2013 Cambridge Business & Economics Conference
ISBN : 9780974211428
An Assessment of APT’s Performance on Portfolios
Seetanah B, RV Sannassee, M Lamport and Cuttaree V
University of Mauritius
ABSTRACT
The objective of this paper is to explore the performance of the Arbitrage Pricing
Theory (APT) on the different portfolios quoted on the Stock Exchange of Mauritius
(SEM). Also, a general analysis is undertaken to encapsulate the overall effect of the
local stock market as well as the two major sectors of the Mauritian economy. To
account for the financial crisis, the time frame is divided into two since the stock
market is more volatile during the second period. A set of variable is employed and
an Ordinary Least Square technique is then performed to obtain the factor betas for
each model. The results are quite clear: the risk premium factor is captured in nearly
all models while the other variables display different outcomes. The findings are
similar to Rjoub, Tursoy and Gunsel (2009) as the components exhibit a spread
relationship with the stocks’ returns.
Keywords: Arbitrage Pricing Theory; Stock Exchange of Mauritius; Ordinary Least
Square; Risk premium
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INTRODUCTION
The study of asset’s returns performance is of upmost importance in corporate
finance since it has major repercussion on every facet of the financial management
decision making process. There has been a new lease of life with the materialisation
of the Arbitrage Pricing Theory (APT), formulated by Ross (1976), as a substitute
theory to the famous Capital Asset Pricing Model (CAPM) proposed by Sharp
(1964), Lintner (1965) and Mossin (1966). The APT is broader than the CAPM as it
enables the equilibrium asset’s returns to be captured by not only one factor but
several factors. Under the APT, the return of the stock can be modelled as a linear
function of several macroeconomic variables where the sensitivity of the changes in
each factor is characterised by a factor-exact beta coefficient. The multi-beta model
is only interested in factors that are non-diversifiable in nature. In fact, arbitrage
condition holds where an investor discovers dissimilarity in the asset’s returns with
the same risk. Then, one will automatically indulge in arbitrage opportunities to
fully benefit from it; however arbitrage occasions are only short term in nature.
Originally initiated by Ross (1976), the first empirical work on the APT was
however published by Gehr (1978). Later on, Roll and Ross (1980) employed a
factor analytical approach and discovered that at least three likely factors were
captured by the New York Stock Exchange. Their study was considered as an
extension of Gehr (1978) study. Yet this approach was highly criticised as
generating no meaningful interpretation while Dhrymes, Friend and Gultekin (1984)
found that the number of factors tend to increase with the number of securities in the
group. The first macroeconomic approach of the APT was propounded by Chen et
al. (1986) where they reported four significant factors (unanticipated inflation, risk
premium, term structure and industrial production) were priced in the US stock
market. Consequent studies in the UK and Spanish stocks market were undertaken
by; Martinez and Rubio (1989); Poon & Taylor (1991) respectively where they
found no valid relationship of the variables put forward by Chen et al. (1986). On
the other hand, Gunsel & Cukur (2007) adopted a portfolio analysis of firms’ quoted
on the London Stock Exchange and concluded a mix effect relationship of the
variables with the portfolios. The scattered association was also confirmed in
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another study of Rjoub, Tursoy and Gunsel (2009) on the different portfolios of the
Istanbul stock market.
To date most of the research on this topic was conducted in advanced stock markets,
thereby deserting the emerging one in developing countries. The bubble effect and
the small size market were mainly the reasons for this lack of thorough research.
Also, the mining of the factors is not an easy task when investigating the multifactor model in a particular stock market. The more research is accomplished in this
field, the greater will be the performance of the APT in identifying the correct set of
factors. The lack of research in this domain for a developing stock exchange like
Mauritius has been the driven-factor for embarking on this topic. The study will
focus mainly: on the different portfolios quoted on the SEM where companies will
form portfolios according to the most trading one; on a general approach of the
overall stock market; on the tertiary and secondary sectors. At the end of the thesis,
one will have a clear picture of how well the APT explains the different analysis.
The results will be useful to academic scholars and finance practitioners.
The financial crisis that was originated in the United States had major consequences
on the Mauritian stock market: to account for stability purposes the time frame is
divided into two. A set of hypothesised variables will be utilised where four of them
(oil price, unanticipated inflation, term structure of interest rate and risk premium)
have been used by Chen et al. (1986) and the others have been selected based on
specific criteria. First and foremost, a Principal Component Analysis will be
undertaken to have an idea of the percentage variance explained by the explanatory
variables but the reliability of the test will be determined by the Kaiser-Meyer-Olkin
measure. Thereafter, an Ordinary Least Square technique will be adopted to obtain
the factor betas. The problem of heteroskedasticity will be examined and where
necessary robust regression as suggested by Huber (1967), Eicker (1967), and White
(1980) will be employed
The structure of this paper is as follows: the next two chapters highlight the
literature review and the overview of the SEM respectively; section four produces
the research methodology and the analysis of the results while section five
underscores the conclusions.
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Related Literature
As we have signified earlier, Ross (1976) was the one who developed the Arbitrage
Pricing Theory but the first published empirical study was undertaken by Gehr
(1978). In 1980, Roll and Ross analysis was considered as an extension of Gehr
(1978) study since it was larger in scope concerning tested securities (a more
comprehensive set of data was used instead of 24 industry indices and 41 individual
stocks used by Gehr (1978) previously) and had more capability on succeeding
empirical test. In the study of Ross & Roll (1980), a factor analytical approach was
used to test the New York Stock Exchange for the periods ranging 1962 to 1972. A
five-factor structure was employed out of which three were found to be at least
present in the expected returns of the securities - both authors concluded that there
test might be quite weak.
Dhrymes, Friend and Gultekin (1984) examined the procedures used by Ross & Roll
(1980) and found some drawbacks in their study. Firstly, the number of factors
extracted seemed to increase with the number of securities in the group - “ at 5%
significance level, a group of 30 securities have at most three common risk factors,
with a group of 45 securities, four common risks factors were identified while a
group of 90 securities have at most nine common risk factors”. Secondly, they
recognized the complexity of identifying the actual number of factors characterising
the return generating process.
Chen, Roll & Ross (1986) used a different approach to obtain the factors affecting
asset returns - a macroeconomic variable model. They employed a two-stage
regression that Fama & MacBeth (1973) had used to estimate the correlation of
economic variables with stock returns. The outcome of their two-stage regression
methodology was to create time series of estimated premium for each risk factor and
the latter were then tested to see if they are different from zero. Only four variables:
industrial production, risk premium, term structure of interest rate and measure of
unanticipated inflation of changes in expected inflation were found to be significant.
The first three mentioned had a positive relationship while the last variable
commanded a negative effect on the expected stock returns. They concluded that the
stock returns are exposed to systematic economic news and they are priced in
relation with their exposures.
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Poon & Taylor (1991) examined the same variables as those of Chen, Roll & Ross
(1986) to explain the returns of the UK stock market – they concluded that the
factors did not affect the stock market return as prescribed by Chen et al. (1986).
Martinez and Rubio (1989) also analysed the Spanish stock market by using the
same macroeconomic variables and they did not find any significant relationship
between stock returns and the selected factors. They both stated that there are other
variables that affect stock returns and they even questioned the methodology used by
Chen et al. (1986). However, Hamao (1988) simulated the multi- factor framework
of Chen, Roll & Ross (1986) in the Japanese stock market and found that changes in
expected inflation, risk premium and the slope of the term structure of interest rates
positively influence Japanese stock returns.
Olli and Virtanen (1992) tested the Finnish firms quoted on the Helsinki Stock
Exchange by using monthly data ranging from 1970 to 1986. Factor analysis was
used to find systematic risks for each asset; afterwards transformation analysis was
employed where the sample was divided into three sub-periods for stability
purposes. Three very stable factors were found to be significant and these factors
were used to examine the effects on equilibrium returns. The cross-sectional
regression showed that at least two different factors were significantly greater than
zero. They also reported that factors found to be significant by the factor analysis
may not be so when performing the cross-sectional regression – they can be firm or
industry specific.
