# MULTI-FACTOR MARKET MODELS IN THE SOUTH AFRICAN STOCK MARKET

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1. Abstract This study examines the performance of the CAPM, the three-factor model, the four-factor model and their liquidity adjusted variants in explaining realised returns, and also investigates the importance of higher moments in the African market using the Basic Materials Index in South Africa. The liquidity adjusted four-factor model performs best in explaining realised returns; however book-to-market value factor was found to be insignificant. Beta was consistently significant for all the models along with size, momentum and liquidity, however, unlike popular findings in the developed markets, large stocks were found to outperform small stocks and liquid stocks were found to outperform illiquid stocks. Including a dummy for the financial crisis changed some of the results significantly indicating the importance of model stability and the need to account for structural breaks/time variation. The two higher moment factors were also found to be important in pricing South African Stocks. However, when the higher-order moments are included in the liquidity augmented four-factor model, the alpha term becomes significant. 2

2. Introduction The notion of risk has been proved to differ between emerging and developed markets as identified in Dey (2005), and has to be accounted for in any asset pricing analysis as Lischewski and Voronkova (2012) point out. This difference has become even more important due to the poor performance of the single factor pricing model, especially in emerging markets, as stated in Hearn and Piesse (2009). This is also highlighted in Collins and Abrahamson (2006) who identify the poor performance of one-factor relationships in modelling industry sector time series within a variety of African markets. To highlight the possible difference in the notion of risk within the emerging and developed markets, we contrast the structure of the South African stock market (the South African All share index – JASIN) and that of the UK’s FTSE 100 and the US’s S&P 500 index, as highlighted in section 3. This paper contributes to the growing literature on stock return predictability in African market by investigating the basic Sharpe-Lintner CAPM, the three-factor Fama-French (1993) model, the four-factor Carhart (1997) model and the importance of liquidity in explaining the cross-section of asset returns in the South African stock market. It also investigates the question of whether higher moments have any explanatory power by incorporating the skewness and kurtosis into a liquidity augmented four-factor model. We find that the African market seems to be unique, as that beta, size, momentum, liquidity, skewness 3

and kurtosis are priced in the South African Basic Materials Index while, value was found to be insignificant. The rest of the paper is organized as follows. Section 3 evaluates the structure of the South African stock market while, Section 4 examines the key theoretical issues in the area. Section 5 and 6 analyses the liquidity measure and higher-moment CAPM respectively. In section 7, the sample and the data are described while section 8, assesses the models to be used and also analyses some descriptive statistics. The empirical findings are analysed in section 9. Section 10 summarises and concludes the paper. 3. The Structure of the South African stock market Fig 1a, 1b and 1c below shows the returns structure of the FTSE100, the S&P500 and the South African stock market (JASIN). It is clear that the structure of the FTSE 100 and the S&P 500 are quite similar, with spikes to both the upside and the downside in the fourth quarter of 2008, due to the recession. The spikes to the downside resulted in a highest negative weekly returns of about 23.5% for the FTSE 100 and 20% for the S&P 500, while the spikes to the upside saw weekly return peak at about 12.7% and 11.4% respectively for the FTSE 100 and the S&P 500. On the contrary, the South African All share index – JASIN had spikes in weekly returns of 8.8% and 12.8% to the downside and upside respectively, in the fourth quarter of 2008. Fig 2a, 2b and 2c identifies some interesting characteristics of these different markets using the 30 day moving average standard deviation of 4

the weekly returns. The structure of the standard deviations for the FTSE 100 and the S&P 500 are fairly similar with a negative intercept and a positive slope within the time period shown on the graph. This differs from the structure of the standard deviation of the JASIN which had a positive intercept and a negative slope. Also, within the recessionary period, the standard deviations for FTSE 100 and the S&P 500 peaked at about 7% and 6.8% respectively, while that of the JASIN peaked at about 4.8%. 0.15 0.1 0.05 0 FTSE -0.05 -0.1 -0.15 -0.2 -0.25 2006 2007 2008 2009 2010 2011 2012 Fig 1a: Weekly stock returns for the FTSE 100 between 2006 and 2011.(Data source: Reuters Eikon) 5

0.15 0.1 0.05 0 SPX -0.05 -0.1 -0.15 -0.2 -0.25 2006 2007 2008 2009 2010 2011 2012 Fig 1b: Weekly stock returns for S&P500 between 2006 and 2011.(Data source: Reuters Eikon) 0.15 0.1 JASIN_mkt 0.05 0 -0.05 -0.1 2006 2007 2008 2009 2010 2011 2012 Fig 1c: Weekly stock returns for the South African All Share Index (JASIN) between 2006 and 2011.(Data source: Reuters Eikon) 6

0.08 Y = -2.12 + 0.00107X 0.07 0.06 FTSE_SD 0.05 0.04 0.03 0.02 0.01 2007 2008 2009 2010 2011 2012 Fig 2a:The time series plot of 30-day moving average standard deviation of the weekly returns for the FTSE100from 2006 to 2011 (Data source: Reuters Eikon) 0.07 Y = -3.34 + 0.00168X 0.06 0.05 SPX_SD 0.04 0.03 0.02 0.01 2007 2008 2009 2010 2011 2012 Fig 2b: The time series plot of 30-day moving average standard deviation of the weekly returns for the S&P500from 2006 to 2011 (Data source: Reuters Eikon) 7

0.05 Y = 1.39 - 0.000679X 0.045 0.04 0.035 JASIN_SD 0.03 0.025 0.02 0.015 0.01 2007 2008 2009 2010 2011 2012 Fig 2c: The time series plot of 30-day moving average standard deviation of the weekly returns for South Africa’s All Share Index from 2006 to 2011 (Data source: Reuters Eikon) Mean Median Std. Dev. Skewness Ex. kurtosis FTSE 100 -0.000038513 0.001455 0.031195 -1.3827 11.808 S&P 500 -0.000010413 0.000655 0.030654 -0.85067 6.6565 JASIN 0.0025718 0.003827 0.025874 -0.13707 2.2417 Table 1: Summary statistics using weekly returns from 06/01/2006 to 02/12/2011for the FTSE 100, S&P 500 and the South Africa’s All Share Index(JASIN) (Data source: Reuters Eikon) Table 1, also shows a difference between the developed markets and the South African market, with the JASIN displaying a low negative skewness and lower kurtosis compared to the FTSE 100 and the S&P 500. Fig 3a and 3b shows the weekly volume of trade for the FTSE 100 and the JASIN. The FTSE 100 had periods of high volume up until late 2009 from where it had a continuous downward trend. On the contrary, the JASIN had a very volatile weekly trade volume throughout the 8

sample period. Perhaps, the most visible difference in the structure of these markets is highlighted in fig 4, which shows the bid-ask spread for British American Tobacco listed on the London stock exchange (BATS_L) and the bid-ask spread of British American Tobacco listed on the Johannesburg stock exchange (BTIJ_L). These are calculated using , as identified in Hearn and Piesse (2009). It is quite clear that BTIJ_L has higher spreads than BATS_L through the period. This demonstrates the possible existence of different systematic factors that affect securities in these markets, which will also affect pricing. The difference in the bid-ask spread highlights the presence of severe illiquidity within the African market. As suggested in Hearn and Piesse (2009), this severe illiquidity suggests a high degree of price rigidity which will lower both variance and covariance, adding a significant bias in betas or their proxies in CAPM type pricing models. 9

