj. R2
2.33
0.573
15.1%
2.61
0.417
18.9%
5.53
0.844
54.2%
4.35
0.569
41.7%
0.01
0.004
‐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
β
t(β)
Adj. R2
Low RIX‐beta
1.70
0.153
67.7%
‐1.30
2
‐0.101
74.4%
1.21
3
0.066
85.5%
High RIX‐beta
1.18
0.086
75.4%
0.67
Low ‐ High
0.068
‐0.8%
FXRIX‐beta Portfolios
β
t(β)
Adj. R2
2.11
0.100
58.7%
0.21
0.006
73.8%
0.22
0.005
78.6%
0.52
0.015
74.6%
1.52
0.085
1.2%
BDRIX‐beta Portfolios
β
t(β)
Adj. R2
‐0.18
‐0.004
54.2%
1.18
0.017
52.3%
1.64
0.021
52.0%
‐0.11
‐0.002
50.5%
‐0.08
‐0.002
6.2%
CMRIX‐beta Portfolios
β
t(β)
Adj. R2
‐0.95
‐0.078
46.2%
0.54
0.044
45.2%
1.27
0.108
40.8%
0.72
0.065
26.2%
‐1.18
‐0.142
2.9%
Panel B: quarterly portfolio formation
EQRIX‐beta Portfolios
β
t(β)
Adj. R2
Low RIX‐beta
1.37
0.122
69.4%
‐0.10
2
‐0.006
82.6%
0.84
3
0.047
85.9%
High RIX‐beta
0.73
0.051
78.6%
0.67
Low ‐ High
0.070
‐0.9%
FXRIX‐beta Portfolios
β
t(β)
Adj. R2
2.08
0.093
63.0%
‐0.13
‐0.004
71.9%
‐0.18
‐0.004
81.5%
1.26
0.037
74.2%
1.08
0.056
2.1%
BDRIX‐beta Portfolios
β
t(β)
Adj. R2
‐0.16
‐0.003
56.8%
0.88
0.013
53.7%
1.37
0.019
47.6%
0.22
0.004
52.6%
‐0.30
‐0.007
2.5%
CMRIX‐beta Portfolios
β
t(β)
Adj. R2
0.69
0.065
50.3%
‐0.68
‐0.059
32.2%
1.50
0.134
29.4%
0.66
0.063
19.3%
0.01
0.002
9.7%
Panel C: semi‐annual portfolio formation
EQRIX‐beta Portfolios
β
t(β)
Adj. R2
Low RIX‐beta
0.46
0.042
67.5%
1.44
2
0.091
82.3%
0.28
3
0.015
87.4%
High RIX‐beta
0.82
0.057
78.5%
‐0.14
Low ‐ High
‐0.015
‐1.2%
FXRIX‐beta Portfolios
β
t(β)
Adj. R2
1.99
0.090
61.4%
‐0.20
‐0.005
76.7%
‐0.10
‐0.002
76.9%
0.89
0.026
74.9%
1.20
0.063
0.8%
BDRIX‐beta Portfolios
β
t(β)
Adj. R2
0.10
0.002
53.8%
0.86
0.011
53.8%
0.71
0.009
48.5%
0.61
0.011
54.2%
‐0.35
‐0.008
2.9%
CMRIX‐beta Portfolios
β
t(β)
Adj. R2
‐0.56
‐0.053
44.0%
1.02
0.080
44.5%
0.13
0.012
29.1%
1.32
0.122
22.2%
‐1.36
‐0.174
6.7%
Panel D: annual portfolio formation
EQRIX‐beta Portfolios
β
t(β)
Adj. R2
Low RIX‐beta
0.49
0.043
70.9%
1.46
2
0.094
81.2%
‐0.59
3
‐0.029
88.3%
High RIX‐beta
1.52
0.098
81.1%
‐0.58
Low ‐ High
‐0.054
‐0.6%
FXRIX‐beta Portfolios
β
t(β)
Adj. R2
1.39
0.066
57.8%
0.62
0.016
77.7%
‐0.63
‐0.016
76.8%
1.18
0.036
71.2%
0.55
0.030
1.3%
BDRIX‐beta Portfolios
β
t(β)
Adj. R2
0.00
0.000
51.5%
0.68
0.009
51.6%
‐0.34
‐0.004
49.6%
1.40
0.024
54.3%
‐0.91
‐0.024
5.0%
CMRIX‐beta Portfolios
β
t(β)
Adj. R2
‐0.28
‐0.027
39.2%
0.64
0.059
32.5%
‐0.31
‐0.027
34.3%
1.89
0.161
31.3%
‐1.50
‐0.188
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 Monthly Portfolio Portfolios
Formation
Low RIX‐beta
0.734
(3.06)
0.074
2
(0.42)
0.319
3
(1.94)
High RIX‐beta
0.374
(1.93)
0.360
Low ‐ High
(2.00)
Quarterly Portfolio Formation