Cheng (1995) utilised a different approach to assess the UK stock market: the
canonical correlation analysis. Monthly returns of 61 securities quoted on the UK
stock exchange from 1965 to 1988 were used. Canonical correlation analysis was
employed to investigate the association between the factor scores of the set of
security returns and the set of economic indicators (the factor scores of security
returns and the factor scores of economic indicators). It is viewed as an external
factor analysis that linked economic factors and the stock market returns. While the
systematic economic forces (money supply, unemployment rate, price index)
seemed to be weakly correlated for the UK stock market, the market factor alone
represented the most positive contribution.
Robotti (2002), financial economist, conducted a research to assess the impact of
pre-identified economic and financial variables on the return trade off by analysing
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how the latter affect or predict the mean of asset’s returns. The aim of the study was
to spot the sources of economic risk that investors should track and hedge against
the commanded economic and financial risks. The returns of ten stock portfolios
listed on the NYSE, AMEX and NASDAQ for a monthly period of December 1959
to November 1996 were taken onto consideration. Macroeconomic and financial
market variables that are used to capture non-diversifiable risks of the economy are:
inflation rate, lagged stock return of NYSE-AMEX-NASDAQ, term structure,
dividend yield, real rate of interest, risk premium and consumption-aggregate wealth
ratio. The results were clear cut, the term structure and risk premium displayed a
positive and significant relationship with the stocks’ returns. These outcomes are
consistent with those of Chen, Roll, and Ross (1986) and Ferson and Harvey (1991).
At the same time the inflation rate and real rate of interest were adversely related to
the shares’ returns while the other variables showed a positive relation.
Cauchie, Hoesli & Isakov (2003) investigated on a monthly basis ranging from 1986
to 2002 the Swiss stock market using the APT framework. Both statistical and
macroeconomic methods were used in the study for the 19 industrial sector
portfolios for comparison purposes. They utilized a new method proposed by Xu
(2003), the maximum explanatory component analysis, which is a standard principal
component analysis to derive the factors. On one side, the statistical model produced
five factors while the macroeconomic model generated four variables which are
related (industrial production, changes in expected inflation, market return and term
structure) to the Swiss stock exchange. They confirmed the significance of three
variables with those of Chen et al. (1986) study in the U.S stock market.
Gunsel & Cukur (2007) undertake a portfolio approach to analyse the London Stock
Exchange for the period 1980-1993. The variables explored by the authors were:
term structure of interest rate, unanticipated inflation, unanticipated sectoral
industrial production, risk premium, exchange rate, money supply and unanticipated
sectoral dividend yield. A total of eighty-seven firms were grouped into ten different
portfolios - the firms were categorised according to their respective industries they
belong so as to account for firm size effect. The results demonstrate that the
independent variables have a significant effect on the UK Stock Exchange but the
factors tend to influence each industry in a specific way. They proclaimed that the
money supply variable has mixed effect on the different portfolios’ returns. The
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authors even compared their findings with Clare and Thomas (1994) who have not
found any association of the given factor in their model. Similarly, the exchange rate
was negatively priced for one portfolio and when lag effect of 1 month was
incorporated, a positive relationship was obtained for one industry. A similar
scenario was reproduced for the risk premium and unexpected inflation variable.
However, the oil price showed a negative relation when lag effect 2 months was
introduced in the model. Finally the term structure also exhibit a positive
relationship at 1 month lag term and a weakly negative connection at two months lag
term on the portfolios’ returns. This negative sign was also confirmed by Javid &
Ahmad (2009) on the Karachi stock exchange but no lag term was employed in their
model.
Moreover, another portfolio method as Gunsel & Cukur (2007) was undertaken to
test empirically the Istanbul Stock Exchange. Rjoub, Tursoy and Gunsel (2009) used
monthly data starting from January 2001 to September 2005 to constitute thirteen
industry portfolios for a total of 193 stocks. Six macroeconomic variables (Money
supply, real exchange rate, unemployment rate, unanticipated inflation, risk
premium, term structure) were then tested on the returns of the different industry
portfolios by using regression analysis. The factors seemed to affect each portfolio
in a particular manner ranging from a significance of 1% to 10% level respectively.
Money supply was found to have different movements on the industries’ returns.
Conversely, three variables (the term structure, unanticipated inflation and risk
premium) showed a positive effect on some of the portfolios’ returns. Burmeister
and McElroy (1988) also found a positive relationship of the unanticipated inflation
with the stocks’ returns. However, the real exchange rate and unemployment rate
were not priced in any portfolio. The authors are unanimous that the variables are
weakly correlated with the stocks returns in the Istanbul Stock Exchange even
though they may alter each industry in an another way – there are other factors left
untested.
Instead of using a portfolio approach to examine the Istanbul Stock Exchange, the
returns of the stock market index (Istanbul Stock Exchange Index-100) was tested
against seven macroeconomics variables. Büyükşalvarcı (2010) made use of
monthly data ranging from January 2003 to March 2010. Correlation analysis was
carried out to spot the presence of multicollinearity among the seven variables
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(Consumer price index, money market interest rate, gold price, industrial production
index, international crude oil price, foreign exchange rate and money supply) but the
correlation was pretty weak. Afterwards, a stationarity test was performed to ensure
the underlying time series was stationary to avoid the problem of spurious
regression. Once the series was stationary, the effect of macroeconomic variables on
the ISE-100 index return was observed by Ordinary Least Square estimation. The
ISE-100 index return is explained by nearly 50% of the seven variables out of which
five macroeconomic variables were found to be significant. The money supply
factor had a direct relationship with the Istanbul stock market while the other
variables were negatively related. The oil price effect was consistent with those of
Clare and Thomas (1994) study of the UK stock market. Conversely, gold price and
inflation rate were not priced in the stock index return. The findings were quite
encouraging when the ISE-100 index was used as a proxy regarding the performance
of the Istanbul stock return – five factors were captured by the stock market.
To date, most of the studies are conducted in developed countries even though some
recent one has been carried out in developing countries like Turkey. Two
approaches, a statistics and a macroeconomics study of the APT can be adopted: the
former produce no consequential economic reason while the latter is silent on the
variables to be used. The number of significant variables varies widely among
studies. Although a particular connection may exist, the direction of the relationship
may differ from the findings of other stock markets. Poon and Taylor (1991) did not
find any evidence of the variables used by Chen et al. (1986) in the UK stock market
while Hamao (1988) found three of the variables captured by the Japanese stock
market. When Gunsel & Cukur (2007) examined the UK stock market in a portfolio
approach, they found that the factors adopted in the study produced a separate
relationship with each of the industry.
Rjoub, Tursoy and Gunsel (2009) also
employed a portfolio concept on the firm’s quoted on the Istanbul stock market and
arrived at the same conclusion as Gunsel & Cukur (2007).
RESEARCH METHODOLOGY & ANALYSIS
The scope of the APT-model enables a wide freedom in the selection of the
explanatory variables but of course the assumptions as mentioned in the literature
review must be fully satisfied. A macroeconomic approach was undertaken where
variables were selected according to the appropriate criteria. Four of the variables
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that Chen et al. (1986) had used in their study were employed and the others have
been utilised by subsequent authors. However, the tourist arrival variable remains a
new one and the ideology in the use of it was mainly driven by the important
contribution of the tourism industry for a small island like Mauritius. To sum up,
the aim is to analyse the relationship of the hypothesised list of explanatory
variables pre and post crisis with: the different portfolios quoted on the Stock
Exchange of Mauritius; the official market as a general analysis; the two main
sectors (tertiary and secondary) of the Mauritian economy.
