This table describes the construction of variables used in the traditional valuation model based on Rhodes-Kropf et al. (2005).
Table IA.1: Rhodes-Kropf, Robinson and Viswanathan (2005)
Variable Description
lnm Natural logarithm of market value of equity from CRSP (ln(crsp_market_equity))
lnb Natural logarithm of book equity(ln(be_ac))
lnni Natural logarithm of absolute value of the last four-quarter net income (ln(abs(ni_ac))) negni An indicator variable for loss (ni_ac < 0 & ni_ac != .)
LEV1 Leverage ((dltt+dlc)/at) as in Golubov and Konstantinidi (2019)
LEV2 Book leverage (1-book/at) as in Rhodes-Kropf, Robinson and Viswanathan (2005) LEV3 Market leverage (1 - m2b * book / (m2b * book + debt_book_value)) as in
Rhodes-Kropf, Robinson and Viswanathan (2005)
This table reports the summary statistics of variables used in the traditional valuation model based on Rhodes-Kropf et al. (2005).
Table IA.2: Summary statistics of variables used in RRV models
Variable N Mean SD p1 p10 p50 p90 p99
lnm 1,615,187 5.69 1.98 1.97 3.27 5.51 10.83 10.83
lnb 1,615,187 5.16 1.76 2.40 3.02 4.92 9.88 9.88
lnni 1,615,187 2.93 2.03 -1.65 0.52 2.81 8.01 8.01
negni 1,615,187 0.22 0.42 0.00 0.00 0.00 1.00 1.00
LEV1 1,615,187 0.21 0.18 0.00 0.00 0.18 0.73 0.73
LEV2 1,615,187 0.53 0.25 0.07 0.19 0.52 0.96 0.96
LEV3 1,615,187 0.27 0.25 0.00 0.00 0.21 0.91 0.91
Table IA.3: Coefficient estimates: RRVcs model
This table reports means of coefficient estimates, from cross-sectional regressions by month and FF49 industry based on Rhodes-Kropf et al. (2005). t-statistics are presented in parentheses. Coefficients significant at 10%, 5% and 1% are indicates with ***, ** and *, respectively.
Model1 Model2 Model3
lnb 0.69*** 0.70*** 0.75***
(35.82) (103.40) (41.31)
lnni 0.26*** 0.32*** 0.29***
(8.89) (42.44) (80.45)
negni -0.43*** -0.40*** -0.18***
(-13.63) (-30.24) (-8.52)
LEV1 -0.01
(-0.22)
LEV2 0.20***
(7.98)
LEV3 -1.44***
(-14.32)
Const 1.47*** 1.13*** 1.41***
(8.89) (47.84) (24.80)
Avg. Adj. R2 0.86 0.87 0.89
N of obs 1,597,149 1,597,149 1,597,149
N of models 23,520 23,520 23,520
This table describes the construction of variables used in the traditional valuation model based on Bartram and Grinblatt (2018).
Table IA.4: Bartram and Grinblatt (2018)
Variable Description
at Assets - Total
seq Stockholders Equity > Parent > Index Fundamental > Quarterly
icapt Invested Capital - Total - Quarterly
teq Stockholders Equity - Total
pstkr Preferred/Preference Stock - Redeemable
ppent Property Plant and Equipment - Total (Net)
ceq Common/Ordinary Equity - Total
pstk Preferred/Preference Stock (Capital) - Total
dltt Long-Term Debt - Total
ao Assets - Other - Total
lt Liabilities - Total
lo Liabilities - Other
che Cash and Short-Term Investments
aco Current Assets - Other - Total
lco Current Liabilities - Other - Total
ap Account Payable/Creditors - Trade
dv cash dividend
dvp Dividends - Preferred/Preference
sale Sales/Turnover (Net)
ib Income Before Extraordinary Items
ni Net Income (Loss)
xido Extraordinary Items and Discontinued Operations
ibadj Income Before Extraordinary Items - Adjusted for Common Stock Equivalents ibcom Income Before Extraordinary Items - Available for Common
pi Pretax Income
txt Income Taxes - Total
nopi Non-Operating Income (Expense) - Total
do Discontinued Operations
This table reports the summary statistics of variables used in the traditional valuation model based on Bartram and Grinblatt (2018).