90000 80000 70000 60000 Volume_FTSE 50000 40000 30000 20000 10000 0 2006 2007 2008 2009 2010 2011 2012 Fig 3a: Weekly volume for FTSE100 between 2006 and 2011.(Data source: Reuters Eikon). No volume data for the S&P500 was available on Reuters Eikon 1.2e+007 1e+007 8e+006 Volume_JASIN 6e+006 4e+006 2e+006 0 2006 2007 2008 2009 2010 2011 2012 Fig 3b: Weekly volume for the South African All Share Index between 2006 and 2011. (Data source: Reuters Eikon) 10

0.006 BATS_L BTIJ_J 0.005 0.004 0.003 0.002 0.001 0 2009 2010 2011 2012 2013 Fig 4: Bid-ask spread for British American Tobacco listed on the London stock exchange (BATS_L) and Johannesburg stock exchange (BTIJ_L). The bid-ask spread is derived using (Data source: Reuters Eikon) This illiquidity effect is supported by Bekaert et al. (2007) who highlight the importance of liquidity in markets where both securities and investors are scarce. Lee (2011) found high liquidity risk in stocks listed in emerging markets compared to developed markets. The lack of integration of the Emerging market with the developed market as remarked in Hearn and Piesse (2009) introduces other risk factor in the pricing of assets in the emerging markets. With mixed findings on the explanatory power of the one-factor CAPM or its three-factor and four- factor counterparts, as identified in Martinez et al. (2005) and Liu (2006), the continued use of the risk-return paradigm in asset valuation has become questionable. 11

4. Key Theoretical Issues Establishing the relationship between risk and expected return has become one of the most important areas in modern finance. The expected return from rational equity markets is solely determined by the underlying risk, as established in the Capital Asset Pricing Model (CAPM), which was developed in the early 1960’s by William Sharp (1964), John Lintner (1965a, 1965b) and Jan Mossin (1966). The CAPM implies a positive linear relationship between the beta of a security and the expected return, which means that higher beta securities will demand higher expected returns while lower beta securities will only demand lower expected returns, as disclosed in Sharp, Alexander and Bailey (1999). In the 1970’s a number of authors questioned the relationship established in the CAPM with Miller and Scholes (1972) and Black, Jensen and Scholes (1972) examining stocks in the US between 1937 and 1965. They found that low beta stocks did better than the CAPM predicts, while high beta stocks performed worse. They however still insist that there is a systematic relationship between risk and return. This is also supported by Black (1972) and Fama and MacBeth (1973). However, Roll (1977) insists that the relationship between beta and realized return could remain linear if the market portfolio proxy is mean- variance efficient. This implies that if the proxy for the market portfolio is not efficient, the relationship could not be linear. He argues that the CAPM may not be testable since the linearity test does not indicate whether the market portfolio used is mean-variance efficient. 12

Many other studies after the 1970’s have highlighted deviations from the linear risk-return trade-off established in the CAPM, with some authors revealing that these deviations are explained by other variables such as size, as in Banz (1981), earnings yield, as in Basu (1983), book- value-to-equity ratio, as in Chan et al. (1991)and Rosenberg et al. (1985), leverage in Bhandari (1988), industrial structure in Roll (1992), historical sales growth in Davis (1994) and Lakonishok et al. (1994), annual asset growth rate in Cooper et al. (2008), growth rate of industrial production in Liu and Zhang (2008), cash flow in Chan et al. (1991), dividend yield in Black and Scholes (1974) and Chu (1997), volume in Amihud and Mendelson (1991), liquidity in Pastor and Stambaugh (2003), Correia and Uliana (2004), Martinez et al. (2005) and Hearn and Piesse (2009) and political risk in Mishra and O’Brian (2005). Perhaps the most popular extensions of the CAPM comes from Fama and French (1992, 1996), through the three factor CAPM model. They found that the combination of size and book/market ratio performs best in explaining the cross-sectional variations in stock returns. More interestingly, they found that when these two factors are accounted for, CAPM beta becomes insignificant. Like Fama and French (1992), Banz (1981) found size (value of equity) to be negatively related to average stock returns. Stattman (1980) and Rosenberg et al. (1985) find that on average high book-to-market stocks return more than the CAPM, supporting the findings in Fama and French (1992). Another very interesting variant of the CAPM is the four-factor model of Carhart (1997) using momentum, as measured in Jegadeesh and Titman 13

(1993), within the three-factor model. According to Novy-Marx (2012), momentum trading refers to buying past winners and selling past losers. Evidence have been provided by numerous researchers on the profitability of momentum trading strategies (e.g., Griffin et al., (2003), Jegadeesh and Titman, (1993, 2001), Jagadeesh (1990), Chui et al., (2003), Rouwenhorst (1998, 1999), De Bondt and Thaler (1985)), but there still remains to be seen, a consensus on the source of these profit. Badrinath and Wahal (2002) highlight the implication of momentum trading for the Efficient Market Hypothesis by stating that it destabilizes stock prices, which is in contrast to Friedman’s (1953) argument which insists that rational speculation must stabilize asset prices. Unlike the findings in Fama and French (1992), Carhart (1997) finds beta to be significant. The importance of liquidity has also been highlighted, with Correia and Uliana (2004) and Martinez et al. (2005) pointing to the effect of size and liquidity in explaining variation in returns. Also, Pastor and Stambaugh (2003) suggest that liquidity is an important variable in asset pricing. They find that stocks with higher sensitivity to aggregate liquidity generate higher return than low sensitivity stocks. Using the theory of stochastic discount factor, Wang and Chen (2012) developed a liquidity- adjusted conditional two-moment CAPM and a liquidity-adjusted three- moment CAPM models. They found that using the liquidity-adjusted two-moment model, a security’s conditional expected return consists of the liquidity risk premium, the systematic risk premium and its conditional expected liquidity cost. 14

