coskewness in european real estate equity returns tobias dechant kai-magnus schulte
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Coskewness in European Real Estate Equity Returns Tobias Dechant Kai-Magnus Schulte. Coskewness in European Real Estate Equity Returns Aim of the Paper pricing of European real estate equities cross-section relationship between coskewness and European real estate equity returns - PowerPoint PPT PresentationTRANSCRIPT
Dr. Max MustermannReferat Kommunikation & Marketing Verwaltung
ERES Conference 2012Edinburgh
Coskewness in European Real Estate Equity Returns
Tobias DechantKai-Magnus Schulte
Coskewness in European Real Estate Equity Returns
Aim of the Paper
• pricing of European real estate equities
• cross-section relationship between coskewness and European real estate equity returns
• higher returns on equities which contribute negatively to equity market skewness
Motivation
• real estate characteristics demand for the analysis of coskewness in asset pricing
• almost no evidence for the European real estate market
• some evidence for the explanatory power of coskewness in global real estate equities
Methodology
Time Series Regressions (Fama & French 1993, 1996, 1997)• rolling time series regressions to determine factor risk premia
Cross Section Regressions (Fama & McBeth 1973, Harvey & Siddique 2000) • explaining cross section return differences by regressing equity returns on factor risk premia
Conditional Cross Section Regressions (Pettengill et al. 1995, 2000)• explaining cross section returns differences by regressing equity returns on factor risk premia conditional on the state of the equity market
Data
Thomson Reuters Datastream/Global Property Research (GPR)
• 16 European countries
• June 1988 - June 2009
• data frequency: monthly
• 275 (Ø 102) real estate equities (screening according to Ince und Porter, 2006)
• 9.662 (Ø 3.864) general equities (screening according to Ince und Porter, 2006)
• currency: Euro
• equity market return: equally weighted return on all available equities
• riskless rate of return: equally weighted „One Month Interbank Rate“ of all 16 countries
Constructing Portfolios
• reducing idiosyncratic risk in returns
• sequential sorting (Liew and Vassalou, 2000)
• sorting date: end of June each year from 1988 to 2009
• sorting criteria: market capitalisation (ME) book equity/market equity (BE/ME)
• breakpoints ME: quartiles BE/ME: quartiles
• 16 real estate portfolios for time series regressions
Coskewness and Asset Pricing (1)
Definition Coskewness
•
• contribution of asset skewness to skewness of the market portfolio
• preference for positive skewness (Kraus & Litzenberger 1976; Scott & Horvath 1980)
• asset which increases (decreases) market skewness should, on average, yield a lower (higher) return
• expected prefix in cross section regressions dependent on market skewness
3
2
)()()(
mm
mmititim rErE
rErrErE
Coskewness und Asset Pricing (2)
Coskewness according to Harvey & Siddique (2000)
•
•
• residuals from CAPM regression
• unconditional measures of coskewness (not dependent on market skewness)
• easier interpretation in cross section regressions
3
2,2
, )()(
ˆmm
mmmpmp rEr
rErE
22
,
2,1
,)(
)(ˆ
mmmp
mmmpmp
rErEE
rErE
mp,
Model (1)
Rolling Time Series Regressions
Determination of Factor Risk Premia:
• modelling time variation in factor risk premia
• rolling window of 60 months (check for robustness: 48 months, 72 months)
pppppp HMLhSMBsRMbr
Model (2)
Unconditional Cross Section Regressions
Regression of Equity Returns on Portfolio Factor Loadings (g2i)
• monthly cross section regressions from July 1993 to June 2009
