AN ECONOMIC ANALYSIS

OF FACTORS AFFECTING SOUTH AFRICAN EQUITY RETURNS

By

JUSTIN BEUKES

Submitted in partial fulfilment of the requirements for the degree of

Baccalaureus Commercii Honores (Economics)

IN THE FACULTY OF BUSINESS AND ECONOMIC SCIENCES

AT THE NELSON MANDELA METROPOLITAN UNIVERSITY

Supervisor Mrs. D. Du Preez

JANUARY 2009

I

ACKNOWLEDGEMENTS

I would like to express profound gratitude to the following individuals for their involvement in this dissertation:

Deborah Du Preez, my supervisor, for her continued support throughout the year. Thank you for helping me through a difficult year. Without you, this would not have been possible.

Mario Du Preez, for being willing to always give a hand. Your guidance on the proposed topic was invaluable. Your enthusiasm in economics also rubbed off on me.

Leann Cloete, for being all that a friend can ask for. You did not once doubt my abilities.

Marius Wolmarans, for having a big impact on my life. Thank you for steering me in the right direction.

I am as ever, especially indebted to my family. Thank you for the love, support and counsel I could not do without.

II

EXECUTIVE SUMMARY

The efficient market hypothesis declares that the efforts of investors who attempt to

gain returns on share markets is futile. The current price of a share is said to reflect all

available information (Fama 1970) and that analysing available information with the

goal of earning a return will be unsuccessful.

Nonetheless, share price valuation has sought much attention because of the potential

gains to be realised by investors. The search for ways of reading the share market has

brought about two different approaches to share price valuation, namely, technical and

fundamental analysis. Technical analysis is a short term approach to valuation and is

the study of the action of the market (Edwards & Magee 2001: 4). That is, only the

prices of the companies concerned are studied ignoring forces outside the market.

Fundamental analysis is the second approach to share price valuation; it is basically

the study of value (Bodie et al., 2008: 569). A company’s value is determined by

examining virtually every aspect possible. The macroeconomy is one aspect that is

evaluated in order to determine the company’s macroeconomic environment.

This relationship, however, between certain macroeconomic variables and share

prices is not well established. There is no generally accepted asset pricing model to

explain this link (Asprem 1989). This is particularly the case for South Africa’s

Johannesburg Securities Exchange (JSE), as research on the JSE is limited.

The dissertation takes on a fundamental approach instead of a technical one to share

price valuation, to see whether fundamentals drive the JSE. It examines the

relationship between four macroeconomic variables and the JSE. The variables

considered are real activity, proxied by real GDP growth, the exchange rate as proxied

by the real effective exchange rate, inflation expectations as proxied by inflation

expectations for one year ahead, and the interest rate as proxied by the prime overdraft

interest rate.

An empirical analysis was carried out in order to determine if any of these four

variables help explain movements in the JSE All Share Index (ALSI).

It was hypothesised that an increase in real activity results in higher earnings and

therefore an increase in the ALSI, a depreciation of the currency improves firm’s

III

competitive position, thus increasing earnings and consequently increasing the ALSI,

higher inflation expectations are associated with increased interest rates which results

in a decrease in the ALSI, and lastly higher interest rates would lead to higher returns

through higher than usual short term inflows, thus improving the performance of the

ALSI.

The resultant model had some problems, i.e. it suffered from serial correlation. It

could not , however, be corrected for, as serial correlation still existed after running

the generalized least squares (GLS) equation using the AR(1) method.

Another attempt to correct for serial correlation was to re-specify the equation,

lagging the ALSI by one period and substituting inflation expectations for one year

ahead with current inflation expectations. This did not, however, solve the problem of

serial correlation and made all the variables insignificant. The initial regression was

thus reported on.

It was found that inflation expectations and the interest rate were statistically

significant variables in helping to explain movements in the ALSI. The other two,

namely GDP growth and the exchange rate were found to be insignificant.

Further research should thus be undertaken in order to identify possible significant

variables that will help to give investors a better understanding of the movements in

the ALSI, using the fundamental approach to share price valuation.

IV

LIST OF TABLES

Page

Table 2.1: Comparison of industry profitability ratios in South Africa

(2004 - 2005) 16

Table 3.1: Variables used in estimation 27

Table3.2: Regression output of equation 3.2 30

Table 3.3: Unadjusted R-squares and VIFs of independent variables 32

Table 3.4: The first-order serial correlation coefficient 34

Table 3.5: Generalized least squares AR (1) method 35

Table 3.6: White heteroskedasticity results 36

V

LIST OF FIGURES

Page

Figure 2.1:Bar chart and Point-and-figure chart 12

Figure 2.2:How resistance forms and How support forms 12

Figure 2.3:Dow Theory trends 14

Figure 2.4:Moving average for Microsoft as of 18 January 2005 15

Figure 2.5:Industry cyclicality 17

TABLE OF CONTENTS

Page

ACKNOWLEDGEMENTS I

EXECUTIVE SUMMARY II

LIST OF TABLES IV

LIST OF FIGURES V

CHAPTER ONE: INTRODUCTION

1.1 INTRODUCTION AND PRELIMINARY LITERATURE REVIEW 1

1.2 MODELS USED FOR PREDICTION PURPOSES 1

1.2.1 Technical Analysis 1

1.2.2 Fundamental Analysis 2

1.2.3 Fundamental Analysis Research 2

1.3 THE MACRO-ENVIRONMENT 3

1.3.1 Real Activity 3

1.3.2 Exchange Rates 4

1.3.3 Inflation Expectations 4

1.3.4 Interest Rate 5

1.4 PROBLEM STATEMENT 5

1.5 OBJECTIVES OF THE STUDY 6

1.6 RESEARCH HYPOTHESES 6

1.7 RESEARCH METHODOLOGY 6

1.8 ORGANISATION OF THE DISSERTATION 7

CHAPTER TWO: ALTERNATIVE APPROACHES TO SHARE

PRICE VALUATION

1.0 INTRODUCTION 8

1.1 THE THEORY UNDERLYING THE EFFICIENT MARKET

HYPOTHESIS 8

1.1.1 The Fair Game Model 9

1.1.2 The Submartingale Model 9

1.1.3 The Random Walk Model 9

1.1.4 The Forms of EMH 10

1.2 ALTERNATIVE APPROACHES TO SHARE PRICE VALUATION 10

1.2.1 Technical Analysis 11

1.2.2 Fundamental Analysis 15

2.4 A FUNDAMENTAL ANALYSIS OF SHARE PRICE VALUATION IN SOUTH AFRICA 20

2.4.1 Real Activity 21

2.4.2 Exchange Rate 22

2.4.3 Inflation Expectations 22

2.4.4 Interest Rate 23

2.5 CONCLUSION 24

CHAPTER THREE: AN EMPIRICAL ANALYSIS OF SHARE PRICE

VALUATION USING A FUNDAMENTAL

ANALYSIS APPROACH

3.1 INTRODUCTION 25

3.2 DATA SOURCES USED 26

3.2.1 Data Description 27

3.2.2 The Econometric Method of Estimation 28

3.3 AN EMPIRICAL APPROACH TO SHARE VALUATION

USING FUNDAMENTAL ANALYSIS 29

3.3.1 Model Structure 29

3.3.2 Presentation and Analysis 30

3.3.3 The Overall Fit of the Estimated Model 31

3.3.4 Violations of the Classical Linear Regression Model 31

3.4 CONCLUSION 37

CHAPTER FOUR: CONCLUSION

4.1 INTRODUCTION 39

4.2 GENERAL FINDINGS 39

4.3 CONCLUDING REMARKS 40

LIST OF SOURCES 42

CHAPTER ONE: INTRODUCTION

1.1 INTRODUCTION AND PRELIMINARY LITERATURE REVIEW

Conventional wisdom in economics suggests that share price changes are highly

unpredictable. This unpredictability is mainly caused by the fact that the fundamental

operation of the share market is very well understood. In essence, share prices exhibit

a random walk – this means that if shares did well last week, they are no more likely

to either do well or do poorly this week than at any other time. This so called random

walk is perceived by economists to be an indication of market efficiency and is

termed the efficient market hypothesis (EMH).

Market efficiency is theorised in three forms, namely, the weak, the semi-strong and

the strong. The weak form claims that share prices reflect all information from the

past, and thus an investor cannot predict future share prices on the basis of past share

prices. The semi-strong form argues that all publicly available information is already

represented in the share price; this information includes the quality of management,

fundamental data on the product, and so forth. This information cannot be used for

predictive purposes either. Finally, the strong form states that share prices reflect all

available information i.e. even unpublished information, and this (insider) information

cannot be used for predictive purposes (Bodie, Kane & Marcus 2007: 246) .

Notwithstanding the unpredictable nature of share prices, economists and those

intimately involved with share markets, still require processes or procedures to

explain and predict share market behaviour.

1.2 MODELS USED FOR PREDICTION PURPOSES

In the search for predictive models of share prices, two alternative models have come

to the fore, namely, fundamental analysis and technical analysis.