The study was run from February 2004 to December 2010 where the period was
divided into two sub-periods namely: February 2004 to February 2008 (pre-crisis);
March 2008 to December 2010 (post-crisis). The reason for doing so is purely for
stability purposes: the second period was more volatile in nature. The sub-prime
crisis that was originally initiated in the U.S. had a spill-over effect on the local
market by the end of the second month of 2008: this can be confirmed by analysing
graphically the trend of the SEMDEX. Similarly, a press communiqué from the
Bank of Mauritius issued on February 2009 confirmed that the crisis started in 2008
and on the other hand, in its budget speech, the former Minister of Finance, Dr.
Rama Sithanen rightly pointed out that the economic situation in 2009 will be
difficult due to the financial crisis. Thus, Mauritius was still under the effect of the
financial crisis by the end of 2009.
Firms which are frequently traded on the SEM are selected to constitute different
portfolios/divisions. Each portfolio is then categorised either in a tertiary or
secondary sector (refer to table 3). Here, the Sugar portfolio will not be used in the
sector analysis.
Table 3: Portfolio allocation
Portfolio
Company symbol1
Number of firms
Banks and Insurance
MCB, MUA, SBM
3
Investments
CAUD, FINC, MDIT, POL
4
Leisure and Hotels
NMHL, NRL, SUN
3
Transport
AIRM
1
Sector
Tertiary
1
Refer to Appendix 3 for company name and a brief overview of the firm.
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Commerce
IBL, ROGE, SHEL
3
Industry
PBL, MOR, UBP
3
Sugar
HARF,MTMD, SAVA.N
3
Secondary
-
Seven variables are tested against the return of all firms in the particular portfolio to
see whether they are priced accordingly. Therefore, the variables can be formulated
as a linear model as put forward by Chen et al. (1986):
Ri = αi + βi1F1 + βi2F2 + βi3F3 + βi4F4 + βi5F5 + βi6F6 + βi7F7 + εi
where
Ri = actual return of the firm in the particular portfolio.
αi = intercept term.
βi = reaction coefficient measuring the change of the firm return in the
particular portfolio for change in the risk factor.
F1 – F7 = Exchange rate, Crude oil price, Money supply, Tourist arrival,
Term structure of interest, Risk premium and Unanticipated inflation.
εi = residual error term
The dependent variable represents each firm’s returns in each portfolio. First of all,
the daily closing share prices of the twenty firms under study were extracted from
the website of the State Bank of Mauritius Securities. Then the mean average of the
prices was calculated so as to obtain the average share price of the firm on a monthly
basis. Finally, the return of the monthly share price was obtained as follows:
Ri = ln(Pt) – ln(Pt-1)
where
Ri = return for month t
Pt = average value of the firm’s share price for month t
Pt-1 = average value of the firm’s share price for month t-1
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As far as the independent variables are concerned, the data was obtained from the
Bank of Mauritius monthly report except for the crude oil price which was mined
from the Index Mundi’s website. All variables are captured on a monthly basis. An
“apercu” of the explanatory variables used in the study are described below:
Crude Oil Price
Considered to be of upmost importance when pricing an asset, it has also been used
by several authors like Clare and Thomas (1994) and Büyükşalvarcı (2010) in their
studies. In fact, oil price forms part of the web of systematic factors that negatively
influence the returns of stock market. Since Mauritius does not possess any of this
natural resource, the country is considered to be a net importer of oil. A change in
the price of oil on the international level will have a major repercussion on the
Mauritian economy, leading firm’s production costs to rise and future cash flows to
fall.
Exchange Rate
The exchange rate factor is widely taken into account either directly or indirectly by
investors since they are more involved in international activities. Büyükşalvarcı
(2010) found a negative significant relationship between the exchange rate and the
ISE-100 index returns whereas Günsel et al. (2007) considered that the exchange
rate factor is priced in only some portfolios of the London stock exchange. With
imports representing twice as much as its exports, Mauritius is an import dominated
country. Thus, if the country’s currency depreciates with respect to the other
country’s currency, imported goods and services will appear more expensive
resulting in a decrease in cash flows and profits. In the study, the dollar/Rupee
($/Rs) exchange rate is adopted.
Money Supply
Fama (1981) and Jensen et al. (1996) found the importance of money supply on
stock market returns – an increase in money supply gives rise to more liquidity on
the market and thus higher prices of nominal shares. On the other hand, a fall in
interest rate may be expected if money supply increases, leading investors to
reorient their investment horizons towards equity markets in search of higher
returns. Therefore, unanticipated changes in money supply tend to influence firm’s
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specific returns. This thesis examines broad money supply (M2) since it is widely
used by economists to measure the amount of money in circulation.
Tourist arrival
Since the 20th century, the tourism industry has become a major pillar for the small
volcanic island’s economy. Tourist arrival is expected to have a positive effect
especially on the hotel’s cash flow and level of profits. Also, the latter will enable
the overall Mauritian economy to benefit from its outcome which in return will
generate positive psychological effect from the point of view of the investor. The
new independent variable has not been used by other authors; the end result will
determine whether it is priced in the respective tested models.
Risk premium
The risk premium factor has been extensively employed by authors like Poon and
Taylor (1991) and Hamao (1988) among others. Actually, the risk premium is
simply a measure of the changes in the aggregate risk for the economy. The formula
put forward by Chen et al. (1986) is the difference between the yield of a low grade
bond and the long-term government. During the tested period there was no corporate
bond traded on the Mauritius stock market, the CAPM equation2 was therefore
employed.
Risk Premiumt = βt*(SEMDEX returnt – Risk free ratet)
Given: βt = 13
Risk free ratet = T-bill ratet (365 days) / 12
SEMDEX returnt = ((SEMDEX valuet+1 - SEMDEX valuet) / SEMDEX
valuet)*100
Term Structure of interest rate
The interest rate factor is frequently utilised in many asset pricing model but the
problem is that it is highly correlated with other macroeconomics variables which
may lead to multicollinearity dilemma. To prevent such thing from happening, the
2
This method was also adopted by Rjoub, Tursoy and Gunsel (2009).
3
Beta of the market = 1, refer to I M Pandey, Financial Management, 9 th edition, pp. 97.
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term structure of interest rates as employed by Chen et al. (1986) was utilised in the
study. The term structure of interest rate is calculated as follows:
Term structure of interest ratet = T-bill ratet (1 year) – T-bill ratet (3 months)
Unanticipated inflation
Inflation has an impact on the sales income and borrowings of a firm due to changes
in nominal cash flows or discount rate as proclaimed by Chen et al. (1986). Since
anticipated inflation has already been incorporated in the discount rate or sales price,
only the unanticipated inflation will have an effect on the stock value. According to
Chen, Roll & Ross (1986), the unanticipated inflation is calculated as follows:
UI(t) = I(t) – E(I(t) / t-1)
Given: UI(t) = Unanticipated inflation for period t
I(t) = Realised monthly first differenced in the logarithm of the Consumer
Price Index4 for period t
E(I(t) / t-1) = The series of expected inflation
The components (crude oil price, exchange rate, money supply and tourist arrival)
are measured as rate of change5 rather than absolute values. The motive for taking
logarithmic returns is to ease the assessment with stock’s returns and to render the
series stationary (Nelson and Plosser, 1982; Wasserfallen, 1989; and Eun and Shim,
1989). Also, as stated by Cheng (1995), the unexpected change in the economic
indicator rather than the absolute value will facilitate comparison with market
expectations.
Estimation Techniques
First and foremost, a correlation study will confirm the association of the
macroeconomic variables with each other: it is considered to be important since
highly correlated variables will provide bias results. A Principal Component
4
The computed value of the Consumer Price Index was correctly adjusted by a multiplication index
obtained from the Central Statistical Office, since the basket of goods and services are re-estimated
every five years. The base year was 1996/1997. Multiplication index: 1996/1997 = 1.442; 2001/2002
= 1.3285; 2006/2007 = 1.3526
5
K(Ai)t = ln(Ai)t – ln(Ai)t-1
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Analysis (PCA) will then be conducted to explore the effectiveness of the variables:
how well the study has explained the theory of the APT in choosing the variables
especially the number of factors to be retained. PCA is somehow similar to factor
analysis with objectives data diminution and summarisation. However, the main
purpose is to find out the minimum number of factors that will explain for the
maximum variance in the data that will subsequently be used in further analysis.