• explaining return differences by rolling factor risk premia
• mean value of „gammas“ indicates explanatory power
Model (3)
Conditional Cross Section Regressions
• Conditioning cross section regression depending on the state of the equity market
If an asset is classified as risky there must be some states in which its return is
below that of a less riskier asset
with 01 fmm rrfür 00 fmm rrfür
Results (2) – Base Model (Equally Weighted)
• Almost no explanatory power of coskewness neither unconditional nor conditional
Sample Full Ex FC Sub I Sub II Full Ex FC Sub I Sub II Full Ex FC Sub I Sub II Full Ex FC Sub I Sub II Full Ex FC Sub I Sub II0.000 -0.001 -0.001 0.000 -0.002 -0.002 -0.009 0.001 0.003 0.001 0.011 -0.001 -0.004 -0.005 -0.004 -0.004 0.005 0.006 0.002 0.008
(-0.071) (-0.204) (-0.184) (0.035) (-0.702) (-0.421) (-1.675) (0.248) (0.947) (0.224) (2.114) (-0.309) (-1.263) (-1.336) (-0.712) (-1.029) (1.476) (1.562) (0.411) (1.427)**
Adj. R² 0.176 0.169 0.149 0.191 0.165 0.171 0.136 0.180 0.193 0.166 0.170 0.205 0.183 0.186 0.172 0.188 0.167 0.141 0.130 0.1950.000 -0.001 -0.002 0.001 -0.001 0.000 -0.006 0.002 0.001 -0.002 0.004 -0.001 -0.004 -0.004 -0.002 -0.004 0.004 0.005 -0.003 0.010
(-0.036) (-0.118) (-0.592) (0.169) (-0.208) (0.079) (-1.588) (0.342) (0.237) (-0.434) (0.851) (-0.121) (-0.842) (-0.833) (-0.420) (-0.723) (0.982) (0.930) (-0.600) (1.342)
Adj. R² 0.178 0.171 0.151 0.192 0.166 0.173 0.138 0.181 0.194 0.167 0.171 0.206 0.185 0.188 0.174 0.189 0.168 0.142 0.131 0.196Obs. 192 168 66 126 114 104 40 74 78 64 26 52 110 104 31 79 82 64 35 47
Panel I - Equal-Weighted Euro Currency Including Country-EffectsUncondit ional Stock Market Real Estate Market
Up Down Up Down
HS1
HS2
Results (3) – Controlling for Weighting Effects
• weak conditional explanatory power when weighting effects are considered for
Sample Full Ex FC Sub I Sub II Full Ex FC Sub I Sub II Full Ex FC Sub I Sub II Full Ex FC Sub I Sub II Full Ex FC Sub I Sub II0.000 0.001 0.003 -0.001 -0.002 -0.003 -0.005 -0.001 0.004 0.009 0.017 -0.001 -0.001 -0.002 -0.009 0.002 0.002 0.006 0.014 -0.006
(0.082) (0.376) (0.494) (-0.178) (-0.623) (-0.874) (-0.711) (-0.205) (0.862) (2.540) (2.969) (-0.154) (-0.314) (-0.446) (-1.369) (0.480) (0.540) (1.691) (2.703) (-0.952)** *** * **
Adj. R² 0.173 0.167 0.147 0.188 0.163 0.165 0.126 0.185 0.189 0.172 0.186 0.190 0.184 0.186 0.156 0.196 0.160 0.138 0.137 0.1760.002 0.003 0.003 0.001 0.000 -0.001 -0.002 0.001 0.005 0.010 0.011 0.002 0.001 0.001 -0.007 0.005 0.002 0.007 0.013 -0.004
(0.322) (0.555) (0.470) (0.162) (-0.038) (-0.211) (-0.315) (0.106) (0.790) (1.950) (1.909) (0.215) (0.211) (0.101) (-1.073) (0.614) (0.462) (1.213) (2.290) (-0.535)* * **
Adj. R² 0.175 0.169 0.149 0.189 0.165 0.167 0.129 0.187 0.190 0.173 0.187 0.191 0.187 0.189 0.160 0.198 0.161 0.139 0.138 0.176Obs. 192 168 66 126 113 105 43 70 79 63 23 56 108 102 33 75 84 66 33 51
HS2
Panel II - Value-Weighted Euro Currency Including Country-EffectsUnconditional Stock Market Real Estate Market
Up Down Up Down
HS1
Sample Full Ex FC Sub I Sub II Full Ex FC Sub I Sub II Full Ex FC Sub I Sub II Full Ex FC Sub I Sub II Full Ex FC Sub I Sub II-0.001 -0.002 0.002 -0.003 -0.006 -0.006 -0.009 -0.004 0.005 0.004 0.018 -0.001 -0.004 -0.005 -0.001 -0.006 0.003 0.003 0.004 0.002
(-0.461) (-0.637) (0.333) (-0.954) (-2.472) (-2.047) (-2.184) (-1.443) (1.940) (1.340) (4.153) (-0.205) (-1.767) (-1.793) (-0.168) (-2.028) (1.006) (1.083) (0.808) (0.602)** ** ** * *** * * **
Adj. R² 0.167 0.159 0.133 0.185 0.159 0.163 0.123 0.178 0.178 0.153 0.147 0.193 0.166 0.166 0.136 0.179 0.168 0.146 0.131 0.194-0.001 -0.002 0.001 -0.002 -0.006 -0.005 -0.007 -0.005 0.005 0.003 0.012 0.002 -0.005 -0.006 -0.001 -0.007 0.005 0.005 0.003 0.007