1.2.1 Technical Analysis

Technical analysis is basically the making and interpretation of share charts where the

analysis of averages and moving averages of share prices takes place. Technicians

study records of past share prices in order to find patterns they can profit from in the

1

future. They believe the market is 10 percent logical and 90 percent psychological.

They subscribe to the castle-in-the-air theory. This theory suggests that the crowd of

investors is likely to build their hopes during times of optimism into castles in the air.

The technician attempts to anticipate the crowd behaviour and thus buy before the

crowd makes their move (Malkiel 2003: 127).

1.2.2 Fundamental Analysis

In fundamental analysis, investors believe the market is 90 percent logical and 10

percent psychological. This model is based on the firm-foundation theory; the value

of a share is based on the present value of all future dividends. This value is known as

the intrinsic value. If the intrinsic value is greater than the quoted price the investor

should buy (Malkiel 2003:127). Fundamental analysts start their analysis with a study

of past earnings. In addition, an analysis of the management, the firms’ position in the

industry, and the prospects of the industry are taken into account (Bodie et al.,

2007:247). Fundamental analysts attempt to take all factors into consideration that

affect share prices, both firm specific and those pertaining to the macro-economy.

1.2.3 Fundamental Analysis Research

Asset prices are often thought to react to fluctuations in macroeconomic variables.

Returns on shares have a complicated relationship to macroeconomic variables.

Accordingly, research has being undertaken to understand this complexity.

Previous research by Solnik (1984: 69), was undertaken to find a correlation between

monetary variables and share prices. Variables considered were, interest rates,

inflation and the exchange rate. According to Solnik, the specific influence of

international monetary variables such as exchange rates is weak in comparison to

domestic variables such as changes in inflation expectations and interest rates. This

suggests that domestic variables are more influential.

Asprem (1989: 590) investigates the relationships, in ten European countries, between

the countries’ respective major share index and various macroeconomics variables.

This research showed that changes in share prices are positively correlated to certain

measures of real economic activity. These measures included a) industrial production,

b) real gross national product, c) gross capital formation, and d) exports. Positive

correlations were shown to exist between changes in the share indices and the United

2

States yield curve, as well as the M1 monetary aggregate and lagged values of share

indices themselves. Negative correlations are found between changes in share indices

and employment (a measure of real activity), the exchange rate, imports, inflation and

interest rates.

1.3 THE MACRO-ENVIRONMENT

Based on work done by Asprem (1989), the macroeconomic variables considered in

this dissertation include: a) real activity, b) exchange rates, c) interest rates and d)

inflation expectations.

1.3.1 Real Activity

In fundamental analysis, the constant growth model, also known as the Gordon

growth model, is used in calculating the intrinsic value of a firm. Value is based on

the future series of dividends that grow at a constant rate. Given a dividend per share

that is payable in one year, the required rate of return , and the assumption that the

dividend grows at a constant rate in perpetuity, the model solves for the present value

of the infinite series of future dividends (Howells & Bain 2005: 347).

Asprem (1989: 593), who assumes rational markets, suggests that asset prices should

reflect expectations of these future earnings, which are inclined to be influenced by

measures for real activity.

The perceptions of investor’s on future dividends must be responsive to changes in

the outlook for the economy as a whole. The movement from boom to recession, for

example, will lead to a demoted perception of dividend forecasts. Thus in the Gordon

growth model, this will lead to a reduced dividend in the numerator, and therefore a

downgraded present value.

The business cycle represents different levels of real activity. The different stages of

the cycle will exhibit differing levels of performance. In an expansionary phase,

performance will be greater, and expectations of future earnings thus increase. The

opposite is true for a recession, where expectations will be lower (Bodie et al., 2005:

577).

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These expansionary phases can be accounted to market growth, thus the gross

domestic product (GDP) growth rate will be used as a measure of this growth or

increase in real activity.

1.3.2 Exchange Rates

According to Phylaktis and Ravazzolo (1998), the adoption of more flexible exchange

rate regimes by developing countries has increased the volatility of foreign exchange

markets and the risk associated with such investments. The choice of currency

denomination is an important dimension in the overall portfolio decision of the

investor. Exchange rates volatility also affects real activity in that it changes the prices

of imports and exports.

A depreciation of a currency improves the competitive position of domestic

industries. The earnings of an export or international firm will increase when the

currency depreciates, as domestic goods will be cheaper relative to other international

goods (Asprem, 1989: 596). However, domestic firms that need to import capital

equipment will experience a negative impact on their share prices.

Any investor should be concerned about how their domestic capital market reacts to

international monetary disturbances such as exchange rate fluctuation. Solnik (1984:

71) maintains that the international investor who uses his home currency to value his

portfolio measures return as the sum of his assets’ return, in local currency, plus any

currency movements. The portfolio thus bears both market and currency risk. Leaving

market risk aside by way of diversification, the investor still needs to pay attention to

reactions of share prices to fluctuations in the currency of measure.

It is thus expected that a negative relationship exists between exchange rates and

share prices, due to the impact on domestic industries.

1.3.3 Inflation Expectations

The higher inflationary expectations are, the more likely one’s real returns on share

investments are going to be negatively affected.

Higher inflationary expectations also bring about higher interest rate expectations.

Central banks are generally forward looking in the application of monetary policy,

implying that if they expect higher inflation in the future, then they will apply

4

restrictive monetary policy today. This usually involves an increase in the interest

rates. Indirectly, inflationary expectations in most cases, leads to increases in interest

rates, which generally suppresses share market performance.

1.3.4 Interest Rate

The most considerable source of market wide influences can be contributed to interest

rates or expectations of interest rates. The required rate of return in the denominator of

the Gordon growth model is the sum of a risk-free rate and a risk premium derived

from the market’s current pricing of risk in general and the firm’s relative risk

characteristics. An official change in interest rates causes a change in the risk free rate

which will cause the required rate of return to change. An increase in the denominator

caused by increased interest rates will reduce the present value of the shares in

question; the opposite is true for a decrease (Howells and Bain, 2005: 356).

However, investors consider how much interest can be earned in all investment

opportunities (Malkiel 2003: 112). The risk free rate provides a base for all risky

assets. Once the interest rate changes the opportunity cost for investors in equity

markets changes (Asprem 1989: 598).

Interest rates are thus expected to be positively related to share prices according to the

opportunity costs investors undertake.

1.4 PROBLEM STATEMENT

Investors are observers of numerous factors that might affect return on equity. Returns

on shares have a complex relationship with macroeconomic variables. Thus there is no

consensus on a generally accepted asset pricing model that explicitly takes economic

variables into account (Asprem, 1989: 589).

This complex linkage of macroeconomic variables when related to shares on the

Johannesburg Securities Exchange (JSE) has not found much attention. Research on

this topic with regards to the South African equity market is thus limited. A model

needs to be developed to explain macroeconomic variations in share prices on the JSE.

5

1.5 OBJECTIVES OF THE STUDY

(a) Primary objective:

The primary objective of this work will be to research the link between certain

macroeconomic variables and share prices on the JSE.

(b) Secondary objective:

The secondary objective is to provide a simple and useful model that can be used by

investors and prospective investors in the South African equity market, to predict the

general movement of future equity returns.

1.6 RESEARCH HYPOTHESES

The following hypotheses will be tested:

Increased real activity in the form of GDP growth results in higher earnings and

therefore an increase in the JSE All Share Index (ALSI).

An expected depreciation in the exchange rate places domestic firms in a greater

competitive position, owing to cheaper exports, thus increasing earnings and

therefore increasing the ALSI.

Higher inflation expectations will have a negative impact on the ALSI.

Investors see a chance of higher returns with higher interest rates thus boosting the

short term inflows and increasing the ALSI.

1.7 RESESEARCH METHODOLOGY

Data will be obtained through secondary sources using the following methods:

(a) Historical method:

This involves obtaining data from published sources such as journals, research

reports, articles and the internet.

(b) Analytical method:

This involves the drawing up of an econometric model to establish statistical

relationships between the ALSI and certain macroeconomic variables investigated.

6

1.8 ORGANISATION OF THE DISSERTATION

Chapter two presents a literature overview, which explains both technical and

fundamental analysis. Fundamental analysis is further expanded on with regards to the

four factors considered, namely, real activity, exchange rates, inflation expectations

and interest rates. Chapter three entails an econometric analysis of the correlation

between the considered factors and the ALSI. Chapter four involves an overall

conclusion and highlights key points from each section.

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CHAPTER TWO: ALTERNATIVE APPROACHES TO SHARE PRICE

VALUATION

2.1 INTRODUCTION

The potential gains which the share market holds to those who read it correctly are

colossal; then again, the potential losses to those who don’t can be severe. It has

drawn people from all walks of life in an endeavour to reap these enormous gains

(Edwards & Magee, 2001: 3). The share market has been extensively studied in

finding a way to predict share price behaviour. Early research on share prices could

find no predictable patterns (Kendall 1953). Prices seemed to behave randomly; there

was no economic rationale to explain this until the development of the efficient

market hypothesis (EMH). The EMH explained the random movement in prices as the

result of a well operating market (Bodie et al., 2008: 357). Despite this theory of

market efficiency, two divergent approaches to predicting share prices have evolved,

namely, technical analysis and fundamental analysis.

