Is intrinsic value priced in the cross section of stock returns?

Figures & data

Table 1. Descriptive Statistics—Variables of the research models

	MRP	SMB	HML	WML	HVPLVP
Mean	0.6283%***	0.2113%**	0.7232%**	0.8033%***	0.9845%***
Median	0.8140%	0.2840%	0.5500%	1.2550%	1.0108%
Maximum	12.6700%	4.7400%	6.9400%	1.3800%	3.6660%
Minimum	−21.05%	−6.8300%	−4.5999%	−2.5960%	−6.9689%
Skewness	−0.9176	−0.4988	0.2916	−1.4650	−0.9383
Kurtosis	5.1782	3.3112	4.1354	9.4957	9.4150
Jarque-Bera	3.1800	4.9761	6.7198	2.2851	3.8976
Probability	0.0000	0.0896	0.0332	0.0000	0.0000

*, **, *** denote significance at the 10%, 5% and 1% level of significance, respectively.

Table 2. Regressions of V/P Portfolios against Risk Factors

P/F	ai	bi	si	hi	wi	vi	Adj. R^2
							ex. HVMLV	in. HVMLV
Panel A: (Ri-Rf)t = ai + bi (RM-Rf)t + vi HVMLVt + εi
(1)	−0.5389	0.521				0.232	0.3356	0.3547
	(−1.9498)	(3.1225)				(1.6573)
(2)	−0.6456	0.477				0.378	0.2587	0.2767
	(−1.2523)	(2.6157)				(4.3428)
(3)	−0.4567	0.483				0.567	0.2679	0.3251
	(−1.6587)	(3.2156)				(3.5683)
Panel B: (Ri-Rf)t = ai + bi(RM-Rf)t+ siSMBt + hiHMLt + viHVMLVt + εi
(1)	−0.2548	0.4831	0.8534	0.265		0.027	0.3148	0.3568
	(−1.3186)	(9.5456)	(4.6937)	(1.2651)		(3.8765)
(2)	−0.2254	0.4749	0.1253	0.185		0.064	0.3275	0.3687
	(−0.5753)	(5.2320)	(5.3283)	(1.1761)		(2.4845)
(3)	−0.3864	0.4428	0.1152	0.599		0.853	0.3445	0.4065
	(−0.8798)	(9.9802)	(4.1705)	(1.344)		(3.6568)
Panel C: (Ri-Rf)t = ai + bi(RM-Rf)t+ siSMBt + hiHMLt + wiWMLt + viHVMLVt + εi
(1)	−0.4534	0.5359	0.6518	0.367	−0.3269	0.3978	0.3254	0.3645
	(−4.2575)	(2.8987)	(3.2165)	(0.2657)	(−1.30)	(4.5608)
(2)	−0.2354	0.5047	0.2150	0.274	0.0161	0.6876	0.3366	0.3756
	(−3.5734)	(3.3978)	(4.4734)	(0.9754)	(0.03)	(3.5644)
(3)	−0.4575	0.4725	0.2518	0.506	0.1641	0.9266	0.3565	0.4045
	(−5.1743)	(2.0781)	(6.6767)	(0.2567)	(5.73)	(5.3761)

Notes: bold numbers denote statistical significance at the 1% level. The column labeled “R² in.HVMLV” gives the adjusted R² for a model with the HVMLV risk factor and the column labeled “R² ex.HVMLV” gives the adjusted R² for a model without the HVMLV risk factor.

Table 3. Regressions of V/P portfolios against MRP and HVMLV after controlling for size

P/F		ai	bi	vi	Adj. R^2
					Ex. HVMLV	in. HVMLV
(Ri-Rf)t = ai + bi (RM-Rf)t + vi HVMLVt + εi
Panel A: Large
High V/P	-0.1765(-3.3643)		0.5624(9.6725)	0.4019(4.0497)	0.2492	0.2727
Medium V/P	-0.7965(-3.1567)		0.5664(8.9674)	0.3652(2.4457)	0.2567	0.2654
Low V/P	-0.2667(-2.6412)		0.5796(9.6266)	0.3409(3.1621)	0.2896	0.3098
Panel B: Small
High V/P	-0.7165(-3.2771)		0.4159(5.3571)	0.5417 (2.0703)	0.2594	0.2725
Medium V/P	-0.1572(-2.4704)		0.4142(4.5703)	0.4196(2.9856)	0.2343	0.2587
Low V/P	-0.7475(-3.1644)		0.4171(3.9807)	0.3986 (3.4604)	0.2052	0.2424

Notes: bold numbers denote statistical significance at the 1% level. The column labeled “R² in.HVMLV” gives the adjusted R² for a model with the HVMLV risk factor and the column labeled “R² ex.HVMLV” gives the adjusted R² for a model without the HVMLV risk factor.