(-0.377) (-0.631) (0.202) (-0.520) (-1.896) (-1.501) (-2.230) (-1.174) (1.705) (0.836) (3.440) (0.444) (-1.684) (-1.686) (-0.300) (-1.605) (1.344) (1.291) (0.568) (1.281)* ** * *** * *
Adj. R² 0.168 0.160 0.135 0.185 0.160 0.164 0.127 0.179 0.178 0.153 0.147 0.193 0.167 0.166 0.137 0.179 0.169 0.149 0.133 0.194Obs. 192 168 66 126 111 102 39 72 81 66 27 54 113 108 33 80 79 60 33 46
Panel III - Equal-Weighted Local Currency Including Country-EffectsUnconditional Stock Market Real Estate Market
Up Down Up Down
HS1
HS2
Results (4) – Controlling for Currency Effects
• conditional explanatory power when currency effects are controlled for
Results (1) – Cross Section Results without Coskewness (EW)
Sample Full Ex FC Sub I Sub II Full Ex FC Sub I Sub II Full Ex FC Sub I Sub II Full Ex FC Sub I Sub II Full Ex FC Sub I Sub II
0.010 0.016 0.004 0.014 0.036 0.036 0.022 0.043 -0.026 -0.016 -0.024 -0.028 0.042 0.043 0.031 0.047 -0.033 -0.027 -0.019 -0.042
(1.734) (2.991) (0.647) (1.619) (8.993) (7.926) (4.645) (8.422) (-5.033) (-3.851) (-6.067) (-3.629) (13.783) (12.986) (8.405) (11.854) (-7.987) (-9.041) (-6.132) (-7.328)
* *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** ***
0.001 0.000 0.000 0.001 -0.001 -0.001 -0.004 0.001 0.003 0.002 0.005 0.003 -0.006 -0.005 -0.006 -0.006 0.010 0.008 0.004 0.014
(0.318) (-0.079) (-0.192) (0.391) (-0.385) (-0.470) (-1.364) (0.155) (1.421) (0.592) (2.365) (0.754) (-1.914) (-1.532) (-2.077) (-1.356) (4.068) (2.668) (1.804) (3.860)
** * ** *** *** * ***
-0.003 -0.003 -0.001 -0.004 -0.003 -0.003 0.007 -0.008 -0.003 -0.003 -0.012 0.002 -0.002 -0.003 0.008 -0.006 -0.004 -0.003 -0.009 0.000
(-0.799) (-0.749) (-0.249) (-0.759) (-0.739) (-0.694) (2.223) (-1.392) (-0.800) (-0.666) (-5.278) (0.514) (-0.537) (-0.707) (3.269) (-1.203) (-1.365) (-0.939) (-3.640) (-0.057)
** *** *** ***
Adj. R² 0.175 0.168 0.149 0.189 0.164 0.170 0.136 0.178 0.192 0.165 0.169 0.204 0.182 0.184 0.170 0.186 0.167 0.141 0.130 0.194
Obs. 192 168 66 126 114 104 40 74 78 64 26 52 110 104 31 79 82 64 35 47
Rm - Rf
SMB
HML
Panel I - Equal-Weighted Euro Currency Including Country-Effects
Unconditional Stock Market Real Estate Market
Up Down Up Down
Sample Full Ex FC Sub I Sub II Full Ex FC Sub I Sub II Full Ex FC Sub I Sub II Full Ex FC Sub I Sub II Full Ex FC Sub I Sub II
0.009 0.014 0.003 0.011 0.033 0.034 0.019 0.041 -0.025 -0.016 -0.020 -0.028 0.038 0.037 0.027 0.042 -0.033 -0.027 -0.020 -0.042
(1.466) (2.622) (0.582) (1.355) (8.000) (7.306) (4.159) (7.484) (-5.235) (-4.212) (-4.861) (-4.052) (10.655) (9.766) (6.635) (9.027) (-7.809) (-7.624) (-6.648) (-7.004)
*** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** ***
-0.001 -0.002 -0.001 -0.001 -0.001 -0.002 -0.003 0.000 0.000 -0.001 0.003 -0.001 -0.005 -0.005 -0.004 -0.006 0.006 0.004 0.002 0.009
(-0.336) (-0.657) (-0.447) (-0.201) (-0.493) (-0.550) (-1.454) (-0.053) (0.025) (-0.654) (1.134) (-0.420) (-2.046) (-1.686) (-1.148) (-1.669) (3.190) (2.025) (1.331) (3.072)
** * * *** ** ***
0.000 0.000 0.001 -0.001 -0.001 -0.001 0.009 -0.006 0.000 0.002 -0.012 0.006 0.004 0.003 0.011 0.001 -0.007 -0.006 -0.010 -0.005
(-0.125) (-0.061) (0.164) (-0.176) (-0.209) (-0.310) (3.652) (-0.947) (0.027) (0.344) (-5.971) (1.057) (0.967) (0.672) (3.665) (0.200) (-1.909) (-1.507) (-4.957) (-0.852)
*** *** *** * ***
Adj. R² 0.166 0.158 0.133 0.184 0.159 0.162 0.123 0.178 0.177 0.152 0.146 0.192 0.167 0.166 0.137 0.179 0.166 0.144 0.128 0.193
Obs. 192 168 66 126 111 102 39 72 81 66 27 54 113 108 33 80 79 60 33 46
Up Down Up Down