Thereafter, the descriptive analysis will generate some important statistics like:
standard deviation, mean, kurtosis, jarque-bera and skewness. The latter will reveal
some important findings on the normality assumptions and the fluctuations in the
mean values.
An ordinary least square (OLS) technique was adopted to obtain the factor scores for
each model. The first analysis will concentrate on the constructed portfolio. Then,
the twenty firms that where first grouped in particular portfolios will be examined as
a general analysis (irrespective of the portfolio they belonged) where a single linear
model will explain the whole official market. Finally, the APT model will be tested
on the tertiary and secondary sector of the Mauritian economy. The study will also
account for the financial crisis during the tested time frame. The thesis will therefore
analyse whether the Arbitrage Pricing Theory holds pre and post crisis for: each
portfolio; the overall official market; the two principal sectors.
While undertaking the regression analysis, the presence of heteroskedasticity was
taken into consideration. Heteroskedasticity as termed by White in its influential
paper in the 1980 refers to the conditional variances which are no longer constant,
therefore violating the assumptions underlying the OLS. It does not cause biasness
of the OLS coefficient but it can provide wrong standard errors. This will result in
bias inference and an incorrect hypothesis tests: it may lead to the rejection of the
null hypothesis that is statistically significant. If the null hypothesis (homoscedastic
or constant variance) is rejected at 5 % significance level, heteroskedasticity is
therefore present in the model. So, to obtain valid statistical inference when some of
the regression’s model assumptions are violated, “robust” standard errors 6 are
employed.
6
Huber (1967), Eicker (1967), and White (1980) developed this method to obtain valid statistical
inference in the absence of homoscedastic.
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Analysis
Before conducting a regression analysis, a correlation test will brief us whether two
or more independent variables are linearly dependent on each other. As a rule of
thumb if correlation is in excess of 0.8, multicollinearity will produce inefficient
results. As mentioned earlier, to prevent correlation between interest rate variable
and other macroeconomic components, the term structure of interest rate was
adopted. It can be confirmed that highly correlated values are not present, thus the
multicollinearity dilemma is not present in the two time intervals. The reasons are
mainly due to the transformation of the determinants and also to the nature of the
underlying variable.
The main motive of running Principal Component Analysis (PCA) is to find out how
well the models are interpreted. As provided by Kaiser (1960), only eigenvalues
greater than one should be retained as factors. From tables 5A and 5B, three
components meet the given criteria and the total cumulative variances explained by
the explanatory variables are nearly 67% and 76% respectively which is an accepted
value. The particular variable correlated with each of the component structure is
provided by the highlighted dark grey cell. However, the Kaiser-Meyer-Olkin
measure of the sampling adequacy proposed by Kaiser (1970) reports a very poor
figure (less than 0.6) for the two samples: therefore one cannot make any robust
conclusion on the results provided by the Principal Component Analysis.
Table 5A: Principal Component Factor Analysis (Pre-crisis)
Principal Component Factor Analysis (Pre-crisis)
Components
Eigenvalues
% of variance
Cumulative %
1
1.8562
0.2652
0.2652
2
1.56266
0.2232
0.4884
3
1.26055
0.1801
0.6685
4
0.967771
0.1383
0.8067
Component Loadings
Exchange rate
Crude oil price
Money supply (M2)
Tourist arrival
Term structure of interest
Risk Premium
Unanticipated inflation
1
0.5963
-0.3616
-0.2982
-0.1737
0.1999
0.0755
0.5906
2
-0.1101
0.1991
0.5302
0.1842
0.664
-0.2478
0.3618
3
0.1104
-0.2022
0.1234
0.6154
0.1501
0.7159
-0.1343
Kaiser-Meyer-Olkin measure of sampling adequacy = 0.3342
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Table 5B: Principal Component Factor Analysis (Post-crisis)
Principal Component Factor Analysis (Post-crisis)
Components
Eigenvalues
% of variance
Cumulative %
1
2.53889
0.3627
0.3627
2
1.6331
0.2333
0.596
3
1.12347
0.1605
0.7565
4
0.731756
0.1045
0.861
Component Loadings
Exchange rate
Crude oil price
Money supply (M2)
Tourist arrival
Term structure of interest
Risk Premium
Unanticipated inflation
1
-0.4768
0.5233
-0.257
-0.1081
-0.0531
0.4935
0.4179
2
-0.2781
-0.1104
0.4821
0.4976
-0.4914
-0.1797
0.3959
3
-0.2035
-0.1439
-0.2685
0.6699
0.6398
-0.0358
0.0798
Kaiser-Meyer-Olkin measure of sampling adequacy = 0.4643
Portfolio Analysis
Before jumping on any explanation, it is important to access the significance of the
models for the two periods through the probability of the F-statistics (Prob>F). If the
probability of the computed F-statistics is greater than the critical values, the null
hypothesis that the true slope coefficients are concurrently equal to zero is rejected:
the overall model is considered to be insignificant. In spite of the Transport portfolio
in the post-crisis period, two portfolios (Industry and Sugar) in the first period have
reported a Prob>F greater than the critical value of 10%. This indicates that the
models are not significant and one cannot draw any conclusions on the latter since
the slopes of the coefficients are different from zero. Thus, the multi-index model is
not appropriate under these circumstances. However, all the other regressions’
models (other than those mentioned above) display the existence of a linear
relationship, even though the association in explaining the securities’ logarithmic
excess returns for the portfolios are quite low (few significant factors). This type of
result was quite common in most studies examined.
While most of the variables under study influenced different portfolios in a scattered
way for both periods, the changes in exchange rate and tourist arrival are not priced
in any models. The last one represents an innovating factor which was not employed
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in other studies. According to the end result, the significance of the latter was not
taken into consideration or has been diversified by investors on the market: even
though some relationship was expected with the Leisure portfolio. A plausible
explanation is that the anticipated incoming tourist in the island by investors lies in
the vicinity of the true figure. If one analyse the trend of the tourist arrival, the
highest peak period is achieved in December and low peak period in June. Thus,
investors already have an approximate idea of the number of tourist arrival in the
country and are not surprise by sudden fluctuations in the latter. On the other hand,
the exchange rate variable also exhibits a similar argument as the tourist arrival one.
The findings here are more or less supported by those of Günsel et al. (2007) in that
the named variable does not have any effect on the portfolios’ returns although they
found a relationship for two of them. The companies might have used several tools
to eliminate exchange rate risk: hedging or by covering their transactions. Also,
Mauritius adopts a managed floating exchange rate regime where the Central Bank
intervenes from time to time on the market to provide stability of the currency value.
The intervention was confirmed by the Deputy Governor of the Bank of Mauritius
where the Central Bank intervened on October 2008 on the foreign exchange market
to sold USD 20 millions. There has not been much fluctuations in the trend of the
$/Rs during the period examined even though an appreciation of the local currency
against the dollar was witnessed during February to September 2008 due to the
crisis.
The main concerned remain the four variables (risk premium, unanticipated
inflation, term structure of interest rate and oil price) that were used by Chen et al.
(1986) in their study. They concluded that the first three factors mentioned above
reported a significant relationship while the change in oil prices was not captured by
the New York Stock Exchange returns. Martinez and Rubio (1989); Poon and
Taylor (1991) found no relationship of these components with the firms’ returns.
