Macroeconomic variables and the cross-section of Johannesburg Stock Exchange returns

Van Rensburg, Paul Article Macroeconomic variables and the cross-section of Johannesburg Stock Exchange returns South African Journal of Business Management Provided in Cooperation with: University of Stellenbosch Business School (USB), Bellville, South Africa Suggested Citation: Van Rensburg, Paul (2000) : Macroeconomic variables and the cross-section of Johannesburg Stock Exchange returns, South African Journal of Business Management, ISSN 2078-5976, African Online Scientific Information Systems (AOSIS), Cape Town, Vol. 31, Iss. 1, pp. 31-43, https://doi.org/10.4102/sajbm.v31i1.732 This Version is available at: https://hdl.handle.net/10419/218220 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ S.Afr.J.Bus.Manage.2000.31 (I) JI Macroeconomic variables and the cross-section of Johannesburg Stock Exchange returns Paul van Rensburg Head of Research, Future-Growth Asset Management Part-time Senior Lecturer. School of Management Studies, University of Cape Town. Rondebosch. 7700 South Africa Received September 1999 This study adopts the Chen. Roll & Ross prespecified variable approach to priced arbitrage pricing theory factor (APT) identification on the Johannesburg Stock Exchange (JSE). It is observed that the dichotomy in the return generating processes underlying South African mining and industrial shares leads to cross-sectional correlations in the residual errors of linear factor models that do not employ factor analytically extracted explanatory variables. As a result. a ·two residual market factor' approach is introduced in this study. Employing the iterated non-linear seemingly unrelated regression technique of McElroy & Burmeister ( 1988). it is found that the rand gold price. the rate on long bonds. the Dow-Jones Industrial Index and the level of gold and foreign exchange reserves together with the Industrial and All-Gold residual market factors represent priced sources of risk within the framework of the APT over the period 1985 to 1995. The pricing relationships estimated are found to be inconsistent with those implied by the capital asset pricing model. These results arc robust across the ·unconstrained intercept' and 'zero beta· cross-sectional model specifications. The findings of the study. however. imply that the influence of macroeconomic variables on the JSE is most parsimoniously expressed in the two factor APT model of Van Rensburg & Slaney ( 1997). Introduction and prior research The majority of studies investigating the relationship between macroeconomic forces and the cross-section of equity returns have been conducted within the framework of the Ross ( 1976; 1977) arbitrage pricing theory (APT). As is the case in American literature, South African research concerning the number and nature of the priced APT factors can be broadly subdivided into (i) those studies adopting a factor analytic approach (see Roll & Ross, 1980; Reinganum, 1981; Brown & Weinstein, 1983; Chen, 1983; Cho, 1984; Cho, Elton & Gruber, 1984; Pari & Chen, 1984; Dhrymes, Friend & Gultekin, 1984; Conway & Reinganum, 1988; Lehmann & Modest, 1988; Connor & Korajczyk, 1988; Brown, 1989; Kryzanowski, Lalancette & To, 1994 inter a/ia) and (ii) those studies that preselect certain macroeconomic variables and proceed to test whether sensitivities to these variables are associated with statistically significant risk premia (see Chen, Roll & Ross, 1986; Chen, Chan & Hseih, 1985; Burmeister & McElroy, 1988; and Mc Elroy & Burmeister. 1988). This study adopts the latter approach to APT factor identification on the JSE. Although links between the above two branches of research are seldom made, factor analytic evidence is germane to the appropriate specification of a linear factor model that employs only prespecified macroeconomic variables as explanatory forces. In particular, factor analytic findings are relevant with regard to the possible violation of the 'diagonality' assumption of such a model. Prior South African factor analytic studies support the extraction of at least two but no more than three principal components as a parsimonous representation of the return generating process on the JSE (Page. 1986, 1989; Biger & Page, 1993; and Van Rensburg & Slaney, 1997). With regard to the economic interpretation of these statistical constructs, Page ( J 986) found that mining shares tended to load on the first principal component extracted while industrial firms tended to load on the second: 'What the findings do suggest is that the underlying macroeconomic variables determining the return generating process can be divided into those that influence the mining sector to a greater extent and those that influence the industrial sector to a greater extent' (1996: 42). Van Rensburg & Slaney ( 1997) included observable marker variables in their promax rotation of the factor pattern and found that the JSE Actuaries