Panel III - Equal-Weighted Local Currency Including Country-Effects
Unconditional Stock Market Real Estate Market
Rm - Rf
SMB
HML
Summary & Implications
Coskewness and Returns on European Real Estate Equities• no explanatory power in unconditonal models
• indication for the explanatory power of coskewness in conditional models
• explanatory power of coskewness depends on the model
• coskewness proves to be significant when currency effects are considered
• relationship between market capitalisation , momentum and coskewness
Role of Coskewness requires• more attention in real estate asset pricing
• more research
Backup
Sample Full Ex FC Sub I Sub II Full Ex FC Sub I Sub II Full Ex FC Sub I Sub II Full Ex FC Sub I Sub II Full Ex FC Sub I Sub II0.000 0.000 -0.001 0.000 -0.001 0.000 -0.002 0.000 0.001 0.001 0.000 0.001 -0.001 -0.001 -0.001 -0.001 0.001 0.002 0.000 0.002##### (0.361) ##### (0.330) ##### ##### ##### ##### (1.765) (2.005) (0.579) (1.621) ##### ##### ##### ##### (2.100) (3.431) ##### (2.836)
*** * ** * *** ** *** ***Adj. R² 0.172 0.163 0.145 0.186 0.158 0.164 0.130 0.174 0.191 0.161 0.166 0.203 0.176 0.178 0.168 0.180 0.165 0.137 0.124 0.195
-0.001 0.000 -0.001 -0.001 -0.001 -0.001 -0.001 -0.001 0.000 0.001 0.000 0.001 -0.002 -0.002 -0.001 -0.002 0.001 0.002 0.000 0.002##### ##### ##### ##### ##### ##### ##### ##### (0.868) (1.322) (0.202) (0.853) ##### ##### ##### ##### (1.055) (2.996) ##### (1.345)
** *** *** ** *** ** ***Adj. R² 0.172 0.162 0.143 0.187 0.160 0.163 0.127 0.177 0.189 0.160 0.168 0.200 0.176 0.177 0.164 0.180 0.167 0.138 0.125 0.198
Obs. 192 168 66 126 114 104 40 74 78 64 26 52 110 104 31 79 82 64 35 47
Gamma 2
Panel IV - Equal-Weighted Euro Currency Excluding Country-EffectsUnconditional Stock Market Real Estate Market
Up Down Up Down
Gamma 1
Ergebnisse (1) – Querschnittsregressionen ohne Coskewness
Sample Full Ex FC Sub I Sub II Full Ex FC Sub I Sub II Full Ex FC Sub I Sub II Full Ex FC Sub I Sub II Full Ex FC Sub I Sub II
0.010 0.016 0.004 0.014 0.036 0.036 0.022 0.043 -0.026 -0.016 -0.024 -0.028 0.042 0.043 0.031 0.047 -0.033 -0.027 -0.019 -0.042
(1.734) (2.991) (0.647) (1.619) (8.993) (7.926) (4.645) (8.422) (-5.033) (-3.851) (-6.067) (-3.629) (13.783) (12.986) (8.405) (11.854) (-7.987) (-9.041) (-6.132) (-7.328)
* *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** ***
0.001 0.000 0.000 0.001 -0.001 -0.001 -0.004 0.001 0.003 0.002 0.005 0.003 -0.006 -0.005 -0.006 -0.006 0.010 0.008 0.004 0.014
(0.318) (-0.079) (-0.192) (0.391) (-0.385) (-0.470) (-1.364) (0.155) (1.421) (0.592) (2.365) (0.754) (-1.914) (-1.532) (-2.077) (-1.356) (4.068) (2.668) (1.804) (3.860)
** * ** *** *** * ***
-0.003 -0.003 -0.001 -0.004 -0.003 -0.003 0.007 -0.008 -0.003 -0.003 -0.012 0.002 -0.002 -0.003 0.008 -0.006 -0.004 -0.003 -0.009 0.000
(-0.799) (-0.749) (-0.249) (-0.759) (-0.739) (-0.694) (2.223) (-1.392) (-0.800) (-0.666) (-5.278) (0.514) (-0.537) (-0.707) (3.269) (-1.203) (-1.365) (-0.939) (-3.640) (-0.057)
** *** *** ***
Adj. R² 0.175 0.168 0.149 0.189 0.164 0.170 0.136 0.178 0.192 0.165 0.169 0.204 0.182 0.184 0.170 0.186 0.167 0.141 0.130 0.194
Obs. 192 168 66 126 114 104 40 74 78 64 26 52 110 104 31 79 82 64 35 47
Panel I - Equal-Weighted Euro Currency Including Country-Effects
Unconditional Stock Market Real Estate Market
Up Down Up Down
pb
ps
ph
Descriptive Statistics
B1 B2 B3 Mean Break B1 B2 B3 Mean Break
S1 147.94 145.33 152.81 148.26 < 297.15 31.87 40.49 42.82 38.6 < 110.10
S2 1206.43 1068.27 934.68 1069.85 > 297.15 1580.53 2538.94 2433.81 2220.08 > 110.10
Mean 686.53 613.49 549.41 616.16 806.68 1290.02 1238.86 1129.34
Obs. 252 252 252 252 252 252
B1 B2 B3 Mean Obs. B1 B2 B3 Mean Obs.