Table 4. Regressions of V/P portfolios against Fama-French factors and HVMLV after controlling for size

P/F	ai	bi	si	hi	vi	Adj. R^2
						ex. HVMLV	in. HVMLV
(Ri-Rf)t = ai + bi (RM-Rf)t + si SMBt + hi HMLt + vi HVMLVt + εi
Panel A: Large
High V/P	−0.0224 (−0.9609)	0.5605 (8.5138)	0.4083 (1.9273)	0.3366 (1.0092)	0.4987 (3.3447)	0.3538	0.3774
Medium V/P	−0.1044 (−1.5321)	0.5437 (7.3136)	0.4285 (1.9143)	0.1187 (0.3848)	0.4277 (2.4578)	0.3583	0.3706
Low V/P	−0.7039 (−1.4779)	0.5311 (8.1049)	0.4449 (2.1535)	0.1609 (0.5074)	0.3749 (2.4778)	0.3654	0.3634
Panel B: Small
High V/P	−0.1318 (−1.2186)	0.4035 (4.0219)	0.1614 (0.7814)	0.2543 (0.8954)	0.5577 (1.7229)	0.3584	0.3938
Medium V/P	−0.0213 (−0.7735)	0.3908 (3.2808)	0.2449 (1.1437)	0.5304 (1.3586)	0.4946 (2.3216)	0.3496	0.3766
Low V/P	−0.1027 (−0.4233)	0.3974 (2.6221)	0.2345 (1.0134)	0.6499 (1.2542)	0.4813 (2.4196)	0.3254	0.4468

Notes: bold numbers denote statistical significance at the 1% level. The column labeled “R² in.HVMLV” gives the adjusted R² for a model with the HVMLV risk factor and the column labeled “R² ex.HVMLV” gives the adjusted R² for a model without the HVMLV risk factor.

Table 5. Regressions of V/P portfolios against Carhart factors and HVMLV after controlling for size

P/F	ai	bi	si	hi	wi	vi	R^2-bar
							ex. HVMLV	in. HVMLV
(Ri-Rf)t = ai + bi (RM-Rf)t + si SMBt + hi HMLt + wi WMLt + vi HVMLVt + εi
Panel A: Large
High V/P	0.0728 (0.5317)	0.4789 (6.4187)	0.2641 (1.9496)	0.5727 (1.1748)	−0.3599 (−3.3468)	0.2099 (3.7422)	0.3926	0.4117
Medium V/P	−0.0743 (−0.2532)	0.48135 (5.5343)	0.2843 (1.9485)	0.4995 (1.6257)	−0.2831 (−3.2768)	0.1586 (2.6207)	0.3941	0.4997
Low V/P	−0.0176 (−0.4733)	0.4711 (6.4889)	0.3515 (2.4451)	0.4362 (0.8138)	−0.3559 (−3.3669)	0.1271 (2.318)	0.3019	0.4065
Panel B: Small
High V/P	−0.0726 (−0.9321)	0.3191 (2.3433)	0.1326 (2.6047)	0.4346 (1.4375)	−0.4801 (−4.3039)	0.1627 (1.8326)	0.3941	0.4017
Medium V/P	0.0679 (0.4431)	0.3541 (2.7817)	0.1176 (2.2232)	0.7522 (0.7647)	−0.3543 (−4.0289)	0.1403 (2.5081)	0.3775	0.4926
Low V/P	0.0176 (0.2331)	0.3157 (3.1195)	0.1212 (2.8319)	1.1323 (0.7387)	−0.2572 (−3.8987)	0.1374 (3.081)	0.3551	0.4778

Notes: bold numbers denote statistical significance at the 1% level. The column labeled “R² in.HVMLV” gives the adjusted R² for a model with the HVMLV risk factor and the column labeled “R² ex.HVMLV” gives the adjusted R² for a model without the HVMLV risk factor.

