Table 1: Risk Factor Proxies: Descriptive Statistics
The table reports the means (percentage), standard deviations, first-order autocor-relations (ρ), and corautocor-relations of the market return proxy (rW), SMB, HML, and patenting growth (pg). The sample period is 1927-2008, and the sampling frequency is annual.
Correlations Mean×100 Std. Dev.×100 rW HML SMB ρ
rW 11.4 20.7 0.04
HML 5.1 14.0 0.12 -0.01
SMB 3.6 14.4 0.40 0.08 0.28
pg 2.4 13.7 -0.06 -0.21 -0.21 0.00
Table 2: Portfolio Excess Returns: Descriptive Statistics
The table shows the summary statistics for yearly excess returns (percentage) of the 25 size- (vertical) and B/M- (horizontal) sorted portfolios from 1927-2008.
Panel A: Value-Weighted Portfolios
Mean Std. Dev.
Low 2 3 4 High Low 2 3 4 High
Small 3.7 9.5 13.0 16.0 18.7 38.2 35.3 34.1 37.0 40.2 2 7.2 11.9 13.4 14.7 15.4 32.3 31.4 30.3 32.7 33.2 3 8.4 11.1 12.4 12.7 14.3 30.6 27.5 26.8 27.7 32.1 4 8.0 9.1 10.8 12.0 13.1 24.1 25.4 26.3 27.3 34.5 Big 7.2 7.1 8.3 8.5 10.0 21.5 19.5 22.1 25.2 31.8
Panel B: Equally-Weighted Portfolios
Mean Std. Dev.
Low 2 3 4 High Low 2 3 4 High
Small 6.9 14.6 16.5 19.8 25.8 41.6 42.8 38.6 47.0 51.0 2 7.3 12.6 14.8 15.0 15.6 35.2 34.0 33.3 35.1 35.1 3 7.9 11.4 12.7 13.1 15.1 30.0 29.3 27.6 28.0 32.4 4 7.9 9.2 10.9 12.2 13.5 24.6 26.1 27.2 28.2 36.6 Big 6.6 8.2 9.1 9.7 10.8 21.3 20.4 24.1 27.0 32.9
Table 3: CDRM: Time-Series and Cross-Sectional Regression Results - Value-Weighted Portfolios
Panel A reports the beta estimates that result from time-series regressions of excess returns on the CDRM risk factors. Test assets are the 25 value-weighted portfolios sorted by size (vertical) and book-to-market value (horizontal). The sample period is 1927-2008, and the sampling frequency is annual. The t-statistics are formulated for the null hypothesis that the true parameter is zero. The table also displays the R2 of each time-series regression. Panel B reports the estimated λfrom a cross-sectional regression of average excess returns on estimated betas. For details on statistical inference, see the Appendix.
Panel A: Time-Series Regressions
Low 2 3 4 High Low 2 3 4 High
βˆW tW
Small 1.428 1.394 1.359 1.412 1.539 10.16 12.69 14.29 9.34 9.86 2 1.314 1.306 1.235 1.317 1.327 13.38 11.14 11.67 10.69 11.88 3 1.283 1.175 1.131 1.151 1.248 10.79 13.45 14.81 16.50 10.70 4 1.064 1.079 1.136 1.122 1.374 20.50 11.66 14.40 14.18 9.10 Big 0.969 0.898 0.965 1.068 1.286 26.03 36.66 14.83 12.86 10.55
βˆN tN
Small -0.187 -0.270 -0.329 -0.426 -0.461 -1.27 -1.90 -2.48 -2.67 -2.47 2 -0.170 -0.216 -0.296 -0.291 -0.295 -1.34 -1.91 -2.42 -2.05 -2.07 3 -0.073 -0.228 -0.212 -0.292 -0.267 -0.69 -2.26 -1.94 -2.54 -1.84 4 0.070 -0.137 -0.164 -0.261 -0.153 1.07 -1.73 -1.66 -2.72 -1.10 Big 0.138 -0.044 -0.049 -0.105 -0.141 1.86 -0.92 -0.72 -1.26 -1.40
R2
Small 61.1 69.2 71.4 67.0 67.1
2 72.7 76.3 74.5 72.6 71.6
3 76.3 80.9 79.1 78.0 67.7
4 83.7 79.2 81.8 75.8 69.3
Big 87.2 91.6 82.2 78.5 71.3
Panel B: Cross-Sectional Regression
ˆλW 0.066 tW 2.84
ˆλN -0.148 tN -2.36
Table 4: CDRM: Time-Series and Cross-Sectional Regression Results - Equally-Weighted Portfolios
Panel A reports the beta estimates that result from time-series regressions of excess returns on the CDRM risk factors. Test assets are the 25 equally-weighted portfolios sorted by size (vertical) and book-to-market value (horizontal). The sample period is 1927-2008, and the sampling frequency is annual. The t-statistics are formulated for the null hypothesis that the true parameter is zero. The table also displays the R2 of each time-series regression. Panel B reports the estimated λfrom a cross-sectional regression of average excess returns on estimated betas. For details on statistical inference, see the Appendix.
