Cross-Sectional Asset Pricing with Individual Stocks: Betas versus Characteristics. Tarun Chordia, Amit Goyal, and Jay Shanken
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1 Cross-Secional Asse Pricing wih Individual Socks: Beas versus Characerisics Tarun Chordia, Ami Goyal, and Jay Shanken
2 Main quesion Are expeced reurns relaed o Risk/beas, OR Characerisics If boh, which is more imporan? 2
3 How o answer? Use porfolios Helps miigae EIV problem Fama and MacBeh (1973) Bu, Less efficien Ang, Liu, and Schwarz (2010) Mehod of grouping is imporan Lewellen, Nagel, and Shanken (2010) Use individual securiies Bu, EIV problem 3
4 Wha we do Use individual securiies Correc for EIV bias Lizenberger and Ramaswamy (1979), Shanken (1992), Kim (1995) Allow beas o change over ime Two year rolling regressions Quanify conribuion of beas vs characerisics in explaining he cross-secion of reurns 4
5 Mehodology Two Pass Mehodology: Fama-MacBeh Time-series regression (TSR) R B B F i 0i i i Cross-secional regression (CSR) R Bˆ Zcs Beas are esimaed wih error ˆ ˆ, ˆ, ˆ ' ˆ ˆ ˆ 1 ˆ ˆ ˆ ( X X ) X R, where X 1 N : B 1: Zcs 1 5
6 Mehodology Sandard-error correcion New formulas o accoun for condiional beas; exension of Shanken (1992) Maer lile in pracice for raded facors Bias correcion N 1 ˆ EIV ˆ ˆ ˆ ˆ X X M ˆ M X R, B i1 i1 where ˆ ˆ, and 0 0, Whie ˆ Zs 1 ˆ* B i Zsi 1 M k 1 Ik k k k i1 B i 2 6
7 Inuiion For a one-facor model cov ( ˆ, R ) cov (, R ) var ( ˆ ) var ( ˆ ) OLS cs i i cs i i cs i cs i The denominaor is equal o he cross-secional variaion of beas (his is wha we wan) plus he cross-secional variaion of bea esimaion error (his is wha we wan o remove). Forunaely var ( ˆ ) var ( ) var ( ˆ ) cs i cs i cs i i 2 1 var cs( i ) var cs( ei F ) cov (, R ) EIV cs i i ˆ 2 1 var cs( i ) var cs( ei F ) 7
8 Relaive imporance Using average CSR esimaes E R ˆ E R E R bea char char,and,where E R Bˆ ˆ E R Zcs ˆ bea Using cross-secional variaion a ime bea E 1 R E 1 R %(Beas) var var cs cs char E 1 R E 1 R %(Chars) var var cs cs 8
9 Simulaion Number Acual Facor Mean Acual Truh of Bias RMSE Bias RMSE FMSE socks OLS EIV OLS EIV OLS EIV OLS EIV OLS EIV Premia on B Mk , , , Premia on B SMB , , , Premia on B HML , , , Premia on B RMW , , , Premia on B CMA , , ,
10 Daa All common socks on NYSE, AMEX, and NASDAQ Sample: July 1963 o December 2013 Price greaer han $1 (for CSR) Sample of all socks and non-microcap socks (>20% NYSE percenile) Monhly average of over 3000 socks wih abou 1500 nonmicrocap socks Fama-French (2014) five facor model plus Momenum Mk, SMB, HML, RMW, CMA Characerisics include size, B/M, pas six monh reurn (exclude las monh), operaing profiabiliy and invesmen Assumed o be available 6 monhs afer fiscal year-end Winsorized a he 99 h and 1 s perceniles 10
11 Daa Panel A: Cross-secional saisics B Mk B SMB B HML B RMW B CMA Mean Sdev % % Median % % Panel B: Correlaions B SMB B HML B RMW B CMA Sz B/M Re6 Profi Inves B Mk B SMB B HML B RMW B CMA Sz B/M Re Profi
