Return predictability and valuation ratios: sector-level evidence on the Johannesburg stock exchange

Figures & data

Table 1. Descriptive statistics

Sector	Variable	Mean	Median	$\sigma$	Kurtosis	Skewness	Min.	Max.
J510	Returns	0.0887	0.0538	7.5996	1.8401	−0.1042	−25.7352	34.6562
	EY	0.0002	0.0613	1.0018	−0.3289	−0.3064	−2.8773	1.9328
	DY	0.0001	−0.0726	1.0018	−1.0349	0.0325	−1.9694	2.4905
J530	Returns	0.6164	0.8885	6.5711	2.2233	−0.5925	−25.9125	19.5953
	EY	0.0073	0.1217	1.0039	−1.0062 –0.2365	−0.0832	−1.8947	2.0927
	DY	−0.0003	−0.1060	1.0070		0.5184	−1.8254	3.0460
J550	Returns	0.6063	1.0016	6.5402	5.6621	−1.1925	−41.7638	14.0648
	EY	0.0129	0.2814	0.9994	−0.9744	−0.4692	−2.0550	1.5694
	DY	0.0148	0.4634	0.9939	−0.6922	−0.8190	−2.0965	1.2920
J580	Returns	0.1933	0.2385	6.0025	20.9529	−2.2843	−52.2968	21.1140
	EY	0.0208	0.1325	0.9870	−0.9359	−0.2615	−2.4870	1.9215
	DY	6.5451	6.5519	1.0574	1.8490	−0.3545	0.7991	8.9606
J540	Returns	−0.5621	0.4443	14.7580	18.63036	−12.4558	−222.2209	16.7077
	EY	0.0079	0.0804	1.0044	−1.2430	−0.3067	−1.8764	1.5646
	DY	−0.0004	−0.4028	1.0072	−1.5567	0.0871	−1.7862	1.6086
J520	Returns	0.2624	0.2881	5.8082	4.4858	−0.9857	−33.9490	13.7644
	EY	0.0150	0.1046	0.9967	−1.2855	−0.1784	−1.9284	2.0335
	DY	0.0119	0.0661	1.0006	−1.1235	−0.1813	−1.9958	1.9160
J560	Returns	0.3110	0.0875	8.6842	2.8059	−0.2232	−40.6570	31.1613
	EY	0.0133	0.1718	0.9988	5.1142	−1.9103	−5.1039	1.6185
	DY	−0.0108	0.0629	1.0016	−0.8680	−0.2311	−2.4116	1.9307

EY and DY denote the real log earnings yield and real log dividend yield, respectively.

Table 2. Augmented Dickey-Fuller unit root test

Sector	Returns	Dividend Yield		Earnings Yield
	ADF I(0)	ADF I(0)	ADF I(1)	ADF I(0)	ADF I(1)
J510	−4.6646***	−2.7938	−5.7610***	−3.6442**
J530	−3.9787**	−2.9512	−5.1947***	−2.5354	−5.9249***
J550	−3.9432**	−1.5986	−5.6213***	−2.2476	−4.4394***
J580	−3.4292**	−2.2483	−4.5186***	−2.5838	−5.2442***
J540	−4.2907***	−1.5425	−4.1270***	−2.4488	−5.0950***
J520	−3.7962**	−3.5275**		−3.2626**
J560	−3.6646**	−3.4972**		−3.1779**
J203	−4.5183***	−3.7048**		−3.1812**

*, **, *** denotes significance at 10%, 5% and 1% levels, respectively. Critical values are based on a sample size of 276 observations allowing for the inclusion of intercept and trend and lag selection based on SBIC.

Table 3. Zivot and Andrews unit root test

Sector	Returns	Dividend Yield		Earnings Yield
	ZA I(0)	ZA I(0)	ZA I(1)	ZA I(0)	ZA I(1)
J510	−17.350***	−4.275	−16.262***	−4.825***
J530	−8.318***	−4.517	−10.760***	−3.883	−17.447***
J550	−14.793***	−4.803	−9.751***	−4.350	−9.936***
J580	−16.559***	−4.329	15.799***	−5.027*
J540	−17.816***	−5.867***		−3.909	−18.289***
J520	−16.291***	−4.794	−10.809***	−5.692***
J560	−8.553***	−4.177	−16.921***	−6.300***
J203	−17.469***	−5.152**		−4.338	−8.995***

*, **, *** denotes significance at 10%, 5% and 1%, respectively. Critical values are based on 276 observations allowing for the structural break, the inclusion of intercept and trend and lag selection based on SBIC.