Within emerging markets, the importance of liquidity has been highlighted by Bekaert et al. (2007). They compared the performance of models that incorporate only risk factors against those that account for liquidity risk and find that those that account for liquidity risk outperform. As noted in Lesmond (2005), liquidity is quite difficult to define and estimate, however, Liu (2006) describe it as the ability to trade large quantities quickly at low cost with little price impact. Empirical definitions of liquidity span depth and resiliency (indirect trading costs), price impact to tightness (direct trading costs), and bid- ask spread. Other empirical studies employ other liquidity measures, like employing the concept of price impact to capture the price reaction to trading volume, as identified in Amihud (2002) and Pastor and Stanbaough (2003) and the turnover measure which captures the trading quantity dimension as detailed in Datar et al (1998). Even with the evidences provided against the CAPM, Omran (2007) insists that it still remains widely used in practice as it offers a statistical framework that allows a comprehensive analysis of the behaviour in the capital markets. However, as stated in Alagidede (2011), most tests of the CAPM are focused primarily on developed economies and the emerging markets in Asia and Latin America, with only very few in the African market, (also see Datar, Naik and Radcliffe (1998), Fiori(2000), Chordia, Subranmanyam and Anshuman (2001), Appiah-Kusi and Manyah, (2003) and Smith and Jefferis, (2005)). Recently though, there has been an increase in interest in the African stock market, primarily due to their relatively low and sometimes negative correlation with 15

developed markets and their fast economic growth, as identified in Harvey (1995) and Alagidede (2011). 5. Liquidity Measure The liquidity construct to be used follows the measure developed in Lesmond (2005), which measures trading costs directly using the bid-ask spread as identified in Jain (2002). As stated in Lesmond (2005), the most demostratable indicator of overall liquidity still remains the bid-ask quote, however, the quotes are not always available in all emerging and African markets and for all time periods. For the South African basic material index, the bid-ask quotes required are all available. The weekly quoted spread used is defined as The bid-ask spread is calculated using the average of the available weekly quotes; and the average bid-ask spread for a 6-weekly period is used for the estimation of the spread. This minimizes outliers and averages out the highs or lows resulting from weekly sampling. 16

6. Higher-moment CAPM Jean (1971) and Scott and Horvath (1980) argue that the higher moments of returns distribution are very important beyond the mean- variance context established by the CAPM. This also follows the findings in Kraus and Litzenberger (1976) who expanded the utility function beyond the second moment to examine the importance of skewness. Unlike the Sharpe-Lintner (standard) CAPM which implies that investors are only compensated for bearing the systematic covariance risk, Fang and Lai (1997) found that investors are compensated for bearing the systematic co-kurtosis risk, as well as the systematic covariance and co- skewness risks with higher expected returns. However the importance of co-skewness and co-kurtosis risk measures (third and fourth moment of return distribution) in supplementing the covariance risk in asset pricing remains debatable. Mandelbrot (1963) and Fama (1963) inferred that the return on stocks may have fat tails. Sears and Wei (1988) insist that ignoring the co- skewness risk may bias the estimates in tests for the risk-return trade- off. Others who explored the importance of skewness in asset pricing include Friend and Westfield (1980), Barone-Adesi (1985), Peiro (1999) and Harvey and Siddique (1999, 2000). Christie-David and Chaudhry(2001) also provide evidence for the pricing of co-kurtosis in the futures market.Huang,Shackleton and Xu(2004) show that the square and cube of the excess market return are modestly significant in explaining the size effect. Using the Bayesian framework Harvey, Liechty and Muller (2004) analyse the use of higher moments of multivariate 17

returns in portfolio selection, highlighting their importance in respect to maximising utility. Other recent studies to investigate the importance of co-skewness and co-kurtosis include Cremers, Kritzman and Page (2005), Davies, Kat and Lu (2009), Ranaldo and Favre (2005), Wang (2010), Beaulieu et al. (2010) and You and Daigler (2010). Most of the studies continue to investigate investor preference for positive skewness and kurtosis in the developed equity markets, with only a few investigating the emerging markets.Chiao, Hung and Srivastava (2003) observe that the reason for this paucity of studies may be due to the relative newness of the markets. Hartmann and Khambata (1993) highlight that emerging markets have low market capitalization, lower turnover and trading volume, small number of listed stocks, few large stocks dominating the market and high volatility. Those who investigated emerging markets include Korajczyk (1996) and Bekaert and Harvey (1997), Chunhachinda et al. (1997), Mitra and Low (1998), Eftekhari and Satchell (1999), Hwang and Satchell (1999). 18

7. Sample selection and data description The Johannesburg stock exchange represents one of the most developed stock markets in Africa, and it also has the highest market capitalization within Africa as reported in Yartey (2008). Within the Johannesburg stock exchange, the mining stocks remain the best known, however, according to Page Reyaneke (1997), the growth of the commercial and industrial sectors of the South African economy and the decline in international commodity prices have reduced their relative importance. However the mining and mining financial stock remain very important within the Johannesburg stock exchange. Our dataset consists of 31 stocks on the basic material index (.JBASM) as at September 2012. Weekly prices were collected on all 31 companies and the market index (the South African All share index – JASIN)from January 2006 to December 2011, given an observation of 310, which provides a good basis for a reasonable portfolio-sorting. Descriptive statistics of the constituents of the South African basic materials index are shown in table 2. 19