All-Gold and Industrial Indices could be employed as observable proxies for the first two factor analytic factors on the JSE. It is argued that using these proxies (i) alleviates the primary difficulty of factor analytic procedures, that is the economic interpretability of estimated factor loadings and risk premia (Fama. 1991: 594-595): and (ii) allows access to the powerful system equation methodologies adopted by Mc Elroy & Burmeister ( 1988) when conducting cross-sectional testing. These observable proxies are of relevance to the 'two residual market factor· approach introduced in later on in this article. Prior research adopting the µrespecified variable approach to APT factor identification on the JSE is limited to Var. Rensburg ( 1996) who found that unexpected movements in the Dow-Jones Industrial Index. sho11-term interest rates. the term structure of interest rates and the ·residual market factor'l of Burmeister & Wall ( 1986) were associated with statistically significant risk prem ia over the decade of the 1980s. These findings do not preclude the poss ibi I ity of other macrovariables also being priced over this period. For example. default premia (the difference in yields between corporate and government bonds) were consistently found to be an important explanatory variable in the US environment (Ross. S. · personal correspondence; see also Chen. Roll & Ross. 1986: and McElroy & Burmeister. 1988 infer uliu). Due to the 32 perceived poor quality of the data in the thinly traded South African corporate bond market, this variable was not selected for testing. In addition, the caveat is applied that, due to the fact that the term structure and short-term interest rate variables displayed a marked degree of multicollinearity, in the multiple regression context the former variable may actually be more representative of a 'long bond' rather than a term structure effect. Most importantly. the prespecified variable approach adopted in Van Rensburg ( 1996) does not take account of the dichotomy in the return generating processes underlying mining and industrial shares on the JSE. Consequently, a factor analytic augmentation to the prespecified approach is suggested in Van Rensburg ( 1997) where the residual errors of linear factor models, employing the preidentified priced factors, are factor analysed. The factor scores derived in this manner are then employed alongside the prespecified macrovariables in order to provide a more comprehensive specification of the return generating process than would otherwise be the case. It was found that (i) the factors more than doubled the explanatory power of models employing only macroeconomic variables to explain both 'market' and individual asset returns; (ii) all but three shares loaded significantly on one of the residual factors; and (iii) one of the factor analytically extracted factors was also able to significantly explain the crosssection of share returns thereby justifying its inclusion in the LFM underlying the APT. As expected, following varimax and promax factor rotation, it was found that mining shares tended to load on the first 'residual factor' while industrials loaded on the second. In a recent study, Van Rensburg (1999) reinvestigated the issue of the macroeconomic identity of candidate APT factors on the JSE. A comprehensive list of macroeconomic series were investigated in the context of the socioeconomic and institutional factors that shaped the South African economy over the turbulent period of democratic transition, 1965 to 1995. Based on a time-series analysis of the data, the following variables were selected as candidate APT factors for future cross-sectional testing: (i) the rand gold price, (ii) the three month Banker's Acceptance rate, (iii) the IO-year long bond rate, (iv) the Dow-Jones Industrial Index, (v) the balance on the current account, and (iv) the money market shortage. This study extends prior South African research in the following ways. First, an independent and more recent share sample than that employed by Van Rensburg ( 1996, 1997) is analysed in this study. The search for candidate factors is also based on the more extensive time-series investigation conducted in Van Rensburg ( 1999) (the second section). Second, employing the vector autoregressive (VAR) methodology, unexpected movements in the factors are extracted accounting for the predictive power of other series (in addition to past factor realisations) in the formation of investor expectations (first part, third section). Third, to avoid the problem of contemporaneous correlation of residual errors in the models, two residual market factors are employed throughout the subsequent analysis. These (' All-Gold' and 'Industrial') residual market factors are employed as observable and economically interpretable proxies for the factor analytic augmentation proposed in Van Rensburg (1997). The econometric nature of the S.i\ fr.I .Bus.Manag.e.2000.31(1) bias