Table 4. KPSS stationarity test

Sector	Returns		Dividend Yield			Earnings Yield
	KPSS I(0)	KPSS I(0)		KPSS I(1)	KPSS I(0)		KPSS I(1)
J510	0.0910***	0.1650*			0.0743***
J530	0.0847***	0.1269**			0.0898***
J550	0.0978***	0.4969		0.0375***	0.4287		0.1041***
J580	0.0500***	0.3234		0.0987***	0.2411		0.0280***
J540	0.1084***	0.2758		0.1070***	0.2204		0.1120**
J520	0.1097***	0.1406**			0.2152*		0.0594***
J560	0.0832***	0.3101		0.0305***	0.2677		0.0219***
J203	0.0669***	0.0797***			0.278		0.0423***

*, **, *** denotes significance at the 10%, 5% and 1%, respectively. Critical values are based on a sample size of 276 observations allowing for the inclusion of intercept and trend and lag selection based on SBIC.

Table 5. Gregory Hansen cointegration test

J510	ADF		Zt		Za
Statistic		Breakpoint	Statistic	Breakpoint	Statistic	Breakpoint
Int. shift	−16.93***	08-Mar	−16.96***	08-Mar	−283.48***	08-Mar
Int. shift + trend	−16.95***	08-Mar	−16.98***	08-Mar	−183.80***	08-Mar
Int. shift + slope	−17.03***	08-Mar	−17.06***	08-Mar	−285.10***	08-Mar
J530	ADF		Zt		Za
Int. shift	−7.84***	15-Jul	−18.32***	03-Apr	−302.28***	03-Apr
Int. shift + trend	−8.24***	03-May	−18.56***	03-Apr	−307.08***	03-Apr
Int. shift + slope	−8.01***	03-Jun	−18.66***	03-Apr	−307.24***	03-Apr
J550	ADF		Zt		Za
Int. shift	−14.76***	03-Mar	−14.79***	03-Mar	−244.22***	03-Mar
Int. shift + trend	−14.65***	03-Feb	−14.67***	03-Feb	−242.38***	03-Feb
Int. shift + slope	−14.64***	02-Feb	−14.67***	02-Feb	−242.13***	02-Feb
J580	ADF		Zt		Za
Statistic		Breakpoint	Statistic	Breakpoint	Statistic	Breakpoint
Int. shift	−16.41***	07-Mar	−16.43***	07-Mar	−273.30*	07-Mar
Int. shift + trend	−16.43***	03-Feb	16.46***	03-Feb	−273.98*	03-Feb
Int. shift + slope	−16.30***	07-Mar	−16.33***	07-Mar	−271.58*	07-Mar
J540	ADF		Zt		Za
Statistic		Breakpoint	Statistic	Breakpoint	Statistic	Breakpoint
Int. shift	−17.24***	14-Aug	−17.28***	14-Aug	−287.32***	14-Aug
Int. shift + trend	−17.35***	14-Aug	−17.39***	14-Aug	−289.00***	14-Aug
Int. shift + slope	−17.33***	14-Aug	−17.36***	14-Aug	−288.58***	14-Aug
J520	ADF		Zt		Za
Int. shift	−15.78***	03-Mar	−15.80***	03-Mar	−261.38***	03-Mar
Int. shift + trend	−15.33***	03-May	−15.38***	03-May	−1254.62***	03-May
Int. shift + slope	−15.72***	07-Mar	−15.75***	07-Mar	−261.03***	07-Mar
J560	ADF		Zt		Za
Int. shift	−7.86***	10-Oct	−15.70***	02-Sep	−260.79***	02-Sep
Int. shift + trend	−8.09***	02-Dec	−15.92***	02-Aug	−264.80***	02-Aug
Int. shift + slope	−7.97***	Nov-00	−15.98***	Mar-00	−265.73***	Mar-00
J203	ADF		Zt		Za
Int. shift	−17.10***	07-Aug	−17.13***	07-Aug	−283.92***	07-Aug
Int. shift + trend	−16.92***	07-Apr	−16.95***	03-Mar	−281.40***	03-Mar
Int. shift + slope	−17.21***	07-Apr	−17.24***	07-Apr	−285.64***	07-Apr

*** denotes statistical significance at the 1%. Critical values of the models with intercept shift, intercept shift and trend, and intercept shift and slope are based on SBIC lag selection and sample size of 276 observations.