Table IA.5: Summary statistics of variables used in BG models
Variable N Mean SD p1 p10 p50 p90 p99
crsp_market_equity 362,852 6573.52 27734.44 10.01 54.40 827.16 1.1e+05 1.1e+05
at 362,852 8224.79 42091.52 20.97 69.52 823.20 1.3e+05 1.3e+05
seq 362,852 2332.56 9659.91 11.31 34.33 347.58 36088.00 36088.00
icapt 362,852 4341.48 18267.76 14.37 45.69 570.29 69133.00 69133.00
teq 362,852 2400.77 9900.84 11.42 34.74 353.84 36834.00 36834.00
pstkr 362,852 2.82 57.26 0.00 0.00 0.00 54.71 54.71
ppent 362,852 1857.63 8693.21 0.14 4.66 121.99 30712.00 30712.00
ceq 362,852 2310.89 9589.47 11.09 33.59 343.48 35334.00 35334.00
pstk 362,852 21.67 453.96 0.00 0.00 0.00 325.00 325.00
dltt 362,852 1922.76 10865.04 0.00 0.00 116.08 27261.00 27261.00
ao 362,852 2945.08 16761.71 0.09 4.62 161.72 49699.00 49699.00
lt 362,852 5806.07 35642.60 3.64 20.04 389.10 96263.00 96263.00
lo 362,852 1253.02 10680.02 0.00 0.06 29.26 26779.00 26779.00
che 362,852 1013.89 8433.81 0.17 4.58 81.55 14098.00 14098.00
aco 362,852 194.66 1294.39 0.00 0.66 17.06 3244.00 3244.00
lco 362,852 513.77 2293.64 0.00 2.46 53.31 9096.00 9096.00
ap 362,852 1068.98 11839.36 0.30 2.54 39.22 15419.00 15419.00
dv 362,852 118.83 643.19 0.00 0.00 0.00 2437.00 2437.00
dvp 362,852 2.23 36.57 0.00 0.00 0.00 31.90 31.90
sale 362,852 4594.98 18299.25 13.79 50.03 655.81 74415.00 74415.00
ib 362,852 306.06 1807.57 -692.28 -44.57 20.55 6011.00 6011.00
ni 362,852 310.16 1824.41 -713.69 -46.39 20.80 6120.00 6120.00
xido 362,852 4.10 174.94 -83.30 -0.23 0.00 149.10 149.10
ibadj 362,852 303.30 1804.12 -704.72 -45.35 20.22 5933.00 5933.00
ibcom 362,852 303.83 1804.91 -704.14 -45.33 20.31 5955.00 5955.00
pi 362,852 437.59 2491.10 -777.00 -46.01 29.45 8391.00 8391.00
txt 362,852 123.09 859.36 -287.00 -5.51 8.04 2353.00 2353.00
nopi 362,852 35.04 404.94 -125.00 -3.55 0.44 743.20 743.20
do 362,852 4.42 173.93 -70.00 -0.14 0.00 146.72 146.72
Table IA.6: BG model estimation
This table reports means of coefficient estimates, from monthly cross-sectional regressions based on Bartram and Grinblatt (2018). t-statistics are presented in parentheses. Coefficients significant at 10%, 5% and 1%
are indicates with ***, ** and *, respectively.
Estimates
Coeff. t-stat
at 0.44** (2.02)
seq -13.13 (-0.20)
icapt 0.68*** (3.76)
teq -28.69 (-0.91)
pstkr -1.95** (-2.47)
ppent -0.29*** (-6.11)
ceq 41.68 (0.46)
pstk 41.87 (0.46)
dltt -0.37* (-1.96)
ao 0.02 (0.67)
lt -0.78*** (-3.96)
lo 0.20*** (3.75)
che 0.63*** (8.78)
aco 1.22*** (8.20)
lco 0.93*** (7.62)
ap 0.19*** (2.72)
dv 3224.65 (1.07)
dvp 394.63 (1.46)
sale 0.03* (1.96)
ib 86.23** (2.45)
ni -453.47* (-1.68)
xido 447.61* (1.65)
ibadj -4.75 (-0.53)
ibcom 389.95 (1.44)
pi -12.07*** (-6.71)
txt 16.83*** (7.60)
nopi -2.52*** (-4.21)
do 6.61 (0.89)
Const 368.30*** (8.26)
Avg. Adj. R2 0.89 N of obs 1,433,047
N of models 480
This table describes the construction of variables used in the traditional valuation model based on Bhojraj and Lee (2002).
Table IA.7: Bhojraj and Lee (2002)
Variable Description
m2b Market value to book equity
v2a Enterprise value to total assets
v2s Firm value (market value of equity + total debt) to sales (sale) multiple indm2b Cross-sectional industry harmonic mean of market to book multiple
indv2a Cross-sectional industry harmonic mean of firm value to total assets multiple indv2s Cross-sectional industry harmonic mean of firm value to sales multiple
adjopmad Industry adjusted opearting profit margain (actual - median); opmad_wr-opmad_wm negadjopmad adjopmad * an indicator variable for negative adjopmad
adjsalesgrowth Industry adjusted sales growth (actual - median)
d2e Total debt (dltt + dlc) to book equity
pretret_noa_wr Pre-tax Return on Net Operating Assets: ebit/noa; Net operating assets: ppent+act-lct
roe_wr Return on Equity: ib/be if be>0
RD_SALE_wr R&D/Sales: max(xrd/sale,0), missing xrd replaced with zero
This table reports the summary statistics of variables used in the traditional valuation model based on Bhojraj and Lee (2002).