resulting from the omission of th is procedure is elaborated on and illustrated through an example in the second part of the third section. Fourth. three cross-sectional model specifications are estimated using the systems equations technique of McEiroy & Burmeister ( 1988): the 'exact APT restrictions' model, the 'unconstrained intercept' model and the 'zero beta' version of the APT. The results are compared across model specifications to draw inferences on the validity of the APT pricing restrictions and the robustness of the findings with respect to the proxy employed for the default free asset. Sample selection In comparison to investigators of the major US equity markets, thin-trading is a far more serious concern for South African researchers.' The implications for South African researchers are considered by Bradfield ( 1989) and Bowie & Bradfield ( 1993) in the context of the estimation of systematic risk on the JSE: 'The main cause of the bias associated with estimation problems in environments characterised by thin-trading is the fact that recorded prices are used to represent true underlying prices. For example. when a security has not been traded in a period in question then the recorded price of the security remains unchanged, and represents the outcome of some transaction in a previous period. The underlying (theoretical) price of the security, by contrast would reflect the arrival of any new information in the period in question' (Bradfield, 1989: 23). Finance researchers must either correct for the presence of thin-trading, through the trade-to-trade approach (as suggested by Bowie & Bradfield. 1993: 19) or omit thinly traded securities from their sample. incurring a self-selection bias. In this study thinly-traded securities are omitted from the sample. A prominent environmental feature germane to interpret· ing the sample employed in this study. is the dominant and focused nature of South African institutional investment policy: 'The ... dominant position of financial institutions in trading activities on the JSE has been reflected in the buying policies of these institutions. The latter concentrate their buying activities on a narrow range of equities amounting to about 50 shares which are of a blue chip status, and reasonably marketable. The great majority of shares quoted on the JSE do not attract the attention of these institutions· ( Economi,: Focus. J 990. 84[6]; see also The .!SE Centenwy Puhlication. J 987: 134). The inferences drawn from this research are appropriately interpreted to apply to this coterie of JSE shares that constitute the bulk of investor trade and interest. All of the shares comprising the JSE Actuaries All-Share Index on 3 January 1995 were initially considered for inclusion in the sample. Any shares listed after 31 January 1985 were excluded. Also. any share that had zero volume traded for more than 20 weeks out of the 520 weeks available in the sample period was excluded. In this manner the econometric problems associated with thin tradin!! were avoided. This reduced the sample. from the 141 sha;es comprising the index S.Atr.J.Bus.Managc.2000.31 (I) as at 3 January 1995, to 55 that met both of these criteria. Gold shares were found to be, on average, more actively traded than industrials. This led to a higher representation of mining shares than industrials in terms of both market capitalTable 1 Sectoral overview of the sample Sector :\lining producers Coal Diamonds Rand and others Evander Klerksdorp West Witwatersrand OFS Curtailed operations Copper Manganese Platinum Other metals & minerals Minini.: financial Mining houses Mining holding Mining exploration Financial Banks & fin. Services Insurance Investment trusts Property Property trusts Property loan stock Industrial Industrial holdings Be\' .. hotels & leisure Build .. rnnstr. & allied Chem .. oils & plastics Clothing Electronics Engineering Food Furn .. hous .. & allied .\fotor Paper & packaging Phann. & medical Print. & publishing Steel and allied Stores Transport Percentage of sector No. of shares in the market capitalization sample as a represented by percentage of total sample 39.8% 75.3% 69.6% 93.2% 71.1% 98.3% 12.8% 0.0% 83.0% 89.6% 75.3% 8.2% 72.9% 94.3% 4.5% 64.3% 57.3% 43.6% 55.8% 23.9% 0.0% 37.9% 48.9% 36.6% 92.2% 0.0% 8.6% 34.7% 52.4% 0.0% 0.0% 73.1% 0.0% 0.0% 26.8% 20.3% o O'\o shares in the sector 11.1% 11.1% 25.0% 50.0% 44.4% 60.0% 37.5% 0.0% 20.0% 33.3% 20.0% 15.4% 25.0% 26.7% 6.7% 7.3% 12.5% 4.8% 14.3% 25.0% 0.0% 13.6% 6.3%, 4(J% 30.8% ().(J"o 2 '0' __ ., 0 15.6% ().()% 0.0% 12.5°0 (J.0°o (J.0% 16.7% 103% ().