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1. INTRODUCTION
The study of risk and return continues to be an area of vital
importance for researchers however the theorizing and empirical
findings in this area continue to present a series of problems. The
riskreturn relationship has been presented in the literature in two
distinct ways. The history of the stock and bond markets shows that
risk and reward are inextricably intertwined. One does not expect
high returns without high risk nor should one expect safety without
correspondingly low return. Investors are faced with difficult
decisions as they contemplate what assets to invest in. The most
important decision that an investor has to make is what assets to
invest in and this is a very crucial issue given tfhat one bad decision
can have severe repercussions. The investor hence as to take into
account the risk and return of the asset of interest in order to makesound and stable decisions about investments. However,
understanding the risk and return of assets is not an easy matter.
(Leon, Nave and Rubio, 2005). Therefore because one first need to
understand the relationship of risk and return and this can be done
by understanding economic theory so as to understand how these
two terms affect investments. One is the discussion on the literature
has been presented by analysing existing literature. Different
theories have been discussed and existing empirical evidence had
been highlighted in relation to South Africa
2. BACKROUND
The relationship between risk and return is a fundamental financial

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relationship that affects expected rates of return on every existing
asset investment. The RiskReturn relationship is characterized as
being a positive relationship meaning that if there are expectations
of higher levels of risk associated with a particular investment then
greater returns are required as compensation for that higher
expected risk. Alternatively, if an investment has relatively lower
levels of expected risk then investors are satisfied with relatively
lower returns (Fiegenbaum, Hart, & Schendel, 1996).
This riskreturn relationship holds for individual investors and
business managers hence greater degrees of risk must be
compensated for with greater returns on investment. Since
investment returns reflects the degree of risk involved with the
investment, investors need to be able to determine how much of a
return is appropriate for a given level of risk. This process is referred
to as pricing the risk. In order to price the risk, we must first be able
to measure the risk and then we must be able to decide an
appropriate price for the risk we are being asked to bear
(Fiegenbaum et al, 1996).
3. PROBLEM STATEMENTInvestors are faced with difficult decisions as they contemplate what
assets to invest in. The most important decision that an investor has
to make is what assets to invest in and this is a very crucial issue
given that one bad decision can have severe repercussions. The
investor hence as to take into account the risk and return of the
asset of interest in order to make sound and stable decisions about

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investments. However, understanding the risk and return of assets
is not an easy matter. This riskreturn tradeoff is a long standing
phenomenon in investments analysis and is the foundation of
financial economics (Leon et al, 2005). Therefore because one first
need to understand the relationship of risk and return and this can
be done by understanding economic theory so as to understand
how these two terms affect investments. Therefore this research
sought to provide this analysis that would form the background that
would help investors understand risk and return by concerning
investments in shares and return (Fiegenbaum, et al, 1996).
4. AIM OF RESERACH
The aim of this research is to provide a theoretical background into
the relationship of risk and return of long term bonds and all share
financial index. It sought to do this by understanding the modernportfolio theory that was developed by Harry Markowitz between
1952 and 1959 and other theories whose background was based on
the modern portfolio theory such as the Capital Asset Pricing Model,
the Arbitrage Model and Tobin Q's Theory.
5. THEORIES OF RISK AND RETURN
THE MODERN PORTFOLIO THEORY
The modern portfolio theory was developed by Harry Markowitz
between 19521959. Markowitz formulated the portfolio problem as
a choice of mean and variance of a portfolio asset namely holding
constant variance, maximise expected return, and holding constant
expected return minimise variance. The mean is the measure of
return of the investment namely usually follows the formula
= iiKPK