Panel A: Time-Series Regressions
Low 2 3 4 High Low 2 3 4 High
βˆW tW
Small 1.498 1.671 1.451 1.625 1.740 10.79 12.35 11.56 5.78 6.48 2 1.388 1.363 1.310 1.371 1.363 10.39 8.65 8.81 8.40 9.67 3 1.259 1.214 1.165 1.158 1.261 12.16 10.77 13.89 15.80 10.76 4 1.085 1.104 1.172 1.165 1.456 19.23 11.51 13.66 14.26 8.46 Big 0.981 0.931 1.069 1.133 1.277 31.19 24.98 19.03 11.58 9.74
βˆN tN
Small -0.237 -0.338 -0.405 -0.522 -0.603 -1.36 -1.97 -2.69 -2.43 -2.40 2 -0.250 -0.249 -0.336 -0.335 -0.305 -1.90 -2.02 -2.49 -2.24 -2.04 3 -0.067 -0.249 -0.219 -0.283 -0.288 -0.63 -2.26 -2.10 -2.51 -1.99 4 0.055 -0.144 -0.176 -0.277 -0.164 0.83 -1.76 -1.84 -2.78 -1.14 Big 0.125 -0.077 -0.128 -0.106 -0.178 2.70 -1.63 -1.68 -1.15 -1.69
R2
Small 57.3 68.0 64.5 55.3 54.1
2 68.9 71.2 69.8 68.9 67.5
3 76.0 76.7 79.0 76.9 68.0
4 83.7 78.5 81.7 76.9 69.1
Big 90.9 90.4 86.4 76.7 66.2
Panel B: Cross-Sectional Regression
ˆλW 0.061 tW 2.52
ˆλN -0.187 tN -2.90
Table 5: CDRM: Risk Compensations
The table shows estimated expected excess return compensations (percentage) that are associated with market risk ( ˆβW ·ˆλW) and creative destruction risk ( ˆβN ·λˆN).
Test assets are the 25 portfolios sorted by size (vertical) and book-to-market value (horizontal). The sample period is 1927-2008, and the sampling frequency is annual.
Panel A shows the results for value-weighted Fama-French portfolios; Panel B shows the results for equally-weighted Fama-French portfolios. The delta method is used to compute the t-statistic for a test that the respective risk compensation is zero. For details on statistical inference, see the Appendix.
Panel A: Value-Weighted Portfolios
Small 9.2 10.2 8.9 10.0 10.7 2.43 2.35 2.38 2.14 2.17
2 8.5 8.4 8.0 8.4 8.4 2.32 2.26 2.29 2.26 2.33
Table 6: Model Comparison: CAPM, Fama-French, and CDRM
The table reports theλestimates for CAPM, Fama-French model, and CDRM. Test assets are the 25 size and book-to-market sorted portfolios, and the sample period is 1927-2008 at annual frequency. The t-statistics (in parentheses) are formulated for the null hypothesis that the true parameter is zero. The table also reports thep-values of the first-stage GMM J-statistics and the cross-sectionalR2, both in percentages.