()% ization and the proportion of total shares listed in each sector. As a result, all of the shares listed in the non-mining sectors at 19 April 1995 were examined and all shares that met the above criteria were included in the sample. This procedure resulted in a final sample of 84 shares. Table I presents a overview of the sectoral composition of the sample. Arithmetic returns were calculated as follows: R = D;, + (P,,- P,u11 ) II p 1( I - I I (I) where: R,. = return on share i in period t D,. = the dividend on share i for which the last date to register fell within period t P,, = the price of share i at the end of period t. Note that dividends are recognised 111 their 'ex dividend" rather than payment months (see Van Rensburg, Slaney & Hardy, 1997). Following the prior research of Van Rensburg ( 1999 ). the first differences in levels or natural logarithms (prefixed · D' and 'DL' respectively) of the following macroeconomic variables were initially selected as candidates for cross-sectional testing: A: Share indices: I. The JSE All-Share Index (L)LALSI) 2. The Industrial Index (DLINDI) 3. The All-Gold Index (DLGOLDI) B: Sector earnings I. All-Share Indexed Earnings (DLAE) 2. Industrial Indexed Earnings (DLIE) 3. All-Gold Indexed Earnings (DLGE) C: Economic forces I. The Dow-Jones Industrial Index ( DLDJ) 2. The rand gold price (DLGOLRJ 3. The R 150 IO year government bond ( DR 150) 4. The three month Bankers Acceptance rate (DRBASJ 5. The level of gold and foreign exchange reserves (DLGFX) 6. The money market shortage (DL:\11M'.')J Note that sectoral earnings were included due to the strong theoretical prior that unexpected mowments in these series should influence equity returns. The balance on the current account was excluded from the analysis as only quarter!: data was available for this variable Month-end data \\·as dO\\ n loaded from the IN ET database at the University of '.;atal. Durban. over the period Januar: )980 to December 1994 while the cross-sectional analysis was conducted over the sub-period 1985 .0 I to 1994. 12. In this way it was ensured that the inclusion of lagged variables in the modelling of unexpected movements in the factors did not consume any degrees of freedom in the ensuing cross-sectional tests. Indexed sector earnings were derived for each of the three JSE price indices from their earnings yields for example AE = [ E P] ''" * A LSI where Ar. the · index.:d accounting earnings· of the .JSE All-Share Index. [E!P]" '' · the 34 earnings yield of the All-Share Index and ALSI = the level of the All-Share Index. All of the underlying series except. for the level of gold and foreign exchange res~r~es~ ar~ pu_bltcly observable on a daily basis and, thus, their mclus1on m t~e forecastino model, which uses monthly data, will not result m any mean;gful Banz & Breen ( 1986) 'look-ahead' bias. Results Estimation of candidate factors The linear factor model underlying the Ross ( 1976) Arbitrage Pricino Theory assumes that all risk factors have a mathe;atical expectation of zero i.e E(h,) = 0 for all factors k = /, .... A.") and are void of autocorrelation (E(/~/i..,.,) = 0 where s;tQ) due to their theoretical depictions of innovations in certain pervasive risk factors.; In this study a vector autoreoressive (VAR) model is employed to forecast future values 0 /' the candidate macrovariables and the residuals of this model are taken as a proxy for unexpected movements in the factors. This methodology is a generalisation of the BoxJenkins transfer function technique and appropriate when forecasting interrelated economic series. Following the intuition of Sims ( 1980) each variable in the VAR model is treated symmetrically -all of the variables are specified as being endogenous. The time path of each series in the _sys.tern is specified as being dependent on its own past realtsat1ons and both contemporaneous and past values of all of the other variables in the system. Using matrix notation, the general form of such a model in n variables and k lags can be depicted as: k By, = ro + L r,.r, -A + E, I= I Where: [ I b 12 b,, B= . b., b., Y;,.JVJ,&, =[~'] r.., s., B is a symmetric (nxn) matrix of coefficients with unities on the main diagonal (to ·pick out' the dependent variable from y, in the case of each equation in the system); y, is the (nx I) vector of variables included in the VAR system; r., is a (nx I) vector of intercept coefficients; r, is a (11x11) matrix of coefficients for each lagj= I, ...• k and i::, is a (nx I) vector of residual disturbances. Such a system is characterised by feedback as contemporaneous values of y,, and y1 ,, for example, are allowed to influence each other. If b 11 ;tQ then a given unit shock to i:: 21 will affect y1, and indirectly y,,. As a result, the error term E2, will be correlated with y, which is a violation of the classical assumptions and, thus, the system cannot be directly estimated using conventional least squares analysis. However, this system may be manipulated into ·reduced form' (where each variable depends on its own lags, lags of other endogenous variables and error terms) by premultiplication by B· 1: A Y, = Ao+ LA,y,_,+<', j = I Where: A 11 =B· 1 r,, A = B· 1r for all i= I ..... k I I · e, = B· 1 i::, S.Alr.J llus.Manag~.:woo.31(1) Although it is