The purpose of this chapter is to expand on the EMH and the two approaches

mentioned above, and give a more comprehensive explanation of each. The grounding

theory of the EMH is illustrated by Fama (1970) in three models namely, a) the Fair

Game model, b) the Submartingale model and c) the Random Walk model. The

differing versions of the EMH are explained by Bodie et al. (2008). Technical

analysis will be divided into two areas, according to Teweles and Bradley (1982:

373), namely; a) patterns on price charts, and b) trend-following methods.

Fundamental analysis is explained by Bodie et al. (2008) using macroeconomic and

equity analysis. Lastly, macroeconomic factors based on work done by Asprem

(1989), namely: a) real activity, b) exchange rates, c) interest rates and d) inflation

expectations, are applied to share price valuation in South Africa.

2.2 THE THEORY UNDERLYING THE EFFICIENT MARKET HYPOTHESIS

The EMH plays an important part in financial economic literature. An asset market is

said to be efficient if the asset price reflects all information. If this is true, investors

are wasting their time in an attempt to earn abnormal returns.

8

Fama (1970) suggested the following models for testing stock market efficiency: the

Expected Return or Fair Game model, the Submartingale model, and the Random

Walk model.

2.2.1 The Fair Game Model

The fair game model states that investors cannot achieve above average returns based

on historic information because such information is fully integrated into the share

price (Bhatti et al., 2006: 230). Fama (1970: 384) defines more exactly what is meant

by the term “fully reflected”. He hypothesizes that equilibrium prices are generated in

a two parameter world. These prices are conditional on some information set, and the

equilibrium expected return on a share is a function of its risk. This information is

fully utilised in determining equilibrium expected returns i.e. “fully reflected”.

Furthermore, the model hypothesises, that expected profits or returns in excess of

equilibrium are a fair game with respect to this information set. What is meant by

“fair game” is that expected profits or returns are zero.

2.2.2 The Submartingale Model

This model is similar to the fair game model, but the dissimilarity is that the expected

return is positive. Prices are expected to increase over time. Returns on investments

are expected to be positive due to the risk involved in capital markets. The expected

value of next period’s price, as forecast on the basis of the information set, is equal to

or greater than the current price. If the expected value of next period’s price is equal

to the current price, then the price sequence follows a martingale (i.e. zero expected

return) (Fama 1970:386).

2.2.3 The Random Walk Model

Two hypotheses constitute the random walk model. Firstly, the statement that the

current price of a share “fully reflects” available information is assumed to imply that

successive price changes are independent. Secondly, it is assumed that successive

price changes are identically distributed (Fama 1970: 387). The random walk model

states more than the fair game model. The fair game model states that the mean return

of the next period is independent of the current information set, however, the random

9

walk model, in addition, states that the entire distribution is independent of the current

information set.

2.2.4 The Forms of EMH

The EMH can now be described in more detail in accordance with the available

information that is reflected in the price. Fama (1970: 383) classified the information

set into three groups and put three forms of EMH forward, depending on the

definition of the relevant information set. These three forms are the weak, semi-strong

and strong forms.

The weak form hypothesis is the lowest form of efficiency. It maintains that share

prices already reflect all information that can be obtained by examining market

trading data, for example, past prices and trading volume. This form implies that past

data cannot be used for predictive purposes (Bodie et al., 2008: 361). The information

set applicable in the semi-strong form is publicly available information. This

information includes, in addition to past prices; annual reports, quality of

management, interest rates, information on money supply and the exchange rate, to

name a few. Consequently, investors are unable to reap superior returns from

analysing this data available to the public (Bodie et al., 2008: 361). The strong form is

concerned with whether given investors or groups have monopolistic access to any

information relevant to price formation (Fama 1970: 383). This version of the

hypothesis is extreme in that both private (inside information) and public information

is reflected in the price (Bodie et al., 2008: 361).

2.3 ALTERNATIVE APPROACHES TO SHARE PRICE VALUATION

The two different approaches to share price valuation include technical and

fundamental analysis. These theories have been put forward despite the EMH, which

states that both past and public information cannot be used for predicting future share

prices. Technical analysis is concerned with the market and the reading of charts (i.e.

past information), whereas fundamental analysis takes a scope of variables that lie

outside the market into account (i.e. public information).

10

2.3.1 Technical Analysis

Technical analysis is the study of the action of the market and ignores the study of the

goods in which the market deals (Edwards & Magee 2001: 4). In contrast,

fundamental analysis looks carefully at fundamental economic and political

conditions – forces inside and outside of the market. Technicians do not reject the

value of fundamental information, but believe prices only gradually close in on

intrinsic value (Bodie et al., 2008: 407). Technical analysts, primarily, are short run

traders and only seek capital gains. The technical approaches of patterns on price

charts and trend following methods, will be discussed below (Teweles & Bradley

1982: 372).

Patterns on Price Charts

Among the most oldest and popular approaches is the use of patterns on price charts.

Chartists believe that patterns repeat themselves and that charts can be used to

forecast significant price movements (Teweles & Bradley 1982: 373). Charts are used

to record historical movements of share prices and to forecast future movements

(Badger & Coffman 1967: 187). The two most commonly used charts are bar charts,

and point and figure charts.

An illustrative comparison of a bar chart and a point and figure chart is given in figure

2.1 for the same price fluctuation and time period. Bar charts indicate time on the

horizontal axis and price on the vertical axis in figure 2.1 (a). Price is represented by a

vertical line for a specified length of time, usually a day. The bar drawn indicates the

price range from high to low. Tick marks are added to indicate the opening and the

close of the market, and the midrange may be specified. Each period is plotted

chronologically from left to right. Additional data may be added that may be of

importance to the trader, such as volume (Teweles & Bradley 1982: 374).

Point and figure charts in contrast, in figure 2.1 (b), take no consideration of time or

volume – they are only designed to indicate price change. Significant changes,

considered by the individual trader, are represented by each box. Increases of this

amount are indicated by an X. Each successive rise is indicated by an X on top of the

previous X. If there is a decrease of the selected amount, an X is entered in the

following column and one box down. This is called a reversal. To make interpretation

11

easier, rises may be indicated by X’s and falls by O’s. Closing prices can also be

blacked in (Teweles & Bradley 1982: 375).

Figure 2.1: (a) Bar chart (b) Point-and-figure chart ( from Teweles & Bradley 1982 ).

Since technicians are only interested in the action of the market, much analysis is

centered around the interaction between demand and supply for a share. Increasing

prices are indicative of more demand than supply, and decreasing prices indicate the

opposite. Accordingly, a support level is a price at which a considerable increase in

the demand for a share is to be expected, whereas a resistance level is the price where

a substantial increase in the supply of a share develops. At these levels, a relatively

large amount of shares change hands (Badger & Coffman 1967: 198).

Figure 2.2: (a) How resistance forms (b) How support forms (from Badger &

Coffman 1967).

In panel (a) of figure 2.2, for example, a number of investors may have purchased

shares between R20 and R22. Say the share slips to R18 then recovers to the R20-R22

range. Holders hope the share will rise above R22, but some are happy to get out even

and start to sell when the share hits R22. This liquidation prevents the share from

going above R22, thus R22 forms as a resistance line. Perhaps this pressure from

12

Pri

ce

Pri

ce

Weeks

(a)

Weeks

(b)

Pri

ce

Pri

ce

(a) (b)

liquidation overwhelms new buying of the share, and the share breaks through the

lower support line. Then this range of R20-R22 (a congestion range) is interpreted as

a resistance level. In panel (b) of figure 2.2, the opposite is illustrated. Buyers in the

range R20-R24 are content with their purchase. When the share drops to R20, buyers

are attracted, and the resistance level of R24 meets sustained pressure. Eventually, the

prices break out on the upside, the area R20-R24 becomes known as a support level

(Badger & Coffman 1967).

Although many statistics books show how to construct charts, none present any

statistics indicating that charts will probably lead to significant profits over time

(Teweles & Bradley 1982: 375).

Trend Following Methods

A great deal of technical analysis is the identification of trends in market prices.

Technical analysts believe that once a trend is established, it is more likely to continue

than to reverse (Teweles & Bradley 1982: 377). This is basically the search for

momentum in market prices. Momentum can be absolute - where a trader searches for

upward or downward price trends, or it can be relative - when an analyst seeks to

invest in one sector over another (Bodie et al., 2008: 407).

a) Dow Theory

Trend analysis has its origins in the Dow Theory, established by Charles Dow. The

Dow theory hypothesises three forces working at the same time on share prices,

namely the primary, secondary and tertiary trend. The primary trend is the long term

change of prices over a number of months to a number of years. The secondary (or

intermediate) trends are brought about by short term deviations of prices from the

underlying trend line. The tertiary (or minor trends) are fluctuations on a daily basis,

which are insignificant (Bodie et al., 2008: 408).

13

.

Figure 2.3: Dow Theory trends (from Bodie et al., 2008).

