7. PRELIMINARY ANALYSIS AND METHODOLOGY
7.3. Risk factor selection and analysis
7.3.3. Risk factor selection
Aside from being in agreement with the theory embodied by equation (4.1), the APT framework requires that risk factors have a pervasive influence upon returns (section 3.1.1, 3.2.2 & 4.2; Berry et al., 1988). This can be demonstrated by showing that there is a level of correlation between major indices and the candidate risk factors. To identify risk factors that impact returns on the South African stock market, the approach of Van Rensburg (2000) of establishing correlation between the risk factors and returns on market aggregates is adopted.
This approach is almost identical to the approach employed by Chan et al. (1985), Chen et al.
(1986) and Hamao (1988).
Candidate risk factors found to be correlated with returns on the market index are retained and used in further testing. If a risk factor is correlated with the market index, then this factor should have a pervasive influence on other indices and also individual series. This follows from the fact that the market index compromises various indices, which represent economic groupings and industries which in turn consist of individual stocks. The market index, the JSE All-Share Index, is therefore representative of the South African stock market.
Following Poon and Taylor (1991), Van Rensburg (2000) and Clare and Thomas (1994), risk factors are entered contemporaneously and with lags into the correlation matrix. Factors such as interest rates or exchange rates are known instantaneously and therefore, can be considered contemporaneously. On the other hand, measurements of factors such as inflation or industrial production are reported with a lag. For example, January’s inflation rate is announced in February, hence stock prices react to January’s inflation in February. Therefore, incorporating lags ensures that prices respond to announcements of macroeconomic factors (see Clare & Thomas, 1994). However, as Poon and Taylor (1991) and Van Rensburg (1996)
suggest, risk factors for which data is not instantaneously available may also enter into the model contemporaneously. It is however the former approach (coinciding with announcements, lags), rather than the latter approach, that is more in-line with the APT framework. The level of correlation between each risk factor and returns on the JSE All-Share Index is reported in Table 7.7.
Table 7.7: Correlation of JSE All-Share Index returns with candidate risk factors Factor
1. *** Indicates statistical significance at the 1 percent level of significance.
** Indicates statistical significance at the 5 percent level of significance.
* Indicates statistical significance at the 10 percent level of significance.
2. Correlation coefficients indicate the level of correlation over the period 1995M07-2011M03.
Source: Compiled by author
The correlation coefficients in Table 7.7 indicate that returns on the JSE All-Share Index are, as expected, positively and significantly correlated with returns on the international and
foreign indices; namely, the DJIA, UDJ , the FTSE World Index, t UFTW , the FTSE 100 t Index, UFTSE , the MSCI World Index, t UMSCIt, and the MSCI World Index in local currency (Rands), UMSCIR , and the Nikkei 225,t UNK . These indices can be interpreted as t catch-all proxies for international risk (Van Rensburg, 1996; Clare & Priestley, 1998; Kwon
& Yang, 2008).
The fist lag of the unexpected changes representative of innovations in the inflation rate,
−1
UCPIt , as well as unexpected changes in inflation expectations as measured by the bankers acceptance rate, URBASt, are both negatively and significantly correlated with market returns. Unexpected changes in industrial production, UMPt, are positively and significantly correlated with returns on the JSE All-Share Index. Another measure of real activity, the unexpected changes in the number of building plans passed, UBP , is positively and t significantly correlated with returns contemporaneously and at the first lag. The statistically significant correlation at the first lag potentially reflects the publication lag or the delayed availability of information. Returns are positively and significantly correlated with the unexpected growth rate in retail sales, USLSt, at the second lag. This statistically significant relationship also potentially reflects a publication lag or the delayed availability of information. UMPt, UBPt and USLSt are all proxies for real activity suggesting that stock prices respond positively to unexpected changes in real activity.