now the case that E(v, 'e,) = 0, due to the premuliplication by B· 1 and the multicollinearity inherent in this overparameterised model. a typical element of the estimated coefficient matrix A, cannot be directly interpreted. As a result, these estimates are not reported in the VAR results in Table 2. It is not the purpose of th is ,111alysis to draw economic inferences on the dynamics inherent in this model. Rather the VAR methodology is employed as a pragmatic approach to capturing the dominant lagged interrelationships between the variables to forecast the future values of the system's components. All of the domestic economic series: DLAE (the growth rate of 'All-Share' earnings). DLIE (the growth rate of 'Industrial' earnings). DLGE (the growth rate of 'All-Gold' earnings). DLGOLR (rand gold returns). DRl50 (changes in the rate on 10 year gilts). DRBAS (changes in the rate on three month Banker's Acceptances). DLGFX (the growth rate of the level of gold and foreign reserves). DLMMS (the growth rate of the money markd shortage). together with DLINDI (returns on the Industrial Index) and DLGOLDI (returns on the All-Gold Index). were included in the V,\R model. The equity return variable~ are included due to (i) the aroument that thev will reflect anticipations of the other econo~nic series; (ii) ~o allow for the possibility of bi-directional causality between equity returns and the underlying macroeconomy; and (iii) efficient market considerations prompt an interest in the degree to which the system can predict equity returns. The cross-correlations between all of the above series \\ere examined in order to inform the decision as to the appropriate lag length of the VAR system. It ,, as found that the majority of significant lagged relations oc.:urred at the earlier lags. In order to capture the bulk of the forecasting power available within the system. it ,,as decided to employ three lags in th_e VAR model. Thus. investors are assumed to make their (month-ahead) projections based on the most recent , alues of the economic series anal\'sed as. for example. reported in the Reserve Bank· s 011ur1c~·II' Eco110111ic Rerie1r. Despite the benefits of lon!.!.er la!.!. stru~tures. the addition of each lag con· sumes 11 de!.!.re;s of freedom due to the multivariate nawre of the model. The variable RALSI was also not included in the system as it was felt that the predictiw power of this ,ariabk would be subsumed in DLl\:Dl and DL.GOLDI. (0111.:crns ot tractabilitv motivated the decision not to e,periment ,, ith the inclusion 'or additional economic series to aid the forecasting of the candidate factors. The results of the VAR model esti· mated are presented in Table 2. . The reported F statistics indicate that the system contains statistically significant predictive po,, er regarding the furnre direction of the business c\'cle. short-term interest rate, and the money market shonage: Consistent with notions of infor· mational efficiencv. the s,·srem does 1101 successfully predict those economic s~ries r~presentin!.!. (or containing in their construction) market prices (DLINDI. DLGOLDI. DR150. S.AfrJ Bus.Manage.2000.31( I) Table 2 Vector autoregression results Panel A: Dependent variable DLAE Mean of dependent var: 0.008 Stnd dev. of dependent var: 0.022 Stnd error of regression: 0.019 Panel B: Dependent variable DUE Mean of dependent var: 0.009 Stnd dev. of dependent var: 0.025 Stnd error of regression: 0.021 Panel C: Dependent variable DLGE Mean of dependent var: 0.002 Stnd dev. of dependent var: 0.037 Stnd error of regression: 0.030 Panel D: Dependent variable DUNDI Mean of dependent var: 0.018 Stnd dev. of dependent var: 0.055 Stnd error of regression: 0.055 Panel E: Dependent variable DLGOLDI l\kan of dependent var: 0.006 Stnd dev. of dependent var: 0.095 Stnd error of regression: 0.095 Panel F: Dependent variable DR 150 Mean of dependent var: 0.000 Stnd dev. of dependent var: 0.005 Stnd error of regression: 0.005 Panel G: Dependent variable DLRBAS Mean of dependent var: -0.001 Stnd dev. of dependent var: 0.005 Stnd error of regression: 0.004 Panel H: Dependent variable DLGFX Mean of dependent var: 0.008 Stnd dev. of dependent var: 0.08 Stnd error of regression: 0.08 Panel I: Dependent variable DLMMS Mean of depcndcnt var: 0.003 Stnd dcv. of depcndcnt var: 0.426 Stnd error of regression: 0.395 Panel J: Depcndent variable DLGOLR Mean of depcndcnt var: 0.007 Stnd dev. of dependent var: 0.046 Stnd error of regression: 0.046 R squared: 0.4 7 Adjusted R squared: 0.30 Log likelihood: 322.39 R squared: 0. 48 Adjusted R squared: 0.31 Log likelihood: 310.06 R squared: 0.51 Adjusted R squared: 0.34 Log likelihood: 267.86 R squared: 0.26 Adjusted R squared: 0.01 Log likelihood: 195.35 R squared: 0.25 Adjusted R squared: 0.00 Log likelihood: 129:56 R squared: 0.30 Adjusted R squared: 0.07 Log likelihood: 495.30 R squared: 0.51 Adjusted R squared: 0.34 Log likelihood: 498.18 R squared: 0.30 Adjusted R squared: 0.06 Log likelihood: 154 .. 