Price discovery of South African stocks cross-listed on the New York Stock Exchange

Figures & data

Table 1. Trading Hours for JSE and NYSE

	JSE Opens	JSE Closes	NYSE Opens	NYSE Closes
Johannesburg Time	0900	1700	1530	2200
New York Time	0300	1100	0930	1600

Source: Authors’ Own Illustration

Table 2. Average Stock Prices of South African Stocks Cross-listed on the NYSE

Stock Market	Open	Close	High	Low	Volume
Anglo-Gold Ashanti (AU)
JSE	12,068.87	12,070.25	12,114.52	12,023.65	39,203
NYSE	8.65	8.65	8.69	8.60	307,616
DRD Gold (DRD)
JSE	339.63	340.65	341.87	338.22	22,794
NYSE	2.40	2.40	2.42	2.38	6605
Gold Fields (GFI)
JSE	4191.83	4190.88	4208.21	4175.19	884,445
NYSE	3.04	3.04	3.06	3.02	404,003
Harmony Gold (HMY)
JSE	2380.28	2380.86	2392.24	2369.46	86,879
NYSE	1.72	1.72	1.73	1.70	402,338
Sibanye Gold (SBGL)
JSE	888.87	889.27	895.24	883.31	419,705
NYSE	2.57	2.567926	2.59	2.55	367,354
Sasol (SSL)
JSE	51,336.47	51,337.96	51,505.29	51,172.74	83,486
NYSE	36.65	36.65	36.76	36.55	18,968

JSE and NYSE prices are denoted in South African Rand cents and US Dollar, rounded off to two decimal places.

Table 3. Lag Length Criteria Tests

Price Series	AIC	SBIC
Anglo-Gold Ashanti (AU)	−11.99818(1)	−11.94385(1)
DRD Gold (DRD)	−0.167012(2)	−9.076456 (2)
Gold Fields (GFI)	−11.61746(5)	−11.52325(1)
Harmony Gold (HMY)	−10.83408(4)	−10.76054(1)
Sibanye Gold (SBGL)	−9.993022(1)	−9.938689(1)
Sasol (SSL)	−13.54821(4)	13.47360(1)

AIC: Akaike Information Criterion, SBIC: Schwarz Bayesian Information Criterion.

Lag order selected by model is in parentheses.

Table 4. Augmented Dickey-Fuller and Phillips Perron Unit Root Tests

Stationarity Test	Integration Order	JSE Listed	NYSE Listed
AU
Augmented Dickey Fuller	Level	−2.628	−2.824
	First Difference	−16.146	−16.208
Phillips-Perron	Level	−2.702	−2.94
	First Difference	−22.641	−23.215
DRD
Augmented Dickey Fuller	Level	−2.656	−3.003
	First Difference	−19.07	−16.266
Phillips-Perron	Level	−3.036	−3.168
	First Difference	−27.859	−23.674
GFI
Augmented Dickey Fuller	Level	−1.075	−1.631
	First Difference	−15.947	−16.436
Phillips-Perron	Level	−1.121	−1.649
	First Difference	−22.036	−21.798
HMY
Augmented Dickey Fuller	Level	−1.148	−0.894
	First Difference	−14.987	−15.992
Phillips-Perron	Level	−1.169	−1.059
	First Difference	−21.511	−23.458
SBGL
Augmented Dickey Fuller	Level	−2. 161	−2.143
	First Difference	−16.195	−15.373
Phillips-Perron	Level	−2.217	−2.21
	First Difference	−22.234	−22.42
SSL
Augmented Dickey Fuller	Level	0.808	0.094
	First Difference	−13.217	−16.74
Phillips-Perron	Level	0.804	0.057
	First Difference	−20.625	−21.952

ADF and PP critical values are −3.982, −3.422 and −3.130 at the 1%, 5% and 10% significance levels, respectively.

Table 5. Cointegration Results

Price Series	Johansen’s Cointegration			Phillips-Ouliaris Cointegration
	Rank	Trace	Max-Eigen Value
AUJSE and AUNYSE	0	89.89256*	88.71263*	−8.648416* Cointegrated
	1	1.1799932 (0.2774)	1.179932 (0.2774)
DRDJSE and DRDNYSE	0	31.10901*	26.97267*	−5.053948* Cointegrated
	1	4.136337 (0.0420)**	4.13637 (0.0420)**
GFIJSE and GFINYSE	0	138.2760*	136.8278*	−10.09559* Cointegrated
	1	1.448216 (0.2288)	1.448216 (0.2288)
HMYJSE and HMYNYSE	0	86.88470*	84.91446*	−10.04774* Cointegrated
	1	1.970240 (0.1604)	1.970240 (0.1604)
SBGLJSE and SBGLNYSE	0	88.29471*	84.52144*	−10.03592* Cointegrated
	1	3.773268 (0.0521)***	3.773268 (0.0521)***
SSLJSE and SSLNYSE	0	89.94946*	89.79566*	−10.39739* Cointegrated
	1	0.153892 (0.6949)	0.153892 (0.6949)

Parentheses () are p-values. *Significant at 1%; **Significant at 5%; *** Significant at 10%.