The cross-sectional R2 come from a regression of average realized excess returns on betas and a constant
Panel A: Value-Weighted Portfolios λˆW ˆλHM L ˆλSM B λˆN p-val. R2
CAPM 0.090 0.3 24.1
(3.91)
Fama-French 0.068 0.060 0.035 2.6 70.5
(2.89) (3.73) (2.04)
CDRM 0.066 -0.148 1.4 51.3
(2.84) (-2.36)
Panel B: Equally-Weighted Portfolios λˆW ˆλHM L ˆλSM B λˆN p-val. R2
CAPM 0.096 0.5 49.4
(4.21)
Fama-French 0.061 0.066 0.049 2.2 83.4
(2.45) (4.05) (3.28)
CDRM 0.061 -0.187 3.2 73.1
(2.52) (-2.90)
Table 7: Weights of the Invention-Mimicking Portfolio
The table shows the results of a time-series regression,pgt=γ0+P6
i=1γireB,i,t+vt, used to estimate the weights of the invention-mimicking portfolio. Base assets are the six portfolios sorted by size and book-to-market (growth, neutral, small-value, big-growth, big-neutral and big-value (Fama and French,1993)). The sample period is 1927-2008, at annual frequency. Coefficient estimates are reported on the left-hand side. Thet-statistics (right-hand side) are formulated for the null hypothesis that the true parameter is zero. The table also displays theR2andp-value of a Wald test of the null hypothesis that γ1=γ2=...=γ6= 0.
Portfolio Weights t
Growth Neutral Value Sum Growth Neutral Value
Small 0.098 -0.244 -0.090 -0.236 Small 1.14 -1.31 -0.63
Big 0.243 -0.099 0.092 0.236 Big 2.01 -0.44 0.54
Sum 0.341 -0.343 0.002
R2 (%) 10.3
p-val.(%) 1.5
Table 8: Invention-Mimicking Portfolio: Descriptive Statistics
The table reports descriptive statistics for the invention-mimicking portfolio. It shows the portfolio’s mean excess return, its standard deviation, and its correlation with the market excess return (reW), and the Fama-French factorsHMLandSMB. The sample period is 1927-2008, at annual frequency.
Mean×100 -1.7
Std. Dev.×100 4.4
Correlation with: rWe -0.21
HM L -0.67
SM B -0.66
Table 9: Mimicking Portfolio CDRM: Time-Series and Cross-Sectional Regression Results - Value-Weighted Portfolios
Panel A reports the beta estimates that result from time-series regressions of the test assets’ excess returns on the invention-mimicking portfolio’s excess return,reM, and the return of the wealth portfolio proxy,rW. Test assets are the 25 value-weighted Fama-French portfolios sorted by size (vertical) and book-to-market value (horizontal). The sample period is 1927-2008, and the sampling frequency is annual. The t-statistics are formulated for the null hypothesis that the true parameter is zero. Panel A also displays theR2of each time-series regression. Panel B reports the estimatedλfrom a cross-sectional regression of average excess returns on the estimated betas, as well as
∆ˆλ= ˆλcs−λˆts, and the associatedp-value of a test that ∆ˆλis significantly different from zero. Statistical inference takes into account that the parameters are estimated via three subsequent regressions that yield the mimicking portfolio weights, the beta estimates, and the lambda estimates. For details on statistical inference, see the Appendix.