Figure 2.3 above points out the characteristic components of the Dow Theory. The

primary trend here is upward, the intermediate trend has temporary deviations for a

few weeks and the minor trend has no long run impact (Bodie et al., 2008: 408).

b) Moving averages

The most usual trend following device is the moving average. A moving average adds

a new term periodically, for instance daily or weekly, and at the same time drops the

oldest term, thus recalculating the average per day or week (Teweles & Bradley 1982:

377).

The moving average takes in older and higher prices, thus it will be above current

prices after a period that has been experiencing falling prices. When prices have been

rising, the moving average will be below the current price. A break of the market

price (the irregular curve) through the moving average line (the smoothed curve) from

below, as at point A in figure 2.4, is a bullish signal, as it implies a shift from a falling

trend to a rising trend. The opposite is true for point B, the market line cuts the

moving average line from above and is thus a bearish signal.

The followers of trends must decide on the average lengths of time to utilize and what

events induce market action. The method can be checked with respect to past markets

without risking capital as the device allows them to get out of the market as well as

into it. Traders will profit from a major fluctuation in the market, and not lose much

money before the position is abandoned (Teweles & Bradley 1982: 379).

14

Pri

ce

Time

Figure 2.4: Moving average for Microsoft as of 18 January 2005 (from Bodie et al.,

2008).

2.3.2 Fundamental Analysis

The alternative method to share price valuation is fundamental analysis. Fundamental

analysis not only looks at the action of the market but also examines variables outside

of the market. The core of fundamental analysis is the analysis of the determinants of

value. Value is analysed at a micro and macro level. Analysis takes place at firm

level looking at the financials and even the personal characteristics of management.

However, the individual firm is tied to the broader economy, and thus

macroeconomics factors can have an influence on its future prospects as well (Bodie

et al., 2008: 569).

Macroeconomic and Industry Analysis

If the fundamental analyst first reviews the macro-economy and the specific industry,

a top down approach is being taken. This approach is a way of evaluating a firm’s

prospects by looking at the bigger picture first. After the macroeconomic influences

are considered, the fundamental analyst examines the firms’ position in the particular

industry (Bodie et al., 2008: 571).

Macroeconomic factors can be organised into demand and supply shocks. Demand

shocks are events that affect the demand for goods and services in an economy,

whereas supply shocks are events that influence production capacity and costs.

Demand shocks usually occur by aggregate output moving in the same direction as

interest rates and inflation, while supply shocks are the converse, with output moving

in the opposite direction of inflation and interest rates (Bodie et al., 2008: 574).

15

Pri

ce (

in m

illi

ons)

Time

Industry analysis, similarly with macroeconomic analysis, is important in evaluating a

firms’ performance, as it is generally impossible for a firm to do well in its industry

when the industry in question is suffering. This importance of selecting the correct

industry is illustrated in table 2.1. The profitability ratio1 for industries in South Africa

for 2004 and 2005 are given. In 2005, the profitability ratio for trade was only 4%

whereas real estate and other business services (excluding financial intermediation

and insurance) was 15%. An investor must choose the correct industry, as profitability

between differing industries can be large.

Table 2.1: Comparison of industry profitability ratios in South Africa (2004 –

2005)

Industry Profitability ratio

2004 2005

Forestry and fishing - 0.10

Mining and quarrying 0.06 0.07

Manufacturing 0.06 0.08

Electricity, gas and water supply 0.10 0.10

Construction 0.03 0.05

Trade 0.03 0.04

Transport, storage and communication 0.05 0.11

Real estate and other business services, excluding financial intermediation and insurance

0.15 0.15

Community, social and personal services, excluding government institutions

0.08 0.10

All industries 0.06 0.07

Source: Statistics South Africa (2005)

After the state of the macroeconomy is forecast, the analyst must determine the

implications of the forecast for specific industries. Industries have differing

sensitivities to the business cycle. Three factors determine the sensitivity of a firm’s

earnings to the business cycle. Firstly, is the sensitivity of sales. Necessities show

little sensitivity, as demand for these goods remain intact during recessions. Also,

industries for which income is not a crucial determinant of demand, for example, have

low sensitivity. Secondly, operating leverage determines sensitivity. This refers to the

ratio of variable to fixed costs. A firm with more variable costs with respect to fixed

costs is less sensitive to the conditions of business. During a recession, costs can be

reduced as output falls. Whereas, a firm with high fixed costs is more sensitive as

1 Net profit after providing for company tax divided by turnover

16

costs cannot be reduced. Operating leverage is measured by how sensitive profits are

to changes in sales. A degree of operating leverage of greater than 1 represents some

operating leverage. The third factor that influences sensitivity is financial leverage.

The use of debt incurs interest payments which must take place regardless of business

conditions. These payments represent a fixed cost similar to the operating leverage

case (Bodie et al., 2008: 586).

Differing sensitivity to the business cycle of the passenger car and cigarette industries

is demonstrated in figure 2.6 below. Cigarettes (the black curve in figure 2.6) will be

consumed regardless of whether economic times are good or bad and thus are less

sensitive. This is illustrated by the fairly smooth movement within the industry.

Durable goods, however, such as passenger cars (grey curve in figure 2.6) are

sensitive to the swings of the business cycle (Bodie 2008: 586). This is illustrated

through the large fluctuations in the passenger car industry.

Figure 2.5: Industry cyclicality (from Bodie et al., 2008)

Equity valuation

This valuation is at the firm level. Here, individual firm’s shares are valued according

to dividend models and are compared using price-earnings ratios.

17

a) Dividend Models

Fundamental analysts are always on the search for mispriced shares using information

concerning the current and prospective profitability of a company to calculate its fair

value (Bodie et al., 2008: 603). Dividend models are the most accepted and

conventional approaches used by fundamentalists for asset valuation. Investors in

shares expect a return consisting of dividends and capital gains or losses (Bodie et al.,

2008: 605).

This approach states that the present value of an asset is the sum of its future earnings,

each discounted at an appropriate rate that takes time and risk into account (Howells

& Bain 2005: 346). The price of a share at time period zero P0 is the present value

PV of the expected future dividend streamD1. The expected capital gain realised upon

the sale of the share is included in the expected future dividend stream since its size

also depends on the present value of this stream. The approach assumes that expected

dividends grow at a constant rateg, thus eliminating the problem of forecasting an

infinite number of dividends. Finally, the required rate of return is given byk . Taking

these elements into account gives the constant growth model, also known as the

Gordon growth model, in equation 2.1 (Howells & Bain 2005: 347):

P0=PV =D1

( k−g ) ................................................................................................. (2.1)

In theory, the present value model asserts that share prices are determined by

dividendsD and the discount ratek . Therefore any factor that influences the dividend

stream or the discount rate will systematically influence share prices (Moolman & Du

Toit 2005: 81).

b) Price earnings ratios

A great deal of market valuation centres on the firm’s price earnings multiple, i.e. the

ratio of price per share to earnings per share, generally called the price earnings ratio

(P/E ratio). This ratio can serve as a useful indicator of expectations of growth

prospects. Bearing in mind that dividends are earnings not reinvested in the firm;

D1=E1(1−b)....................................................................................................... (2.2)

18

Where, E1 is future earnings and b is the plowback ratio (the fraction of earnings

reinvested in more capital).

Dividends initially fall under a policy of reinvestment. However, subsequent growth

in the assets of the firm because of these reinvested profits will generate growth in

future dividends. The return on capital invested in the firm is the return on equity

(ROE). The capital stock increases by the rate at which income was generated i.e.

ROE multiplied by the plowback ratio(b). With more capital the firm earns more

income and therefore pays out higher dividends, growing at a rate of g;

g=ROE ×b.......................................................................................................... (2.3)

Substituting forD1 and g into equation 2.1 and rearranging gives the P/E ratio;

P0

E1

= 1−bk−ROE× b

..........................................................................................................

(2.4)

The P/E ratio increases withROE. High ROE gives the firm good growth prospects.

Higher plowback ratios also increase the P/E ratio, as long as the ROE exceedsk

(Bodie et al., 2008: 622). This shows that a firms’ P/E ratio will be higher if its return

on projects is higher than the return that can be earned elsewhere¿). The P/E ratio thus

gives an indication of the firms’ growth with respect to the industry.

In summary, the main difference between the dividend model and the price earnings

ratio is cited. In the dividend model, fundamental analysts analyse shares to find the

intrinsic value and hope that there are some cracks in the efficient market to uncover

shares whose market value is out of line with the intrinsic value. If the intrinsic value

is greater than market price, the investor makes a purchase, and holds for the long

term until the two values approach each other. Price earnings ratios, however, are

mainly used as comparables, as here the investor is interested in relative evaluation.

Other things being equal, the investor is more willing to pay the lowest price per rand

of earnings. Therefore a firm with a P/E ratio lower than another firm in the same

industry will be regarded as cheap (Howells & Bain 2005: 352). The P/E ratio should

be equivalent to the growth rate; if the P/E ratio is less than the growth rate of

equation 2.3, then a bargain is found (Bodie et al., 2008: 623).