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. and the return of an asset is measured by the mean return over
time. The variance is measure of risk of the investment and is the
probability that actual return may differ from expected return and
follows the formula (Howell and Bain,
2008).The Modern Portfolio Theory provided a framework for the
construction and selection of portfolios based on the expected
performance of the investments and risk of the investor. The
modern portfolio theory has also been commonly to as referred as
meanvariance analysis. The theory sought to describe the
behaviour that investors should engage in when they constructing
the portfolio (Markowitz, 1999:516).
The modern portfolio theory provided a framework by specifying
and measuring investment risk and developed a relationship
between expected asset return and risk. The theory dictated thatthe given estimates of the return, volatilities and correlations of set
of investments and constraints on the investment choices. The
modern portfolio theory sought to provide results of the greatest
possible expected return for that level of risk or the results in the
smallest possible risk for that level of expected return. In Modern
Portfolio Theory, the terms variance, variability, volatility, and
standard deviation are often used interchangeably to represent
investment risk (Markowitz, 1999:516).
The Importance of theory is that it illuminated the tradeoffs
between the risk and return and provided a framework on which
construction of the portfolio was based on expected performance of
the investment and the risk appetite of the investor. The theory
22 )(iii
KKP
=

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dictated that given estimates of the returns, volatilities, and correlations of a set of
investments and constraints on investment choices (for example, maximum
exposures and turnover constraints), it was possible to perform an optimization
that results in the risk/return or meanvariance efficient frontier. The theory
allowed for the formulation of an efficient frontier from which the
investor could choose his or her preferred investment depending on
the riskreturn/meanvariance preference. The theory also gave
insight on how each security comoved with all other securities i.e.
bond versus shares. Comovements resulted in ability to construct a
portfolio that had the same expected return and less risk than one
that ignored the interaction between the securities (Howell and
Bain, 2008).
The theory followed the process of selecting a set of asset classes to
obtain estimates of the return and volatilities and correlation by
beginning with historical performance of the indexes representing
these asset classes. The estimates were used as inputs in the mean
variance optimization. The modern portfolio theory assumed that all
estimates are precise or imprecise thus treated all assets equally.
Most commonly, practitioners of meanvariance optimization
incorporated their beliefs on the precision of the estimates by
imposing constraints on the maximum exposure of some assetclasses in a portfolio. The asset classes on which these constraints
are imposed are generally those whose expected performances are
either harder to estimate, or those whose performances are
estimated less precisely (Markowitz, 1999:516).
AN EXAMPLE OF PORTFOLIOS SELECTION

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Using an explicit example, it has been illustrated how asset
managers and financial advisor used Modern Portfolio theory to
build optimal portfolios for their clients. In this example there were
two assets namely S A bonds and S A international equity, and this
shed some light on the selection of an optimal portfolio (Markowitz,
1991:460477).
These inputs were an example of estimates that were not totally
based on historical performance of these asset classes. The
expected return estimates were created using a risk premium
approach and then were subjectively altered to include the asset
manager's expectations regarding the future longrun (5 to 10
years) performance of these asset classes. The risk and correlation
figures were mainly historical. This showed the risk/return tradeoff
that the client faces and attempted to answer the question does theincrease in the expected return compensate the client for the
increased risk that she will be bearing?. Additionally it was seen that
a portfolio that may have not be acceptable to the investor over a
short run may have be acceptable over a longer investment horizon.
In summary, it is sufficient to say that the optimal portfolio depends
not only on risk aversion, but also on the investment horizon
(Markowitz, 1991:460477).
Application of meanvariance analysis for portfolio construction
required a significantly greater number of inputs to be estimated
expected return for each security, variance of returns for each
security, and either covariance or correction of returns between
each pair of securities. For example, a meanvariance analysis that

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allowed 50 securities as possible candidates for portfolio selection
required 50 expected returns, 50 variances of return, and 4975
correlations or covariances. An investment team tracking 50
securities may reasonably be expected to summarize its analysis in
terms of 50 means and variances, but it is clearly unreasonable for
it to produce 4975 carefully considered correlation coefficients or
covariances (Markowitz, 1991:460477).
It was clear to Markowitz (1959:100) that some kind of model of
covariance structure was needed for the practical application of
normative analysis to large portfolios. He did little more than point
out the problem and suggest some possible models of covariance
For research one model Markowitz proposed to explain the
correlation structure among security returns assumed that the
return on the ith security depends on an "underlying Factor, thegeneral prosperity of the market as expressed by some index".
Mathematically, the relationship is expressed as Follows:
Ri= i+ iF + ui
where Ri= the return on security i;
F = value of some index; and
ui= error term ( Markowitz,1991:460477).
The expected value of ui is zero and ui is uncorrelated with F and
every other uj. Markowitz Further suggested that the relationship
needed not be linear and that there could be several underlying
Factors.
In 1963, Sharpe used the above equation as an explanation of how
security returns tend to go up and down together with a general