S1 1.88 0.97 0.52 1.1 252 5.97 0.68 0.27 2.14 252
S2 3.88 0.96 0.49 1.67 252 4.97 0.52 0.22 1.77 252
Mean 2.9 0.96 0.51 1.39 5.47 0.6 0.25 1.95
Break > 1.18 > 0.76 < 0.76 > 0.85 > 0.40 < 0.40
B1 B2 B3 Mean H-L t(H-L) B1 B2 B3 Mean H-L t(H-L)
S1 1.03% 0.79% 0.56% 0.48% 1.55 1.44% 0.72% 0.09% 1.34% 7.9
S2 0.82% 0.53% 0.31% 0.52% 2.07 1.09% 0.64% 0.30% 0.79% 4.65
Mean 0.50% 2.19 1.07% 6.69
S-B 0.21% 0.26% 0.25% 0.24% 0.34% 0.08% -0.21% 0.07%
t(S-B) 0.96 1.42 0.85 1.49 2.66 0.67 -1.53 0.64
Obs. 252 252 252 252 252 252
Panel III: Returns
Panel II: BE/ME
Real Estate Equities 2x3 Panel I: Size General Equities 2x3
Formung der systematischen Risikofaktoren HML und SMB
• Nach Portfolioformierung: S1/B1, S1/B2, S1/B3, S2/B1, S2/B2, S2/B3
• SMB: S1/B1 + S1/B2 + S1/B3 – (S2/B1 + S2/B2 + S2/B3)
Risikofaktor assoziiert mit der Größe einer Firma
• HML: S1/B1 + S2/B1 – (S1/B3 + S2/B3)
Risikofaktor assoziiert mit der Bewertung einer Firma
Ergebnisse (1)
Zeitreihenregressionen – 6 Portfolien
S1/B1 S1/B2 S1/B3 S2/B1 S2/B2 S2/B3 S1/B1 S1/B2 S1/B3 S2/B1 S2/B2 S2/B3 S1/B1 S1/B2 S1/B3 S2/B1 S2/B2 S2/B3
-0.003 -0.003 -0.005 -0.006 -0.007 -0.009 -0.002 -0.001 -0.008 -0.006 -0.006 -0.010 -0.001 -0.002 -0.001 -0.003 -0.005 -0.008
(-0.971) (-1.437) (-1.729) (-2.026) (-3.558) (-3.993) (-0.578) (-0.481) (-1.947) (-2.011) (-2.636) (-3.818) (-0.214) (-0.517) (-0.135) (-0.790) (-1.387) (-1.868)
* ** *** *** * ** *** *** *
1.000 0.750 0.719 0.954 0.816 0.744 1.167 0.829 0.780 1.022 0.931 0.634 0.904 0.722 0.673 0.915 0.766 0.810
(12.356) (14.824) (11.243) (14.317) (13.898) (10.476) (8.642) (12.092) (5.879) (8.863) (11.537) (9.726) (7.562) (8.624) (7.168) (10.234) (7.980) (7.328)
*** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** ***
0.056 0.052 0.021 -0.643 -0.498 -0.362 0.272 0.226 0.051 -0.553 -0.207 -0.198 -0.079 -0.039 -0.029 -0.709 -0.675 -0.524
(0.394) (0.579) (0.138) (-3.480) (-3.409) (-2.063) (1.079) (1.458) (0.162) (-1.985) (-1.366) (-1.340) (-0.424) (-0.407) (-0.125) (-3.505) (-2.531) (-1.679)
*** *** ** ** *** ** *
0.584 0.361 0.373 0.678 0.574 0.537 0.338 0.064 0.283 0.520 0.169 0.529 0.544 0.377 0.334 0.662 0.583 0.562
(6.133) (7.097) (3.551) (6.953) (7.846) (6.438) (1.332) (0.363) (0.947) (1.974) (0.895) (3.168) (4.035) (5.172) (2.464) (5.483) (5.548) (5.069)
*** *** *** *** *** *** * *** *** *** ** *** *** ***
F-Statistic 129.500 149.300 48.760 150.300 167.100 105.800 54.880 55.280 28.790 65.080 88.000 49.140 84.060 108.900 20.880 84.260 86.070 57.560
(p-value) 0.000 0,000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
Adj. R2 0.606 0.639 0.363 0.641 0.665 0.556 0.564 0.566 0.400 0.606 0.676 0.536 0.666 0.721 0.323 0.667 0.671 0.576
Obs. 252 252 252 252 252 252 126 126 126 126 126 126 126 126 126 126 126 126
Full Sample: 1988:07 – 2009:06 Subsample I: 1988:07 – 1998:12 Subsample II: 1999:01 – 2009:06
Ergebnisse (2)
Zeitreihenregressionen – 25 Portfolien: 1988 – 2009
S1/B1 S1/B2 S1/B3 S1/B4 S1/B5 S2/B1 S2/B2 S2/B3 S2/B4 S2/B5 S3/B1 S3/B2 S3/B3 S3/B4 S3/B5 S4/B1 S4/B2 S4/B3 S4/B4 S4/B5 S5/B1 S5/B2 S5/B3 S5/B4 S5/B5