Table IA.8: Summary statistics of variables used in BL models
Variable N Mean SD p1 p10 p50 p90 p99
m2b 1,308,512 2.90 8.31 0.22 0.64 1.72 19.11 19.11
v2a 1,308,512 1.64 2.18 0.30 0.59 1.11 8.75 8.75
v2s 1,308,512 2.50 9.24 0.14 0.38 1.23 19.93 19.93
indm2b 1,308,512 1.43 0.58 0.45 0.78 1.33 3.04 3.04
indv2a 1,308,512 1.07 0.35 0.32 0.72 0.99 2.13 2.13
indv2s 1,308,512 1.10 0.66 0.25 0.42 0.94 3.47 3.47
adjopmad 1,308,512 -0.03 0.45 -1.46 -0.13 0.01 0.51 0.51
negadjopmad 1,308,512 -0.08 0.43 -1.46 -0.13 0.00 0.00 0.00
adjsalesgrowth 1,308,512 0.67 64.61 -0.66 -0.22 0.00 3.04 3.04
d2e 1,308,512 0.83 3.27 0.00 0.00 0.40 7.49 7.49
pretret_noa_wr 1,308,512 0.16 20.03 -1.28 -0.12 0.14 1.47 1.47
roe_wr 1,308,512 0.02 1.10 -1.57 -0.21 0.08 0.62 0.62
RD_SALE_wr 1,308,512 0.06 0.32 0.00 0.00 0.00 1.05 1.05
Table IA.9: BL model estimation
This table reports means of coefficient estimates, from monthly cross-sectional regressions based on Bhojraj and Lee (2002). t-statistics are presented in parentheses. Coefficients significant at 10%, 5% and 1% are indicates with ***, ** and *, respectively.
m2b v2s v2a
indm2b 1.87*** 0.26** 0.60***
(18.34) (2.29) (12.84)
indv2a 0.29* 0.14 0.43***
(1.66) (1.30) (8.82)
indv2s -0.32*** 0.94*** -0.16***
(-6.33) (23.05) (-8.03)
adjopmad 4.99*** 8.16*** 4.27***
(13.64) (28.84) (25.71) negadjopmad -5.98*** -13.15*** -4.44***
(-15.81) (-28.50) (-23.75) adjsalesgrowth 0.10*** 0.11*** 0.05***
(7.47) (7.18) (7.48)
d2e 0.75*** 0.04*** -0.03***
(12.73) (7.50) (-12.90) pretret_noa_wr 0.25*** -0.04*** 0.11***
(5.24) (-2.86) (5.69)
roe_wr 2.04*** 0.39*** 0.18***
(8.29) (7.35) (11.87)
RD_SALE_wr 1.38*** 4.19*** 0.81***
(9.12) (8.68) (8.33)
Const -1.08*** -0.26*** 0.17***
(-6.51) (-2.95) (5.11)
Avg. Adj. R2 0.32 0.42 0.22
N of obs 1,307,283 1,307,283 1,307,283
N of models 480 480 480
Table IA.10: Model performance comparison (assets, book equity, sales > 0)
This table reports summary statistics of valuation errors of non-IPO firm-months from different models. This table uses the same methodology as in Table 2 except that this table includes “tiny” firm-month observations with assets, book equity or sales between 0 and 10 million USD while Table 2 excludes them.
N med(|ε|) avg(|ε|) med(ε) avg(ε) sd(ε) ρy,ˆy
MLlnm2b 2,143,842 31.3 55.0 0.1 23.7 152.3 0.90
MLlnv2a 2,143,842 33.0 63.9 1.9 27.4 270.2 0.89
MLlnv2s 2,143,842 34.3 72.2 1.3 30.4 864.7 0.87
RRVcs 2,021,470 38.2 67.2 1.6 32.1 171.4 0.86
BLm2b 1,669,514 81.5 216.9 38.3 119.8 885.9 0.40
BLv2a 1,669,514 84.6 229.8 79.5 199.5 8798.5 0.55 BLv2s 1,669,514 411.2 1657.1 29.4 88.1 14554.6 0.10 INDm2bhm 2,143,842 44.4 58.4 -21.3 -0.0 108.5 0.80 INDv2ahm 2,143,842 48.9 84.3 -15.9 11.9 400.5 0.61 INDv2shm 2,143,842 68.4 125.1 -39.5 -5.9 617.4 0.39
BG 1,840,002 122.6 616.8 85.0 464.3 2721.6 0.93
Table IA.11: Most important variables (assets, book equity, sales > 0)
This table presents 10 most important variables as measured by the magnitude of SHAP values for each machine learning model. This table uses the same methodology as in Table 4 except that this table includes tiny firm-month observations with assets, book equity or sales between 0 and 10 million USD while Table 4 excludes them.