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market index, F. He called the model given by the above equation
the market model. It should be noted that the beta for the market
model is different from the beta under the capital asset pricing
model (Sharpe, 1964).
The now widely used valueatrisk framework (VAR) for the
measurement and management of market risk for financial markets
is based on the concepts first formalized in MPT. The need to
consider each security or financial instrument in the context of the
overall exposure and not in isolation was the key to obtaining more
precise estimates of the daytoday risks faced by a financial
institution, and thereby allowing the institution to keep the VaR
within tolerable levels (Markowitz, Gupta and Fabozzi,2002: 716).
An example may assist in clarifying the impact of correlations on the
daytoday VaR of a financial institution. If a South African basedinvestor holds a position in a eurodenominated bond, then the
investor has exposure to two risk factors:1) interest rate risk that
can directly impact the value of the bond and 2) foreign exchange
risk (i.e., the volatility of the Euro/RSA exchange rate).But when
computing the risk of this position, it is important to keep in mind
that the total risk of this position is not simply the sum of the
interest rate risk and the foreignexchange risk, but rather must
incorporate the impact of the correlation that exists between the
returns on the denominated bond (i.e., the interest rate risk) and
the Euro/RSA exchange rate (i.e., foreign exchange risk). Extensive
work and research has been done so as to collect more accurate
data on the performance of a vast array of financial instruments and

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to improve the methods used to compute the estimates of the
variances and covariances (Markowitz, Gupta and Fabozzi, 2002: 7
16).
By now it is evident that Modern Portfolio Theory first expounded by
Markowitz 50 years ago, has found applications in many aspects of
modern financial theory and practice. We have illustrated a few of
the most widely used applications in the areas of asset allocation,
portfolio management, and portfolio construction. Though it did take
a few years to create a buzz, the late 20th and early 21st centuries
saw no letup in the spread of the application of Modern Portfolio
Theory. Further, it is unlikely that its popularity will wane any time in
the near or distant future. Consequently, it seems safe to predict
that MPT will occupy a permanent place in the theory and practice
of finance (Markowitz, Gupta and Fabozzi, 2002:716).The modern portfolio theory has been extended today to formulate
the post modern portfolio theory. In summary it was seen that under
the Modern Portfolio Theory, risk was defined as the total variability
of returns around the mean return and is measured by the variance,
or equivalently, standard deviation. The Modern Portfolio Theory
treated all uncertainty the same in that variability) on the upside
were penalized identically to surprises on the downside. Therefore
the variance was a symmetric risk measure, which was counter
intuitive for realworld investors (Rom and Ferguson, 1993:2733).
However while variance captured only the risks associated with
achieving the average return, the Post Modern Portfolio Theory
sought to recognize that investment risk should be tied to each

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investors specific goals and that any outcomes above this goal did
not represent economic or financial risk. Post Modern Portfolio
Theory downside risk measure made a clear distinction between
downside and upside volatility. In Post Modern Portfolio Theory only
volatility below the investors target return incurred risk; all returns
above this target caused uncertainty which was the riskless
opportunity for unexpectedly high returns. In Post Modern Portfolio
Theory this target rate of return was referred to as the minimum
acceptable return (MAR). It represented the rate of return that must
be earned to avoid failing to achieve some important financial
objective (Rom and Ferguson, 1993:2733).
CAPITAL ASSET PRICING MODEL
Standard asset pricing theory claimed a direct relationship between
expected excess stock returns and risk. This riskreturn tradeoff is along standing phenomenon in investments analysis and is the
foundation of financial economics (Leon, Nave and Rubio, 2005).
The rate of return on an investment was weighted by the perceived
risk of undertaking such an investment. This implied a direct
relationship between market risk and return for the reason that risk
averse investors required additional compensation for assuming
extra risk. Markets which were perceived by investors to be high risk
were associated with higher returns in order to compensate for the
risk involved in investing in such markets. Conversely, lower risk
markets were characterised by relatively lower returns. Thus it was
unambiguous that the riskreturn relationship is a fundamental
concept in investment decision making and that it is accepted as