Table 2: Descriptive statistics of the constituents of the South African basic materials index, sorted in descending order of market capitalization. The data set is for the duration January 2006 and December 2011 while the market capitalization is as at 30/12/2011. (Source: Reuters Eikon database) Mkt cap on Ex. Name Avg return Std. Dev. Median Minimum Maximum Skewness 30/12/2011 kurtosis Bhp Billiton PLC 528706 0.00293 0.05553 0.00428 -0.20086 0.36204 0.69230 6.31038 Anglo American PLC 419420 0.00111 0.05888 0.00479 -0.22432 0.25744 -0.19544 2.23710 Kumba Iron Ore Ltd 167470 0.00563 0.06393 0.00746 -0.27996 0.24253 -0.58511 2.95944 Anglo American Platinum Ltd 142231 0.00066 0.06623 0.00028 -0.24590 0.21851 -0.43113 1.97386 AngloGold Ashanti Ltd 135218 0.00089 0.05509 0.00098 -0.19756 0.18566 0.04002 1.38250 Impala Platinum Holdings Ltd 107707 0.00115 0.06427 0.00479 -0.21655 0.23531 -0.40753 1.46270 Gold Fields Ltd 79678 0.00073 0.06474 -0.00135 -0.24490 0.26446 0.39276 2.69944 Exxaro Resources Ltd 61885 0.00539 0.06145 0.00167 -0.21131 0.22525 0.07145 1.37862 Harmony Gold Mining 41566 0.00100 0.07030 0.00165 -0.32816 0.28947 -0.00237 3.08861 Company Ltd African Rainbow Minerals 37201 0.00471 0.06451 0.00432 -0.27837 0.27126 -0.00461 2.69381 Ltd ArcelorMittal South Africa 30708 -0.00005 0.06166 0.00294 -0.32314 0.30979 -0.31844 5.56351 Ltd Assore Ltd 29743 0.00669 0.05127 0.00004 -0.22300 0.23639 0.09937 3.30001 Mondi PLC 21704 -0.00046 0.05439 -0.00501 -0.24535 0.21462 0.00099 2.67367 Lonmin PLC 13574 -0.00069 0.07475 0.00224 -0.42187 0.42351 -0.30919 8.49080 Sappi Ltd 12837 -0.00232 0.06180 -0.00212 -0.29826 0.29826 0.05057 4.50415 Northam Platinum Ltd 11855 0.00195 0.06716 0.00298 -0.35159 0.27397 -0.52803 3.44862 20

Mkt cap on Ex. Name Avg return Std. Dev. Median Minimum Maximum Skewness 30/12/2011 kurtosis AECI Ltd 10055 0.00141 0.03382 0.00131 -0.13665 0.11333 -0.25225 1.16662 Royal Bafokeng Platinum Ltd 9164 -0.00391 0.02797 -0.00382 -0.07432 0.07657 0.40357 0.65733 Mondi Ltd 7099 -0.00025 0.05246 -0.00436 -0.26260 0.22306 0.05967 3.70797 Palabora Mining Company 6707 0.00329 0.07059 0.00000 -0.34183 0.26570 -0.42848 3.89433 Ltd Omnia Holdings Ltd 5908 0.00292 0.04226 0.00092 -0.19062 0.21981 0.13099 5.35885 African Oxygen Ltd 5599 -0.00149 0.03396 0.00000 -0.11352 0.08224 -0.36353 0.53311 Coal of Africa Ltd 5100 0.00384 0.09938 -0.00159 -0.42640 0.36624 0.28959 1.92292 Hulamin 2692 -0.00588 0.05206 -0.00479 -0.16508 0.16998 0.08724 0.90580 Pan African Resources PLC 2579 0.00213 0.09470 0.00000 -0.32850 0.62713 1.81525 13.29770 Wesizwe Platinum Ltd 2360 -0.00205 0.09060 -0.00883 -0.28518 0.57793 1.42094 8.14600 Merafe Resources Ltd 2319 0.00143 0.07471 0.00000 -0.33178 0.31131 -0.42862 2.80934 DRDGOLD Ltd 1792 -0.00153 0.08191 -0.00914 -0.32622 0.29195 0.20704 1.63019 Petmin Ltd 1471 0.00333 0.06112 0.00000 -0.26826 0.23245 -0.17388 3.61735 Sentula Mining Ltd 1144 -0.00208 0.07814 0.00000 -0.76547 0.30932 -2.93272 29.99020 Argent Industrial Ltd 598 -0.00199 0.04448 0.00000 -0.17327 0.19832 -0.38220 2.66786 21

Other data on bid-ask spread, size (market capitalization) and book-to- market value were collected from Reuter’s Eikon database. The formulation of the size and book-to-market portfolios followed the process detailed in Fama and French (1993). Carhart (1997) developed the 4-factor model using the 3-factor model of Fama and French (1993) and an additional factor capturing Jegadeesh and Titman’s (1993) momentum anomaly. The process detailed in Carhart (1997) was used to form the momentum portfolio, while the liquidity portfolio was based on the bid-ask and commission cost measure in Lesmond (2005). The risk free rate was estimated using the South African 3 Month Benchmark (ZAR) divided by 52 to obtain the weekly short term rate, as identified in Omran (2007). This represents the risk free rate adjusted to take account of weekly excess returns rather than the quoted equivalent annualised rates. 8. Empirical models This study expands the CAPM framework by modifying the model to take account of size, book-to-market value, momentum and liquidity that offer improved performance in capturing anomalies across the cross section of stock returns. Thus, in addition to market excess returns, the model is augmented by the excess returns attributed to size (SMB), book-to-market value (HML), momentum (WML) and illiquidity (IMV). However, to investigate the diverse factors on asset pricing I employ a 22

stepwise approach using six alternative pricing models. I start off with the estimation of the standard CAPM: This model will then be extended by the SMB and HML factors to become the Fama-French 3-factor model: The third model follows the Carhart 4-factor model: This allows an investigation of whether size, book-to-market value and momentum are priced factors on the South African stock market. These models are extended further to test for the importance of liquidity by the IMV-factor in the time-series regression: 23

I construct my 5-factor model using Carhart (1997) 4-factor model and the additional factor capturing liquidity. This 5-factor model is consistent with a model of market equilibrium with five risk factors. Hence, performance will be estimated relative to the 5-factor models as where , , , , are expected premiums and the factor sensitivities or loading, , , , and , are the slopes in the time-series regression, is a random shock distributed IN(0, ) As identified in Barberis (2000), parameters of these models are typically estimated with considerable uncertainty and according to Pettenuzzo and Timmermann (2005), one aspect that receives less attention is model instability. This supports the long lasting view in finance which suggests that the probability of return distribution changes over time, leading practitioners and academics to rely on more recent data, as identified in Pastor and Stambaugh (2001). Pettenuzzo and Timmermann (2005) relate this change to ‘‘structural breaks’’. Stock and Watson (1996) highlight that structural instability affects most finance and macroeconomic variables and some of the causes include changes to tax 24

policy or monetary targets, financial crisis and other large shocks to the economy and technological, legislative and institutional changes. To Account for the effect of the financial crisis, a variant of the models with dummy for the period 18/05/2008 to 08/03/2009 (as shown in fig. 5) will be used. 36000 34000 32000 30000 28000 Price (Close) 26000 24000 22000 20000 18000 16000 14000 2006 2007 2008 2009 2010 2011 2012 Fig 5: Daily closing price for the Johannesburg Stock Exchange All Share Industrials Index from 02/01/2007 to 31/12/2010 The intercept, , in Eqs. 2 – 8 is the risk-adjusted return of asset relative to the factors in the model. If the model explains asset returns, the intercept in Eqs. 2 – 8 should not be significantly different from zero. The size, book-to-market value, momentum and liquidity factors used in the CAPM are formed from the South African basic material index and sorted into portfolios with rebalancing undertaken in January and July 25