59 R squared: 0.36 Adjusted R squared: 0.14 Log likelihood:- 40.82 R squared: 0.24 Adjusted R squared: -0.02 Log likelihood: 215.54 (p values of F statistics significant at the 95% level are in hold) F statistic: 2.68 Proh (F): 0.00 D.W. statistic 1.88 F statistic: 2. 76 Proh (F): 0.00 D.W. statistic U16 F statistic: 3.06 Prob (F): 0.00 D.W. statistic: 1114 F statistic I 02 Prnh (F): 0.45 D.W. statistic: 1.88 F statistic:0.99 l'roh (F): 0.50 D.W. statistic 2.00 F statistic 1.28 Proh(F)018 D.W statistic 1.99 F statistic: 3.06 Proh (F): 0.00 D.W. statistic: 1.99 F statistic: 1.27 Proh (F): 0 19 D. W. statistic: 1.97 F statistic: 1.64 Proh ( Fl 0.04 D.W. statistic: 2.00 F statistic: 0 94 Pnih (F): 0.% D W. statistic: 1.92 construction) market prices (DLINDI, DLGOLDI. DR150, DLGFX and DLGOLR). The fact that the standard error of each of these series is identical to the standard error of the residual of its forecasting equation (rounded to three places) clearly confirms this inference. In these cases the mean of the dependent variable is its optimal forecast value. The multi-equation residuals were taken as estimates of unexpected movements in the candidate series and prefixed by a · U'. All were found to be characterised by a mean value of zero. Ljung-Box stat1st1cs conducted over 12 lags also found all of these series to be void of autocorrelation. with the exception ofUDLGOLR. The correllogram of the latter series revealed significant ti fth and sixth order autocorrelation and partial autocorrelation. As a result. UDLGOLR was regressed on values of itself lagged by five and six periods and the residuals of this model were taken as revised values of this factor. The international series DLDJ (which was not included in the VAR model) was found to be void of autocor- .,h S ;\frJ.Bus.Man,1gc.2000Jl(ll Table 3 Correlation matrix: candidate factors (1985-1995) lDL\E LDLIE l'DLGE lJDLDJ DI .. \I SI 0.20 0.13 0.13 0.41 l>U'I.DI 0.06 --0.02 0.08 0.54 DL<iOLDI 0.20 0.23 0.14 007 I DI II 0.58 IDI !ii 0.35 0.10 II.DJ 0.03 ~)05 0.01 I DRB \S 0.08 0.20 0.11 --0.06 I DR 1,11 --0.16 ~) 13 --0.13 --0 06 I DU,F\ 0.03 0.06 0.03 0.01 I DI \I\IS 0 12 11.15 0.09 0.10 DIJ,<>1.R 11.24 0.30 0.18 --0.17 (n.:latinnships significant at the 95% level are in bold) relation over 12 lags consistent with Fama ( 1970) 'weak form· market efficiency. The mean value of DLDJ over the sample period was, thus, subtracted from its realised values to derive a proxy for unexpected movements in this variable.The correlations of the candidate factors estimated in the manner described above both with each other and with DLA LSI. DLINDI and DLGOLDI are reported in Table 3. The upper portion of Table 3 presents the correlations of each of the candidate factors derived above with returns on the major sectoral equity indices. As the variables UDRBAS and UDL\1MS were not found to have significant relations with the time series of equity returns over the sample period, they were omitted from further analysis. All of the correlations observed have signs consistent with those implied by the dividend discount model of equity valuation. The lower portion of Table 3 tabulates the correlations of the candidate explanatory variables with each other. Due to the close relation between UDLAE and UDLGE. only the former was retained for cross-sectional testing. The most pronounced cases of multicollinearity between the candidate factors exist between UDLGOLR and UDLGFX and between UDLGOLR and UDLAE. The variables UDLGFX and UDLAE also share significant correlations with UDR 150 explaining the dilution of their ceteris paribus influence in the multiple regression model presented in Panel A of Table 4 in the following section. Factor analytic augmentation revisited Van Renshurg ( 1997) points out that the assumption that E(F:.,£") = 0 for all i-ctc- /. which underlies all linear factor models. i~ likely to be violated in those specifications of the JSE return generating process that employ prespecified macroeconomic series as explanatory forces in the manner of Chen. Roll & Ross ( 1986).'' A factor analytic augmentation to the prespecified variable approach is suggested. The rationale underlying this procedure can be presented as follows: assume that we have (mis)specified the following return generating process: llDRBAS UDR 150 l iDL<iFX ! l[)LMMS l 'DUiOLR 0.01 --0.23 0.IH 0.02 0.23 --0 06 --0.18 0.17 -0 01 -0 01 -0.06 --0.15 0.17 -001 0.37 0.36 0.05 --0.10 0.11 --0.18 ~J.08 0.15 --0.03 0.25 ~)04 ( i R =a+'bj+r. JI I ~ l}:.J.:I II (3) i:" J where: E(E,.