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the cornerstone of rational expectations asset pricing models
(Levhari and Levy, 1977:92104).
The Capital Asset Pricing Model was developed in the early 1960's
by Jack Treynor, William Sharpe, Jan Mossin and John Lintner. The
capital asset pricing model was built n the work of harry markowitz
of the modern portfolio theory. The modern portfolio theory was also
commonly know as the meanvariance model and provided an
algebraic conditions on the asset weights in meanvariance efficient
portfolios. In its simplest form the theory predicted that the
expected return on an asset above the riskfree rate was
proportional to the nondiversifiable risk, which was measured by the
covariance of the asset return with a portfolio composed of all the
available assets in the market. The capital asset pricing model was
a static one period model but there have been some intertemporalextension made to it (Levhari and Levy, 1977:92104).
The capital asset pricing model is based on a number of
assumptions. It assumed that investors chose assets that they had
perceived to be the mean variance efficient and they all that the
belief in the expected return variance pair E,V. It model assumed
that the risk premium for any asset was linearly related to its
covariance and that the asset risk premia was dependent on the
relationship of the asset to the whole market and not on the total
risk of the asset. Therefore the competitive equilibrium asset earned
premia over the riskless rate that increased with the assets risk. The
determining influence on the risk premia was the covariance
between the asset and the market portfolio. The expected returns

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were linearly related to the beta if the market portfolio was the
meanvariance (Ross,1977:2830).
The capital asset pricing model concluded that not all risk should
affect the asset prices. The investors were risk averse and
evaluated their investments portfolios solely on the terms of the
expected returns and the standard deviations of the returns that
were measures over the same single holding period. Another
important factor in the development of the capital asset pricing
model was the assumption of the capital markets that they were
prefect (Merton, 1973:867887). This meant that there were no
transaction and information costs, information was easily available
to everyone, there were no short selling transaction, there were no
taxes, assets were infinitely divisible and that investors could
borrow and lend at the riskfree rate Additionally investors hadaccess to the same investment opportunities and they made the
calculated the estimates of the individual assets expected
return,standard deviations of return and correlations among the
asset returns (Merton, 1973:867887).
The investors also determined the same highest Sharpe ratio
portfolio of the risky asset. The expected return of the asset was
given by Es=Rf+B(EmRy) and it shows the relationship between
expected return and risk that was consistent with investors
behaving according to the prescriptions of portfolio theory. Es and
Em were the expected return on the asset and the market portfolio
respectively, rfwas the riskfree rate and the B was the sensitivity
of the asset's return to the return on the market portfolio (Perold,

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2004:324).
Example, under the capital asset pricing model to calculate the
expected return on the tock one would need to know the premium
of the overall equity market (Em) and the stock beta versus that of
the market. The stock's risk premium was determined by the
component of its return that was perfectly correlated with the
market only and the expected return of the asset would not depend
on the stand alone risk and that the beta offered a method of
measuring the risk of an asset that would not be diversified away.
Additionally the stock of the expected return did not have to depend
on the growth rate of the expected cash flows hence it was not a
requirement that one conduct an extensive financial analysis of the
company and forecast the expected future cash flows. Therefore in
line with what as been discussed above on the capital asset pricingmodel one would only need to take into account the beta of the
stock and a parameter that would be easy to estimate (Perold,
2004:324).
As mentioned in the beginning the capital asset pricing model has
undergone several intertemporal extensions such as elimination of
the possibility of the riskfree lending and borrowing, allowing for
multiple time periods and investment opportunities that change
between time periods,extensions to the international investing and
having some assets be nonmarketable however the most important
has been the relaxation of some of the assumptions through
employing weaker assumptions by relying on the arbitrage pricing
model(Brennan, Wang and Xia, 2004: 17431774).