each year, between 2005 and 2011. All stocks are held for a further 6 months before rebalancing. The market portfolio is the mean of the cross section of total return on the South African All Share Index. The South African basic material index is first sorted by each stocks market capitalization into a small, medium and big portfolio which is further sorted into another three portfolios based on the book-to-market value measure. The stocks within the portfolios were not weighted to market capitalization as Hall, Hwang and Satchell (2002) and Omran (2007) highlight that size weighted portfolios and equal weighted portfolios are proxies of each other. Following Fama and French (1993), the size factor is formed from a cross-section mean return of the small-size portfolio minus the big size portfolio and is referred to as the SMB (small minus big) factor. Also, the book-to-market value factor is formed from a cross-section mean return of high book-to-market portfolio minus the low book-to-market portfolio. Following Carhart (1997) the momentum factor is formed from a cross-section mean return of the winner portfolio minus the looser portfolio and is referred to as the WML (winner minus looser) factor. The illiquidity factor is formed from a cross-section mean return of the portfolio of illiquid stocks minus that of the very liquid stocks and is referred to as the IMV (illiquid minus very liquid) factor. Low values of the illiquidity measure indicate high liquidity whereas high values of the measure indicate high illiquidity. Table 3 below, presents selected descriptive statistics of the factors in the Carhart model and the liquidity factor portfolio return. The 26

distribution of the weekly market excess return has a positive mean of 0.00093 and is negatively skewed. This is supported by the findings in Hearn and Piesse (2009). This may be explained by the fact that the South African stock market has had very positive returns for a number of years, with a relatively short period of negative returns during the 2008 recession. This is obvious from the broadest stock exchange index, the all share index (FTSE JSE ICW) which had returns of 33%, 15%, -20%, 24%, 22%, 6% in 2006, 2007, 2008, 2009, 2010 and 2011 respectively. The moderate volatility in the market excess returns is confirmed by the standard deviation. This volatility is relatively low compared to other African stock markets due to a higher degree of integration between the South African market and the developed markets. Table 3 also presents the returns on the SMB and HML portfolios as both negative at -0.041% and -0.204% respectively. This seems to identify no presence of size (SMB) and value (HML) premiums in the South African stock market. This is quite different from the popular findings on the effect of size within asset prices as reported in Reinganum (1981),Banz (1981), Fama and French (1993), Rouwenhorst (1999) and Bauer et al., (2010). Table 3 Descriptive Statistics Minimum Maximum Mean Std. Deviation Skewness Kurtosis Statistic Statistic Statistic Statistic Statistic Statistic MKT -.08914 .12745 .0009282 .02588598 -.162 2.263 SMB -.12830 .08984 -.0004062 .02623583 -.462 2.184 HML -.09747 .06082 -.0020370 .02293070 -.566 1.760 WML -.17648 .19271 .0003655 .03636305 .089 6.018 IMV -.15708 .09067 .0026461 .02846931 -.563 3.770 27

The relevant issue is whether the size premium is still positive, and, if so, whether its magnitude is substantial, as noted in Horowitz et al. (2000a). However, Horowitz et al. (2000b) and Dimson and Marsh (1999) have identified that this size anomaly may have disappeared or even reversed over time, which is consistent with our SMB portfolio. This may be due to failure of out-of-sample tests, as is often the case with academic predictions. Blume and Stambaugh (1983) and Keim (1983) find that size has explanatory power only in January, while Horowitz et al. (2000b) even suggest that the size effect may not have really existed in the first place. Popular findings also document a value premium in average returns as in Fama and French (1992, 2000) and Ang and Chen (2007). However, Loughran (1997) provide evidence that there is no value premium among large stocks. On the other hand, Ritter and Chopra (1989) attribute the performance of value firms to the January effect only, documenting the lack of consistent book-to-market effect outside January. Using data between 1940 and 1963, Davis’ (1994) finds that book-to-market value has no explanatory power outside of January. Turning to the momentum risk premium, we observe that it is positive for the sample, conforming to the findings in Jegadeesh and Titman (1993) and Carhart (1997). Lastly, the liquidity risk premium is also positive for the sample as supported by Hearn and Piesse (2009) and Lischewski and Voronkova (2012), and has a higher magnitude than the other risk premiums. 28

Table 4 shows the correlation coefficient between the risk factors, with all but one correlation coefficient being well below 0.5. Table 4 does not detect any overly high value of the correlation coefficient that may give rise to concerns of multicollinearity problem. Table 4 Correlation Coefficients Rm-Rf SMB HML WML IMV 1.0000 -0.2489 -0.1029 0.1976 -0.1772 Rm-Rf 1.0000 0.3740 -0.2724 0.5627 SMB 1.0000 -0.1575 0.3806 HML 1.0000 0.0102 WML 1.0000 IMV Notes: Correlation Coefficients, using the observations 2006-01-01 - 2011-12-04 5% critical value (two-tailed) = 0.1114 for n = 310 Tables 2 and 3 report descriptive statistics and correlation for the market, size, book- to-market, momentum and liquidity factors, indicated by MKT, SML, HML, WML and IMV Fig 6 plots the weekly value of the market factor (MKT (Rm-Rf)), the size factor (SMB), the value factor (HML), the momentum factor (WML) and the liquidity factor (IMV), respectively. Their co-movements are observable from the plots; they however, do not seem to be perfectly correlated. 29

0.15 0.1 0.05 Rm_Rf 0 -0.05 -0.1 2006 2007 2008 2009 2010 2011 2012 0.1 0.05 0 SMB -0.05 -0.1 -0.15 2006 2007 2008 2009 2010 2011 2012 30

0.08 0.06 0.04 0.02 0 HML -0.02 -0.04 -0.06 -0.08 -0.1 2006 2007 2008 2009 2010 2011 2012 0.2 0.15 0.1 0.05 WML 0 -0.05 -0.1 -0.15 -0.2 2006 2007 2008 2009 2010 2011 2012 31

0.1 0.05 0 IMV -0.05 -0.1 -0.15 -0.2 2006 2007 2008 2009 2010 2011 2012 Fig6.Weekly values of the market factor (MKT), the size factor (SMB), the value factor (HML), the momentum factor (WML) and the liquidity factor (IMV) Following Karus and Litzenberger (1976), Homaifar and Graddy (1988) and Fang and Lai (1997), we further augment the liquidity adjusted Carhart (1997) four factor model by incorporating the systematic measures of skewness and kurtosis. This is denoted as Where the represents the systematic coskewness and is the systematic cokurtosis of asset . 32