19

A focus on fundamental analysis, using macroeconomic variables, is embarked on,

since the relationship between share prices and macroeconomic variables is not fully

understood. The analysis is carried out in the South African economy specifically

with respect to the Johannesburg Securities Exchange (JSE), as not much research in

this area has occurred for this developing economy.

2.4 A FUNDAMENTAL ANALYSIS OF SHARE PRICE VALUATION IN SOUTH

AFRICA

This dissertation is based on macroeconomic variables studied by Asprem (1989).

Asprem (1989) examines the relationship between share indices, asset portfolios and

macroeconomic variables in ten European Countries. The countries considered where;

Denmark, Finland, France, Germany, Italy, Norway, Netherlands, Sweden,

Switzerland and the United Kingdom. The macroeconomic variables taken into

account were; several measures of real activity (changes in industrial production, real

gross national product, gross capital formation, employment and exports), the

effective trade-weighted exchange rate, consumption (measured by changes in

imports), the interest rate (measured by interest rates on long term bonds and the

United States yield curve), and inflation (measured by past and future values and the

money supply). Share indices were also regressed on the S&P 400 and a basket of

European share indices.

However, Asprem’s (1989) study was about European markets and not about a

developing market such as South Africa’s. Sources of literature on the study of share

markets are dominated by studies on developed economies, whereas studies on

emerging markets and in particular, South Africa’s are scarce. However, according to

Moolman and Du Toit (2005: 77) the most important studies that examine structural

determinants of the JSE are those of Van Rensburg (1995), and Barr and Kantor

(2002).

Van Rensburg (1995), estimates the simultaneous linear relationship between the JSE

and four macroeconomic factors, namely the unexpected changes in the term

structure, unexpected returns on the New York Stock Exchange, unexpected changes

in inflation expectations and unexpected changes in the gold price. The results of this

study indicate that all four variables significantly influence share prices.

20

Barr and Kantor (2002), developed an econometric model of the South African

economy that focused on the linkages between the real and financial markets and

between domestic and foreign financial markets. They identify the gold price, the

short term interest rate, foreign share markets and local business confidence as factors

that significantly influence returns on the JSE (Barr and Kantor 2002: 53).

Another contribution to the study of returns on the JSE is that of Jefferis and

Okeahalam (2000). Research was carried out for the share markets of South Africa,

Botswana and Zimbabwe. Their approach lacked a theoretical background and was

empirical in nature. Variables investigated in the South African case consisted of the

real exchange rate, real GDP, long term interest rates and United States (US) interest

rates.

According to Jefferis and Okeahalam (2000: 24), the prices of individual company

shares should be influenced by the following sets of economic factors: those relating

to individual firms; to specific sectors of the economy; to the national economy; and

to the international economy. Given that this dissertation considers a national share

market index, the JSE All Share Index (ALSI), only the national and international

factors will be taken into account. This dissertation will limit the number of factors

considered to real activity, the exchange rate, the interest rate and inflation

expectations.

2.4.1 Real Activity

The Gordon growth model reflected by equation 2.1 dominates the literature on

fundamental analysis. Also referred to as the present value model, it maintains that

share prices are determined by dividends and the discount rate (Moolman & Du Toit

2005: 81). Since growth of dividends are assumed to be constant, anything that

changes expected future profits (i.e. dividends), or the discount rate will therefore

affect share valuation (Jefferis & Okeahalam 2000: 24).

Asprem (1989: 593) states that, assuming rational markets, asset prices should reflect

expectations of future earnings (dividends) which are likely to be influenced by

measures of real activity. Jondea and Nicolai (1993), show that only in the case of US

shares do dividends directly explain share prices, while in other countries, dividends

have to be replaced by proxies. Since dividends are usually proxied by variables such

21

as industrial production, unemployment or the state of the business cycle, the Gross

Domestic Product (GDP) growth rate will be used as a proxy in this dissertation

(Moolman & Du Toit 2005: 81).

2.4.2 Exchange Rate

Fang (2002: 195) mentions that little empirical research has examined the interaction

between share returns and foreign exchange rates. According to Branson and

Henderson (1985), the portfolio balance model contends that investors will usually

hold a greater proportion of any asset the higher return it offers and the lower the

return offered on competing assets, other things being equal. Fang (2002: 195)

focuses on the effects of currency depreciation and states that if the domestic currency

is expected to depreciate, against the dollar, for example, investors would shift their

funds from domestic assets to American assets. According to this model, currency

depreciation should have negative effects on stock prices and returns, and hence it is

assumed that an appreciation will have the opposite effect.

Asprem (1989: 596) moves away from the focus on the investors’ portfolio decisions

and looks at the possible effect of currency depreciation on domestic industries. A

depreciation of a currency improves the competitive position of domestic industries as

their prices relative to international industries are cheaper. Together the prices and

volume of production can result in higher earnings. This is especially the case for

international or export orientated firms that have a large foreign customer base.

2.4.3 Inflation Expectations

The discount rate in the Gordon growth model of equation 2.1 is determined by three

factors: 1) the economy’s real risk-free rate, 2) the expected rate of inflation, and 3) a

risk premium (Reilly 1989). According to Van Rensburg (1995: 51), rational investors

are only concerned about real returns and thus nominal returns should offset the

inflation rate. Investors want to be compensated for expected inflation (Moolman &

Du Toit 2005: 81). An upward revision in inflationary expectations should lead to a

higher discount rate and thus a drop in the current share price, other things being

equal (Van Rensburg 1995: 51).

According to Van Rensburg (1995: 51), three studies have examined the relationship

between inflation and share returns in South Africa. Bethlehem (1972) studied the

22

inflation adjusted performance of a randomly selected sample of industrial shares over

twenty years. It was found that these shares yielded positive real returns; however, the

study occurred prior to the high rates of inflation experienced in the late 1970’s.

Gultekin (1983) tested the Fisher Hypothesis that a unitary relationship exists between

share returns and inflation, yet no significant relationship was found. Lastly, Correia

and Wormald (1987) found no significant relationship when using the present rate of

inflation as a proxy for expected inflation when regressed on the ALSI. However,

Correia and Wormald (1987) used the short term interest rate on three month

negotiable certificates of deposit as a measure on inflationary expectations, and found

a negative relationship with share returns.

Asprem (1989: 603) investigated the relationship between share returns and inflation

(past, present and future measures on inflation). It was found that there is a stronger

correlation between share returns and future measures of inflation. Asprem (1989:

604) also considered the money supply, since most economic theory relates inflation

and the money supply. This is the monetarists approach to inflation that indicates that

increased money supply results in increased inflation. It was found that the monetary

base generally showed negative relationships, but this was only significant in the

United Kingdom. However, broader measures of money supply, showed a stronger

relationship to share returns than base measures of money. Positive coefficients

indicated that there was a liquidity effect in place. The effect of changing monetary

supply is to increase the liquidity in the financial markets. Increased liquidity is

transferred into demand for financial assets which results in asset prices being bid up

(Asprem 1989: 604).

2.4.4 Interest Rate

As mentioned above, Reilly (1989) states that the discount rate in the Gordon growth

model is determined by three factors. These factors are summed up by the long term

interest rate. The expected future short term interest rates are used to discount future

earnings in the Gordon growth model. However, these short term interest rates are

usually captured by the long term rate as the long term rate is considered as the

average of all future short term interest rates expected to prevail over the duration of

the shares’ life (Moolman & Du Toit 2005: 81).

23

The interest rate represents the discount rate in the denominator in equation 2.1. All

else being equal, an increase in the interest rate, results in a decrease in the price of

shares. The opposite is true for a decrease in interest rates (Asprem 1989: 598).

Van Rensburg (1995: 53) investigates the relationship between the JSE and the term

structure of interest rates. The term structure of interest rates refers to the yield to

maturity of bonds that display different terms to maturity. The term structure

influences the discount rate in the Gordon growth model. The measure used by Van

Rensburg (1995: 53) was the difference in yields between three month and ten year

default free bonds. He found a significant negative relationship between the

unexpected changes in the term structure and the ALSI.

2.5 CONCLUSION

In both developed and emerging markets, there have been times when share market

indices experienced substantial declines or crashes. These crashes ask the question

whether share prices reflect fundamental economic factors (Jefferis & Okeahalam

2000: 23). Share markets play the important role of pricing and allocating capital

within the economy in accordance with risk and expected return. This role is

particularly important in developing economies such as South Africa. If the share

market does not allocate financial capital efficiently to competing uses, then share

markets are unlikely to contribute to economic development.

It is thus important to improve the general understanding of the relationship between

the JSE and macroeconomic variable to see if the market is driven by fundamentals. If

so, share markets should be promoted for economic development.

The following chapter moves from theory to empirical analysis. A model is built,

taking into account the four variables discussed above, namely GDP growth, the

exchange rate, inflation expectations and the interest rate. These variables are

regressed against the ALSI. The results are critically analysed, using the appropriate

econometric methods, in order to determine whether share markets are indeed driven

by fundamentals.