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THE ARBITRAGE MODEL
The Arbitrage Model was formulated by Ross in 1976 and deals s
with more than one risk factor and provided theoretical support to
the capital asset pricing model discussed above. The arbitrage
model was proposed as an alternative to the mean variance capital
asset pricing model that had been introduced by Sharpe, Lintner,
and Treynor. The Arbitrage Model has become the major analytic
tool for explaining phenomena observed in capital markets for risky
assets. The Arbitrage Model unlike the modern portfolio theory and
the capital asset pricing model is a multifactor risk model instead of
the full meanvariance.
The arbitrage model is assumptions that arise from the neoclassical
school of though of perfectly competitive and frictionless asset
markets and its main foundation is the assumption of returngenerating process where individuals homogeneously assumed that
the random returns on the set of assets was ruled the kfactor
generating model of the form
rt=Ei+ bi11 + ***+ bik k +i
il, ..., n.(Ross, 1980:10731103)
The first term Eit, was the expected return on the ith asset. The
next k terms were of the form bi11, where denoted the mean zero
jth factor common to the returns of all assets under consideration.
The coefficient bi1 quantified the sensitivity of asset i's returns to the
movements in the common factor. The common factors captured
the systematic components of risk in the model. The final term i is
a noise term which represented an unsystematic risk component,

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idiosyncratic to the ith asset.
The Arbitrage Model was also based on two main assumptions of no
arbitrage opportunities in the capital market and that there was
linear relationship between the actual returns and the k common
factors. The expected returns were linearly related to the weights of
the common factors in the assumed linear process and the that
factor analysis was used to extract the k factors from the sample
covariance matrices and then to test the hypothesis by the
regressing returns on the average returns against the factor
amplitudes of the common factors (Trzcinka, 1986:347368). One of
the models used that shows the basic relationship that had to be
estimated in the multifactor model was Ri Rf= i, F1RF1+ i,
F2RF2+ ...i, FHRFH+ ei
whereRi= rate of return on stock i;
Rf= riskfree rate of return;
i, Fj= sensitivity of stock i to risk factor j;
RFj= rate of return on risk factor j; and
ei= nonfactor (specific) return on security i.(Ross, 1980:10731103)
This model is called the Barra fundamental factor model and it used
the industry attributes or market data called descriptors that were
not risk factors but candidates for the risk factors selected based on
their ability to explain the returns.
The descriptors were potential risk factors that were statistically
significant so that they be grouped together as risk indices that
captured the related industry attributes. The model used the market

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index as a benchmark and variance was a tracking error that
measured the risk exposure and not the risk itself. This therefore
shows that the arbitrage model allowed for the generations of more
than one factor and demonstrates that every equilibrium would be
characterised by the linear relationship between each assets
ex[expected return and its returns response magnitude on the
common factors since every market equilibrium was consistent with
no arbitrage profits (Ross, 1980:10731103).
TOBIN Q THEORY
Tobin contribution to the theories is the addition of the riskfree rate
to the risky assets. James Tobin (1969) introduced the ratio of the
market value of a firm to the replacement cost of its capital stock
and he called the Q which sought to measure the incentive to
invest in capital. Tobins Q, was the empirical implementation ofKeyness notion that capital investment became more attractive as
the value of capital increases relative to the cost of acquiring the
capital (Abel and Eberly, 2008: 230). The q ratio was defined as
the market value of the company's assets that is divided by assets
replacement cost. This q ratio is also known as the average q
(Richard and Weston, 2008: 112). The Q ratio is therefore the ratio
of the market valuation of real capital assets that can be reproduced
to the current replacement costs of those assets and follows the
formula q = MV/V (Tobin and Brainard, 1977). I f the Q ratio is
greater than 1 then the investment is pursued because the capital is
more highly valued than the cost to produce it in the market.
However if the Q ratio is less than 1 then it would mean that the