Table 6. Regressions of V/P portfolios against MRP and HVMLV after controlling for BE/ME ratio

P/F	ai	bi	vi	R^2-bar
				ex. HVMLV	in. HVMLV
(Ri-Rf)t = ai + bi (RM-Rf)t + vi HVMLVt + εi
Panel A: High BE/ME
High V/P	0.010	0.4674	0.4290	0.2166	0.2524
	(−0.5675)	(4.5536)	(4.6634)
Low V/P	−0.0010	0.4510	0.3955	0.2045	0.2582
	(−1.1846)	(3.0952)	(2.6626)
Medium V/P	−0.0012	0.4640	0.3793	0.2353	0.2742
	(−1.2646)	(3.8541)	(2.9195)
Panel B: Medium BE/ME
High V/P	−0.0026	0.3990	0.3850	0.2645	0.3151
	(−1.6828)	(4.8332)	(2.1033)
Low V/P	−0.0003	0.3935	0.3726	0.2905	0.3693
	(−0.8484)	(3.4099)	(2.0263)
Medium V/P	−0.0011	0.3959	0.3388	0.2959	0.3535
	(−1.0773)	(3.3281)	(2.3925)
Panel C: Low BE/ME
High V/P	0.0019	0.4636	0.2959	0.2774	0.3453
	(−0.2616)	(5.9236)	(2.9337)
Low V/P	−0.0006	0.4763	0.2806	0.2197	0.3485
	(−1.2456)	(6.7298)	(2.4104)
Medium V/P	−0.0003	0.4566	0.2654	0.2044	0.3432
	(−1.1644)	(6.4220)	(2.8725)

Notes: bold numbers denote statistical significance at the 1% level. The column labeled “R² in.HVMLV” gives the adjusted R² for a model with the HVMLV risk factor and the column labeled “R² ex.HVMLV” gives the adjusted R² for a model without the HVMLV risk factor.

Table 7. Regressions of V/P portfolios against Fama-French factors and HVMLV after controlling for BE/ME ratio

P/F	ai	bi	si	hi	vi	R^2-bar
						ex. HVMLV	in. HVMLV
(Ri-Rf)t = ai + bi (RM-Rf)t + si SMBt + hi HMLt + vi HVMLVt + εi
Panel A: High BE/ME
High V/P	−0.0001	0.4710	0.3789	0.5099	0.4867	0.3626	0.4243
	(−0.8000)	(5.1512)	(1.6156)	(2.0401)	(2.8000)
Low V/P	−0.0021	0.4583	0.3555	0.1308	0.4153	0.3452	0.4465
	(−1.3558)	(3.8149)	(1.4062)	(1.1835)	(2.3558)
Medium V/P	−0.0025	0.4684	0.4227	0.0475	0.3975	0.3723	0.4698
	(−1.5283)	(4.5012)	(1.7262)	(0.4310)	(3.5283)
Panel B: Medium BE/ME
High V/P	−0.0042	0.3971	0.5219	0.1801	0.4256	0.3097	0.4157
	(−2.1651)	(2.5277)	(2.0812)	(1.6576)	(2.1651)
Low V/P	−0.0024	0.3752	0.7016	0.2638	0.4145	0.3743	0.3891
	(−1.3187)	(4.1088)	(2.5642)	(2.2329)	(3.3187)
Medium V/P	−0.0029	0.3800	0.6347	0.1975	0.3964	0.3697	0.3762
	(−1.4611)	(4.0614)	(2.2872)	(1.6454)	(2.4611)
Panel C: Low BE/ME
High V/P	0.0012	0.4689	0.2848	0.3042	0.3865	0.3215	0.4448
	(−0.3982)	(6.5408)	(1.3419)	(2.3016)	(3.3982)
Low V/P	−0.0014	0.4859	0.2781	0.0040	0.3665	0.3448	0.4424
	(−1.3765)	(7.2461)	(1.3301)	(0.0183)	(3.3765)
Medium V/P	−0.0016	0.4562	0.4333	0.1199	0.3465	0.3407	0.4430
	(−1.5146)	(6.9261)	(2.1299)	(1.4091)	(2.5146)

Notes: bold numbers denote statistical significance at the 1% level. The column labeled “R² in.HVMLV” gives the adjusted R² for a model with the HVMLV risk factor and the column labeled “R² ex.HVMLV” gives the adjusted R² for a model without the HVMLV risk factor.