As disclosed in Doan and Lin (2012), Systematic skewness can be defined as the co-movement between an asset’s return and the variance of the market portfolio, while systematic kurtosis refers to the co-movement between an asset’s return and the skewness of the market portfolio. As Identified in Hwang and Satchell (1999) and Chiao et al. (2003), the co- skewness and co-kurtosis measures can be expressed as (10) (11) The and are the returns of asset and the market respectively, and and are the expected returns on asset and the expected market returns respectively. This skewness and kurtosis measure follows the measures in Kraus and Litzenberger (1976) and Barone-Adesi (1985) to avoid the risk of spurious correlation between the systematic risks of the portfolio. Applying these in eqn. 9, we will be testing the importance of higher moments in capturing variations in average returns within the South African Basic Materials Index. Fig 7 shows the distribution of the returns on the index, while tables 5 and 6 show the descriptive statistics of the distribution and the correlation matrix of all the risk factors respectively. 33

12 Test statistic for normality: JBASM_RTN N(0.0017673,0.047144) Chi-square(2) = 108.720 [0.0000] 10 8 Density 6 4 2 0 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 JBASM_RTN Fig 7: Distribution of the returns on the Johannesburg stock basic material index Mean 0.0017673 Median 0.0043292 Minimum -0.1703 Maximum 0.26697 Standard deviation 0.047144 C.V. 26.675 Skewness 0.26682 Ex. kurtosis 4.2268 5% percentile -0.078185 95% percentile 0.068849 Interquartile range 0.053667 Missing obs. 0 Table 5: Descriptive statistics of the distribution of the returns on the Johannesburg stock basic material index 34

MKT SMB HML WML IMV Skew Kurt 1.0000 -0.2489 -0.1029 0.1976 -0.1772 -0.1760 -0.0035 MKT 1.0000 0.3740 -0.2724 0.5627 0.0753 -0.0949 SMB 1.0000 -0.1575 0.3806 -0.1083 -0.0603 HML 1.0000 0.0102 0.0335 -0.0059 WML 1.0000 -0.0242 -0.0661 IMV 1.0000 0.1978 Skew 1.0000 Kurt Table 6. Correlation Coefficients, using the observations 2006-01-01 - 2011-12-04. 5% critical value (two-tailed) = 0.1114 for n = 310 Table 6 shows the correlations between the explanatory variables. It does not detect any overly high value of the correlation coefficients that may give rise to any more concerns of multicollinearity problem. 9. Empirical Findings This study analyses the Sharpe-Lintner CAPM, the Fama-French three- factor model and the Carhart four-factor model, and also includes the liquidity factor within each model. It also examines the explanatory power of higher moments within the liquidity augmented four-factor model, with adjustment for the financial crisis (18/05/2008 – 08/03/2009) using a dummy variable. The objective of this approach is to investigate the role of the different risk factors in explaining asset pricing within the South African Basic Material Index. Table 71: Time series regression using equally weighted weekly contemporaneous market excess return for the CAPM, three-factor model and the four-factor model, using observations 2006-01-01:2011-12-04 (T = 310) 1 Heteroskedasticity-corrected 35

CAPM Fama-French's 3-factor Carhart's 4-factor model Coeff. performance model performance performance -0.00110871 -0.00106947 -0.000447738 (0.00197686) (0.00133890) (0.00132014) 1.16812*** 0.880607*** 0.850363*** (0.0920584) (0.0576336) (0.0591658) -0.871156*** -0.886990*** (0.0726090) (0.0696063) -0.130936* -0.0671721 (0.0667739) (0.0645737) 0.0982075* (0.0547490) 0.343294 0.632825 0.639003 Table 82: Includes a dummy for the financial crisis (18/18/2008 – 08/03/2009) Coeff. CAPM Fama-French's 3-factor Carhart's 4-factor model performance model performance performance - 0.000370028 0.000444102 0.000150700 (0.00194933) (0.00130940) (0.00130224) 1.11365*** 0.823902*** 0.804321*** (0.0849139) (0.0616621) (0.0630372) -0.856435*** -0.857975*** (0.0703026) (0.0688443) -0.115414 -0.0829898 (0.0699673) (0.0715486) 0.0846059 (0.0524252) Dummy -0.00556932 -0.0107902* -0.00772508 (0.00785363) (0.00607783) (0.00604437) 0.366900 0.614843 0.613009 Notes: The table7 (and 8) report estimated results for the standard CAPM, the Fama- French three-factor model and the Carhart four-factor model (and the models with a dummy variable) *, ** and *** indicates statistical significance of the coefficient at the 10%, 5% and 1% levels. Table 93: Time series regression using equally weighted weekly contemporaneous market excess return for the liquidity augmented CAPM, the liquidity augmented 2 Heteroskedasticity-corrected 3 Heteroskedasticity-corrected 36

three-factor model and the liquidity augmented four-factor model, using observations 2006-01-01:2011-12-04 (T = 310). CAPM Fama-French's 3-factor Carhart's 4-factor model performance Coeff. model performance performance (Liquidity (Liquidity (Liquidity adjusted) adjusted) adjusted) 0.000618477 -0.000528182 -0.000404742 (0.00176471) (0.00130670) (0.00135245) 0.893608*** 0.816498*** 0.848551*** (0.0821804) (0.0619216) (0.0587069) -0.805907*** -0.802354*** (0.0813115) (0.0802716) -0.106899 -0.0238405 (0.0703723) (0.0601097) 0.117811** (0.0507547) - -0.113758* -0.202243*** 0.668190*** (0.0786015) (0.0682193) (0.0609669) 0.458350 0.604827 0.671013 37