24

CHAPTER THREE: AN EMPIRICAL ANALYSIS OF SHARE PRICE VALUATION USING A FUNDAMENTAL ANALYSIS APPROACH

3.1 INTRODUCTION

Over the history of share market research, much concentration has been on the more

developed economy’s share markets while developing economy’s share markets, such

as South Africa’s Johannesburg Securities Exchange (JSE), has received less

attention. However, with the ending of apartheid in South Africa, the country has

become more attractive to portfolio investors (Jefferis & Okeahalam 2000: 28). This

increase in popularity is evident in the proliferation of research on the JSE in the

pursuing years.

According to Asprem (1989: 589) returns on shares have a complicated relationship to

macroeconomic variables. Chen, Roll and Ross (1986) recognised the spread between

long and short term interest rates, the expected and unexpected inflation rate,

industrial production, and the spread between high and low grade bonds, as

systematically affecting share returns. The link between share returns, real activity,

inflation and money was investigated by Fama (1981). Keim and Stambaugh (1986)

explored the relationship between share returns and the yield differential between low

grade bonds and Treasury bills, the ratio of the Standard and Poor’s composite index

to its previous long run level, and the level of small firms’ prices. The relationship

between share prices and exchange rates was found to be significant by Fang (2002).

A great deal of this empirical research was carried out with respect to international

and developed countries. Nonetheless, according to Moolman and Du Toit (2005: 77)

the most important studies that examine structural determinants of South Africa’s JSE

are those of Van Rensburg (1995) and Barr and Kantor (2002).

Van Rensburg (1995) estimates the simultaneous linear relationship between the JSE

and four macroeconomic factors, namely the unexpected changes in the term structure

of interest rates, unexpected returns on the New York Stock Exchange, unexpected

changes in inflation expectations and unexpected changes in the gold price. All four

variables were found to be statistically significant in explaining movements in share

prices. A further study by Van Rensburg (1998) used bivariate Granger causality tests

25

and correlations to investigate relationships between macroeconomic variables and

share prices. He tested factors affecting the discount rate and dividend in the Gordon

growth model and also tested international factors. Finally, Van Rensburg (1999) also

analysed macroeconomic relationships on the JSE All Share Index (ALSI), the

Industrial Index and Gold Index of the JSE. For all three indices, he found long term

interest rates, the gold and foreign reserve balance and the balance on current account

to be significant influences on share returns (Moolman & Du Toit 2005: 82).

Barr and Kantor (2002) identified the gold price, the short term interest rate, foreign

stock markets and local business confidence as factors that significantly influence

returns on the JSE (Barr and Kantor 2002: 53).

Lastly, Jefferis and Okeahalam (2000) carried out empirical research on several

Southern African markets. Variables investigated in the South African case consisted

of the real exchange rate, real GDP, long term interest rates and US interest rates.

Chapter three shifts from the theoretical premise established in chapter two, and has

an empirical focal point. A model is built using certain macroeconomic variables, as

mentioned above, in an attempt to explain movements in the ALSI.

3.2 DATA SOURCES USED

The data used for this dissertation is a quarterly data series, which was extracted

from the first quarter of 2000 to the second quarter of 2008. This resulted in 32 data

points. The majority of the data, for the independent variables, was from the

electronic database of the South African Reserve Bank. Data for the dependent

variable was supplied by the JSE. The dependent variable in this case is quarterly

index values of the ALSI. The variables are explained in more detail in the

following section.

26

3.2.1 Data Description

The following table presents a list of all the independent variables to be used in the

estimation procedure:

Table 3.1: Variables used in estimation

Independent

Variable

Variable name Unit of

Measurement

Functional form

InfExp Inflation

Expectations

% Linear

Exchange Real Effective

Exchange Rate

% Linear

GDPGrowth Gross Domestic

Product Growth

% Linear

IntRate Prime Overdraft

Interest Rate

% Linear

Source: www.resbank.co.za

The dependent variable is the ALSI. The top 99 per cent of all companies are included

in the ALSI and the remaining 1 per cent forms the FTSE/JSE Africa Fledgling Index.

The ALSI is further divided into the FTSE/JSE Africa Top 40 Index containing the

forty highest ranking companies, the FTSE/JSE Africa Mid Cap Index containing the

sixty highest ranking companies outside the top forty, and the FTSE/JSE Small Cap

Index containing the remaining companies (Forssman 2005). The ALSI is ranked by

full market capitalization (shares in issue multiplied by price). The weighting of a

constituent in the index is Free Float Market Cap weighted (free float multiplied by

shares in issue multiplied by price). Free float is the number of shares that are freely

tradable among investors.

Inflation expectations considered here are for one year ahead in relation to the

reference quarter when the expectations were surveyed. In each instance, the annual

average CPIX inflation rate for the calendar year which is expected by the participants

is asked.

27

The exchange rate is the real effective exchange rate. This is a weighted average

exchange rate against the most important currencies, it is measured in percentage

changes of averages.

Gross domestic product (GDP) growth is growth in GDP for one term. GDP is

compared with the preceding period. Quarterly changes reflect annual rates based on

seasonally adjusted data

The prime overdraft rate, is the lowest rate at which a clearing bank will lend money

to its clients on overdraft. Competition forces all banks to set the same prime rate.

3.2.2 The Econometric Method of Estimation

Regression analysis is used by economists to make quantitative estimates of economic

relationships that previously have been completely theoretical (Studenmund 2006: 6).

The lifeblood of regression analysis is estimation of the coefficients of econometric

models with a technique called Ordinary Least Squares (OLS) (Studenmund 2006:

35). It is very rare that one independent variable explains all the variation in a

dependent variable, thus multivariate regression models (models with more than one

independent variable) are employed. The general multivariate regression model with

K independent variables is represented by equation 3.1:

Y i=β0+β1 X1 i+β2 X2 i+…+βk X ki+∈i ....................................................... (3.1)

Where i indicates the observation number, therefore, X1 i indicates the ith observation

of independent variable X1, while X2 i indicates the ith observation of another

independent variable X2. In this model, Y is referred to as the dependent variable and

∈ is the stochastic error term that is added to the model to account for all the variation

in the model not explained by the independent variables. The coefficients β in a

multivariate regression model are often called partial regression coefficients. The

word “partial” implies that researchers are able to distinguish the impact of one

variable on the dependent variable from that of other independent variables. The

intercept is given by β0 (Studenmund 2006: 41).

28

The above gives some insight into the statistical theory used in this dissertation. The

subsequent section will present the model used in this study.

3.3 AN EMPIRICAL APPROACH TO SHARE VALUATION USING

FUNDAMENTAL ANALYSIS

3.3.1 Model Structure

As mentioned before, Asprem (1989: 589) states that share prices have a complicated

relationship to macroeconomic variables. There is no generally accepted asset pricing

model that explicitly takes economic variables into account. However, this

econometric model is specified in equation 3.2, and attempts to explain this complex

relationship:

ALSI=bo+b1 InfExp+b2 Exchange+b3GDPGrowth+b4 IntRate+∈t .. (3.2)

The variables considered are the ALSI, inflation expectations for one year ahead

(InfExp), the real effective exchange rate (Exchange), gross domestic product growth

for one term (GDPGrowth), and the prime overdraft interest rate (IntRate). The

stochastic error term ∈t is added to represent all possible variables omitted from the

model as well as random errors from the estimation process. Economic theory predicts

a positive relationship between share prices and real activity (represented by

GDPGrowth) as additional real activity results in higher earnings and therefore higher

prices. Theory also suggests a negative relationship between share prices and inflation

expectations, since higher inflation expectations bring about higher interest rate

expectations, and with forward looking monetary policy, this generally suppresses

share market performance. Higher interest rates lead to above average short term

inflows, thus improving the performance on share markets. However, theory is

inconclusive on the relationship between share prices and the exchange rate – a

negative or positive relationship could exist, due to the point of view taken. From an

export orientated firm’s perspective, depreciation in currency will have positive

effects on share prices. However, depreciation from an investor’s viewpoint will have

a negative effect on share prices.

29

3.3.2 Presentation and Analysis

The model specified in equation (3.2) is regressed using Eviews and the results are

displayed in table 3.2 below:

Table 3.2: Regression output of equation 3.2

Dependent Variable: ALSI

Method: Least Squares

Date: 11/22/08 Time: 09:38

Sample(adjusted): 2000:3 2008:2

Included observations: 32 after adjusting endpoints

Variable Coefficient Std. Error t-Statistic Prob.