Variable Description Category SHAP CSHAP rho Expected sign
MLlnm2b
industry Fama French 49 industries Industry 9.0 9.0 -0.133 N.A.
profitability_an Profitability (pbt/equity) Profitability 6.2 15.3 0.220 +
book Book equity Size 6.2 21.5 -0.117 -
roe_wr Return on Equity Profitability 5.6 27.1 0.234 +
RD_SALE_wr R&D/Sales Growth 5.4 32.4 0.206 +
salesgrowth_an Sales Growth Growth 3.6 36.0 0.248 +
aftret_invcapx_wr After-tax Return on Invested Capital Profitability 3.6 39.6 0.273 +
chbe_an ∆ Book Equity Growth 2.4 42.0 0.267 +
pretret_noa_wr Pre-tax Return on Net Operating Assets Profitability 2.3 44.2 0.009 +
CAPMbeta CAPM beta CAPMbeta 2.2 46.4 0.189 -
MLlnv2a
industry Fama French 49 industries Industry 9.2 9.2 -0.309 N.A.
chbe_an ∆ Book Equity Growth 5.1 14.4 0.330 +
roic_an Return on Invested Capital Profitability 4.7 19.1 0.249 +
curr_debt_wr Current Liabilities/Total Liabilities Financial soundness 4.0 23.1 -0.221 +/-
RD_SALE_wr R&D/Sales Growth 4.0 27.1 0.288 +
debt_at_wr Long-term Debt/Total Assets Solvency 3.8 30.9 -0.094 +/-
de_ratio_wr Total Debt/Equity Solvency 3.4 34.3 -0.445 +/-
salesgrowth_an Sales Growth Growth 3.1 37.5 0.230 +
lt_debt_wr Long-term Debt/Total Liabilities Financial soundness 2.5 39.9 0.008 +/-
lt_ppent_wr Total Liabilities/PP&E Financial soundness 2.5 42.4 -0.307 +/-
MLlnv2s
assetturnover_an Asset Turnover Efficiency 20.8 20.8 -0.749 -
opleverage_an Operating Leverage Efficiency 8.9 29.7 -0.694 -
opmad_wr EBIT Margin Profitability 7.1 36.8 0.236 +
industry Fama French 49 industries Industry 4.7 41.5 0.054 N.A.
sale_ac Sales/Turnover (Net) Size 4.3 45.8 -0.328 -
sales2cash_an Sales/Cash Efficiency 3.9 49.7 -0.585 -
npm_wr Net Profit Margin Profitability 2.7 52.4 0.191 +
RD_SALE_wr R&D/Sales Growth 2.5 55.0 0.139 +
salesgrowth_an Sales Growth Growth 2.2 57.2 0.155 +
chbe_an ∆ Book Equity Growth 2.1 59.3 0.152 +
Table IA.12: Variable importance by category (assets, book equity, sales > 0)
This table presents variable category importance as measured by the magnitude of SHAP values. This table uses the same methodology as in Table 5 except that this table includes tiny firm-month observations with assets, book equity or sales between 0 and 10 million USD while Table 5 excludes them.