0.795
(3.26)
0.163
(0.96)
0.276
(1.71)
0.296
(1.56)
0.499
(2.86)
Semi‐Annual Portfolio Formation
0.802
(3.41)
0.061
(0.35)
0.301
(1.84)
0.342
(1.76)
0.46
(2.72)
Annual Portfolio Formation
0.723
(2.97)
0.093
(0.51)
0.318
(1.88)
0.366
(1.97)
0.357
(1.92)
Panel B: Bond futures interpolated returns of 30‐day constant maturity
BDRIX‐beta Monthly Portfolio Quarterly Portfolio Semi‐Annual Portfolios
Formation
Formation
Portfolio Formation
Low RIX‐beta
0.320
0.252
0.353
(2.82)
(2.37)
(3.17)
0.149
0.153
0.125
2
(2.10)
(2.17)
(1.91)
0.116
0.097
0.085
3
(1.83)
(1.52)
(1.33)
High RIX‐beta
0.102
0.155
0.124
(1.38)
(2.07)
(1.58)
0.219
0.097
0.229
Low ‐ High
(2.38)
(1.17)
(2.62)
Annual Portfolio Formation
0.325
(2.65)
0.095
(1.34)
0.070
(1.06)
0.158
(2.16)
0.167
(1.72)
Panel C: Commodity futures returns of far/back contracts
CMRIX‐beta Monthly Portfolio Quarterly Portfolio Portfolios
Formation
Formation
Low RIX‐beta
0.431
0.652
(1.05)
(1.42)
0.085
0.113
2
(0.23)
(0.29)
0.433
0.203
3
(1.20)
(0.54)
High RIX‐beta
‐0.291
‐0.409
(‐1.18)
(‐0.80)
0.722
1.061
Low ‐ High
(1.66)
(2.22)
Annual Portfolio Formation
0.645
(1.49)
0.001
(0.00)
0.561
(1.44)
‐0.553
(‐1.51)
1.198
(2.75)
Semi‐Annual Portfolio Formation
0.841
(1.94)
‐0.107
(‐0.28)
0.514
(1.35)
‐0.562
(‐1.59)
1.402
(3.20)
Panel D: All assets (GRIX estimated as the simple average of four asset‐class RIXs)
GRIX‐beta Monthly Portfolio Quarterly Portfolio Semi‐Annual Portfolios
Formation
Formation
Portfolio Formation
Low RIX‐beta
0.844
0.750
0.670
(2.68)
(2.40)
(2.02)
0.612
0.507
0.512
2
(2.51)
(2.08)
(2.17)
0.368
0.368
0.258
3
(1.91)
(1.93)
(1.13)
‐0.029
‐0.031
0.100
4
(‐0.09)
(‐0.10)
(0.35)
High RIX‐beta
0.189
0.401
0.391
(0.51)
(1.04)
(1.02)
0.655
0.349
0.279
Low ‐ High
(2.36)
(1.12)
(0.79)
Annual Portfolio Formation
0.589
(1.49)
0.345
(1.24)
0.335
(1.53)
0.040
(0.15)
0.735
(2.03)
‐0.146
(‐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
Excess Excess Excess Alpha
Alpha
Alpha
Return
Return
Return
Low beta
0.971
0.596
0.611
0.305
0.323
0.232
(1.60)
(2.14)
(2.37)
(2.28)
(2.56)
(2.88)
2
0.401
0.076
0.222
‐0.009
0.205
0.174
(0.70)
(0.32)
(1.07)
(‐0.09)
(2.81)
(3.91)
3
0.496
0.161
0.284
‐0.016
0.140
0.146
(0.97)
(0.87)
(1.48)
(‐0.19)
(2.40)
(3.94)
High beta
0.289
‐0.040
0.607
0.289
0.157
0.195
(0.55)
(‐0.22)
(2.93)
(2.65)
(2.26)
(3.96)
Low ‐ High
0.682
0.635
0.005
0.016
0.165
0.037
(2.03)
(1.80)
(0.02)
(0.09)
(1.75)
(0.44)
Commodities
Excess Alpha
Return
0.512
0.322
(1.25)
(1.11)
0.839
0.505
(2.18)
(1.85)
0.709
0.336
(1.77)
(1.48)
‐0.192
‐0.560
(‐0.50)
(‐1.95)
0.705
0.883
(1.64)
(2.06)
Panel B: option‐based implied volatility skew within each asset class