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investment would be forgone because it would be cost more to
replace(Brainard and Tobin, 1968:99122). The market valuation
represents the present value of the expected return in which the
real rate of return gives the discount rate . The replacement cost is
the sum of the present of expected returns that are discounted by
the marginal efficiency of the capita (Mollick And Fariaa, 2010:401
418).
EXISTING EMPIRICAL ANALYSIS
Although it is a long standing phenomenon in investments analysis,
the empirical evidence on the riskreturn tradeoff is ambiguous
with some empirical studies documenting a weak or negative
relationship at best. The paper by Leroi Raputsoane examined the
intertemporal risk and return relationship in South Africa. This study
by Raputsoane examined the intertemporal riskreturn relationshipin the South African stock market based on single factor
intertemporal capital asset pricing model framework. The GARCMM
model by Engle, Lilien and Robins was used to estimate the risk
return tradeoff of 50 daily excess returns of market and industry
stock price indexes of the Johannesburg stock exchange listed
companies (Raputsoane, 2009:313). According to the empirical
results, 95 percent of stock price indexes show a positive and a
highly statistically significant coefficient of risk aversion, while 5
percent are not only statistically insignificant but also show negative
coefficient of risk aversion. This suggests that, generally, the market
and industry stock prices in the South African stock market conform
to the Mertons Intertemporal Capital Asset Pricing Model theoretical

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hypothesis of a positive relationship between excess market returns
and the market risk premium (Raputsoane, 2009:313).
Raputsoane analysed the stock markets and investigated this
relationship by making use of the Merton single factor intertemporal
capital asset pricing model framework. He assumed that investors
were risk averse and processed to conclude that according to shape
there is a positive linear relationship between the expected market
risk and returns. As was discussed above the Capital asset pricing
model implied a positive linear relationship between the market
return and the market risk premium ans assumed that investors had
the power utility and that the rates f return were independent and
identically distributed (Raputsoane, 2009:313). This assumption is
applied to the intertemporal capital asset pricing model.Raputsoane assumes that the relative risk averse is constant ans
that investment opportunities are slowmoving or inactive hence
they have a constant impact on the stock returns in the short term.
This assumption meant that the hedge component could be
excluded and that there was need to use high frequency data so as
to uncover the riskreturn relationship[ precisely (Raputsoane,
2009:313).
Therefore the intertemporal capital asset pricing model was a single
factor model where the conditional variance was directly related to
the conditional excess return in the market and allowed for better
measurement of the risk by producing better estimates of the
conditional volatility process and thus enabled the riskreturn trade

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off to be identified precisely. Raputsoane (2009) carried out his
research by estimation through the use of daily returns on 50
industry and market share price index of the Johannesburg stock
exchange listed companies where the share prices indexes were
weighted by the capital capitalisation (Raputsoane, 2009:313). He
also used the bond exchange yields on the short tern government
bond and the long term government bond to approximate the risk
free rate of the interest. According to the descriptive statistics,
consumer goods, food producers, equity investments, development
and venture capital stock price indexes showed a high volatility
during the sample period based on standard deviations
(Raputsoane, 2009:313).
Henceforth in summary, Raputsoane concluded that the empirical
evidence on riskreturn relationship as obtained by the ICAPM wasambiguous with some empirical studies documenting a weak or
negative relationship at best. However despite this the estimated
results generally supported the robust positive riskreturn
relationship between expected returns and the market risk premium
in the South African stock market (Raputsoane, 2009:313).
In another article the VaR model is used to show that asset return
predictability has important effects oon the variance of long term
returns of shares and bonds by analysing the correlation structures
of the shares and bonds return across investment periods.) to hight
the relevance of the risk horizon effects on the asset allocation the
meanvariance analysis was used .The meanvariance analysis
focused on shortterm expected returns and risks and was extended