Category SHAP rho Expected sign 1980 1990 2000 2010 Pctchg
MLlnm2b
Profitability 32.7 0.196 + 31.8 32.5 33.9 32.6 2.3
Growth 21.0 0.243 + 15.9 24.0 21.9 22.2 40.2
Industry 9.0 -0.133 N.A. 10.9 8.6 8.2 8.3 -23.5
Financial soundness 8.0 0.026 +/- 7.9 7.4 7.8 9.1 14.8
Size 7.9 -0.124 - 13.1 10.1 5.1 3.4 -74.0
Liquidity 6.3 -0.035 +/- 4.6 4.4 7.8 8.3 80.5
Efficiency 5.7 0.164 + 5.8 5.2 6.0 5.8 -0.6
Solvency 5.3 0.162 +/- 4.1 3.8 5.9 7.3 77.9
CAPMbeta 2.2 0.189 - 4.0 2.1 1.7 1.0 -74.8
Capitalisation 1.4 0.103 +/- 1.6 1.7 1.3 1.2 -22.5
MLlnv2a
Profitability 21.0 0.105 + 19.4 20.5 22.4 21.8 12.2
Growth 18.3 0.149 + 16.2 21.8 18.1 17.0 5.4
Financial soundness 17.2 0.002 +/- 18.2 17.4 16.6 16.6 -8.7
Solvency 11.8 0.334 +/- 12.6 13.7 12.0 8.9 -29.1
Industry 9.2 -0.309 N.A. 10.1 7.8 10.9 8.1 -19.7
Efficiency 7.9 0.260 + 5.8 4.8 7.2 13.7 136.9
Liquidity 6.8 -0.168 +/- 3.9 5.9 7.3 10.1 160.6
Size 5.1 -0.214 - 9.0 5.8 3.5 2.0 -78.3
CAPMbeta 1.8 0.221 - 4.0 1.4 1.2 0.8 -80.7
Capitalisation 0.6 0.236 +/- 0.7 0.6 0.6 0.7 -8.3
MLlnv2s
Efficiency 37.8 -0.429 - 39.1 33.4 41.2 37.7 -3.6
Profitability 23.1 0.046 + 20.3 24.4 21.6 26.0 27.7
Growth 11.9 0.292 + 8.5 14.0 12.5 12.6 48.8
Financial soundness 7.1 0.327 +/- 6.4 7.3 6.6 7.9 23.4
Size 5.9 -0.099 - 10.9 6.6 3.7 2.4 -78.2
Industry 4.7 0.054 N.A. 4.7 4.5 4.9 4.6 -1.0
Solvency 4.7 0.109 +/- 5.1 5.1 4.6 3.8 -26.6
Liquidity 2.9 0.370 +/- 2.3 2.8 3.3 3.3 39.7
CAPMbeta 1.1 0.124 - 1.8 1.1 0.8 0.6 -66.6
Capitalisation 0.7 0.017 +/- 0.6 0.7 0.6 0.8 19.5
TableIA.13:Equal-weightedtradingstrategies(assets,bookequity,sales>0) Thistablereportsmonthlymeansandabnormalreturnsofequal-weightedhedgeportfolioreturnsfromtradingstrategiesutilisingvaluationerrors. ThistableusesthesamemethodologyasinTable6exceptthatthistableincludestinyfirm-monthobservationswithassets,bookequityorsales between0and10millionUSDwhileTable6excludesthem. MLlnm2bMLlnv2aMLlnv2sRRVcsBLm2bBLv2aBLv2sINDm2bhmINDv2ahmINDv2shmBG Mean Const0.49***0.53***0.59***0.43***0.220.35*0.170.28*0.35**0.68***0.50*** FF6 MKTRF0.04**0.07***0.06***-0.000.030.08***-0.000.030.07***0.03-0.03 SMB0.08***0.10***0.11***0.11***0.22***0.07*0.040.040.040.11***0.23*** HML0.31***0.34***0.28***0.43***0.11**0.65***-0.12*0.53***0.48***0.18***0.48*** RMW0.18***0.20***0.22***0.19***-0.14***0.28***-0.030.21***0.26***0.65***0.71*** CMA0.040.060.09*0.18***0.30***0.27***0.25***0.24***0.24***0.28***0.19*** UMD-0.38***-0.40***-0.39***-0.35***-0.29***-0.48***0.13***-0.43***-0.38***-0.15***-0.36*** Const0.52***0.52***0.59***0.40***0.29**0.24**0.080.24***0.25***0.38***0.28*** Adj.R20.670.690.670.720.380.740.060.790.740.560.69 FF6+7clustersofanomalies MKTRF0.020.05***0.04**-0.020.020.05**-0.020.010.05**0.02-0.03 SMB0.08***0.11***0.11***0.11***0.22***0.040.030.05*0.040.11***0.23*** HML0.31***0.34***0.28***0.43***0.09*0.63***-0.13**0.53***0.47***0.19***0.49*** RMW0.19***0.22***0.22***0.20***-0.10*0.37***0.030.23***0.32***0.60***0.66*** CMA0.060.09*0.11**0.21***0.29***0.29***0.26***0.25***0.29***0.30***0.17** UMD-0.37***-0.40***-0.38***-0.35***-0.29***-0.45***0.14***-0.42***-0.37***-0.16***-0.36*** EG0.040.010.040.03-0.00-0.19***-0.090.00-0.070.060.09 Accruals0.030.040.020.040.10**0.10**0.10*0.050.07**-0.09***-0.03 STReversal0.10***0.09***0.09***0.09***0.020.05**0.06*0.06***0.06***0.05**0.04* MarginGrowth0.08***0.10***0.08**0.07**-0.01-0.010.090.010.040.08**0.09** epsconsistency-0.02-0.02-0.01-0.010.040.030.02-0.01-0.02-0.02-0.02 ExternalFinance0.040.010.030.010.13***0.08*0.13**0.030.030.03-0.01 seasonality0.010.020.020.01-0.02-0.02-0.020.020.04*0.07***-0.02 Const0.39***0.41***0.46***0.28***0.170.25**-0.020.15*0.17*0.32***0.23* Adj.R20.690.710.690.740.390.750.060.790.750.570.70