Table 6. ARDL bounds tests for the existence of a cointegrating relationship

J510	(1, 1, 2, 0, 1, 2)	Mar-08	72.073***	Cointegration
J530	(1, 2, 1, 1, 1, 1)	Jul-15	85.031***	Cointegration
J550	(1, 1, 1, 2, 0, 0)	Feb-02	35.775***	Cointegration
J580	(1, 2, 1, 0, 0, 0)	Mar-07	129.885***	Cointegration
J540	(1, 0, 1, 1, 0, 1)	Aug-14	52.917***	Cointegration
J520	(1, 1, 1, 0, 1, 0)	May-07	140.055***	Cointegration
J560	(2, 1, 1, 0, 1, 1)	Oct-10	53.453***	Cointegration
J203	(1, 2, 1, 0, 1, 2)	Apr-07	45.814***	Cointegration
Critical Values	1% Lower	1% Upper	5% Lower	5% Upper
	3.41	4.68	2.62	3.79

*** denotes statistical significance at 1%. The lag order selection is based on SBIC, and critical values of the test are based on the sample size of 276 observations. Critical values tabulated by Pesaran et al. (2001).

Table 7. ARDL error correction estimates

Sector	ECT	Long run coefficients			Short run coefficients		Diagnostics		Adj-R^2
		DY	EY	Dummy	DY	EY	BG	DW
J510	−1.0587*	−2.5376*	2.4867**	−1.8739**	−13.2845***	−13.8344**	0.4339	1.9244	0.7886
	(−20.63)	(−3.19)	(−2.61)	(−2.07)	(−6.26)	(−5.45)
J530	−1.1110*	−0.2689	−0.0409	−3.6137**	−3.83968*	−32.4108***	0.8219	2.0137	0.8307
	(−1.71)	(−1.43)	(−1.02)	(−2.04)	(−1.91)	(−7.40)
J550	−1.0008*	0.3308	0.6235	0.7825	−21.5182 ***	−32.6302***	1.9881	1.8725	0.9390
	(−1.79)	(1.00)	(0.63)	(0.78)	(−12.51)	(−17.79)
J580	−1.0211*	0.7566***	−1.4132**	−1.4132	−19.6519***	−3.16974***	0.1539	2.1362	0.7907
	(−1.69)	(3.14)	(−2.57)	(−2.07)	(−20.88)	(2.71)
J540	−0.9886*	−0.0004	−0.5452	−1.1254	−9.48676***	−33.7341***	0.8541	1.9645	0.9686
	(−1.68)	(−1.09)	(−0.78)	(−0.17)	(−5.28)	(−14.62)
J520	−1.0958*	−1.4217***	0.1269	−1.9494*	−8.53492***	−22.6462***	0.2691	1.9560	0.8437
	(−1.72)	(2.66)	(0.93)	(−1.79)	(−6.76)	(−12.30)
J560	−0.9859*	−1.4265**	2.4666**	3.3986**	−13.7426***	−30.1838***	0.4165	2.0685	0.7764
	(−1.85)	(−2.19)	(1.98)	(2.08)	(−9.00)	(−6.13)
J203	−0.9878*	−2.9223**	1.8728	−2.1937*	−24.8602***	−6.49526**	0.2293	2.0318	0.9037
	(−1.87)	(2.20)	(1.07)	(−1.68)	(−10.46)	(2.10)

*, **, *** denotes statistical significance at the 10%, 5% and 1% significance levels, respectively. In parentheses () are t-statistics. The lag order selection is based on SBIC, and critical values of the test are based on the sample size of 276 observations. BG—Breusch Godfrey and DW—Durbin Watson.

Figure 1. CUSUM tests.

Table 8. Multivariate quantile regressions with earnings yield and dividend yield as regressands (without bootstrapped standard errors)