The term structure of interest rate reveals a positive and significant relationship at
10% level with the Banking and Transport portfolios’ returns. The following is also
consistent with Robotti (2002) study on “Asset Returns and Economic Risk”. If one
analyse the trend of the term structure of interest rate in Mauritius during the period
under study: an upward sloping yield curve (long term > short term interest rate) is
witnessed. A positive yield spread represents the excess premium attached to the
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longer maturity instrument due to the element of risk. In Mauritius, the Banking &
Insurance sector are well regulated while the Transport sector (Air Mauritius) is a
majority owned government body – the probability of default in the short term is
nearly impossible and what preoccupies the investors is the uncertainty underlying
the future. Therefore, the higher rate of interest on the 1 year T-bill over the 3
months T-bill entails a higher positive term structure which satisfies the investor in
return. As a result, this will generate a positive movement of the firms’ stocks in the
Banking & Insurance and Transport sector. Conversely, the negative significant
relationship of the term structure with the stock’s returns was also reported by Javid
& Ahmad (2009). The Investment and Commerce portfolio are negatively related to
the term structure at 1% significance level. Here investors believe that a positive
slope is link to future economic growth which in return will be fuelled by higher risk
that inflation will rise in the future than will fall. Also, the Investment and
Commerce industry does not offer the same guarantee as they are involved in more
risky business and they can go bankrupt at anytime compared to the two preceding
portfolios. As a result, this explains the opposite relationship of the term structure on
the respective portfolios’ returns. On the contrary, the term structure was not
captured in any portfolio during the post-crisis period: the particular variable has
less effect in period of more fluctuations. Investors do not price the term structure in
periods of instability.
Although Chen et al. (1986) commanded a negative relationship of the unanticipated
inflation with the U.S. stocks market; Burmeister and McElroy (1988) findings were
also similar as those obtained in the study in that they found a positive and
statistically significant estimate of the unanticipated inflation. The particular factor
is priced in the Investment (first period) at 1% level and Industry portfolio (second
period) at 5% level respectively. Investors therefore overestimate the value of the
expected inflation rate – it will then be incorporated in the discount rate and sales
price as being anticipated inflation. The difference between the predicted
(anticipated) and the real value of inflation is known as the unanticipated inflation.
When the actual rate of inflation is published which is lower than those predicted by
the investors, a positive effect on the market value of the portfolios are observed. In
contrast, the insignificance of the variable on the other portfolios’ returns represents
the near correct inflation rate forecasted by the investors before the proclamation of
actual rate. The Bank of Mauritius estimates projected inflation which can be a
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useful tool for investors to correctly price the latter in the discount rate and sales
price.
The risk premium variable was the most surprising factor since it is priced in almost
all portfolios for both periods. Chen et al. (1986) and Ferson & Harvey (1991) also
found a positive relationship of the variable with the stocks’ returns. When the risk
premium increases, the value of the stocks’ returns also move in the same direction.
The latter is in perfect accord with the investors’ wants: a higher premium is
required to bear the excess risk attached to the assets over the risk free one (T-bill).
Hence, the risk premium factor plays an important role in pricing the portfolios’
returns. As mentioned in the methodology part, the risk premium was derived from
the CAPM model since there was no corporate bond by the time the study was
conducted.
The change in crude oil price on the international market has a direct and significant
relationship at 5% and 10% level for the Leisure & Hotels portfolio before and
during the financial crisis. It was the only portfolio that captured the particular
factor; other industries have already diversified away the risk. The most striking part
is the positive sign obtained even though an inverse relationship was mostly
welcomed. Clare & Thomas (1994) and Büyükşalvarcı (2010) examined a negative
and statistically significant correlation of oil price with the UK and Istanbul stock
markets respectively. Clare & Thomas (1994) proclaim that changes in oil prices
will alter industry costs and revenues. As stated, the crude oil price is measured by
rate of change which is equivalent to unexpected values (logarithmic returns), so a
direct relationship between a change in oil prices and stock returns would indicate
that an increase in oil prices would result to higher returns form the Leisure &
Hotels portfolio. Therefore, the result differs from those of the two authors; the
variable has a different relationship in the study. One cannot draw sudden
conclusion on the findings since a particular factor may report a separate
relationship in other stock market.
Two poles apart association are observed for changes in money supply (M2) on
portfolios returns: a positive relation with the Leisure & Hotels portfolio returns
during the pre-crisis time interval and a negative connection with the Sugar division
returns during the post-crisis period. Rjoub, Tursoy & Günsel (2009); Günsel &
Çukur (2007) also found mix effect relationship between the particular variable and
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the returns’ of portfolios under study. A tangible explanation is that changes in
money supply would alter the money market equilibrium or influence real economic
variables and finally impact the stock returns. Fama (1981) and Jensen et al. (1996)
found the importance of money supply on stock market returns - an increase in
money supply gives rise to more liquidity on the market and thus higher prices of
nominal shares. The result before the crisis reveals a positive relationship of the
Leisure & Hotels portfolio returns with the changes in money supply (M2). During
the period, money supply was exhibiting an upward trend and interest rate was also
displaying a growing movement, from 5% to 8%. The increase money supply will
therefore lead to a portfolio rebalancing vis à vis other real assets and in return cause
share prices to rise (Martikainen et al., 1991). On the other hand, the negative sign
during the post-crisis period reveals a greater coefficient (-2.42) significant at 10 %
level: an increase in money supply had a reverse effect on the sugar portfolio’s
returns. As from February 2008, interest rate has steadily dropped from 7% to attain
4.5% although an increase in money supply (M2) was registered. Usually, a rise in
money supply is accompanied by a fall in equilibrium interest rate. Although an
increase in money supply may have positive relationship on stock returns, it can also
be regarded as a principal indicator of future inflation which can have negative
effect on stocks’ returns. These consequences have also been accelerated by the poor
performance of the sugar sector due to the financial crisis and the continuous effect
resulting from the cut of sugar prices at international level.
General Analysis
This part is conducted as a general analysis to investigate how the Arbitrage Pricing
Theory reacts with the overall Mauritian stock market; the results suggest that only
some of the variables under study have a significant relationship at 1% and 5% level
for both periods. The pre-crisis period seems to outperform the second one since
three variables were found to be significant. The risk premium factor is successfully
priced in the two periods: investors seem to consider the particular variable as an
important component irrespective of the volatility condition during the impact of the
financial crisis. The positive sign reflects the investors’ desire to hedge against
unwanted rise following a rise in uncertainty. Robotti (2002) and Chen et al. (1986)
also concluded a positive effect of the risk premium variable in their findings. On
the other hand, the term structure of interest rate and the unanticipated inflation were
captured in the first period only. Therefore in period of high fluctuations, the
highlighted variables do not exhibit any effect on the stock market returns. The
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negative coefficient of the term structure recorded for the former period relates the
inverse relationship with stock market returns even though Chen et al. (1986) found
a positive sign with the US stock market. Yet, Javid & Ahmad (2009) found
negative relation with the Pakistan stock market. The first period has observed an
upward sloping yield curve of the term structure and the continuous growing trend
of the yield spread. Investors’ reactions have therefore been directed towards higher
economic growth which will be stimulated by an increase in inflation rate in the
future. Thus, the opposite association between the term structure of interest rate and
the stock market return is witnessed. On the other hand, Burmeister and McElroy
(1988) found a positive value of the unanticipated inflation in their study. This can
be explained by the fact that investors overestimate the true value of inflation rate.
Similarly, the money supply (M2) variable displays a negative significant
relationship at 5% level for the post-crisis period only. Even though, increase in
money supply is accompanied by a reduction in interest rate. One may think that
investors would switch towards equity markets but the reverse occurred. During the
period of financial crisis, all the shares quoted on the official market and the overall
index has registered a fall. As a result, albeit the lower interest rate, investors opted
for low returns rather than high risky reward from the equity market. In other words,
the increase in money supply was canalised towards safer instruments rather than the
risky stock market. The factors (exchange rate, oil price and tourist arrival) are not
priced in the two periods; this explains the presence of other variables than those
mentioned in the study that have an impact on the stock market returns. Chen et al.
(1986) also tested the impact of change in oil prices on asset pricing and found no
relationship whereas Büyükşalvarcı (2010) found a negative significant relationship
with the ISE-100 index returns.