0.000 0.000 0.000 0.000 -0.020 0.000 0.000 0.000 0.000 0.000 0.000 -0.010 -0.010 -0.010 -0.010 -0.010 -0.010 -0.010 0.000 -0.010 -0.010 -0.010 -0.010 -0.010 -0.010
(-0.07) (-0.97) (-0.71) (-1.45) (-2.45) (-0.74) (-0.37) (-0.60) -0.580 (-0.66) (-0.38) (-1.55) (-2.63) (-2.29) (-2.00) (-1.71) (-1.78) (-2.51) (-1.06) (-3.17) (-2.53) (-1.89) (-4.08) (-1.54) (-2.62)
** *** ** ** * * ** *** ** * *** ***
1.100 0.870 0.830 0.590 0.750 1.140 0.840 0.660 0.740 0.710 0.980 1.020 1.010 0.690 0.750 1.000 0.870 0.670 0.740 0.660 0.930 0.920 0.780 0.800 0.760
(8.980) (10.120) (7.970) (10.880) (3.250) (9.970) (8.640) (8.170) (4.940) (9.100) (10.760) (10.010) (6.650) (9.180) (8.680) (11.970) (11.730) (8.500) (6.600) (6.900) (8.950) (9.410) (12.070) (5.530) (9.130)
*** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** ***
0.440 0.360 0.370 -0.020 0.040 -0.310 -0.330 -0.080 0.210 -0.060 -0.160 -0.360 -0.640 0.000 -0.260 -0.780 -0.350 -0.470 0.050 -0.350 -0.980 -0.860 -0.350 -0.650 -0.370
(1.480) (1.800) (1.680) (-0.12) (0.060) (-1.36) (-1.80) (-0.72) (0.590) (-0.41) (-0.78) (-1.52) (-1.65) (-0.00) (-1.23) (-3.88) (-1.96) (-2.40) (0.200) (-0.99) (-3.45) (-3.59) (-2.53) (-2.16) (-1.86)
* * * * *** * ** *** ** *** ** *
0.370 0.600 0.430 0.200 0.280 0.700 0.380 0.350 0.340 0.360 0.450 0.660 0.900 0.300 0.430 0.690 0.590 0.530 0.470 0.540 0.880 0.830 0.590 0.560 0.590
(1.820) (5.800) (4.130) (1.860) (0.790) (4.750) (3.300) (3.910) (1.380) (3.390) (3.340) (5.200) (3.280) (3.680) (3.050) (4.980) (10.340) (6.190) (2.770) (3.760) (5.550) (5.070) (6.940) (3.750) (4.310)
* *** *** * *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** ***F-
Statist ic 28.420 51.360 48.030 27.070 8.760 77.760 55.900 45.950 8.770 36.630 63.710 76.640 80.780 50.370 33.220 76.360 88.470 64.350 38.710 33.550 82.960 78.510 85.590 51.600 39.950
(p-value) 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
Adj. R2 0.250 0.380 0.360 0.240 0.080 0.480 0.400 0.350 0.080 0.300 0.430 0.470 0.490 0.370 0.280 0.470 0.510 0.430 0.310 0.280 0.490 0.480 0.500 0.380 0.320
Obs. 252 252 252 252 252 252 252 252 252 252 252 252 252 252 252 252 252 252 252 252 252 252 252 252 252
Full Sample: 1988:07 – 2009:06
Ergebnisse (3)
Zeitreihenregressionen – 25 Portfolien: 1988 – 1998
S1/B1 S1/B2 S1/B3 S1/B4 S1/B5 S2/B1 S2/B2 S2/B3 S2/B4 S2/B5 S3/B1 S3/B2 S3/B3 S3/B4 S3/B5 S4/B1 S4/B2 S4/B3 S4/B4 S4/B5 S5/B1 S5/B2 S5/B3 S5/B4 S5/B5
0.000 0.000 0.000 -0.010 -0.020 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -0.010 -0.010 0.000 -0.010 -0.010 -0.010 -0.010 -0.010 -0.010 0.000 -0.010 0.000 -0.020
(-0.06) (-0.44) (-0.33) (-2.19) (-1.81) -0.030 (-0.57) -0.440 (-0.06) (-0.44) (-0.10) (-0.43) (-2.18) (-2.03) (-0.76) (-1.98) (-1.35) (-1.59) (-1.76) (-1.94) (-1.51) (-0.96) (-1.65) (-0.66) (-4.17)
** * ** ** * * * ***
1.370 1.140 1.060 0.610 0.940 1.270 1.040 0.500 0.780 0.670 0.960 1.200 1.020 0.820 0.680 1.010 1.100 0.860 0.780 0.620 0.950 0.940 0.870 0.470 0.750
(5.370) (8.540) (7.590) (5.230) (2.140) (7.190) (8.190) (5.560) (5.630) (5.120) (7.020) (8.390) (9.430) (6.820) (5.650) (6.520) (8.680) (9.810) (4.620) (5.310) (7.160) (6.380) (5.540) (4.820) (5.470)