Equity Indices
Currencies
Govt. Bonds
Excess Excess Excess Alpha
Alpha
Alpha
Return
Return
Return
Low beta
0.715
0.403
0.766
0.420
0.297
0.252
(1.29)
(2.05)
(2.63)
(2.68)
(2.59)
(3.45)
2
0.187
‐0.204
0.257
0.044
0.143
0.145
(0.35)
(‐1.17)
(1.33)
(0.56)
(2.08)
(3.03)
3
0.825
0.525
0.337
0.102
0.163
0.133
(1.61)
(2.65)
(1.90)
(1.34)
(2.29)
(3.32)
High beta
0.446
0.063
0.380
0.025
0.202
0.207
(0.76)
(0.29)
(1.79)
(0.22)
(2.66)
(3.58)
Low ‐ High
0.269
0.339
0.386
0.395
0.096
0.045
(1.04)
(1.22)
(1.73)
(2.09)
(0.98)
(0.46)
Commodities
Excess Alpha
Return
0.439
0.221
(1.13)
(0.83)
0.502
0.243
(1.32)
(1.07)
0.662
0.205
(1.69)
(0.83)
0.247
‐0.075
(0.65)
(‐0.31)
0.192
0.296
(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 RIX‐
beta 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)
Low RIX‐beta
2
3
High RIX‐beta
Low ‐ High
Excess Return
0.337
(2.65)
0.151
(2.26)
0.191
(3.12)
0.155
(2.23)
0.182
(1.95)
Alpha
0.267
(3.71)
0.111
(2.64)
0.193
(5.05)
0.190
(3.77)
0.077
(0.97)
Foreign Currency (Long or Short)
Excess Alpha
Return
0.892
0.545
(2.83)
(2.94)
0.241
‐0.005
(1.07)
(‐0.06)
0.280
0.046
(1.63)
(0.53)
0.356
0.030
(1.68)
(0.29)
0.536
0.515
(2.31)
(2.48)
Commodity (Long or Short)
Excess Alpha
Return
0.746
0.442
(1.80)
(1.40)
0.869
0.569
(2.17)
(2.35)
0.325
‐0.028
(0.78)
(‐0.12)
‐0.087
‐0.371
(‐0.24)
(‐1.24)
0.833
0.813
(1.84)
(1.79)
Table IA‐14: Prediction of GRIX on future economic fundamentals
We report coefficient estimates and Newey‐West t ‐statistics (in parentheses) of time‐
series predictive regressions. The dependent variable (y ) is one of the following macroeconomic measures: global real GDP growth, recession indicator, inflation, default risk, MSCI world equity market return, and aggregated funding liquidity (see Table IA‐8 for details of constructing these variables). The predictor is the global rare disaster concern index (GRIX) based on the first principal component of the correlation matrix of four asset‐class rare disaster concern indices (see Figure 1 in detail). a
b
Adj. R‐Square
a
b
Adj. R‐Square
Real GDP Default Market Recession Inflation
Growth
Risk
Return
3‐month prediction: y(t+3) = a + b × GRIX(t) + e(t)
‐0.018
0.287
1.443
0.051
0.003
(‐0.13)
(5.00)
(24.12)
(0.51)
(0.79)
0.004
0.062
‐0.067
‐0.195
0.003
(0.03)
(2.66)
(‐2.99)
(‐4.55)
(1.00)
‐0.01
0.10
0.10
0.08
0.00
6‐month prediction
‐0.028
0.284
1.435
0.047
0.003
(‐0.21)
(4.59)
(25.78)
(0.55)
(0.80)
0.178
0.015
‐0.074
‐0.143
0.005
(2.01)
(0.58)
(‐3.30)
(‐2.50)
(2.32)
0.13
0.00
0.12
0.04
0.02
Funding Liquidity
0.026
(0.35)
‐0.236
(‐5.58)
0.06
0.022
(0.30)
‐0.144
(‐4.01)
0.02