TableIA.14:Value-weightedtradingstrategies(assets,bookequity,sales>0) Thistablereportsmonthlymeansandabnormalreturnsofvalue-weightedhedgeportfolioreturnsfromtradingstrategiesutilisingvaluationerrors. ThistableusesthesamemethodologyasinTable7exceptthatthistableincludestinyfirm-monthobservationswithassets,bookequityorsales between0and10millionUSDwhileTable7excludesthem. MLlnm2bMLlnv2aMLlnv2sRRVcsBLm2bBLv2aBLv2sINDm2bhmINDv2ahmINDv2shmBG Mean Const0.37***0.38***0.39***0.37***0.240.290.160.130.200.29*0.26 FF6 MKTRF-0.020.010.030.07***-0.040.000.020.020.09***-0.050.05* SMB0.060.060.07**0.29***0.10**0.16***-0.090.12***0.07*0.10**0.62*** HML0.34***0.29***0.25***0.45***0.070.53***-0.090.57***0.48***-0.14**0.47*** RMW0.070.050.11**-0.14***-0.14**0.000.06-0.24***0.010.57***0.38*** CMA-0.11-0.020.090.010.17*0.15*0.32***-0.100.080.54***0.20*** UMD-0.28***-0.30***-0.31***-0.24***-0.27***-0.42***0.13***-0.31***-0.26***-0.12***-0.47*** Const0.45***0.46***0.41***0.37***0.40***0.34***-0.000.26**0.140.060.13 Adj.R20.360.370.420.500.200.540.050.520.480.240.72 FF6+7clustersofanomalies MKTRF-0.04-0.010.010.05**-0.03-0.01-0.00-0.010.07**-0.07**0.03 SMB0.050.040.050.27***0.12**0.12**-0.070.11***0.060.080.56*** HML0.36***0.31***0.26***0.47***0.080.53***-0.080.58***0.47***-0.13**0.48*** RMW-0.04-0.050.04-0.24***-0.26***-0.060.10-0.26***0.030.49***0.28*** CMA-0.12-0.030.080.000.150.140.39***-0.090.080.55***0.18*** UMD-0.27***-0.28***-0.28***-0.20***-0.28***-0.39***0.12***-0.29***-0.23***-0.10***-0.43*** EG0.18***0.12*0.090.15**0.29***-0.01-0.050.03-0.050.030.02 Accruals-0.15***-0.16***-0.12***-0.13***-0.12**-0.12**0.03-0.05-0.06-0.24***-0.15*** STReversal0.12***0.09***0.11***0.14***0.040.05*0.020.11***0.05*0.040.13*** MarginGrowth0.10**0.08*0.05-0.01-0.03-0.040.070.070.000.030.03 epsconsistency-0.06**-0.06**-0.04-0.03-0.060.02-0.04-0.05*-0.08***-0.10**0.03 ExternalFinance0.020.030.04-0.10**-0.070.04-0.020.030.04-0.000.03 seasonality0.040.06*0.05*0.010.050.010.09*0.040.040.12***-0.02 Const0.35***0.41***0.36***0.35***0.28*0.40***-0.070.200.180.150.17 Adj.R20.420.410.460.550.220.550.050.540.490.280.74
Table IA.15: Model performance comparison: IPOs (assets, book equity, sales > 0)
This table reports summary statistics of valuation errors of IPOs from different models. This table and Table 8 use the same methodology except that this table includes firm-month observations with with assets, book equity and sales between 0 and 10 million USD while Table 8 excludes them.
N med(|ε|) avg(|ε|) med(ε) avg(ε) sd(ε) ρy,ˆy
MLlnm2b 4,348 47.5 64.8 -34.4 -6.8 355.7 0.83
MLlnv2a 4,348 45.3 69.9 -27.1 5.8 410.5 0.83
MLlnv2s 4,348 46.4 79.5 -27.0 14.2 544.8 0.82
RRVcs 4,139 65.0 244121.8 -60.5 244015.5 1.6e+07 0.00
BLm2b 2,623 73.9 121.1 -58.0 -1.0 552.6 0.38
BLv2a 2,623 60.9 162.5 -24.3 95.9 1918.2 0.36
BLv2s 2,623 256.2 1372.8 -36.2 288.8 12976.4 0.18
INDm2bhm 4,348 82.5 80.5 -81.5 -61.8 173.4 0.72
INDv2ahm 4,348 75.5 85.1 -72.6 -47.4 210.2 0.63
INDv2shm 4,348 78.8 130.0 -71.5 -11.5 1256.1 0.18
BG 4,055 88.6 254.3 51.7 172.3 1182.3 0.61
Table IA.16: Long-run abnormal returns on IPOs: the event-time approach (assets, book equity, sales > 0)
This table reports long-run buy-and-hold abnormal cumulative returns on IPOs. This table and Table 8 use the same methodology except that this table includes firm-month observations with with assets, book equity and sales between 0 and 10 million USD while Table 8 excludes them.