Panel A: Time-Series Regressions
Low 2 3 4 High Low 2 3 4 High
βˆW tW
Small 1.391 1.306 1.236 1.256 1.371 9.17 8.03 6.47 5.48 5.57
2 1.268 1.218 1.124 1.186 1.203 10.34 8.25 7.01 6.26 6.04
3 1.265 1.105 1.046 1.053 1.125 11.66 9.78 8.75 7.68 5.64
4 1.082 1.028 1.066 1.043 1.286 17.08 10.16 10.35 7.86 7.32 Big 1.018 0.899 0.933 1.026 1.233 14.29 33.51 14.71 11.73 8.76
βˆM tM
Small -1.021 -2.230 -3.110 -3.937 -4.232 -0.93 -2.13 -2.83 -2.86 -2.88 2 -1.210 -2.198 -2.791 -3.236 -3.086 -1.44 -2.55 -3.01 -2.92 -2.54 3 -0.474 -1.816 -2.137 -2.501 -3.040 -0.54 -2.63 -3.10 -2.95 -2.39 4 0.472 -1.279 -1.740 -2.042 -2.136 0.75 -1.94 -2.57 -2.25 -1.71 Big 1.249 -0.027 -0.775 -1.064 -1.318 3.12 -0.11 -1.34 -1.41 -1.16
R2
Small 62.0 75.5 85.1 85.6 85.2
2 74.8 84.5 88.5 89.3 86.2
3 76.7 87.7 89.7 91.0 83.1
4 84.2 83.4 89.2 84.5 76.1
Big 92.7 91.5 84.4 81.5 74.1
Panel B: Cross-Sectional and Time-Seriesλ
λˆW 0.061 tW 2.60
λˆcsM -0.021 tcsM -2.80
λˆtsM -0.017 ttsM -1.85
∆ˆλ -0.005 p-val. (%) 56.1
Table 10: Mimicking Portfolio CDRM: Time-Series and Cross-Sectional Regression Results - Equally-Weighted Portfolios
Panel A reports the beta estimates that result from time-series regressions of the test assets’ excess returns on the invention-mimicking portfolio’s excess return, reM, and the return of the wealth portfolio proxy, rW. Test assets are the 25 equally-weighted Fama-French portfolios sorted by size (vertical) and book-to-market value (horizontal). The sample period is 1927-2008, and the sampling frequency is annual.
The t-statistics are formulated for the null hypothesis that the true parameter is zero. Panel A also displays the R2 of each time-series regression. Panel B reports the estimated λ from a cross-sectional regression of average excess returns on the estimated betas, as well as ∆ˆλ = ˆλcs−λˆts, and the associated p-value of a test that ∆ˆλ is significantly different from zero. Statistical inference takes into account that the parameters are estimated via three subsequent regressions that yield the mimicking portfolio weights, the beta estimates, and the lambda estimates. For details on statistical inference, see the Appendix.
Panel A: Time-Series Regressions
Low 2 3 4 High Low 2 3 4 High
βˆW tW
Small 1.430 1.575 1.312 1.437 1.531 8.20 8.14 5.87 4.47 4.45
2 1.322 1.263 1.188 1.230 1.226 8.42 7.02 6.23 5.67 5.43
3 1.234 1.132 1.075 1.056 1.135 12.06 8.31 8.38 7.32 5.66
4 1.094 1.048 1.099 1.082 1.365 17.63 9.64 9.91 7.86 7.25
Big 1.014 0.913 1.017 1.068 1.214 20.52 21.82 14.24 9.37 7.78
βˆM tM
Small -1.766 -2.489 -3.531 -4.750 -5.298 -1.34 -2.07 -2.66 -2.47 -2.64 2 -1.737 -2.504 -3.079 -3.495 -3.372 -1.65 -2.34 -2.78 -2.80 -2.52 3 -0.626 -2.086 -2.248 -2.574 -3.115 -0.74 -2.49 -3.00 -2.92 -2.40 4 0.253 -1.397 -1.818 -2.153 -2.208 0.43 -2.03 -2.56 -2.43 -1.70 Big 0.882 -0.473 -1.285 -1.573 -1.582 3.00 -1.58 -2.40 -1.81 -1.31
R2
Small 60.0 73.1 78.0 72.0 71.5
2 72.5 80.3 83.7 85.7 83.3
3 76.7 84.8 90.2 90.6 83.7
4 83.8 83.3 89.2 85.9 75.5
Big 93.5 91.1 91.2 82.7 69.9
Panel B: Cross-Sectional and Time-Seriesλ
λˆW 0.055 tW 2.19
λˆcsM -0.026 tcsM -2.86
λˆtsM -0.017 ttsM -1.85
∆ˆλ -0.010 p-val. (%) 33.5
Table 11: Mimicking Portfolio CDRM: Risk Compensations
The table reports estimated expected excess return compensations (percentage) that are implied by the mimicking portfolio version of the CDRM. Test assets are the 25 portfolios sorted by size (vertical) and book-to-market value (horizontal). The sample period is 1927-2008, and the sampling frequency is annual. Panel A shows the results for value-weighted Fama-French portfolios; Panel B shows the results for equally-weighted Fama-French portfolios. The delta method is used to compute thet-statistic for a test that the respective risk-compensation is zero. Statistical inference takes into account that the parameters are obtained by three subsequent regressions that yield the mimicking portfolio weights, the beta estimates, and the lambda estimates. For details on statistical inference, see the Appendix.