Table 104: Depicts table 9 but includes a dummy for the financial crisis (18/05/2008 – 08/03/2009) CAPM Fama-French's 3-factor Carhart's 4-factor model performance Coeff. model performance performance (Liquidity (Liquidity (Liquidity adjusted) adjusted) adjusted) 0.00195635 0.000732763 0.000652449 (0.00164322) (0.00126933) (0.00129212) 0.861516 *** 0.774066 *** 0.757394 *** (0.0724444) (0.0618735) (0.0612195) -0.782749 *** -0.761203*** (0.0793974) (0.0790416) -0.0947918 -0.0602946 (0.0706596) (0.0699135) 0.0986594 ** (0.0500409) -0.648042 -0.152335 ** -0.189462 *** *** (0.0736845) (0.0667771) (0.0679255) -0.0107580 -0.0103222 -0.00806636 Dummy (0.00771850) (0.00646442) (0.00603566) 0.505711 0.622405 0.637460 Notes: The table 9 (and 10) reports estimated results for the liquidity augmented standard CAPM, Fama-French three-factor model and Carhart four-factor model (and the models with a dummy variable) *, ** and *** indicates statistical significance of the coefficient at the 10%, 5% and 1% levels. 9.1. Diagnostics Classic autocorrelation and heteroscedasticity diagnostics were carried out as identified earlier. Table 6 shows the correlation coefficient among the risk factors, with all but one correlation coefficient being well below 0.5. Apart from the correlation between skewness and kurtosis, Table 6 does not detect any other overly high value of the correlation coefficient that may give rise to concerns of multicollinearity problem. On the other 4 Heteroskedasticity-corrected 38

hand, it is quite possible to eliminate or at least mitigate the problem of autocorrelation by specifying the dynamics of the model more fully i.e. by including relevant lagged variables on a time series model. However, the autocorrelation tests are carried out using Cochrane-Orcutt, Hildreth-Lu andPrais-Winsten in gretl did not indicate the presence of autocorrelation. Tests for heteroskedasticity were carried out using White’s test, Breusch-Pagan tests (See Greene, 2003) and Keonker tests. Where one or more of the tests indicated that heteroskedasticity is present in the form of an unknown function of the regressors which can be approximated by a quadratic relationship, a heteroskedasticity- corrected model within gretl is applied. This offers the possibility of consistent standard errors and more efficient parameter estimates as compared with OLS. The procedure involves (a) OLS estimation of the model of interest, followed by (b) an auxiliary regression to generate an estimate of the error variance, then finally (c) weighted least squares, using as weight, the reciprocal of the estimated variance. In the auxiliary regression (b) we regress the log of the squared residuals from the first OLS on the original regressors and their squares. The log transformation is performed to ensure that the estimated variances are non-negative. We call the fitted values from this regression u*. The weight series for the final WLS is then formed as 1/exp(u*). 39

9.2. Performance of the standard CAPM against the three- factor and the four-factor CAPM models This analysis focuses on investigating the role of different risk factors in explaining asset pricing using the standard CAPM, the Fama-French three-factor model, the Carhart four-factor model and their liquidity augmented variants. It also investigates the role of higher moments in explaining returns within the liquidity augmented four-factor model. Table7 reports the result estimation for the standard CAPM, the three- factor and the four-factor models, representing three alternative risk- specifications. The explanatory power of the model increases with additional size, book-to-market value and momentum factors. This demonstrates the improved explanatory power of the Fama-French and the Carhart models. The intercepts are negative for the respective models and continue to go closer to zero with the addition of the size, book-to-market factor and the momentum factor. However, the Jensen alpha terms, , are not statistically different from zero, indicating a good fit with established theoretical CAPM assumptions.This is also in line with Hearn and Piesse (2009) who point out that within Africa, the Jensen alpha terms , , are not statistically different from zero The importance of the size, book-to-market and momentum factors are highlighted in the of 34% for the one-factor model and an increase to 63% for the three-factor model and a further marginal increase to 64% for the four-factor model. The estimated beta for the standard CAPM is positive and significantly different from zero, indicating that the return on the South African basic material index increases when the market risk premium increases. This behaviour is expected as identified in Sharpe 40

(1964), Lintner (1965), and Sharp, Alexander and Bailey (1999). When compared to the Fama-French three-factor model, the market beta remains positive and significant but the size premium is negative and statistically significant, indicating that large firms’ outperform small firms within the South African Basic Materials Index. Hawawini and Keim (1995, 2000) and Hearn and Piesse (2009) also found this negative relationship. The negative relationship between size and returns in this study can be explained by industry specific factors. The sizes of companies in the industry vary widely as shown in table 2, with the big companies dominating the market. This reduces the revenue source for the small companies; translating into smaller profit margins compared to the large companies. According to Sadorsky (2001) the natural resources sector has remained quite volatile, complicating the business for the industry players. These complications come from the capital intensive nature of the industry as new mining projects can cost billions to build. Secondly, industry players are dealing with depleting resource base which pushed competitive advantage towards the ability to locate and extract low cost natural resources deposit to replace their depleting asset base. The products made by these companies are quite homogeneous, as product differentiation is not possible due to identical raw commodities. The best performing natural resource companies (in terms of return on investment and stock price appreciation) are generally those companies that are the lowest cost producers, and these tend to be the large companies due to economies of scale and scope. 41

Other papers which assert that the size effect disappeared after the early 1980’s include Eleswarapu and Reinganum (1993), Dichev (1998),Chan et al. (2000), Horowitz et al. (2000a,b), and Amihud (2002),while Martinez et al. (2005) presents evidence on the limited explanatory power of the Fama and French three factor model. This contradicts popular findings on the effect of size on returns, which report that small firms outperform big firms as observed in Banz(1981) and Fama and French (1992, 1996). Others who present evidence on the size effect in the United States include Reinganum (1981), Keim (1983), Brown et al. (1983)and Lamoureux and Sanger (1989). International studies which find evidence of a size effect include Heston et al. (1999), Barry et al. (2002), Chan et al. (1991) and Annaert et al. (2002). However, these studies mostly focus on the developed markets. The value beta is negative and statistically insignificant at the 10% level. This is contradictory to the findings of Fama and French (1992, 1996), who find a positive and significant relationship between book-to-market value and returns. Loughran (1997) insist that there is no consistent relationship between book-to-market value and realised return. Other authors have proffered some explanation for the value premium in Fama and French (1992, 1993), with Black (1993) suggesting that the value premium was due to data-spooning, and this is supported by MacKinaly (1995). Kothari et al. (1995) argue that value premium is due to survivorship bias, while Lakonishok et al. (1994) insist that it results from investor over-reaction. 42