Table 8. Regressions of V/P portfolios against Carhart Factors and HVMLV after controlling for BE/ME ratio

P/F	ai	bi			si	hi		wi		vi	R^2-bar
											ex. HVMLV	in. HVMLV
(Ri-Rf)t = ai + bi (RM-Rf)t + si SMBt + hi HMLt + wi WMLt + vi HVMLVt + εi
Panel A: High BE/ME
High V/P	−0.0093		0.4277	0.3405			0.5830		−0.4121	0.5393	0.3243	0.4295
	(0.1478)		(3.4783)	(1.5517)			(1.5867)		(−2.7919)	(2.8803)
Low V/P	−0.0044		0.4111	0.3147			0.4331		−0.3720	0.4709	0.3465	0.4565
	(−0.3781)		(2.1990)	(1.3361)			(1.0677)		(−2.8238)	(2.1010)
Medium V/P	−0.0046		0.4186	0.3805			0.4025		−0.2095	0.3851	0.3698	0.4828
	(−0.4669)		(2.8401)	(1.6666)			(1.0256)		(−3.0942)	(2.2421)
Panel B: Medium BE/ME
High V/P	−0.0011		0.3489	0.4806			0.4638		−0.2855	0.5104	0.3157	0.5293
	(−1.1420)		(3.9580)	(2.0321)			(1.1671)		(−2.9183)	(3.3600)
Low V/P	−0.0046		0.3279	0.6608			0.9318		−0.3732	0.4940	0.3891	0.4987
	(−0.4042)		(2.6436)	(2.5241)			(1.2332)		(−2.6159)	(2.0456)
Medium V/P	−0.0001		0.3360	0.5959			0.9949		−0.4216	0.3269	0.3762	0.4823
	(−0.6121)		(2.6386)	(2.2380)			(1.3442)		(−2.3812)	(2.0406)
Panel C: Low BE/ME
High V/P	−0.0007		0.4156	0.2405			0.8837		−0.3640	0.3355	0.3448	0.4635
	(−0.5937)		(4.8456)	(1.2681)			(1.1940)		(−3.8998)	(4.2476)
Low V/P	−0.0034		0.4348	0.2351			0.5923		−0.3302	0.3496	0.3424	0.4596
	(−0.1199)		(5.5265)	(1.2553)			(1.8508)		(−3.7788)	(4.9285)
Medium V/P	0.0017		0.4050	0.3902			0.7050		−0.3323	0.2890	0.3430	0.4624
	(−0.2143)		(5.2286)	(2.1045)			(2.3117)		(−3.9330)	(4.6306)

Notes: bold numbers denote statistical significance at the 1% level. The column labeled “R² in.HVMLV” gives the adjusted R² for a model with the HVMLV risk factor and the column labeled “R² ex.HVMLV” gives the adjusted R² for a model without the

Table 9. GRS statistics of the empirical models

Model	GRS F-Statistic
	ex. HVMLV	in. HVMLV
Part A: Dependent Variables 3 V/P Portfolios
CAPM	4.72***	3.97***
Fama & French 3 Factor Model	3.38**	3.30***
Carhart 4 Factor Model	2.95***	2.65**
Part B: Dependent Variables 3 Large Cap V/P Portfolios
CAPM	5.11***	4.38**
Fama & French 3 Factor Model	3.69**	3.08***
Carhart 4 Factor Model	2.94***	2.78***
Part C: Dependent Variables 3 Small Cap V/P Portfolios
CAPM	4.93**	4.72***
Fama & French 3 Factor Model	3.95***	3.59***
Carhart 4 Factor Model	3.37***	2.85**
Part D: Dependent Variables 3 High BE/ME—V/P Portfolios
CAPM	2.75***	2.30**
Fama & French 3 Factor Model	2.93***	2.38***
Carhart 4 Factor Model	3.01**	2.69***
Part E: Dependent Variables 3 Medium BE/ME—V/P Portfolios
CAPM	2.85***	2.55**
Fama & French 3 Factor Model	2.15**	2.05***
Carhart 4 Factor Model	1.93***	1.88***
Part F: Dependent Variables 3 Medium BE/ME—V/P Portfolios
CAPM	2.86**	2.73***
Fama & French 3 Factor Model	2.65***	2.43***
Carhart 4 Factor Model	2.53***	2.31**

Notes: The null hypothesis is that model intercepts are jointly equal to zero for all 3 V/P portfolios. *, ** and *** denote statistical significance at the 10%, 5% and 1% level, respectively.