Phillips-Ouliaris Cointegration presents the tau-statistic based on MacKinnon (1996) Critical Values

Table 6. Vector Error Correction Model

	JSE Series	NYSE Series	Price Discovery
$\alpha$ (ECT)	−0.285258 * (−8.123295)	0.051352 (1.26070)	JSE Leads
AUJSE (t-1)	0.002295 (0.04679)	−0.044419 (−0.78070)	Previous NYSE relevant to current JSE (10% stat.sig.)
AUJSE (t-2)	−0.016329 (−0.33913)	−0.02897 (−0.50665)
AUNYSE (t-1)	−0.128488*** (−2.52346)	−0.037000 (0.62647)
AUNYSE (t-2)	−0.056379 (−1.15375)	0.006203 (0.10943)
$\alpha$ (ECT)	−0.077217 * (−4.56256)	0.041004 ** (2.40287)	Bi-Directional
DRDJSE (t-1)	−0.256447 * (−5.57536)	−0.089601 ** (−1.93196)	Previous JSE relevant to current JSE and NYSE. (5% stat.sig.)
DRDJSE (t-2)	−0.105800** (−2.31492)	−0.088217 *** (−1.91429)
DRDNYSE (t-1)	−0.032911 (−0.69645)	−0.072564 (−1.50105)
DRDNYSE (t-2)	−0.006090 (−0.12850)	0.005029 (0.10522)
$\alpha$ (ECT)	−0.382277 * (−9.00417)	0.124799 ** (2.25631)	Bi-Directional
GFIJSE (t-1)	0.061856 (1.21298)	0.007355 (0.11072)	Previous NYSE relevant to current JSE. (1% stat.sig.)
GFIJSE (t-2)	0.021873 (0.44132)	0.028422 (0.44017)
GFINYSE (t-1)	−0166484 * (−3.41983)	0.039656 (0.62526)
GFINYSE (t-2)	−0.152257 * (−3.25178)	−0.037613 (−0.61660)
$\alpha$ (ECT)	−0.285163 * (−8.07302)	0.057252 (1.37480)	JSE Leads
HMYJSE (t-1)	0.057445 (1.17312)	0.066678 (1.15500)	Previous NYSE relevant to current JSE. (10% stat.sig.)
HMYJSE (t-2)	0.0475559 (1.00356)	0.012928 (0.23138)
HMYNYSE (t-1)	−0.096298 *** (−1.91761)	−0.076713 (−1.29574)
HMYNYSE (t-2)	−0.075313 (−1.59361)	0.000440 (0.00790)
$\alpha$ (ECT)	−0.297848 * (−6.46069)	0.104843 ** (2.10721)	Bi-Directional
SBGLJSE (t-1)	0.033654 (0.60269)	0.029158 (0.48384)	No significant lags. Potential for any lead to be less than 30 mins.
SBGLJSE (t-2)	−0.044777 (−0.83551)	−0.031500 (−0.54461)
SBGLNYSE (t-1)	−0.096356 (−1.62489)	−0.012789 (−0.19983)
SBGLNYSE (t-2)	0.005480 (0.09766)	0.052762 (0.87129)
$\alpha$ (ECT)	−0.240825 * (−6.76771)	0.175965 * (3.32826)	Bi-Directional
SSLJSE (t-1)	0.050706 (1.05633)	−0.028038 (−0.39313)	Previous JSE relevant to current JSE and NYSE. (5% stat.sig.)
SSLJSE (t-2)	0.106953 ** (2.28986)	0.146848 ** (2.11608)
SSLNYSE (t-1)	−0.044035 (−1.10081)	0.087786 (1.47704)
SSLNYSE (t-2)	0.026825 (0.69893)	−0.038443 (−0.67417)

*Significant at 1%; **Significant at 5%; *** Significant at 10%.

t-statistics in parentheses to the right of each ECT and lag coefficient.

Table 7. Common Factor Weights

Price Series	Primary Contributor to Price Discovery (CFW)	Contribution of NYSE	Contribution of JSE
AU	NYSE	0.8474	0.1525
DRD	NYSE	0.6532	0.3468
GFI	NYSE	0.7539	0.2461
HMY	NYSE	0.8328	0.1672
SBGL	NYSE	0.7396	0.2604
SSL	NYSE	0.5778	0.4222
Average	NYSE	0.7341	0.2659