*** *** *** *** ** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** ***
0.670 0.590 0.740 0.150 -0.220 -0.090 -0.220 -0.170 0.380 0.030 -0.100 -0.140 0.180 0.320 -0.480 -0.720 -0.300 -0.040 0.050 0.240 -0.940 -0.460 -0.100 -0.510 -0.680
(1.160) (1.970) (2.330) (0.570) (-0.19) (-0.24) (-0.66) (-0.97) (1.270) (0.110) (-0.33) (-0.45) (1.060) (1.340) (-1.77) (-2.04) (-1.06) (-0.19) (0.130) (0.920) (-3.12) (-1.46) (-0.54) (-2.32) (-2.20)
* ** * ** *** ** **
0.140 0.760 0.340 0.440 -0.700 0.040 0.240 0.210 0.600 0.240 0.120 -0.070 -0.280 -0.010 0.370 1.310 0.150 0.250 1.140 -0.060 0.430 0.540 0.030 0.390 1.170
(0.210) (2.220) (0.940) (1.470) (-0.64) (0.130) (0.700) (0.630) (2.190) (0.710) (0.340) (-0.18) (-1.07) (-0.02) (1.200) (3.300) (0.580) (1.120) (2.720) (-0.19) (1.270) (1.430) (0.060) (1.560) (2.680)
** ** *** *** ***F-
Statist ic 10.430 29.520 21.100 11.760 3.620 31.960 25.780 8.020 9.290 11.000 21.120 29.960 52.040 22.770 18.400 28.280 54.170 41.240 18.080 10.190 33.140 28.760 27.990 16.440 21.050
(p-value) 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
Adj. R2 0.180 0.410 0.330 0.210 0.060 0.430 0.370 0.140 0.170 0.190 0.330 0.410 0.550 0.340 0.290 0.400 0.560 0.490 0.290 0.180 0.440 0.400 0.390 0.270 0.320
Obs. 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126
Subsample I: 1988:07 – 1998:12
p
pb
ps
ph
Ergebnisse (4)
Zeitreihenregressionen – 25 Portfolien: 1999 – 2009
S1/B1 S1/B2 S1/B3 S1/B4 S1/B5 S2/B1 S2/B2 S2/B3 S2/B4 S2/B5 S3/B1 S3/B2 S3/B3 S3/B4 S3/B5 S4/B1 S4/B2 S4/B3 S4/B4 S4/B5 S5/B1 S5/B2 S5/B3 S5/B4 S5/B5
0.000 0.000 0.000 0.000 -0.010 0.000 0.000 -0.010 0.010 0.000 0.000 0.000 -0.010 0.000 -0.010 0.000 0.000 0.000 0.000 -0.010 -0.010 -0.010 -0.010 -0.010 0.000
(-0.460) (-0.35) (-0.340) (-0.360) (-1.55) (-0.41) (-0.590) (-1.74) (0.710) (-0.20) (-0.19) (-0.87) (-1.34) (-0.18) (-1.89) (-0.41) (-0.55) (-1.12) (-0.53) (-2.09) (-1.86) (-1.24) (-2.06) (-1.45) (-0.03)
* * ** * **
0.930 0.660 0.670 0.520 0.700 1.110 0.700 0.800 0.670 0.750 1.030 0.970 1.090 0.610 0.820 0.920 0.750 0.550 0.640 0.740 0.960 0.930 0.770 1.060 0.670
(7.480) (5.550) (7.900) (7.220) (3.380) (7.050) (4.400) (11.130) (2.670) (7.460) (9.380) (6.260) (5.800) (4.940) (5.040) (9.760) (6.480) (8.490) (5.810) (8.060) (6.690) (7.110) (8.280) (4.770) (4.340)
*** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** ***
0.280 0.160 0.080 -0.280 0.380 -0.370 -0.430 0.040 -0.020 -0.130 -0.150 -0.400 -1.110 -0.260 0.000 -1.000 -0.310 -0.770 -0.090 -0.750 -0.930 -1.140 -0.470 -0.710 -0.340
(1.000) (0.760) (0.590) (-1.11) (1.050) (-1.42) (-2.12) (0.280) (-0.04) (-0.73) (-0.57) (-1.11) (-2.11) (-1.42) (-0.010) (-4.29) (-1.41) (-3.33) (-0.27) (-1.44) (-2.15) (-3.40) (-2.31) (-1.26) (-1.07)
** ** *** *** ** *** **
0.270 0.430 0.320 0.070 0.390 0.770 0.290 0.490 0.220 0.380 0.520 0.730 1.100 0.250 0.530 0.500 0.570 0.470 0.290 0.640 0.960 0.850 0.650 0.760 0.400
(1.000) (3.160) (4.570) (0.570) (1.790) (3.790) (1.900) (5.340) (0.610) (3.150) (3.600) (4.390) (4.440) (2.170) (3.040) (3.700) (5.390) (3.680) (2.120) (4.080) (4.900) (5.030) (5.990) (3.720) (2.540)