Panel A: Median abnormal cumulative return
12m 24m 36m
MLlnm2b
Low ML error (over-valued IPOs) -21.65 -40.25 -48.25
Med ML error -13.00 -25.81 -32.32
High ML error -11.67 -19.18 -18.24
High minus low 9.98 21.07 30.01
p-value (0.003) (< 0.001) (< 0.001)
MLlnv2a
Low ML error (over-valued IPOs) -22.53 -41.97 -51.17
Med ML error -15.62 -26.00 -35.12
High ML error -8.54 -17.28 -14.06
High minus low 13.99 24.70 37.11
p-value (< 0.001) (< 0.001) (< 0.001)
MLlnv2s
Low ML error (over-valued IPOs) -22.55 -42.95 -49.59
Med ML error -13.69 -27.27 -35.13
High ML error -9.59 -14.70 -13.95
High minus low 12.96 28.24 35.64
p-value (< 0.001) (< 0.001) (< 0.001)
All IPOs -14.40 -28.08 -31.84
Number of IPOs 4,335 4,301 4,259
Panel B: Mean abnormal cumulative return
12m 24m 36m
MLlnm2b
Low ML error (over-valued IPOs) -1.97 -8.03 -15.01
Med ML error -2.06 -8.95 -18.17
High ML error -4.69 -5.90 -9.66
High minus low -2.72 2.13 5.35
p-value (0.327) (0.706) (0.382)
MLlnv2a
Low ML error (over-valued IPOs) -3.20 -11.42 -21.56
Med ML error -3.66 -8.84 -15.41
High ML error -1.85 -2.60 -5.83
High minus low 1.34 8.82 15.73
p-value (0.621) (0.107) (0.008)
MLlnv2s
Low ML error (over-valued IPOs) -4.51 -11.51 -19.65
Med ML error -0.95 -8.43 -17.85
High ML error -3.25 -2.93 -5.30
High minus low 1.26 8.59 14.35
p-value (0.639) (0.122) (0.018)
All IPOs -2.90 -7.63 -14.31
p-value (0.008) (0.000) (0.000)
Number of IPOs 4,335 4,301 4,259
Table IA.17: Long-run abnormal returns on IPOs: the calendar-time portfolio approach (assets, book equity, sales > 0)
This table reports monthly average abnormal returns on IPOs using the calendar-time portfolio approach.
This table uses the same methodology as in Table 10 except that this table includes tiny firm-month obser- vations with assets, book equity or sales between 0 and 10 million USD while Table 10 excludes them.
Panel A: Equal-weighted
Mean FF3 FF5 FF6
MLlnm2b
P1 0.31 -0.47 -0.13 0.02
(0.404) (0.020) (0.521) (0.921)
P2 0.50 -0.33 -0.07 0.09
(0.117) (0.044) (0.688) (0.559)
P3 0.41 -0.36 -0.02 0.14
(0.197) (0.057) (0.918) (0.437)
P3-P1 0.10 0.11 0.11 0.12
(0.685) (0.628) (0.642) (0.614)
N 480 480 480 480
MLlnv2a
P1 0.18 -0.60 -0.25 -0.07
(0.621) (0.003) (0.219) (0.731)
P2 0.49 -0.30 -0.08 0.01
(0.148) (0.098) (0.668) (0.939)
P3 0.56 -0.23 0.11 0.26
(0.067) (0.193) (0.523) (0.111)
P3-P1 0.38 0.37 0.36 0.33
(0.088) (0.075) (0.102) (0.134)
N 480 480 480 480
MLlnv2s
P1 0.25 -0.54 -0.20 -0.05
(0.509) (0.007) (0.324) (0.815)
P2 0.40 -0.34 -0.07 0.09
(0.226) (0.045) (0.673) (0.583)
P3 0.48 -0.32 0.01 0.17
(0.129) (0.070) (0.976) (0.296)
P3-P1 0.23 0.22 0.20 0.22
(0.316) (0.317) (0.368) (0.335)
N 480 480 480 480
All IPOs 0.47 -0.30 0.03 0.19 (0.147) (0.045) (0.835) (0.169)
N 480 480 480 480
Panel B: Value-weighted
Mean FF3 FF5 FF6
MLlnm2b
P1 0.35 -0.39 -0.03 -0.05
(0.413) (0.103) (0.911) (0.831)
P2 1.02 0.21 0.35 0.28
(0.003) (0.334) (0.112) (0.212)
P3 0.57 -0.13 0.10 0.08
(0.045) (0.494) (0.616) (0.662)
P3-P1 0.22 0.26 0.12 0.14
(0.514) (0.374) (0.687) (0.658)
N 480 480 480 480
MLlnv2a
P1 0.17 -0.55 -0.18 -0.16
(0.679) (0.019) (0.455) (0.506)