Sector Analysis
The purpose of conducting this analysis is mainly the contribution of the tertiary and
secondary sector to the Mauritian economy. The tertiary sector in itself accounts to
68.5% of Gross Domestic Product compared to 27% for the secondary sector. The
remainder is shared by the primary sector: as result the analysis will concentrate on
the first two sectors highlighted. Yet, the risk premium factor was the only
significant variable at 1% and 5% levels for the tertiary and secondary sectors
during the two periods. One can proclaim that the given factor is of upmost
importance to investors since it is captured in both sectors irrespective of the time
frame: the positive relationship is in perfect accord with Chen et al. (1986) findings
with the U.S. stock market. The positive risk premium reflects the investors’ want to
protect against unexpected rise in the aggregate risk premium due to uncertainty.
The coefficient of the risk premium factor for the tertiary sector is superior
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compared to the secondary one. It corresponds to the excess rewards attached to
those companies grouped in the services sector. However, the APT model seems to
underperform in this analysis compared to the two previous one: there are other
variables other than those studied which are priced by the two sectors.
Table 7A: Regression results for Portfolio and Overall analysis (Pre-crisis)
Regression results for Portfolio and Overall analysis (Pre-crisis)
Bank and
insurance
Industry
Investm
ents
Sugar
Commerc
Leisure &
e
Hotels
Transport
Overall
-0.0148
0.0115
0.0917
0.1766
0.0119
-0.0119
-0.0602
0.0413
(0.270)
(0.569)
(0.001)*
(0.290)
(0.469)
(0.438)
(0.082)
(0.008)*
0.2508
0.2228
0.3671
-2.7606
-0.3566
0.0270
0.1674
-0.3107
(0.618)
(0.659)
(0.684)
(0.414)
(0.544)
(0.960)
(0.880)
(0.578)
Crude oil
-0.0204
0.0077
0.1277
0.0590
0.1062
0.1934
-0.1508
0.0700
price
(0.811)
(0.939)
(0.402)
(0.853)
(0.294)
(0.037)**
(0.424)
(0.428)
Money supply
0.0660
-0.1668
0.6230
0.4941
-0.0812
0.3655
-0.0367
0.2244
(M2)
(0.746)
(0.374)
(0.136)
(0.569)
(0.724)
(0.085)***
(0.943)
(0.193)
-0.0310
-0.0172
0.0560
-0.1909
0.0117
-0.0462
-0.0350
-0.0316
(0.369)
(0.487)
(0.232)
(0.360)
(0.244)
(0.178)
(0.544)
(0.351)
0.0112
-0.0048
-0.0332
-0.0492
-0.0084
-0.0123
0.0283
-0.0148
(0.055)***
(0.671)
(0.005)*
(0.124)
(0.009)*
(0.129)
(0.057)**
(0.025)**
0.0049
0.0001
0.0059
0.0064
0.0027
0.0045
0.0030
0.0041
(0.000)*
(0.882)
(0.000)*
(0.320)
(0.518)
(0.000)*
(0.054)***
(0.000)*
Unanticipated
-0.0011
0.0006
0.0103
0.0207
0.0012
-0.0022
-0.0046
0.0047
inflation
(0.473)
(0.761)
(0.001)*
(0.640)
(0.518)
(0.195)
(0.226)
(0.021)**
F-statistics
13.53
1.79
6.04
1.48
2.36
13.84
2.27
5.39
(Prob>F)
(0.000)*
(0.104)
(0.000)*
(0.190)
(0.033)**
(0.000)*
(0.079)***
(0.000)*
Yes
Yes
No
Yes
Yes
Yes
No
Yes
(Prob>chi2)
(0.023)**
(0.005)*
(0.552)
(0.000)*
(0.011)**
(0.035)**
(0.802)
(0.029)**
Remarks
Robust
Robust
Ok
Robust
Robust
Robust
Ok
Robust
Intercept
Exchange rate
Tourist arrival
Term
structure of
interest
Risk Premium
Presence of
Heteroskedasti
city
* significant at 1% level; ** significant at 5% level; *** significant at 10% level: p-values are
reported in parentheses for white and dark grey cells.
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Table 7B: Regression results for Portfolio and Overall analysis (Post-crisis)
Regression results for Portfolio and Overall analysis (Post-crisis)
Bank
and
insuranc
Industry
Investm
ents
Sugar
Commerc
Leisure &
Transp
e
Hotels
ort
Overall
e
0.0097
0.0345
-0.0031
0.0327
-0.0101
-0.0168
0.0294
0.0084
(0.484)
(0.012)**
(0.748)
(0.150)
(0.640)
(0.274)
(0.603)
(0.269)
0.2454
0.3379
-0.0530
0.1526
0.0531
0.5492
-1.1990
0.1302
(0.527)
(0.232)
(0.831)
(0.809)
(0.944)
(0.203)
(0.450)
(0.539)
0.0445
0.0052
-0.0430
-0.1039
0.1083
0.1510
-0.3092
0.0067
(0.544)
(0.914)
(0.438)
(0.386)
(0.237)
(0.066)***
(0.307)
(0.867)
Money supply
0.0117
-0.6624
0.0874
-2.4210
-1.6100
-1.1735
-0.7112
-0.9070
(M2)
(0.989)
(0.394)
(0.845)
(0.072)***
(0.338)
(0.196)
(0.830)
(0.043)**
-0.0032
-0.0445
-0.0183
-0.0257
0.0383
0.0725
-0.1948
-0.0078
(0.944)
(0.342)
(0.604)
(0.730)
(0.637)
(0.154)
(0.302)
(0.755)
Term structure
-0.0281
0.0076
-0.0023
-0.0067
-0.0289
0.0110
-0.0054
-0.0062
of interest
(0.174)
(0.705)
(0.820)
(0.842)
(0.384)
(0.381)
(0.948)
(0.584)
0.0040
0.0015
0.0027
0.0017
0.0030
0.0068
0.0035
0.0033
(0.000)*
(0.001)*
(0.000)*
(0.052)**
(0.003)*
(0.000)*
(0.127)
(0.000)*
Unanticipated
-0.0009
0.0032
-0.0005
0.0023
-0.0041
-0.0010
0.0036
0.0000
inflation
(0.602)
(0.024)**
(0.660)
(0.423)
(0.283)
(0.618)
(0.612)
(0.993)
F-statistics
17.92
7.81
8.99
2.3
7.13
47.57
1.43
43.35
(Prob>F)
(0.000)*
(0.000)*
(0.000)*
(0.039)**
(0.000)*
(0.000)*
(0.268)
(0.000)*
No
Yes
Yes
No
Yes
No
No
No
(Prob>chi2)
(0.837)
(0.084)***
(0.000)*
(0.251)
(0.009)*
(0.385)
(0.101)
(0.921)
Remarks
Ok
Robust
Robust
Ok
Robust
Ok
Ok
Ok
Intercept
Exchange rate
Crude oil price
Tourist arrival
Risk Premium
Presence of
Heteroskedastic
ity
* significant at 1% level; ** significant at 5% level; *** significant at 10% level: p-values are
reported in parentheses for white and dark grey cells.
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Table 8: Regression results for Sector analysis (Pre-crisis & Post-crisis)
Tertiary sector
Secondary sector
Pre-crisis
Post-crisis
Pre-crisis
Post-crisis
0.0206
-0.0004
0.0117
0.0123
(0.227)
(0.963)
(0.362)
(0.321)
0.2245
0.0884
-0.0669
0.1955
(0.546)
(0.733)
(0.863)
(0.623)
0.0800
0.0096
0.0570
0.0568
(0.544)
(0.852)
(0.419)
(0.277)
0.3409
-0.3497
-0.1240
-1.1717
(0.107)
(0.429)
(0.413)
(0.242)
-0.0038
-0.0054
-0.0027
-0.0031
(0.853)
(0.851)
(0.900)
(0.947)
-0.0098
-0.0035
-0.0066
-0.0107
(0.200)
(0.739)
(0.323)
(0.586)
0.0050
0.0043
0.0014
0.0022
(0.000)*
(0.000)*
(0.028)**
(0.000)*
0.0024
-0.0004
0.0009
-0.0005
(0.233)
(0.750)
(0.501)
(0.828)
F-statistics
18.83
29.7
2.87
12.33
(Prob>F)
(0.000)*
(0.000)*
(0.008)*
(0.000)*
Heteroskedasticity
Yes
Yes
Yes
Yes
(Prob>chi2)
(0.000)*
(0.024)**
(0.000)*
(0.004)*
Remarks
Robust
Robust
Robust
Robust
Intercept
Exchange rate
Crude oil price
Money supply (M2)
Tourist arrival
Term structure of interest
Risk Premium
Unanticipated inflation
Presence of
* significant at 1% level; ** significant at 5% level; *** significant at 10% level: p-values are
reported in parentheses for white and dark grey cells.