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to take into account multihorizon setting (Campbell and Viceira,
2002:3444). The model of return dynamics showed that commonly
used return forecasting variables had a substantial effect on the
asset allocation and that the effects worked through the term
structure of the riskreturn tradeoff. Campbell and Viceira (2002:34
44) used American treasury bonds and American stock to
characterise the term structure of the risk so as to show that the
variance and correlation of the returns of the assets changes dram
by the investment time period due to changes in factors such as
share market risk, inflation risk and real interest risk at different
time periods. Campbell and Viceira (2005: 2030), based on their
returnforecasting model, have concluded that longhorizon returns
on stocks were significantly less volatile than their shorthorizon
returns. However for bonds, they concluded that bonds real returnvolatility increased with the investment horizon. This could have
been attributed to the fact that shares rick estimated standard
deviations were considerably larger than the bond risk estimated
standard deviation whilst the mean risk of bonds and shares had
different signs. Therefore this meant that bond and shares returns
will move in opposite directions in future periods (Campbell and
Viceira, 2005: 2030) and (Campbell, 1987: 373399).
6. CONCLSUION
The Modern Portfolio Theory defined risk as the total variability of
the returns around the mean return and the risk is measured by the

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variance or standard deviation. It treated all uncertainty the same
whether on the upside or the down side therefore the variance is an
symmetrical risk measure. The variance under the modern portfolio
theory takes only into account the risk that are associated with
achieving the average return. However under the Post Modern
Portfolio Theory the down side risk measure clearly distincts the
downside volatility form the upside volatility. In Post Modern
Portfolio Theory the target rate of return is referred to as the
minimum acceptable return and it represents the rate of return that
must be earned to avoid failing to achieve some important financial
objective (Rom and Ferguson, 1993:2733).
In the capital asset pricing model the return is linearly related to the
systematic risk and the market does not pay for any risk that is
unsystematic because it can be avoided through diversification. Itwas also shown that the beta was the measure of the systematic
risk. The assumptions under which the capital asset pricing model
was developed was that investors seek to maximise their wealth
utility and are risk averse (Fama and French, 2004:2546).
Information is readily available and costless, there are no taxes, no
transaction costs and that all assets are divisible. Investors are
homogeneous in their expectations regarding expected return and
expected risk of the assets and that they face similar time periods.
Additionally investors borrow and lend at riskfree rates and that the
capital market is in equilibrium (Fama and French, 2004:2546).
Furthermore it was seen that under the Arbitrage Pricing Theory the
most important assumption was that K factors generate security

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returns. this assumption is equivalent to assuming that K
eigenvalues of the covariance matrix of returns increased as the
number of securities increased. The theoretical relationship between
eigenvalues and the number of securities provided a natural
method for estimating the number of factors in the APT (Trzcinka,
1986:347368).
The Tobin Q theory looked at maximisation of the present
net worth of the business and the market value of outstanding
stock. Investments were done on the basis that there would be
increase stock value in relation to the expected contribution to the
future earnings of the business and risk (Yoshikawa, 1980:739743).
The q therefore was a representation of the ratio of the businesses
stock to the replacement of the businesses physical assets.Hence if
the investors q value was greater than 1, then additional returnwould be expected because the cost of the firms asset will be less
than the profits generated and hence the investor would have
invested in assets. However if the q value is less than 1 then an
investor will not invest in any assets because the profits would be
less than the cost of the businesses assets (Yoshikawa, 1980: 739
743).
The different theories above all explain the risk and return
relationship that exits. Therefore the aim of this research next will
be to conduct an empirical analysis of this relationship. The data
that will be used will be the south African 3 month treasury bills, the
long term government bonds and the Johannesburg financial share
index. The methodology is thus one of descriptive statistics and will

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include calculating variables such as the mean and variance , the
expected mean and expected variance and to find out riskreturn
relationship of each asset and the covariance.