MULTI-FACTOR MARKET MODELS IN THE SOUTH AFRICAN STOCK MARKET

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

                 By

          Uchenna Tony-Okeke

                                    1
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

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