£ 11 ) *- 0 for all i ~ j. The resulting contemporaneous correlation of residuals across shares can be thought of as being generated by the following process: (4) where: f\, = the principal factor score of factor h at time t b,h = the factor loading of asset i to factor h ~ .. = the residual error at time t. where E(.;".; 11 ) = 0 for all i :it j. Seen in this light. the specification error associated with (3) can be seen as a problem resulting from the omission of relevant explanatory variables. A natural solution is to substitute (4) into (3) and to estimate the resulting model: <i H R,, = a,+ L bi: 11 1, 111 + L h, 1/•,,,+;,, (5) i: -I I, 0 I Fortunately, the nature of the problem ( E( E,,£ 11 ) :it O for all # )) is such that its factor analytic identification and incorporation within the model allows not only its solution but also reveals potentially important information regarding the return generating process underlying the security. Information regarding the comovement of securities returns. which was previously relegated to the error term of the LFM. is explicitly utilised (as manifested in a set of factor scores) as a contributory explanatory force in the LFM. The properties of the est_i· mators in the underspecified model 3 are discussed 111 Gujarati ( 1988: 403-404) and are derived in Kmenta ( 1990: 443-446): (i) The estimator of a, will be unbiased as the mean value of //~ 1*/ = 0, for each g = /. .0. (ii) The estimators of h,l will be unbiased assuming that E(fs,r.,J = 0, for each g = I ..... 0. s.Afr . .l.Aus.Managc.2000.31( I) (iii)The variance of the estimators of both a, and b,g will be upwardly biased as cr,>cr,. As a result, prior South African research employing prespecified macroeconomic variahles to explain ./SE returns has overly tended to accept the null hypothesis ol no relation being present between the series investigated and ./SE returns.' This malady is avoided by using the two residual market factor approach outlined below which can be viewed as an econometric correction for omitted variable bias. Following the findings of Yan Rensburg & Slaney (1997), reviewed earlier in the article. returns realised on the JSE Industrial and All-Gold Indices are employed as convenient observable proxies for the first two factor analytically extracted factors. Accordingly, two ·residual market factors' are estimated using the residuals of ordinary least squares and included in the analysis reported in Table 4: DLGOLDI, = a, .. ,,, -r l\ .. uLDLAE, + b,.,,_,UDLDJ, + h., ... C'DR/501 -r !\.,"UDLGFX, +b, .. ,, DLGOLR,+r,,.,,, where: Ui, = r,""" = the 'All-Gold' residual market/actor. Dl!.\'DI, -- a.,.,,10 + b .... 11UDLAE, + b.,,J:UDLDJ, T h .... , LDR 150, + h, .. .i,UDLGFX, -rh,,,,,, UDLGOLR,+r,,,,J, where: L:I, - 1:,,,, 11 = the "Industrial· residual market.factor. Table 4 compares the results when the · All-Gold' and 'Industrial' residual market factors are included as explanatory .17 forces when describing the return generating process on the JSE All-Share Index. It is evident that, while the coefficent estimates of the underspecifed model in panel A are identical to those estimated in the augmented model reported in panel B, the standard are smaller in the latter case errors (and consequently the t statistics are larger). As a result, the ceteris paribus influences of DLAE and UDLGFX now pass tests of statistical significance at the 5% level. Had this augmentation not been conducted. the resulting estimation bias would mislead the researcher into inferring that these variables do not contribute to explaining the time-series of equity returns. Further. the large t statistics associated with UG and Ul and the surge in ad_iusted R · from 0.26 to 0.90 when these factors are included in the model, confirm the relevance of this adjustment when employing macroeconomic forces to describe the return generating process operational on the JSE. Table 5 reports the results when the series UDLINDI and UDLGOLDI are employed as explanatory variables instead ofthe residual market factors Ul and UG. UDLINDI and UDLGOLDI respectively represent deviations of DLINDI and DLGOLDI from their mean values and Ljung Box statistics indicate that both of the series arc void of serial correlation up to twelve lags. Unlike the residual market factors. UI and UG. these variables represent the entire variation in the Industrial and All-Gold Indices without controlling for the influence of the prespecified macrovariables. Table 4 Multiple regression results (dependent variable: DLALSI) Panel A: Linear factor model results Variable Coefficient c 0.019 LDI.AI: 0336 l DI.DJ 0.510 l DRI 50 -2.871 LDI.CilX ()094 LDl.(iOI.R 0.371 \kan "r <leren<lcnt \ar O 017 ',tnd <le\ of dercmknt var O 056 ',tn<l emir of regrcs,inn 11 (J:,(J Standard error 0 005 0285 (J 102 I 182 0 071 () 130 R ,quarcd O 29 Adjusted R ,quarc<l 0.26 l.og likelihood 191 14 t-,tatistic 4 074 1.178 5 002 -2.428 1.336 2.863 Panel B: · Aurmcnte<l· linear factor model result, Variahlc (_ Pefticient (_ 0.019 l DI. \L 0.33(, l DI.DJ 0.510 l DRI 50 -2.871 1·Du,1x 0.094 l DI.CiOI.R 0.371 l Ci U.317 l I 0.666 \lean ,,f Jeren<lcnt \ar O OJ., 'imd <le\ ,,f <lert:ndent \ ar o 056 ',tnd error ,,r regression: 0.02 Standard error O 002 (J I 05 () 038 (J 437 0.026 () 048 0 020 (J 039 R ,quar,:d 0.91 ..