Sector	Reg.	25^th quantile		50^th quantile		75^th quantile		95^th quantile
		Coefficient	t-stat	Coefficient	t-stat	Coefficient	t-stat	Coefficient	t-stat
J510	DY	−18.5478***	−6.55	−20.1817***	−6.55	−27.1487***	−6.98	−24.0179***	−3.22
			[0.000]		[0.000]		[0.000]		[0.001]
			(3.303306)		(3.081805)		(3.890377)		(7.465179)
	EY	−10.7624***	−3.34	−11.4979***	−3.34	−3.0465	−0.70	−0.9797	−0.12
			[0.004]		[0.001]		[0.484]		[0.906]
			(3.68765)		(3.440377)		(4.343028)		(8.333762)
J530	DY	−11.5071***	−5.42	−0.8569***	−11.78432	−10.9777***	−4.96	−8.0941	−1.08
			[0.000]		[0.000]		[0.000]		[0.283
			(2.12389)		(1.813505)		(2.21419)		(7.517733)
	EY	−25.0242***	−5.44	−0.5058***	−21.25499	−21.1727***	−4.41	−19.5955	−1.20
			[0.000]		[0.000]		[0.000]		[0.230]
			(4.603851)		(3.931045)		(4.799591)		(16.29582)
J550	DY	−9.7666	−1.16	−11.2462	−1.48	−20.5075*	−1.71	−20.7571**	−2.26
			[0.246]		[0.139]		[0.089]		[0.025]
			(8.403364)		(7.574644)		(12.02043)		(9.185113)
	EY	−40.1672***	−3.75	−36.3198***	−6.12	−31.4462***	−2.83	−26.6727*	−2.64
			[0.000]		[0.000]		[0.005]		[0.09]
			(10.71146)		(5.929818)		(11.11858)		(10.10567)
J580	DY	−13.7293**	−2.24	−10.7303	−1.61	−8.1813	−1.22	−3.1485	−0.56
			[0.026]		[0.108]		[0.222]		[0.573]
			(6.140912)		(6.663396)		(6.685719)		(5.575706)
	EY	−5.9752	−0.88	−10.4689	−1.53	−12.7698*	−1.73	−14.9776***	−2.76
			[0.379]		[0.127]		[0.084]		[0.006]
			(6.783733)		(6.846172)		(7.371848)		(5.421938)
J540	DY	−7.2762	−1.03	−7.5096	−1.61	−11.2804***	−2.01	−18.5910**	−2.00
			[0.302]		[0.109]		[0.012]		[0.047]
			(7.040022)		(4.667882)		(5.62405)		(9.29899)
	EY	−35.5745***	−4.11	−32.9996***	−5.69	−24.6126***	−3.49	−30.1926***	−4.88
			[0.000]		[0.000]		[0.000]		[0.000]
			(8.646307)		(5.794948)		(7.058395)		(6.1882593)
J520	DY	−10.0933***	−3.75	−5.1815*	1.79	−2.8714	−0.97	−4.4798	−0.58
			[0.000]		[0.075]		[0.334]		[0.560]
			(1.2.693717)		(2.897033)		(2.967401)		(7.671563)
	EY	−18.0740***	−5.26	−25.5851***	−6.93	−26.4657***	−7.00	−17.8977*	−1.83
			[0.000]		[0.000]		[0.000]		[0.068]
			(3.433517)		(3.692671)		(3.782366)		(9.778474)
J560	DY	−18.3005***	−5.50	−13.8738***	−6.24	−14.3185***	−4.51	−10.0391	−0.98
			[0.000]		[0.000]		[0.000]		[0.328]
			(3.32993)		(2.224634)		(3.174483)		(10.25142)
	EY	−2.0516	−0.72	−6.6452***	3.49	−9.7706***	−3.59	−4.14464	−0.47
			[0.472]		[0.001]		[0.000]		[0.637]
			(2.85158)		(1.905062)		(2.718463)		(8.778786)
J203	DY	−20.7334***	−3.89	−20.4285***	−5.10	−25.7195***	−6.18	−16.0902	0.82
			[0.000]		[0.000]		[0.000]		[0.410]
			(5.324934)		(4.004283)		(4.164412)		(19.51631)
	EY	−5.7340	−0.80	−7.6414	−1.42	−3.9782	−0.71	−16.0560	0.61
			[0.425]		[0.158]		[0.479]		[0.542]
			(7.172546)		(5.393664)		(5.609353)		(26.28796)

*, **, *** denotes 10%, 5% and 1% statistical significance, respectively. [] are p-values and () are standard errors.