Table IA‐15: Disaster concern innovation and returns of portfolios within and across asset classes
Within an asset class, we estimate an asset's beta with respect to the innovation of its asset‐class RIX, and then form four ΔRIX‐beta portfolios. Across all global assets from four asset classes, we estimate such beta with respect to the innovation of the GRIX, and then form four ΔGRIX‐beta portfolios. Both within and across asset classes, we also form hedge portfolios by going long in low beta assets and short in high beta assets. The rolling‐window regression setup is similar to that in Table 3. We form portfolios monthly and calculate equal‐
weighted portfolio returns. This table presents monthly mean excess returns (in percent) and alphas benchmarked on the five‐factor global asset pricing model. Newey‐West t ‐statistics are reported in parentheses.
Beta estimated using ΔRIX (or ΔGRIX)
Low ‐ beta
2
3
High ‐ beta
Low ‐ High
Equity Indices
Excess Alpha
Return
0.759
0.404
(1.19)
(1.15)
0.402
0.100
(0.78)
(0.42)
0.316
0.006
(0.66)
(0.04)
0.679
0.356
(1.31)
(1.71)
0.080
0.048
(0.25)
(0.16)
Currencies
Excess Alpha
Return
0.549
0.248
(1.91)
(1.47)
0.385
0.111
(1.86)
(1.25)
0.355
0.115
(1.87)
(1.30)
0.448
0.174
(2.09)
(1.60)
0.101
0.074
(0.53)
(0.38)
Sovereign Bonds
Excess Alpha
Return
0.254
0.263
(2.11)
(3.44)
0.174
0.179
(2.54)
(4.56)
0.198
0.202
(3.25)
(4.76)
0.172
0.176
(2.34)
(3.36)
0.082
0.087
(0.83)
(0.96)
Commodities
Excess Alpha
Return
0.508
0.251
(1.13)
(0.77)
0.564
0.339
(1.65)
(1.34)
0.381
0.148
(0.98)
(0.57)
0.353
0.129
(0.91)
(0.50)
0.155
0.122
(0.39)
(0.31)
All Assets
Excess Alpha
Return
0.633
0.090
(1.65)
(0.27)
0.385
‐0.081
(1.71)
(‐0.46)
0.188
‐0.090
(0.78)
(‐0.52)
0.449
‐0.157
(1.44)
(‐0.82)
0.184
0.247
(0.72)
(0.71)
Table IA‐16: Kelly‐Jiang tail risk and returns of portfolios within and across asset classes
Within an asset class, we estimate an asset's return beta with respect to the Kelly‐Jiang (2014) tail risk factor, and then form four tail‐risk‐β portfolios (the 18‐24 month rolling‐window regression specifications are the same to those of our baseline RIX‐beta analysis as reported in Table 3). We also estimate tail risk β and form portfolios across all global assets from four asset classes. Both within and across asset classes, we also form hedge portfolios by going long in low‐β assets and short in high‐β assets. We form portfolios monthly and calculate equal‐weighted portfolio returns. This table presents monthly mean excess returns (in percent) and alphas benchmarked on the five‐factor global asset pricing model. Newey‐West t ‐statistics are reported in parentheses.