9.3. The Carhart four-factor model In the Carhart four-factor model, the market beta remains positive and significant while the size discount is significant. However the interesting relationship is that there does not appear to be any value premium as the book-to-market value factor was found to be insignificant. This is consistent with the findings of Wang and Xu (2004) and Shum and Tang (2005) in the Asian market and the assertions in Gaunt (2004) using Australian data. There is a lack of empirical evidence on whether the value premium is present in emerging equity markets generally, and particularly in the emerging African stock markets, as stated in Bundoo (2008). There is also a momentum premium within the South African basic material index, with the momentum factor being positive and significant at the 10% level. This is similar to the findings in Jegadeesh and Titman’s (1993), Carhart (1997), Liew and Vassalou (2000) and L’Her, Masmoudi and Suret (2004). Momentum has also been found to be significant in the Asian market (Rouwenhorst, 1998 and Chui et al., 2000) and in the emerging markets (Rouwenhorst, 1999).However, the sources of momentum has remained contentious with Conrad and Kaul (1998) and Bulkley and Nawosah (2009) insisting that momentum is mainly explained by risk. However, Jegadeesh and Titman (2002) and Bhoota (2011) found that momentum largely results from behavioural biases. Another explanation comes from Lo and Mackinlay (1990) who suggest that the sources of momentum profits are positive serial correlation (negative cross-sectional correlation), and dispersion in unconditional 43

mean returns. This will be discussed in greater detail in relation to the African market in our future research. One interpretation of the evidence in this study comes from Hong and Stein (1999) who indicates that information which is initially private is gradually incorporated into prices. This is particularly severe in the Africa market due to relative difficulty in information circulation. Also, stocks tend to experience further drifts usually in the same direction as the direction of the original event impact. Some of these original events include earnings announcements (see Bernard, 1992), stock issues (see Spiess and Affleck-Graves (1995). Others events are detailed in Hong and Stein (1999). Lo and Mackinlay (1990) also suggest that momentum can be due to the lead-lag relationship among securities. We also found that including a dummy to account for the financial crisis from18/05/2008 to 08/03/2009 (as in table 8), does significantly change the resultsas the book-to-market value factor was found to be insignificant in the 3-factor model and momentum was found to be insignificant in the 4-factor model. This suggests that the significance of the book-to-market value and the momentum factors may have been because of the effect of the bear market resulting from the financial crisis. Hence we can identify that the financial crisis may have had a regime switching effect on the models. Indeed structural instability is known to affect many financial and macroeconomic variables as identified in Pettenuzzo and Timmermann (2005). Further studies will account for structural breaks using the univariate approach in Pastor and 44

Stambaugh (2001) and the multivariate approach in Pettenuzzo and Timmermann (2005). 9.4. Liquidity Augmented CAPM, three-factor and the four- factor models With the introduction of the liquidity factor, in table 8,the market beta, size and momentum remained significant, but the book-to-market value factor was found to be insignificant for both the three-factor and the four-factor liquidity augmented variants. This corresponds to the findings of Bundoo (2008) who highlight that there is a lack of empirical evidence of whether the value premium is present in emerging equity markets generally, and particularly in the emerging African stock markets. Hence we can conclude that accounting for beta, size, momentum and liquidity factors eliminates the relevance of the value factor in asset pricing within the African market. The liquidity factor is significant in all the models but has a negative relationship with returns, which is in contrast to the findings in Amihud and Mendelson (1986), pastor and Stambaugh (2003) and Chordia, Roll and Subrahmanyam (2000). A recent study by Lam and Tam (2011) show that liquidity continues to be an important factor even after accounting for other well-established risk factors. Lee (2011) supports this view, revealing that liquidity is priced after controlling for market risk, size and value. However, as stated in Lischewski and Voronkova (2012), a number of studies have examined the relevance of liquidity in asset pricing, producing conflicting results 45

Hearn (2011) identified that the effect of liquidity on asset pricing depends on the structure of the surveyed stock market. The study finds evidence of size and liquidity being priced in Morocco, whereas the results for other North African countries were mixed. This will seem to be the case for the liquidity discount found in this study which is somewhat related to the size discount as the larger companies tend to be the most liquid in the African market, this was evident in table 2. This could be driven by larger capital raising opportunities available to large companies in these markets, resulting from high interest of foreign investors in large stocks, lower-cost international financing and/or availability of domestic government-subsidized credit. Similar findings are reported in Claessens and Dasgupta (1995) who investigated nineteen emerging markets. They disclose that the contradictory behaviour of these emerging markets may be due to tax systems, market microstructure, improvements in market structures and the opening of markets to foreign investors.Further evidences of this negative relationship are reported in Amihud, Mendelson and Wood (1990) and Amihud (2002). The liquidity adjusted models cannot be rejected at conventional levels of confidence. Also, they fare better in term of goodness of fit, , for cross-sectional returns, and they also fare better in terms of p-values in specification tests. When the dummy variable for the financial crisis was included, see table 10, the liquidity variables remained negative and significant, while the dummies themselves remained insignificant. 46

9.5. Higher moment CAPM using the liquidity adjusted four- factor model Table 11: Heteroskedasticity-corrected, using observations 2006-01-01:2011-12-04 (T = 310) Dependent variable: Ri_Rf Coefficient Std. Error t-ratio p-value const -0.532533 0.25729 -2.0698 0.03932 ** MKT 0.793098 0.0599234 13.2352

7 6 5 4 3 Skew 2 1 0 -1 -2 -3 2006 2007 2008 2009 2010 2011 2012 Fig 8: Time series skewness of the South African basic material index. 1.01 1.005 1 Kurt 0.995 0.99 0.985 2006 2007 2008 2009 2010 2011 2012 Fig 9: Time series kurtosis of the South African basic material index. 48

Unlike our result, Hung (2008) found that skewness does not explain return variation but found kurtosis to have some explanatory power. The findings in Harvey and Siddique (2000), Errunza and Sy (2005) and Smith (2007) show some evidence that co-skewness helps to explain cross- sectional returns. Friend and Westfield (1980) investigated the explanatory power of skewness in the US security markets and found that contrary to the conclusions of Kraus and Litzenberger (1976), investors do not pay a premium for positive skewness of portfolio returns. According to DeMiguel and Nogales (2007) and Hung (2008), this may be due to parameter uncertainty resulting from the use of observed information in estimating unknown parameters and also due to unstable predictive relations and time variation as identified in Lewis (2006) and Paye and Timmermann (2006). This is supported by Bekaert et al (1998) who highlight that the skewness and kurtosis present in emerging market returns change over time. Sanchez-Torres and Sentana (1998) showed no evidence of preference for positive-skewness by investors using the Spanish stock market. Singleton and Wingender (1986) and Peiro (1999) insist that despite evidence that the co-skewness and co-kurtosis risk in asset return are priced, fundamental questions remain as to how these studies confirm the existence of higher moments of return distributions. They also point to the possibility of incorrect assumptions resulting in the observed skewness asymmetry in returns. Chiao, Hung and Srivastava (2003) question the ability of higher moments of return distribution to persist 49

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