\dju,te<l R ,quarcd O 90 Log likelihood 310 65 !·statistic 11.026 3.189 13.535 -6.570 3.615 7.746 15461 16.988 2-tail ,ignilicance 0.000 0 241 0.000 0.017 (JI 84 0.005 I ,tati.,tic 'U4 Prop (I·) 0.00 I) \\ ,tati,tic I 97 2-tail ,ignilicance 0.000 0.002 0.000 0.000 0.001 0.000 0.000 0.000 F ,tati,tic 151 16 Pror (I·) 0.00 I) W ,tati,tic 1.97 (coefticients and r \aluc, nft and F ,tatistics ,ignilicant at the 95% lc\el an: in hold) SAld.Bus.ManagdOOOJl{I) Table 5 Multiple regression results (dependent variable: DLALSI) Economic forces and the two index model Variable Coefficient Standard error !-statistic 2-tail signitkancc (' 0.018 0.002 10.924 0.0000 lJDI.AE 0 178 0.103 1.732 0.0860 IJl)L()J 0.055 0.043 1.281 0.4174 UDR 150 -0.476 0.432 -1.102 0173 l 11)1.( iFX -0 021 0.026 -0 814 0.417 lJDl.<iOLR ().()23 0.050 0.468 O.MI lJ DI.< iOLDI 0.321 0.020 16.170 0.0000 lJDI.INDI 0.<,59 0.038 17.3 35 0.0000 Mean of dependent var: 0.017 R squared: 0 91 F statistic: I 65. 77 Stnd dcv. of dependent var: 0.056 Adjusted R squared: 0.90 Prop (F) 0.00 Stnd error of regression: 0.02 Log likelih01.Jd: 314.48 D.W. statistic: 1.97 (weflicients and p values oft and F statistics significant at the 95% level arc in hold) The t statistics of the coefficients reported in Table 5 indicate that none of the macrovariables offer a marginal contribution to the two index model (using only returns on the JSE Industrial and All-Gold Indices as explanatory variables) that is significant at the 95% level of confidence. A test for omitted variables with F statistic of 1.526 with a p value of 0.188 confirms that the cumulative contribution of the macrovariables is not significant at conventional levels. Thus. the important result can be inferred that the 111·0 mdex model proposed hr I ·un Re11sh11rg & Slaney ( I 99 7J s11h.rn111es the infl11- ,·11n· o/the other 111acroecono111ic 1·ariables and. in this sense. of/as u 11ur1i1111111io11s represelllation ol the i11/!11e11ce ol eco110111ic /orc,·s 011 .!SE listed shares. Cross-sectional analysis The defining characteristic of a priced factor is that it explains the cross-seer ion of expected returns or. equivalently. that it is associarcd \\ irh a non-zero risk premium. The cross-sectional analysis is conducted using the iterated non-linear seemingly unrelared regression (ITNLSUR) methodology. In this model the sensiti\ ity coefficients (h,,s) for each share in the sample and the risl-. premia (A.,s) associated with each factor k are measured simultaneously. Those factors associated with statisticall~ significant risk premia are identified as being priced. The motivation for adopting this more powerft(I methodolog~ o\'er the two-step Fama-Mac Beth ( 1973) technique used by Chen. Roi I & Ross ( 1986) and Page ( 1986) is outlined by McElroy & Burmeister (1988: 32-33): ( i) Incorporating seemingly unrelated regression techniques into the non-linear regression allows across-equation restrictions to be specified which are the exact pricing restrictions postulated by the APT m('del . (ii) There is no need to partition the assets into portfolios in order to c1void the ·errors in the variables· problem.' This procedure consumes a large number of degrees of freedom. considerably diminishing the power of the crosssectional analysis. For South African researchers this is a serious practical problem due the relative Iv smal I size of JSE share sample<,. Further. both Campb~II ( 1979) and Chen. Roll & Ross (1986) find that the (essentially arbitrary) criteria under which the portfolios are formed meaningfully impact on the results of the cross-sectional analysis. (iii) The NLSUR procedure is robust with respect to the nonnormality of the distribution of asset returns and factor values. Even in the absence of normally distributed error terms. the estimates obtained through this technique ll'ill be strongly consistent. asymptotically normally distributed and able to be utilised in standard hypothesis testing. (iv) If it is the case that the error terms are normal I~ distributed then iterating on the contemporaneous covariance matrix (ITNLSUR) provides full information ma,imumlikelihood estimators. The following system was initially estimated using the ITNLSUR technique: " " I?,, - R,, = L b,1,i-1, -L h,1,/1,, - 1:,, k O I k /<ir i = I . ... 11 and t = I. T where: R,, = realised returns on asset i in time period t R,i = the risk free rate of return at time t b,, = the sensitivity of asset i to factor k ),, = the risk premium associated\\ ith factor k (6) [., = the unexpected 1110\'ement in factor k c11 time t E,, = the error term for asset i at time t Equation 6 may be written in matrix notation as: " P, L (i .• ,, - j~)h,1, - i:, k -I where: p, = ( R , - R, ..... R, - R., )' for i = I .... n fork= I. ... K E, =(£, 1 ••••• E1 )' fori~ 1. ... 11 and tT is a T dimensional column wctor of ones. Using the Kronecker or direct product operator. '.S. this S) ,- tem may be condensed as :