β Estimated using Kelly‐Jiang (2014) tail risk factor
Low ‐ beta
2
3
High ‐ beta
Low ‐ High
Equity Indices
Excess Alpha
Return
0.787
0.303
(1.40)
(1.09)
0.648
0.313
(1.33)
(1.62)
0.739
0.293
(1.27)
(1.28)
0.559
0.168
(0.93)
(0.83)
0.228
0.135
(0.61)
(0.40)
Currencies
Excess Alpha
Return
0.502
0.170
(2.62)
(1.65)
0.467
0.147
(2.67)
(1.75)
0.375
0.149
(2.00)
(1.48)
0.406
0.131
(1.89)
(1.20)
0.096
0.039
(0.59)
(0.24)
Sovereign Bonds
Excess Alpha
Return
0.155
0.137
(1.80)
(1.93)
0.171
0.160
(2.63)
(3.28)
0.174
0.159
(2.61)
(3.67)
0.259
0.243
(2.67)
(4.64)
‐0.104
‐0.106
(‐1.23)
(‐1.19)
Commodities
Excess Alpha
Return
‐0.108
‐0.407
(‐0.32)
(‐1.69)
0.406
0.135
(1.06)
(0.68)
0.798
0.519
(1.80)
(1.67)
0.329
‐0.002
(0.88)
(‐0.01)
‐0.437
‐0.405
(‐1.11)
(‐1.04)
All Assets
Excess Alpha
Return
0.329
‐0.098
(1.28)
(‐0.51)
0.303
‐0.006
(2.00)
(‐0.05)
0.399
‐0.176
(1.16)
(‐0.87)
0.749
0.371
(1.41)
(1.36)
‐0.420
‐0.469
(‐0.91)
(‐1.40)
Table IA‐17: US exchange trade funds (ETFs)
This table presents ETFs that have available monthly returns in CRSP. We use these 28 ETFs to track our sample of international equity indices in the main analysis. The two ETFs ("iShares MSCI Denmark Cppd Investable Mkt" and "iShares MSCI Finland Capped Inv Mkt") have no available CRSP returns, and hence we exclude them in tracking market index returns of Denmark and Finland. ETF Full Name
Ticker
Inception Date
CUSIP
SPDR S&P 500
iShares MSCI Australia Index
iShares MSCI Austria Capped Invstbl Mkt
iShares MSCI Belgium Capped Invstbl Mkt
iShares MSCI Canada Index
iShares MSCI France Index
iShares MSCI Germany Index
iShares MSCI Hong Kong Index
iShares MSCI Italy Capped Index
iShares MSCI Japan Index
iShares MSCI Mexico Capped Invstbl Mkt
iShares MSCI Netherlands Invstbl Mkt Idx
iShares MSCI Singapore Index
iShares MSCI Spain Capped Index
iShares MSCI Sweden Index
iShares MSCI Switzerland Capped Index
iShares MSCI United Kingdom Index
iShares MSCI South Korea Capped Index
iShares MSCI Taiwan Index
Vanguard FTSE Europe ETF
iShares MSCI Israel Cap Invest Mkt Index
iShares MSCI Thailand Capped Invstbl Mkt
Global X FTSE Nordic Region ETF
iShares S&P India Nifty 50 Index
iShares MSCI Poland Capped Invstbl Mkt
Global X FTSE Norway 30 ETF
iShares MSCI Russia Capped Index
Global X FTSE Greece 20 ETF
SPY
EWA
EWO
EWK
EWC
EWQ
EWG
EWH
EWI
EWJ
EWW
EWN
EWS
EWP
EWD
EWL
EWU
EWY
EWT
VGK
EIS
THD
GXF
INDY
EPOL
NORW
ERUS
GREK
22-Jan-1993
12-Mar-1996
12-Mar-1996
12-Mar-1996
12-Mar-1996
12-Mar-1996
12-Mar-1996
12-Mar-1996
12-Mar-1996
12-Mar-1996
12-Mar-1996
12-Mar-1996
12-Mar-1996
12-Mar-1996
12-Mar-1996
12-Mar-1996
12-Mar-1996
9-May-2000
20-Jun-2000
4-Mar-2005
26-Mar-2008
26-Mar-2008
17-Aug-2009
18-Nov-2009
25-May-2010
9-Nov-2010
9-Nov-2010
7-Dec-2011
78462F103
464286103
464286202
464286301
464286509
464286707
464286806
464286871
464286855
464286848
464286822
464286814
464286673
464286764
464286756
464286749
464286699
464286772
464286731
922042874
464286632
464286624
37950E101
464289529
46429B606
37950E747
46429B705
37950E366