Table 9. Multivariate quantile regressions with earnings yield and dividend yield as regressands (with bootstrapped standard errors)

Sector	Reg.	25^th quantile		50^th quantile		75^th quantile		95^th quantile
		Coefficient	t-stat	Coefficient	t-stat	Coefficient	t-stat	Coefficient	t-stat
J510	DY	−15.38789***	−2.58	−19.59721***	−3.88	−22.88913***	−5.40	−11.973664***	−3.12
			[0.006]		[0.000]		[0.000]		[0.000]
			(5.970601)		(5.428771)		(4.236432)		(3.837713)
	EY	−7.509189**	−2.46	−7.198456**	−2.15	−2.509189	−0.41	−0.798456	−0.10
			[0.015]		[0.027]		[0.115]		[0.927]
			(3.056561)		(3.199314)		(6.056561)		(8.199314)
J530	DY	−7.104032***	−2.89	−0.731028	−0.59	−8.884281**	−2.42	−4.334478*	−0.66
			[0.004]		[0.275]		[0.016]		[0.631]
			(2.459639)		(1.247846)		(3.674758)		(6.567391)
	EY	−18.50263***	−3.17	−0.65273	−0.09	−19.42869**	−2.25	−18.76358	−1.08
			[0.000]		[0.978]		[0.025]		[0.402]
			(5.828159)		(7.252556)		(8.635084)		(17.383523)
J550	DY	−6.646865	−0.92	−8.336336	−1.23	−13.23075*	−1.13	−19.09349*	−1.90
			[0.287]		[0.175]		[0.192]		[0.058]
			(7.224853)		(6.777509)		(10.756707)		(10.02839)
	EY	−26.705661**	−2.21	−21.39702***	−4.35	−27.44629**	−2.20	−22.67275*	−1.92
			[0.016]		[0.000]		[0.038]		[0.064]
			(12.061946)		(4.922263)		(12.474148)		(11.74631)
J580	DY	−7.714904**	−2.18	−6.76885	−1.28	−6.39443	−1.15	−1.467841	−0.22
			[0.03]		[0.143]		[0.291]		[0.824]
			(3.538947)		(5.292853)		(5.565010)		(6.602215)
	EY	−4.565684*	−1.83	−5.892299	−0.83	−8.96655*	−1.79	−13.80229**	−2.06
			[0.073]		[0.406]		[0.093]		[0.042]
			(2.490313)		(7.08066)		(5.014523)		(6.563554)
J540	DY	−7.298712	−0.93	−6.341751	−1.52	−10.12431**	−1.94	−13.894414*	−1.88
			[0.265]		[0.158]		[0.037]		[0.072]
			(7.84808)		(4.172204)		(5.218765)		(7.390646)
	EY	−24.67914***	−2.65	−26.92175***	−3.27	−17.72355***	−3.11	−21.32119***	−3.84
			[0.002]		[0.000]		[0.000]		[0.000]
			(9.312883)		(8.23295)		(3.448088)		(5.552393)
J520	DY	−9.589963**	−2.64	−4.562886*	−1.69	−1.23204	−0.83	−3.477928	−0.43
			[0.014]		[0.087]		[0.542]		[0.213]
			(3.632562)		(2.699933)		(1.48439)		(8.088205)
	EY	−16.17244***	−2.87	−19.15093***	−3.76	−22.37833***	−3.26	−12.28367*	−1.69
			[0.000]		[0.000]		[0.000]		[0.086]
			(5.634997)		(5.093332)		(6.864518)		(7.268444)
J560	DY	−12.11507***	−4.25	−11.87489***	−3.65	−10.14558***	−2.92	−6.897273	−0.36
			[0.000]		[0.000]		[0.004]		[0.686]
			(2.850605)		(3.253395)		(3.474515)		(19.159092)
	EY	−1.409692**	−0.43	−4.250787***	−2.78	−7.525716***	−2.76	−2.620073	−0.17
			[0.838]		[0.013]		[0.007]		[0.932]
			(3.278353)		(1.529060)		(2.718462)		(15.412194)
J203	DY	−15.04854***	−2.33	−14.22996***	−4.77	−18.943215***	−4.48	−13.46974	−0.43
			[0.018]		[0.000]		[0.000]		[0.654]
			(6.458601)		(2.983220)		(4.228396)		(31.324977)
	EY	−4.085077	−0.38	−3.4182845	−1.02	−2.379966	−0.51	−10.25381	−0.25
			[0.768]		[0.472]		[0.543]		[0.910]
			(10.750203)		(3.351259)		(1.383701)		(41.015240)

*, **, *** denotes 10%, 5% and 1% statistical significance, respectively. [] are p-values and () are robust standard errors bootstrapped with 1000 replications.

Pesaran, M. H., Shin, Y., & Smith, R. J. (2001). Bounds testing approaches to the analysis of level relationship. Journal of Applied Economics, 16(1), 289–326. https://doi.org/https://doi:10.1002/jae.616

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