*** *** * *** * *** *** *** *** *** ** *** *** *** *** ** *** *** *** *** *** **F-
Statist ic 31.430 26.330 38.250 16.270 13.570 48.800 33.740 70.260 2.960 27.640 44.910 57.310 48.150 30.730 16.040 58.930 40.210 29.520 26.100 25.900 49.730 49.930 74.750 35.400 20.860
(p-value) 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.040 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
Adj. R2 0.420 0.380 0.470 0.270 0.230 0.530 0.440 0.620 0.040 0.390 0.510 0.570 0.530 0.420 0.270 0.580 0.480 0.410 0.380 0.370 0.540 0.540 0.640 0.450 0.320
Obs. 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126
Subsample II: 1999:01 – 2009:06
p
pb
ps
ph
p
pb
ps
ph
Coskewness and Asset Pricing (2)
market Skewness coskewness expected sign (CS)
positive negative
positive
negative negative
positive positive
negative
negative Positive
• expected sign in cross section regressions should be opposite to market skewness
Modell (2)
Rollierende Zeitreihenregressionen – Bestimmung der Faktorrisikoprämien• Monatlich rollierend durchgeführte Zeitreihenregressionen von Juni 1988 bis Juni 2008
• Zeitraum jeder einzelnen Regression: 60 Monate
Abbildung der Zeitvariation des systematischen Risikos
Coskewness und Asset Pricing
Empirische Evidenzen
• Kraus & Litzenberger (1976)
• Friend & Westerfield (1980)
• Barone-Adesi (1985)
• Fang & Lai (1997)
• Harvey and Siddique (2000)
• Smith (2007)
• Ngyen & Puri (2009)
Coskewness und Asset Pricing (2)
Coskewness nach Harvey & Siddique (2000)
•
•
• Beide Coskewness-Maße unkonditioniert (nicht abhängig von der Marktschiefe)
• Einfachere Interpretation in Querschnittanalysen
• Risikomaße rollierend über 60 Monate bestimmt
2
,2
,
2,,1
,ˆmMmp
mMmpmp
EE
E
3,
2,,2
,ˆmM
mMmpmp
E
Model (4)
Robustness of Results
• currency effects
• weighting effects
• country effects
iji
J
jji Cx
,
1
1
Results (4) – Controlling for Country Effects
• conditional explanatory power when country effects are considered for
Sample Full Ex FC Sub I Sub II Full Ex FC Sub I Sub II Full Ex FC Sub I Sub II Full Ex FC Sub I Sub II Full Ex FC Sub I Sub II-0.005 -0.001 -0.006 -0.004 -0.011 -0.007 -0.010 -0.011 0.003 0.007 0.000 0.005 -0.007 -0.009 -0.005 -0.007 -0.003 0.010 -0.008 0.000
(-1.135) (-0.367) (-1.139) (-0.720) (-2.365) (-1.538) (-1.956) (-1.718) (0.749) (1.783) (0.007) (0.829) (-1.602) (-2.221) (-0.922) (-1.325) (-0.481) (2.036) (-1.179) (0.029)** * * * ** **
Adj. R² 0.170 0.161 0.142 0.185 0.159 0.162 0.126 0.176 0.187 0.159 0.166 0.198 0.175 0.176 0.162 0.180 0.164 0.136 0.123 0.195-0.006 -0.002 -0.007 -0.005 -0.012 -0.008 -0.012 -0.013 0.004 0.009 0.001 0.005 -0.011 -0.013 -0.008 -0.012 0.001 0.017 -0.006 0.006
(-0.967) (-0.282) (-1.230) (-0.611) (-1.947) (-1.271) (-2.410) (-1.348) (0.648) (1.560) (0.150) (0.631) (-1.949) (-2.193) (-1.723) (-1.530) (0.151) (2.503) (-0.872) (0.525)* ** * ** * **
Adj. R² 0.172 0.162 0.143 0.187 0.160 0.163 0.127 0.177 0.189 0.160 0.168 0.200 0.176 0.177 0.164 0.180 0.167 0.138 0.125 0.198Obs. 192 168 66 126 114 104 40 74 78 64 26 52 110 104 31 79 82 64 35 47
HS2
Panel IV - Equal-Weighted Euro Currency Excluding Country-EffectsUnconditional Stock Market Real Estate Market
Up Down Up Down
HS1