C 10616.57 12758.39 0.832124 0.4126

INFEXP -7745.243 2470.989 -3.134471 0.0041

EXCHANGE -410.8546 252.2541 -1.628733 0.1150

GDPGROWTH 1360.849 985.2728 1.381190 0.1785

INTRATE 3678.538 1423.635 2.583905 0.0155

R-squared 0.364679 Mean dependent var 15396.41

Adjusted R-squared 0.270557 S.D. dependent var 7897.919

S.E. of regression 6745.410 Akaike info criterion 20.61371

Sum squared resid 1.23E+09 Schwarz criterion 20.84273

Log likelihood -324.8194 F-statistic 3.874546

Durbin-Watson stat 0.618148 Prob(F-statistic) 0.012971

The estimated equation is given below:

ALSI=10616.57−7745.24 InfExp−410.85 Exchange+1360.85 GDPGrowth+3678.54 IntRate

..................................................................................................... (3.3)

Equation (3.3) indicates that a one percentage point increase in inflation expectations

decreases the ALSI by 7745.24 points; a one percentage point increase in the

exchange rate (i.e depreciation) leads to a 410.85 point decrease in the ALSI; a one

percentage point increase in the GDP growth rate increases the ALSI by 1360.85

points; and a one percentage point increase in the interest rate increases the ALSI by

3678.54 points.

30

All coefficients conform to the expected signs. However, the only coefficients that

are statistically significant at the 5 per cent level are b1 and b4 . Further aspects will be

scrutinised before accepting this initial result.

3.3.3 The Overall Fit of the Estimated Model

The R-squared indicates that 36% of the variation in the ALSI is explained by

inflation expectations, the exchange rate, GDP growth and the interest rate. A more

accurate measure is the adjusted R–squared as it takes into account the sample size

and the number of independent variables. The adjusted R-squared shows that the

models explanatory power drops to 27%. That is a 9% downward adjustment from the

original R-squared measure. The following section examines equation (3.3)’s

violations of the classical model.

3.3.4 Violations of the Classical Linear Regression Model

In order for OLS to be the best estimator available for regression models the

following classical assumptions must be met (Studenmund 2006: 89):

I. The regression model is linear, is correctly specified, and has an additive error

term;

II. The error term has a zero population mean;

III. All explanatory variables are uncorrelated with the error term;

IV. Observations of the error term are uncorrelated with each other (no serial

correlation);

V. The error term has a constant variance (no heteroskedasticity);

VI. No explanatory variable is a perfect linear function of any other explanatory

variable(s) (no perfect multicollinearity);

VII. The error term is normally distributed.

This lays down the criteria to be met by the model so that the OLS estimates are the

best, linear, unbiased estimators.

31

The next section deals with violations of the classical model of econometrics in the

form of multicollinearity, serial correlation and heteroskedasticity. Corrections will

be made where necessary.

Multicollinearity

Perfect multicollinearity is the violation of Classical Assumption (VI) that no

independent variable is a perfect linear function of one or more other independent

variables. Perfect multicollinearity is a rare phenomenon; however, harsh imperfect

multicollinearity can cause several problems. The more correlated two or more

independent variables are, the trickier it is to accurately estimate the coefficients of

the true model (Studenmund 2006: 245). Thus, multicollinearity reveals itself through

low t-statistics. This is due to the chief consequence of multicollinearity, that is, the

variance and the standard errors of the estimates will increase (Studenmund 2006:

251).

The variance inflation factor (VIF) is a means of exposing the severity of

multicollinearity. The VIF is an index of how much multicollinearity has increased

the variance of an estimated coefficient. A VIF is calculated for each independent

variable using EViews. There is no table of formal critical VIF values, however, the

widely accepted rule is that if the VIF of a coefficient is greater than five, then severe

multicollinearity is considered to exist (Studenmund 2006: 259).

Table 3.3: Unadjusted R-squares and VIFs of independent variables

Variable R2 VIF

InfExp 0.815 5.41

Exchange 0.159 1.19

GDPGrowth 0.348 1.53

IntRate 0.835 1

Table 3.3 gives the unadjusted R-squares and VIFs of each independent variable.

Using the rule given by Studenmund (2006: 259), only inflation expectations appears

to show severe multicollinearity. Since inflation expectations are statistically

significant at the 5 per cent level with a p-value of 0.0041, it is not dropped from the

32

equation. All other variables show no severe multicollinearity. Therefore, the

estimated equation is not altered for multicollinearity.

Serial Correlation

Serial correlation is a violation of Classical Assumption (IV). The theory assumes that

observations of the error term are uncorrelated with each other. Serial correlation can

exist in any research study in which the order of the observations has some

significance. Therefore, it often occurs in time series data. In effect, serial correlation

entails that the value of the error term from one time period depends in some

systematic way on the value of the error term in other time periods (Studenmund

2006: 313). The Durbin-Watson d test is the most commonly used test for serial

correlation. If serial correlation is detected using this test, the generalised least squares

technique is used to reduce it or remove it.

(a) First order serial correlation coefficient

First order serial correlation is the most usual form of serial correlation that is

assumed. This is where the current value of the error term is a function of the previous

value of the error term:

∈t=ρ∈t−1+u t...................................................................................................... (3.4)

Where, ∈ is the error term of the equation; ρ is “rho”, the first-order autocorrelation

coefficient (this variable indicates the strength of the serial correlation if it equals zero

then there is no serial correlation); and u is a classical error term (Studenmund 2006:

314).

Table 3.4, below, shows this functional form regressed for the residuals in equation

(3.3).

33

Table 3.4: The first-order serial correlation coefficient

Dependent Variable: EMethod: Least SquaresDate: 11/26/08 Time: 10:52Sample(adjusted): 2000:4 2008:2Included observations: 31 after adjusting endpointsVariable Coefficient Std. Error t-Statistic Prob. C 663.0859 884.7689 0.749445 0.4596E(-1) 0.768737 0.168137 4.572077 0.0001R-squared 0.418883 Mean dependent var 186.0182Adjusted R-squared 0.398844 S.D. dependent var 6309.223S.E. of regression 4891.807 Akaike info criterion 19.89085Sum squared resid 6.94E+08 Schwarz criterion 19.98337Log likelihood -306.3082 F-statistic 20.90389Durbin-Watson stat 2.248815 Prob(F-statistic) 0.000083

The coefficient of the variable E(-1) represents rho (ρ). In this case, the value of ρ is

positive and significant, confirming first order serial correlation. However, this is not

a test of serial correlation but is important for the Durbin-Watson d test described

below.

(b) Durbin-Watson d test

The Durbin-Watson d statistic is used to establish if there is first order serial

correlation in the error term of the equation by investigating the residuals of a specific

estimation of that equation (Studenmund 2006: 325). The typical hypotheses are:

H 0 : ρ ≤0 ................................................................................................................ (3.5)

H A : ρ>0 ................................................................................................................ (3.6)

Here, the null hypothesis is no serial correlation and the alternate hypothesis is

positive serial correlation. The Durbin-Watson d statistic is 0.618 as indicated by table

3.2. Also indicated by table 3.2 is that 32 observations are included in the regression.

Therefore using the number of observations and number of explanatory variables, and

reading the critical values of the Durbin –Watson test statistics, the lower and upper

limit is 1.18 and 1.73 respectively. Therefore the Durbin-Watson d statistic lies below

the lower limit and the null hypothesis may be rejected at the 5 per cent level of

significance. Thus there is positive serial correlation and the generalized least squares

(GLS) method will be used as a remedy.

34

(c) Generalized least squares

The GLS equation is estimated using the AR(1) method, the results are displayed in

table 3.5 below.

Table 3.5: Generalized least squares AR(1) method

Dependent Variable: ALSIMethod: Least SquaresDate: 11/26/08 Time: 14:57Sample(adjusted): 2000:4 2008:2Included observations: 31 after adjusting endpointsConvergence achieved after 74 iterationsVariable Coefficient Std. Error t-Statistic Prob. C 474418.0 8783324. 0.054013 0.9574INFEXP -252.3288 472.2942 -0.534262 0.5979EXCHANGE 45.76945 29.80164 1.535803 0.1371GDPGROWTH 175.4081 129.1097 1.358598 0.1864INTRATE -38.28460 251.1317 -0.152448 0.8801AR(1) 0.998396 0.030736 32.48279 0.0000R-squared 0.985717 Mean dependent var 15629.62Adjusted R-squared 0.982861 S.D. dependent var 7915.680S.E. of regression 1036.294 Akaike info criterion 16.89667Sum squared resid 26847636 Schwarz criterion 17.17422Log likelihood -255.8985 F-statistic 345.0755Durbin-Watson stat 0.953639 Prob(F-statistic) 0.000000Inverted AR Roots 1.00

The equation is re-estimated as:

ALSI=474418.03−252.33 InfExp+45.77 Exchange +175.41 GDPGrowth

−38.28 IntRate ...................................................................................................... (3.7)

[ AR (1 )=0.9983956357 ]

The coefficients b2 and b4 have changed signs. The change in b2 indicates the

uncertainty with regard to the theory relating to exchange rates. The negative sign of

the coefficient b4 now conforms to the theory of the Gordon growth model and shows

the negative relationship between share prices and interest rates. All coefficients

reduce significantly in magnitude. The p-values show that all variables are not

statistically significant at the 5 per cent level. However, the adjusted R-squared of the

model has increased dramatically from 27 per cent to 98 per cent. The Durbin-Watson

d statistic has increased from 0.62 to 0.95, showing that serial correlation may still be

present.