Panel A: Value-Weighted Portfolios
Table 12: Mimicking Portfolio CDRM: Time-Series and Cross-Sectional Regression Results - Value-Weighted Portfo-lios, Quarterly Postwar Data
Panel A reports the beta estimates that result from time-series regressions of excess returns on the CDRM risk factors using the invention-mimicking portfolio instead of patenting activity. Test assets are the 25 value-weighted portfolios sorted by size (ver-tical) and book-to-market value (horizontal). The sample period is 1950:Q1-2008:Q4, and the sampling frequency is quarterly. The t-statistics are formulated for the null hypothesis that the true parameter is zero. Panel A also displays theR2of each time-series regression. Panel B reports the estimated λfrom a cross-sectional regression of average excess returns on the estimated betas, as well as ∆ˆλ= ˆλcs−λˆts, and the associated p-value of a test that ∆ˆλ is significantly different from zero. Statistical inference takes into account that the parameters are obtained by three subsequent regressions that yield the mimicking portfolio weights, the beta estimates, and the lambda estimates. For details on statistical inference, see the Appendix.
Panel A: Time-Series Regressions
Low 2 3 4 High Low 2 3 4 High
βˆW tW
Small 1.422 1.190 0.985 0.921 0.973 7.22 5.32 4.47 4.09 3.63
2 1.384 1.100 0.943 0.894 0.930 10.30 6.31 5.04 4.51 4.07
3 1.335 1.030 0.881 0.855 0.847 16.38 8.30 5.53 4.69 3.92
4 1.275 0.993 0.910 0.873 0.921 18.71 9.65 6.95 6.18 4.30
Big 1.108 0.913 0.776 0.761 0.802 10.39 23.65 11.78 6.58 5.64
βˆM tM
Small -1.582 -2.122 -2.197 -2.242 -2.720 -1.11 -1.84 -2.12 -2.16 -2.20 2 -1.013 -1.720 -1.843 -2.044 -2.336 -0.93 -2.11 -2.53 -2.47 -2.23 3 -0.272 -1.266 -1.631 -1.848 -2.173 -0.32 -2.42 -2.82 -2.66 -2.24 4 0.136 -0.978 -1.287 -1.433 -2.043 0.22 -2.41 -2.62 -2.45 -2.30 Big 1.113 0.003 -0.427 -0.983 -1.147 2.76 0.01 -0.83 -1.42 -1.17
R2
Small 71.2 81.0 82.4 82.6 82.4
2 80.1 87.1 90.6 89.3 84.0
3 82.9 90.2 91.1 90.2 81.0
4 87.0 89.3 90.7 88.4 85.5
Big 95.8 88.0 79.1 81.5 72.9
Panel B: Cross-Sectional and Time-Seriesλ
λˆW 0.013 tW 2.09
λˆcsM -0.007 tcsM -2.30
λˆtsM -0.005 ttsM 5.43
∆ˆλ -0.003 p-val. (%) 58.5
Table 13: Mimicking Portfolio CDRM: Risk Compensations -Value-Weighted Portfolios, Quarterly Postwar Data
The table reports estimated expected excess return compensations (percentage) that are implied by the mimicking portfolio version of the CDRM. Test assets are the 25 value-weighted portfolios sorted by size (vertical) and book-to-market value (horizon-tal). The sample period is 1950:Q1-2008:Q4, and the sampling frequency is quarterly.
The delta method is used to compute thet-statistic for a test that the respective risk compensation is zero. Statistical inference takes into account that the parameters are obtained by three subsequent regressions that yield the mimicking portfolio weights, the beta estimates, and the lambda estimates. For details on statistical inference, see the Appendix.