12 1-facor 3-facor 4-facor 5-facor 6-facor OLS EIV OLS EIV OLS EIV OLS EIV OLS EIV Panel A : Wih fewer characerisics in CSR Cns (5.31) (5.20) (5.37) (4.89) (5.47) (5.26) (5.35) (4.23) (5.37) (4.80) B Mk (0.38) (0.39) (0.74) (1.49) (0.71) (1.23) (0.85) (2.16) (0.84) (1.79) B SMB ( 1.52) ( 2.21) ( 1.58) ( 2.10) ( 1.40) ( 2.44) ( 1.33) ( 2.18) B HML (0.87) (0.76) (0.61) (0.29) (0.63) ( 0.43) (0.33) ( 0.67) B MOM ( 0.43) ( 0.51) ( 0.37) (0.42) B RMW (1.64) (2.46) (1.72) (2.34) B CMA (1.43) (2.33) (1.38) (2.00) Sz ( 2.15) ( 2.17) ( 3.01) ( 4.38) ( 2.95) ( 4.05) ( 3.01) ( 4.68) ( 2.96) ( 4.36) B/M (6.04) (6.24) (6.34) (5.85) (6.66) (6.20) (6.55) (6.23) (6.77) (6.69) Re (9.85) (10.24) (10.31) (10.37) (10.47) (10.72) (10.28) (10.33) (10.38) (10.76) % Beas % Chars % Diff (97.5, 104.9) (96.9, 106.4) (77.7, 108.1) (68.6, 117.8) (85.0, 108.8) (77.6, 118.8) (54.9, 104.2) (35.8, 103.6) (62.0, 104.0) (54.5, )
13 1-facor 3-facor 4-facor 5-facor 6-facor OLS EIV OLS EIV OLS EIV OLS EIV OLS EIV Panel B : Wih all characerisics in CSR Cns (4.90) (4.58) (5.04) (4.32) (5.10) (4.75) (5.01) (3.96) (5.01) (4.35) B Mk (0.96) (0.98) (1.25) (1.95) (1.27) (1.77) (1.36) (2.36) (1.37) (2.21) B SMB ( 1.04) ( 1.83) ( 1.12) ( 1.82) ( 0.95) ( 1.99) ( 0.92) ( 1.89) B HML (0.45) (0.58) (0.19) (0.09) (0.21) ( 0.51) ( 0.05) ( 1.00) B MOM (0.03) (0.21) (0.04) (0.99) B RMW (1.25) (2.01) (1.27) (2.00) B CMA (0.95) (1.72) (0.91) (1.44) Sz ( 2.80) ( 2.82) ( 3.57) ( 4.76) ( 3.56) ( 4.56) ( 3.57) ( 4.79) ( 3.55) ( 4.70) B/M (5.54) (5.77) (5.76) (5.21) (6.12) (5.76) (5.96) (5.71) (6.18) (6.28) Re (8.93) (9.31) (9.30) (9.36) (9.45) (9.54) (9.34) (9.41) (9.41) (9.67) Profi (7.00) (7.04) (7.06) (6.83) (7.21) (6.99) (7.12) (6.04) (7.23) (6.28) Inves ( 11.23) ( 11.26) ( 11.45) ( 10.81) ( 11.46) ( 10.68) ( 11.28) ( 10.08) ( 11.25) ( 9.99) % Beas % Chars % Diff (102.3, 105.1) (103.0, 106.5) (91.8, 108.7) (86.5, 117.6) (97.8, 110.3) (97.1, 121.3) (77.9, 106.2) (62.9, 109.7) (84.1, 106.8) (70.5, 113.0) 13
14 1-facor 3-facor 4-facor 5-facor 6-facor OLS EIV OLS EIV OLS EIV OLS EIV OLS EIV Panel A : Wih fewer characerisics in CSR non-microcap Cns (5.26) (5.25) (5.48) (5.38) (5.81) (5.98) (5.50) (5.19) (5.72) (5.56) B Mk ( 0.10) ( 0.11) (0.41) (0.77) (0.30) (0.64) (0.63) (1.31) (0.54) (1.11) B SMB ( 1.77) ( 1.82) ( 2.30) ( 2.60) ( 1.71) ( 1.95) ( 2.09) ( 2.45) B HML (1.51) (1.63) (1.13) (1.00) (1.06) (0.73) (0.66) (0.18) B MOM ( 0.24) (0.14) ( 0.21) (0.26) B RMW (2.21) (2.31) (2.48) (2.81) B CMA (1.62) (2.17) (1.49) (1.93) Sz ( 2.06) ( 2.07) ( 3.65) ( 4.18) ( 4.09) ( 5.25) ( 3.50) ( 4.25) ( 3.90) ( 5.11) B/M (3.27) (3.31) (2.78) (2.01) (3.24) (2.87) (3.17) (2.79) (3.37) (3.25) Re (6.47) (6.53) (6.74) (6.74) (7.24) (7.55) (7.09) (7.12) (7.28) (7.53) % Beas % Chars % Diff (86.4, 102.0) (82.5, 102.3) (34.6, 106.6) (20.4, 113.1) (54.2, 109.6) (44.9, 120.9) (7.0, 95.0) ( 1.9, 92.6) (14.1, 96.7) (9.1, 99.5) 14