35

Heteroskedasticity

Heteroskedasticity is the violation of Classical Assumption (V). The assumption

asserts that the observations of the error term are drawn from a distribution that has a

constant variance. This assumption of constant variances for different observations of

the error term is not often observed in real world scenarios. Heteroskedacticity is

more likely to be found in cross-sectional data than time series data (Studenmund

2006: 346). Tests for heteroskedacticity include the Park test and White test. The

latter will be used in this dissertation.

(a) Testing for Heteroskedasticity: The White Test

Table 3.6: White heteroskedasticity results

White Heteroskedasticity Test:F-statistic 1.698085 Probability 0.149121Obs*R-squared 18.65790 Probability 0.178437

Test Equation:Dependent Variable: RESID^2Method: Least SquaresDate: 11/26/08 Time: 16:57Sample: 2000:3 2008:2Included observations: 32Variable Coefficient Std. Error t-Statistic Prob. C 2.65E+09 1.44E+09 1.839862 0.0833INFEXP -1.20E+09 3.86E+08 -3.104620 0.0064INFEXP^2 77911246 60579271 1.286104 0.2156INFEXP*EXCHANGE 153350.8 6786077. 0.022598 0.9822INFEXP*GDPGROWTH

81007631 26517614 3.054861 0.0072

INFEXP*INTRATE -13392751 58529419 -0.228821 0.8217EXCHANGE 47807019 47878242 0.998512 0.3320EXCHANGE^2 28716.78 682760.6 0.042060 0.9669EXCHANGE*GDPGROWTH

-2224612. 3637875. -0.611514 0.5490

EXCHANGE*INTRATE

-3460873. 4613380. -0.750182 0.4634

GDPGROWTH -3.80E+08 2.10E+08 -1.808611 0.0882GDPGROWTH^2 13369940 9345185. 1.430677 0.1706GDPGROWTH*INTRATE

-19188864 12058046 -1.591374 0.1299

INTRATE 2.88E+08 2.06E+08 1.398091 0.1801INTRATE^2 -3385866. 17255032 -0.196225 0.8468R-squared 0.583059 Mean dependent var 38391090Adjusted R-squared 0.239697 S.D. dependent var 70410037S.E. of regression 61394299 Akaike info criterion 39.00851Sum squared resid 6.41E+16 Schwarz criterion 39.69557Log likelihood -609.1362 F-statistic 1.698085Durbin-Watson stat 1.203038 Prob(F-statistic) 0.149121

The hypotheses are stated as follows:

36

H 0 : No Heteroskedasticity

H A : Heteroskedasticity is present

The null hypothesis is only rejected if the test statistic is greater than the critical value

obtained from the Chi-square distribution tables.

The results of the white test are displayed in table 3.6 above. The Obs*R-squared

value of 18.66 is the White’s test statistic. It is computed as the number of

observations time the R2 from the test regression. The test statistic has a chi-square

distribution with degrees of freedom equal to the number of slope coefficients in table

3.6. Thus, with 14 degrees of freedom, the critical chi-square value is 23.7 at the 5 per

cent level of significance. Since the test statistic of 18.66 is less than the critical value

of 23.7, the null hypothesis cannot be rejected, and it is thus concluded that no

heteroskedasticity is present.

3.4 CONCLUSION

Theory suggests that the four variables considered in this dissertation should relate to

the ALSI as follows. Higher inflation expectations, according to the Gordon growth

model, should lead to a higher discount rate and thus current share prices

should drop. Theory on the exchange rate was inconclusive (remembering though that

not much research has been done in this area). The portfolio balance model suggests

that a currency depreciation will have a negative effect on share prices. However,

looking at the effect of a currency depreciation on domestic industries, share prices

could rise. Real activity, represented by GDP growth, should have a positive

relationship with the ALSI. Increased GDP should be reflected by higher earnings and

thus higher share prices. Lastly, using the Gordon growth model again, higher

interest rates increase the discount rate and thus share prices should decrease.

Short term inflows, however, from perceived higher returns, associated with higher

interest rates can increase share prices.

In the initial regression (table 3.2) all coefficients obeyed these relationships, except

for the coefficient of the interest rate variable. The overall fit of this regression was

37

not that impressive, with only 27 per cent explanatory power, according to the

adjusted R-squared.

The model was tested for multicollinearity, serial correlation and heteroskedasticity to

see if it conformed to the assumptions of the classical model. With respect to

multicollinearity, only inflation expectations showed severe multicollinearity, with a

VIF of 5.4. Since inflation expectations were statistically significant, no remedial

action was taken. Using the Durbin-Watson d test, positive serial correlation was

found. Therefore the GLS AR(1) method was run to solve the serial correlation.

However, the signs of the exchange rate variable and the interest rate variable

changed signs. Also the p-values for all the variables in table 3.5 show that the

coefficients are insignificant at the 5 per cent level. In an attempt to correct for this

serial correlation, the ALSI was lagged by one period and inflation expectations for

one year ahead was replaced by current inflation expectations. This new equation still

gave disappointing results when the GLS AR(1) method was run, with the outcome of

insignificant coefficients. Therefore the initial regression was kept. According to the

White Test, the initial model showed no heteroskedasticity.

38

CHAPTER 4: CONCLUSION

4.1 INTRODUCTION

The first chapter introduced the topic of research with a preliminary literature review.

The literature review gave an outline of the two models used for predictive purposes,

namely technical and fundamental analysis. Fundamental Analysis was expounded by

the macroeconomic factors that were considered, specifically real activity, exchange

rates, inflation expectations and the interest rate. The problem statement indicated that

a complicated relationship exists between share prices and macroeconomic factors,

and that research in this area for the Johannesburg Securities Exchange (JSE) was

limited. The objective of the study was to investigate the connection between the

performance of the All Share Index (ALSI) and the four macroeconomic variables and

to develop a model to explain these connections.

The second chapter was a theoretical examination of the two approaches to share

price valuation. Despite the efficient market hypothesis (EMH), the two models,

mentioned above, dominate the literature on share price valuation. Technical analysis

is a very vast subject, with many techniques been developed over the years of share

market research. In the dissertation this model was shortened to a discussion on

patterns on price charts and trend following methods. Fundamental analysis was then

explained, with a discussion on value, the macroeconomy and industry, and

equity. The fundamental model was used in the dissertation focusing only on the

four variables mentioned above.

Chapter two concluded with the question of whether shares reflect fundamental

economic factors. Subsequently, chapter three attempts to answer this question and to

find a better understanding of the correlations that exist between the macroeconomic

variables investigated and the ALSI.

4.2 GENERAL FINDINGS

The empirical analysis of chapter three was not as significant as expected. Asprem

(1989: 589) declared that no commonly accepted pricing model exists that only

39

takes macroeconomic variables into account. This declaration was investigated with

respect to the JSE, and it seems as though this is still the case.

A linear multivariate regression model was built using the ALSI as the dependent

variable and inflation expectations, the real effective exchange rate, GDP growth and

the prime overdraft rate as independent variables. The coefficients of inflation

expectations and the interest rate were the only variables that were statistically

significant at the 5 per cent level. According to the adjusted R-squared, all the

variables explained only 27 per cent of the variation in the ALSI. The model was

constructed to obey the classical linear regression model, thus it was checked for

multicollinearity, serial correlation and heteroskedasticity. A remedy was only sought

for serial correlation by estimating the generalized least squares (GLS) equation using

the AR (1) method. However, this did not adequately solve the problem of serial

correlation.

Another equation was regressed, lagging the ALSI for one period and substituting

inflation expectations for one year ahead with current inflation expectations. This was

done to see if better results could be found; in spite of this the results were no more

promising than the initial regression, and thus are not included here.

4.3 CONCLUDING REMARKS

The empirical analysis carried out in this dissertation encountered two major

difficulties. Firstly, not enough data could be found for inflation expectations,

therefore EViews included only 32 observations after adjusting the endpoints. It is

generally accepted that the more sample observations one has, the more reliable ones

estimates can be. Secondly, serial correlation could not be solved regardless of the

efforts made, as mentioned above. This dissertation thus concludes that only inflation

expectations for one year ahead and the interest rate are statistically significant in

explaining the variation in the ALSI. The presence of serial correlation, however,

caused the ordinary least squares (OLS) estimates of the standard errors to be biased,

leading to unreliable hypothesis testing (Studenmund 2006: 324). Given the

unreliable and biased results obtained, it is difficult to determine whether any of the

hypotheses stated in chapter one are true.

40

Increased real activity did lead to an increase in the ALSI, however this result was

insignificant in the initial model. A depreciation in the exchange rate did lead to better

performance on the ALSI, however, this result was also found to be insignificant (see

table 3.2). The interest rate showed a positive relationship with the ALSI, which

highlighted the importance of international investors in South Africa. Short term

inflows increased, leading to a better performing ALSI. This result was significant,

however, this was prior to correcting for serial correlation. Lastly, inflation

expectations had an expected negative relationship with the ALSI. This result was

also significant, but once again, did not account for possible serial correlation.

In conclusion, further research should be carried out in order to identify significant

variables that help explain the performance of the ALSI, under the fundamental

approach to share price valuation.

41

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