Low 2 3 4 High Low 2 3 4 High
βˆW ·ˆλW ×100 tW
Small 1.8 1.5 1.2 1.2 1.2 1.91 1.89 1.89 1.89 1.87 2 1.7 1.4 1.2 1.1 1.2 1.96 1.96 1.97 1.98 1.95 3 1.7 1.3 1.1 1.1 1.1 1.99 2.03 2.04 2.01 1.94 4 1.6 1.3 1.1 1.1 1.2 1.99 2.08 2.07 2.06 1.95 Big 1.4 1.2 1.0 1.0 1.0 2.03 2.10 2.13 2.11 2.08
βˆM ·ˆλM ×100 tM
Small 1.2 1.6 1.6 1.7 2.0 1.07 1.81 2.28 2.53 2.84 2 0.8 1.3 1.4 1.5 1.7 0.87 2.01 2.66 3.26 3.09 3 0.2 0.9 1.2 1.4 1.6 0.32 2.26 3.18 3.26 3.05 4 -0.1 0.7 1.0 1.1 1.5 -0.22 2.32 2.88 2.97 2.53 Big -0.8 0.0 0.3 0.7 0.9 -2.63 -0.01 0.84 1.48 1.18
−40−200204060 Return (in percent)
−40−200204060Patenting Growth (in percent)
1930 1940 1950 1960 1970 1980 1990 2000 2010 Patenting Growth SMB
Panel A: Patenting Growth and SMB
−40−200204060 Return (in percent)
−40−200204060Patenting Growth (in percent)
1930 1940 1950 1960 1970 1980 1990 2000 2010 Patenting Growth HML
Panel B: Patenting Growth and HML
Figure 1: Patenting Growth and Fama-French Factors
The graph shows patent growth (percentage) and the Fama-French factors (SMB) and (HML) over the period 1927-2008.
Panel A: CAPM
Figure 2: Predicted vs. Actual Mean Excess Returns -Value-Weighted Portfolios
The figures compare predicted vs. realized average excess returns (percentage) given by the CAPM (Panel A), the Fama-French model (Panel B), and the CDRM (Panel C). The sample period is 1927-2008; the sampling frequency is annual. The test assets are the value-weighted 25 portfolios sorted by size and book-to-market value, where the first number denotes the size quintile (1 being the smallest and 5 the largest), and the second number refers to the book-to-market quintile (1 being the lowest and 5 the highest).
Panel A: CAPM
Figure 3: Predicted vs. Actual Mean Excess Returns -Equally-Weighted Portfolios
The figures compare predicted vs. realized average excess returns (percentage) given by the CAPM (Panel A), the Fama-French model (Panel B), and the CDRM (Panel C). The sample period is 1927-2008; the sampling frequency is annual. The test assets are the equally-weighted 25 portfolios sorted by size and book-to-market value, where the first number denotes the size quintile (1 being the smallest and 5 the largest), and the second number indicates the book-to-market quintile (1 being the lowest and 5 the highest).
Panel A: Mimick. Portf. CDRM (VWP)
Panel B: Fama-French Model (VWP)
11
Panel C: Mimick. Portf. CDRM (EVP)
11
Panel D: Fama-French Model (EWP)
11
Figure 4: Predicted vs. Actual Mean Excess Returns -Mimicking Portfolio CDRM vs. Fama-French Model
The figures compare predicted vs. realized average excess returns (percentage) given by the Invention Mimicking CDRM and Fama-French model. The sample period is 1927-2008; the sampling frequency is annual. Test assets are the 25 portfolios sorted by size and book-to-market value, where the first number denotes the size quintile (1 being the smallest and 5 the largest), and the second number indicates the book-to-market quintile (1 being the lowest and 5 the highest). Panels A and B show the results for value-weighted portfolios (VWP), and Panels C and D show the results for equally-weighted portfolios (EWP). The cross-sectional R2 (unadjusted) are, for EVPs, 81.1% (Mimicking Portfolio CDRM) vs. 83.4% (Fama-French model), and for VWPs, 65.4% (Mimicking Portfolio CDRM) vs. 70.5% (Fama-French model).