15 1-facor 3-facor 4-facor 5-facor 6-facor OLS EIV OLS EIV OLS EIV OLS EIV OLS EIV Panel B : Wih all characerisics in CSR non-microcap Cns (4.76) (4.62) (5.05) (4.90) (5.36) (5.46) (5.09) (4.75) (5.29) (5.40) B Mk (0.54) (0.54) (0.85) (1.09) (0.80) (1.04) (1.03) (1.56) (0.97) (1.34) B SMB ( 1.22) ( 1.29) ( 1.76) ( 2.15) ( 1.21) ( 1.49) ( 1.57) ( 2.11) B HML (0.95) (1.10) (0.54) (0.47) (0.59) (0.42) (0.18) ( 0.14) B MOM (0.12) (0.44) (0.10) (0.40) B RMW (1.72) (1.89) (1.99) (2.49) B CMA (1.22) (1.83) (1.10) (1.57) Sz ( 2.58) ( 2.58) ( 3.83) ( 3.98) ( 4.31) ( 5.14) ( 3.72) ( 4.03) ( 4.12) ( 5.01) B/M (3.04) (3.09) (2.67) (2.03) (3.17) (2.90) (2.99) (2.56) (3.18) (2.83) Re (6.25) (6.33) (6.48) (6.47) (6.96) (7.28) (6.79) (6.76) (6.96) (7.15) Profi (5.04) (4.94) (4.87) (4.42) (5.15) (4.76) (4.72) (3.57) (4.84) (3.50) Inves ( 7.16) ( 7.34) ( 7.03) ( 6.74) ( 7.09) ( 6.59) ( 6.80) ( 5.99) ( 6.75) ( 5.63) % Beas % Chars % Diff (99.8, 103.6) (100.0, 104.2) (65.6, 107.2) (54.0, 112.6) (85.8, 111.0) (79.1, 120.5) (39.7, 100.8) (22.1, 98.9) (50.5, 102.7) (32.9, )
16 Time variaion in risk premia Allow predicabiliy in risk premia wih dividend-price raio, erm spread, and defaul spread as predicive variables x Calculae fied values c cx v ˆ ˆ ˆ ˆ fi 1 c0 c1 x 1 Recalculae he conribuion numbers as E R ˆ E R E R bea char fi char,and,where E R Bˆ ˆ E R Zcs ˆ bea fi
17 1-facor 3-facor 4-facor 5-facor 6-facor OLS EIV OLS EIV OLS EIV OLS EIV OLS EIV Panel A1 : All socks, Wih fewer characerisics in CSR Fsa Beas (0.59) (0.63) (0.46) (0.63) (0.44) (0.41) (0.38) (0.62) (0.15) (0.23) Fsa Chars (0.01) (0.03) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) % Beas % Chars % Diff (72.1, 102.3) (68.1, 102.8) (71.4, 103.5) (74.7, 111.7) (70.2, 100.8) (64.8, 106.1) (53.6, 96.5) (33.3, 88.7) (53.1, 93.2) (33.4, 83.6) Panel A2 : All socks, Wih all characerisics in CSR Fsa Beas (0.72) (0.77) (0.41) (0.51) (0.44) (0.39) (0.39) (0.44) (0.16) (0.15) Fsa Chars (0.01) (0.01) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) % Beas % Chars % Diff (84.9, 102.9) (83.0, 103.9) (84.8, 106.1) (86.8, 112.9) (81.7, 101.4) (77.3, 106.2) (72.4, 100.7) (62.4, 102.5) (70.2, 97.8) (46.6, 91.9) 17
18 1-facor 3-facor 4-facor 5-facor 6-facor OLS EIV OLS EIV OLS EIV OLS EIV OLS EIV Panel B1 : Non micro-cap socks, Wih fewer characerisics in CSR Fsa Beas (0.80) (0.81) (0.63) (0.77) (0.53) (0.35) (0.35) (0.40) (0.12) (0.13) Fsa Chars (0.03) (0.03) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) % Beas % Chars % Diff (76.5, 100.9) (74.7, 100.9) (56.7, 100.0) (50.7, 100.2) (53.4, 93.2) (35.9, 90.4) (24.4, 82.4) (12.7, 76.4) (21.0, 75.6) (1.4, 59.1) Panel B2 : Non micro-cap socks, Wih all characerisics in CSR Fsa Beas (0.91) (0.92) (0.75) (0.82) (0.59) (0.37) (0.37) (0.40) (0.13) (0.11) Fsa Chars (0.02) (0.02) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) % Beas % Chars % Diff (92.1, 102.5) (92.1, 103.0) (79.8, 101.5) (74.1, 103.4) (70.6, 94.1) (52.7, 93.4) (50.9, 96.5) (34.1, 81.9) (44.2, 78.5) (16.6, 71.8) 18
19 Conclusion Rejec all facor models Rejecion no news Characerisics more imporan han beas Risk premiums Negaive on SMB Posiive on RMW and CMA No premium on HML or MOM Less robus posiive premium on Mk 19
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