Whereas unexpected changes in the narrow and broad money supply (monetary aggregates), 1 t
UM A and UM3t, are positively and significantly correlated with returns at the first lag, the correlation between returns and the second lag of UM3t is statistically significant and negative. This suggests that while positive changes in the money supply may signal falling discount rates or increased real activity, increases in the broad money supply may also result in uncertainty about inflationary pressures in the future (Günsel & Çukur, 2007; Parkin et al., 2008). The correlation between short-term interest rates and long-term interest rates as measured by yields on UTBT3t, USAGB10t, USAGB30t and returns on the JSE All-Share Index is highly negative and statistically significant implying a strong discount rate effect.
Notably, although Chen et al. (1986) find that the term structure of interest rates is correlated with aggregate returns in their study, unexpected changes in the term structure of interest
rates, UDTS , as measured by the difference between long-term and short-term interest rates t are not significantly correlated with South African stock market returns.
There is a statistically significant and positive correlation between returns and growth in commodity prices; namely, the growth in the prices of oil, UOIL , metals, t UMET ,t non-fuel commodities, UNFCIt, and commodity prices in general, UCOM . Within the commodities t risk category, the level of correlation is strongest between returns and UMET . Returns and t unexpected changes in the Rand-Dollar exchange rate, UZARUSt, are negatively and significantly correlated whereas there is a positive and statistically significant contemporaneous relationship between returns and unexpected changes in the terms of trade,
UTTt. Returns on the JSE All-Share Index are positively correlated with local and foreign business cycle indicators, both leading and coincident, as denoted by statistically significant correlation between returns and ULI , t UCI , t ULTT and t UCTTt−1 respectively. This suggests that South African stock returns respond to variations in the domestic business cycle and variations in the business cycles of South Africa’s trading partners.
Factors found to be significantly correlated with returns on the JSE All-Share Index in Table 7.7 are retained and risk factors that are not significantly correlated with returns on the JSE All-Share Index are omitted from further analysis.
The (unreported) correlation matrix120 for the retained risk factors indicates that in most instances correlation coefficients are below 0.5 and therefore, the level of correlation is not large enough to result in a multicollinearity problem (Poon & Taylor, 1991). In most instances where statistically significant, the level of correlation remains well below 0.5 as in the instance of USAGB30t and UCPIt−1 where the correlation between these two factors is 0.163. However, high levels of correlation are observed between URBAS , t UTBT3t,
10t
USAGB and USAGB30t with correlation coefficients nearing 0.5 and even over 0.8 for 3t
UTBT and URBAS . As expected, t URBAS is highly correlated with the interest rate t factors as this measure of inflation expectations is itself based upon short-term interest rates (see Van Rensburg, 1996). A number of other factors are also notably correlated with each
120 The correlation matrix is not reported in-text owing to its size. It is however available from the author upon request.
other. Measures of the money supply at the first lag, UM A1 t−1 and UM3t−1, are significantly correlated. UZARUS is highly correlated with the interest rate factors, t USAGB10t and
30t
USAGB . However, the level of correlation between these factors is well below 0.5.
Commodity risk factors, UCOM , t UMET and t UNFCI , exhibit levels of correlation of over t 0.5 amongst themselves. The leading cyclical indicator for South Africa’s trading partners, ULTT , is highly correlated (correlation coefficients of around 0.5) with the international and t
foreign indices, suggesting that these indices also reflect changes in the economic climate prevailing within South Africa’s trading partners. Statistically significant correlation is observed between the domestic business cycle indicators and commodity prices. The leading domestic business cycle indicator , ULI , and coincident business cycle indicator, t UCI , are t both positively correlated with UOIL , t UCOM and t UMET suggesting that changes in t commodity prices are also indicative of future or current states of the business cycle.
Correlation between the cyclical indicators and the commodity price risk factors is well below 0.3 and usually around 0.2 and therefore, unlikely to result in multicollinearity.
Nevertheless, it is borne in mind when model building that high levels of correlation between risk factors will result in some multicollinearity which may weaken the influence of individual risk factors within a multifactor model (Chen et al., 1986; Blanchard, 1987; Van Rensburg, 2000).