CONCLUSIONS & RECOMMENDATIONS
The findings have been able to provide an in-depth analysis of the multi-factor
model: on some selected companies that were grouped in respective portfolios; on
the overall local stock market as a general analysis; on the two pioneered sectors of
the Mauritian economy. Also the time effect was taken into consideration: the
financial crisis that prevailed in the United States had major repercussion on the
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local companies quoted on the SEMDEX and consequently led to a radical fall in the
stocks’ prices and the overall local index. The aim was not to compare which
models surpass the other, since each one at a particular period was influenced in a
different manner. Even though a principal component analysis was employed to
explore the effectiveness of the model, the Kaiser-Meyer-Olkin measure has
produced a low unaccepted value. Thus, one cannot make any robust conclusion on
the explanatory variables.
On a portfolio basis approach, the risk premium factor was nearly priced in all
portfolios irrespective of the periods; positive and significant results were obtained.
The exchange rate and tourist arrival factor was not captured in any portfolios which
proved that investors have already diversified these risks. The exchange rate
component has produced somehow similar result as Günsel et al. (2007), although
they examined a relationship with some of the portfolios under study. The term
structure and money supply variables reported a mix relationship with some of the
portfolios at different time interval, even though the former factor was not
incorporated in any stocks’ returns during the post-crisis period. Yet, the crude oil
price was positively significant for the Leisure & Hotels division for the two
periods, though Clare and Thomas (1994) found opposite relationship. Despite the
fact that a negative relationship was expected for the unanticipated inflation factor,
the outcome has produced a direct association with the Investments and Industry
portfolios’ returns.
When the overall analysis was conducted, the pre-crisis period related a three factor
structure while the second one reported a two factor structure. Three factors
(unanticipated inflation, risk premium and term structure) that Chen, Roll & Ross
(1986) utilised had a significant relationship in the first period. The risk premium
factor alone was priced in both periods and the positive sign was also consistent with
Chen et al. (1986) study. Money supply (M2) exhibits a negative significant
coefficient during the crisis period although a rise in money supply is accompanied
by a fall in interest rate. One may think that investors would reorient towards equity
market but the reverse occurred, since the financial crisis has caused a fall in share
prices. The increase in money supply was channelled towards safe instruments as
the equity market was under much pressure. Finally, the results obtained for the
sector analysis confirmed only one significant factor (risk premium) for both sectors
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of the economy. Thus, the three analyses have provided different results but the risk
premium factor was the most captured one.
Given the different analyses, the Arbitrage Pricing Theory performed poorly in
pricing the assets’ returns of the Mauritian stock market. With exception of some
variables that were significant in each model, most of the components displayed a
spread relationship. This can be due to the time lag factor which was not taken into
consideration like Gunsel & Cukur (2007) who included lag term in their model.
The latter can prove to be important as the information is not priced as quickly as
one presumed. In addition, the autocorrelation issue was not discussed in the thesis
even though the companies listed on the SEM were grouped in respective portfolios
they belonged to account for the firm size effect. These concerns are left for further
studies. However this does not mean that the given macroeconomic variables are
poor, as the assumptions underlying the choice of the latter has been fully met.
Moreover the variables are not used as absolute values but are measured as rate of
change which is equivalent as innovations or unexpected changes in the latter
(Cheng, 1995).
5.0 REFERENCES
BURMEISTER, E., MARJORIE, B., MCELROY, 1988. Joint estimation of factor
sensitivities and risk premiums for the arbitrage pricing theory. Journal of Finance,
Vol 43, pp. 721–733.
BÜYÜKŞALVARCI, A., 2010. The effects of macroeconomics variables on stock
returns: evidence from Turkey. European Journal of Social Sciences, Vol 14, No
(3), pp. 404-416.
CAUCHIE. S., HOESLI, M., ISAKOV, D., 2003. The determinants of stock returns
in a small open economy: Swiss stock market. National Centre of Competence in
Research Financial Valuation and Risk Management, No (80).
CHEN, N., ROLL, R., and ROSS, S., 1986. Economic Forces and the Stock Market.
Journal of Business, Vol 59, No (3), pp. 383-403.
July 2-3, 2013
Cambridge, UK
26
2013 Cambridge Business & Economics Conference
ISBN : 9780974211428
CHENG, A., 1995. The UK stock market and economic factors: A new approach.
Journal of Business Finance & Accounting, Vol 22, No (1), pp. 129-142.
CLARE, A.D., THOMAS, S.H., 1994. Macroeconomic Factors, the APT and the
UK Stockmarket. Journal of Business Finance and Accounting, Vol 21, No 3, pp.
309-331.
DHRYMES, P.J., FRIEND, I., GULTEKIN, N.B., 1984. A critical reexamination of
the empirical evidence on the APT. Journal of Finance, Vol 39, No (2), pp. 323346.
EICKER, F., 1967. Limit Theorems for Regressions with Unequal and Dependent
Errors. In: L. LeCam and J. Neyman, ed. Proceedings of the Fifth Berkeley
Symposium on Mathematical Statistics and Probability. University of California
Press, pp. 59–82.
ELTON, E.J., GRUBER, M.J., 1973. Estimating the dependence structure of share
prices - implications for portfolio selections. Journal of Finance, Vol 23, pp. 12031232.
ELTON, E.J., GRUBER, M.J., URICH, T., 1978. Are betas best?. Journal of
Finance, Vol 28, pp. 1375-1384.
ELTON, E., GRUBER, M., BLAKE, C., 1996. Survivorship bias and mutual fund
performance. Review of Financial Studies, Vol 9, pp. 1097–1120.
EUN, C., SHIM, S., 1989. International transmission of stock market movements.
Journal Financial and Quantitative Analysis, Vol 24, pp. 241–256.
FAMA, E.F., MACBETH, J.D., 1973. Risk, return and equilibrium: empirical tests.
Journal of Political Economy, Vol 81, No (3), pp. 607-636.
FAMA, E.F., 1981. Stock returns, real activity, inflation and money. American
Economic Review, Vol 71, No (4), pp. 545-565.
July 2-3, 2013
Cambridge, UK
27
2013 Cambridge Business & Economics Conference
ISBN : 9780974211428
FEDERAL RESERVE BANK OF ATLANTA, 2002. Asset Returns and Economic
Risk. Economic Review: ROBOTTI, C., pp. 13-25.
FERSON, WAYNE, E., CAMPBELL R.H., 1991. The variation of economic risk
premiums. Journal of Political Economy, Vol 99 (April), pp. 385–415.
GEHR, A., 1978. Some tests of the Arbitrage Pricing Theory. Journal of the
Midwest Finance Association, Vol 7, No (4), pp. 91–95.
GROENEWOLD, N., FRASER, 1997. Share prices and macroeconomic factors.
Journal of business finance and accounting, Vol 24, No (9), pp. 1367-1381.
GUNSEL, N., CUKUR, S., 2007. The effects of macroeconomic factors on the
London Stock returns: A sectoral approach. International Research Journal of
Finance and Economics, Vol 10, pp. 140-152.
HAMAO, Y., 1988. An Empirical Investigation of the Arbitrage Pricing Theory.