P2 0.78 0.02 0.29 0.15
(0.042) (0.943) (0.199) (0.500)
P3 0.71 -0.01 0.16 0.13
(0.013) (0.937) (0.422) (0.507)
P3-P1 0.54 0.54 0.33 0.29
(0.092) (0.059) (0.258) (0.330)
N 480 480 480 480
MLlnv2s
P1 0.15 -0.57 -0.32 -0.36
(0.700) (0.009) (0.147) (0.110)
P2 0.59 -0.03 0.38 0.35
(0.116) (0.899) (0.061) (0.081)
P3 0.69 -0.04 0.22 0.19
(0.021) (0.860) (0.298) (0.371)
P3-P1 0.54 0.53 0.54 0.55
(0.084) (0.065) (0.069) (0.069)
N 480 480 480 480
All IPOs 0.54 -0.16 0.07 0.01 (0.093) (0.326) (0.645) (0.951)
N 480 480 480 480
TableIA.18:HedgeportfolioreturnsonIPOs:MLandtraditionalmodels(assets,bookequity,sales>0) ThistablereportsmonthlyaverageabnormalreturnsfromhedgeportfoliosonIPOsusingthecalendar-timeportfolioapproach.Thistableusesthe samemethodologyasinTable11exceptthatthistableincludestinyfirm-monthobservationswithassets,bookequityorsalesbetween0and10 millionUSDwhileTable11excludesthem. PanelA:Equal-weighted MLlnm2bMLlnv2aMLlnv2sRRVcsBLm2bBLv2aBLv2sINDm2bhmINDv2ahmINDv2shmBG Mean0.100.380.230.360.500.830.510.360.510.69-0.37 (0.685)(0.088)(0.316)(0.156)(0.136)(0.017)(0.034)(0.249)(0.078)(0.003)(0.139) FF30.110.370.220.350.400.750.510.350.470.74-0.25 (0.628)(0.075)(0.317)(0.137)(0.235)(0.027)(0.034)(0.230)(0.080)(0.001)(0.287) FF50.110.360.200.260.340.380.290.190.240.39-0.37 (0.642)(0.102)(0.368)(0.282)(0.332)(0.262)(0.242)(0.523)(0.387)(0.068)(0.125) FF60.120.330.220.280.340.350.200.230.280.31-0.35 (0.614)(0.134)(0.335)(0.265)(0.334)(0.315)(0.410)(0.463)(0.305)(0.148)(0.150) N480480480480480480480480480480480 PanelB:Value-weighted MLlnm2bMLlnv2aMLlnv2sRRVcsBLm2bBLv2aBLv2sINDm2bhmINDv2ahmINDv2shmBG Mean0.220.540.540.230.380.900.140.230.470.650.03 (0.514)(0.092)(0.084)(0.514)(0.346)(0.031)(0.647)(0.578)(0.225)(0.026)(0.930) FF30.260.540.530.310.470.960.020.300.490.700.07 (0.374)(0.059)(0.065)(0.323)(0.233)(0.016)(0.944)(0.420)(0.150)(0.011)(0.805) FF50.120.330.540.100.150.43-0.090.030.240.44-0.20 (0.687)(0.258)(0.069)(0.757)(0.716)(0.285)(0.768)(0.933)(0.498)(0.118)(0.500) FF60.140.290.550.090.060.25-0.070.020.260.48-0.17 (0.658)(0.330)(0.069)(0.782)(0.886)(0.530)(0.837)(0.951)(0.457)(0.090)(0.558) N480480480480480480480480480480480
Figure 6: Scatter plots of valuation errors
These figures plot actual equity value (x-axis) against predicted equity value by the MLlnm2b machine learning model (y-axis). Stocks are grouped into percentile portfolios based on their actual equity value in each month. Each dot in these scatter plots presents the natural logarithm of an average value of stocks included in a percentile portfolio.
Panel A: Assets, book equity and sales > USD 10 mm
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Log(Avg equity value prediction)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Log(Avg equity value))
Grouped by monthly equity value percentiles
Panel A: Assets, book equity and sales > USD 0 mm
-1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Log(Avg equity value prediction)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Log(Avg equity value))
Grouped by monthly equity value percentiles