Japan and the World Economy, Vol 1, pp. 45-61.
HUBER, P.J., 1967. The behavior of maximum likelihood estimates under nonstandard conditions. In: C.A. Berkeley, ed. Proceedings of the Fifth Berkeley
Symposium in Mathematical Statistics and Probability. University of California
Press, Vol 1, pp. 221–233.
JAVID, A.Y., AHMAD, E., 2009. Testing Multifactor Capital Asset Pricing Model
in Case of Pakistani Market. International Research Journal of Finance and
Economics, Vol 25, pp. 114-139.
JENSEN, G.R., MERCER, J., JOHNSON, R., 1996. Business conditions, monetary
policy, and expected security returns. Journal of Financial Economics, Vol 40, pp.
213-37.
KAISER, H.F., 1960. The application of electronic computers to factor analysis.
Educational and Psychological Measurement, Vol 20, pp. 141-151.
July 2-3, 2013
Cambridge, UK
28
2013 Cambridge Business & Economics Conference
ISBN : 9780974211428
KAISER, H.F., 1970. A second generation little Jiffy. Psychometrika, Vol 35, pp.
401-415.
LINTNER, J., 1965. The valuation of risk assets and the selection of risky
investments in stock portfolios and capital budgets. Review of Economics and
Statistics, Vol 47, No (2), pp. 13–37.
MARTIKAINEN, T., OLLI, Y.P., GUNASEKARAN, A., 1991. Incremental
significance of prespecified macroeconomic factors in testing the arbitrage pricing
theory: empirical evidence with Finnish data. Applied Financial Economics, Vol 1,
No (3), pp. 139-147.
MARTINEZ, M., RUBIO, G., 1989. Arbitrage pricing with macroeconomic
variables: an empirical investigation using Spanish data. Working paper, European
Finance Association, Universidad Del Pais Vasco.
MOSSIN, J., 1966. Equilibrium in a capital asset market. Econometrica, Vol 34, pp.
768-783
NELSON, C., PLOSER, C., 1982. Trends and Random Walks in Macroeconomics
Time Series: Some Evidence and Implications. Journal of Monetary Economics, Vol
10, pp. 139-162.
OLLI, Y.P., VIRTANEN, I., 1992. Some empirical test of the Arbitrage Pricing
Theory using transformation analysis. Empirical Economics, Vol 17, pp. 507-522.
PASTOR, L., STAMBAUGH, R., 2000. Comparing asset pricing models: an
investment perspective. Journal of Financial Economics, Vol 56, pp. 335–381.
POON, S., TAYLOR, S.J., 1991. Macroeconomic Factors and the UK stock market.
The Journal of Business Finance and Accounting, Vol 18, No (5), pp. 619-636.
RENSBURG, P.V., 1997. Investment Basics: XXXIV. The arbitrage pricing theory.
Investment Analysts Journal, No (46), pp. 60-64.
July 2-3, 2013
Cambridge, UK
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RJOUB, H.T., TURSOY, T., GUNSEL, N., 2009. The effects of macroeconomics
factors on stock returns: Istanbul Stock Market. Studies in Economics and Finance,
Vol 26, No (1), pp. 36-45.
ROLL, R., ROSS, S.A., 1980. An Empirical Investigation of the Arbitrage Pricing
Theory. The Journal of Finance, Vol 35, No (5), pp. 1073-1103.
ROSS, S.A., 1976. The arbitrage theory of capital asset pricing. Journal of
Economic Theory, Vol13, pp. 341-360.
SHARPE, W., 1964. Capital Asset Prices: A theory of market equilibrium under
conditions of risk. The Journal of Finance, Vol 19, No (6), pp. 425–442.
WASSERFALLEN, W., 1989. Macroeconomic news and the stock market. Journal
of Banking and Finance, Vol 13 (4/5), pp. 613–626.
WHITE, H., 1980. A heteroskedasticity-consistent covariance matrix estimator and
a direct test for heteroskedasticity. Econometrica, Vol 48, No (4), pp. 817–838.
XU, Y., 2003. Extracting factors with maximum explanatory power. Working paper,
University of Texas, Dallas.
APPENDIX
Table 1: A summary of the empirical studies on the APT
Author
Method used
Findings
Ross & Roll (1980)
Factor Analytical
Approach
At least 3 factors
Macroeconomic
Approach
Four Factors were found to be
significant out of seven:
 Industrial production
 Risk premium
Chen, Roll & Ross
(1986)
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Poon & Taylor
(1991)
Macroeconomic
Approach
Martinez & Rubio
(1989)
Macroeconomic
Approach
Hamao (1988)
Macroeconomic
Approach
Olli & Virtanen
(1992)
Factor Analytical
Approach
Cheng (1995)
Macroeconomic
Approach
Robotti (2002)
Macroeconomic
Approach
Cauchie, Hoesli &
Isakov (2003)
Factor Analytical
Approach +
Macroeconomic
Approach
Gunsel & Cukur
Macroeconomic
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 Term structure
 Unanticipated inflation
Utilised same factors as Chen, Roll
& Ross (1986) - No factors were
found to be significant
Utilised same factors as Chen, Roll
& Ross (1986) - No factors were
found to be significant
Utilised same factors as Chen, Roll
& Ross (1986) – Three factors were
found to be significant:
 Unanticipated inflation of Δ
in expected inflation
 Risk premium
 Term structure
At least 2 factors
Most positive contribution:
 Market factor
Weakly correlated:
 Money supply
 Unemployment rate
 Price index
Significant variables:
 Inflation rate
 Lag stock return of NYSEAMEX-NASDAQ
 Term structure
 Dividend yield
 Real rate of interest
 Risk premium
 consumption-aggregate
wealth ratio
 Factor Analytical Approach –
Five factors
 Macroeconomic Approach –
Four variables were
significant:
 Industrial production
 Δ in expected inflation
 Market return
 Term structure
Similar data as Chen et al. (1986)
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(2007)
Approach
Rjoub, Tursoy and
Gunsel (2009)
Macroeconomic
Approach
Büyükşalvarcı
(2010)
Macroeconomic
Approach
ISBN : 9780974211428
were employed and each variable
tend to influence a particular sector in
a different way
The authors found a weak correlation
among the 6 macroeconomic
variables, even though each variable
influence a specific sector differently
Five out of seven macroeconomic
variables were significant:
 Interest rate
 Industrial production index
 Oil price
 Foreign exchange rate
 Money supply
Table 2: Summary table of the major landmarks of the SEM
Date
Major Landmarks
1989
Setting up of the Stock Exchange of Mauritius (SEM)
1989
Debut of the first trading session
 5 companies were registered
 The trading session was scheduled once a week
for approximately 15 minutes
 Operation of the SEMDEX and SEMTRI index
1990
An Over the Counter (OTC) market was introduced
 9 companies were admitted
1991
Box method was replaced by the order-driven single
price auction system
1994
Stock market opened to foreign investors
1997
Settlement of the CDS
1998
Launch of the SEM-7 index
2001
SEM Automated Trading System (SEMAT) was
initiated
2003
Trading of treasury bills and medium-to-long term
government papers on the SEM
2004
The SEM became a member of the World Federation of
Exchanges
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2005
The OTC market was replaced by the Development &
Enterprise Market (DEM)
2007
SEM was ranked 2nd as the “Best African Stock
Exchange”
2008
Introduction of the turn-around trading
2008
Broadcast of the Mauritian Stock Exchange on a daily
basis on Bloomberg
Figure 3: Number of companies listed on the Official Market and the DEM from 1989 – 2009
The SEMDEX: The SEMDEX is the main index that tracks the Official Market. It is
an index of prices of all listed companies on the SEM where each stock is weighted
according to its contribution in the total market capitalisation. Therefore, the
SEMDEX is sensible to changes in the price of shares whose market capitalisation is
superior.
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Figure 4: The SEMDEX price ranging from 1989 to 2009
Figure 5: The market capitalisation of the Official Market between 1989 and 2009
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