Modern Portfolio Theory Handin-monday

7/29/2019 Modern Portfolio Theory Handin-monday

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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

risk-return 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 Risk-Return 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 risk-return 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 risk-return trade-off 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 1952-1959. 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

mean-variance analysis. The theory sought to describe the

behaviour that investors should engage in when they constructing

the portfolio (Markowitz, 1999:5-16).

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, 1999:5-16).

The Importance of theory is that it illuminated the trade-offs

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 mean-variance 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 risk-return/mean-variance preference. The theory also gave

insight on how each security co-moved with all other securities i.e.

bond versus shares. Co-movements 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 mean-variance 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, 1999:5-16).

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,

1991:460-477).

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 long-run (5 to 10

years) performance of these asset classes. The risk and correlation

figures were mainly historical. This showed the risk/return trade-off

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, 1991:460-477).

Application of mean-variance 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 mean-variance 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, 1991:460-477).

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 i-th 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,1991:460-477).

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 value-at-risk 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 day-to-day risks faced by a financial

institution, and thereby allowing the institution to keep the VaR

within tolerable levels (Markowitz, Gupta and Fabozzi,2002: 7-16).

An example may assist in clarifying the impact of correlations on the

day-to-day VaR of a financial institution. If a South African -basedinvestor holds a position in a euro-denominated 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 foreign-exchange 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 let-up 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, 2002:7-16).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 real-world investors (Rom and Ferguson, 1993:27-33).

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, 1993:27-33).

CAPITAL ASSET PRICING MODEL

Standard asset pricing theory claimed a direct relationship between

expected excess stock returns and risk. This risk-return trade-off 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 risk-return 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, 1977:92-104).

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 mean-variance model and provided an

algebraic conditions on the asset weights in mean-variance efficient

portfolios. In its simplest form the theory predicted that the

expected return on an asset above the risk-free 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, 1977:92-104).

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

mean-variance (Ross,1977:28-30).

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, 1973:867-887). 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 risk-free 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, 1973:867-887).

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(Em-Ry) 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 risk-free rate and the B was the sensitivity

of the asset's return to the return on the market portfolio (Perold,


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2004:3-24).

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,

2004:3-24).

As mentioned in the beginning the capital asset pricing model has

undergone several intertemporal extensions such as elimination of

the possibility of the risk-free 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 non-marketable 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: 1743-1774).


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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 mean-variance.

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 k-factor

generating model of the form

rt=Ei+ bi11 + ***+ bik k +i

i-l, ..., n.(Ross, 1980:1073-1103)

The first term Eit, was the expected return on the i-th asset. The

next k terms were of the form bi11, where denoted the mean zero

j-th 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 i-th 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, 1986:347-368). 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= risk-free rate of return;

i, Fj= sensitivity of stock i to risk factor j;

RFj= rate of return on risk factor j; and

ei= non-factor (specific) return on security i.(Ross, 1980:1073-1103)

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, 1980:1073-1103).

TOBIN Q THEORY

Tobin contribution to the theories is the addition of the risk-free 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: 2-30). 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: 1-12). 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, 1968:99-122). 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 risk-return trade-off 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 risk-return relationshipin the South African stock market based on single factor

intertemporal capital asset pricing model framework. The GARCM-M

model by Engle, Lilien and Robins was used to estimate the risk-

return trade-off of 50 daily excess returns of market and industry

stock price indexes of the Johannesburg stock exchange listed

companies (Raputsoane, 2009:3-13). 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, 2009:3-13).

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, 2009:3-13). 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 slow-moving 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 risk-return relationship[ precisely (Raputsoane,

2009:3-13).

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 risk-return 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, 2009:3-13). 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, 2009:3-13).

Henceforth in summary, Raputsoane concluded that the empirical

evidence on risk-return 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 risk-return

relationship between expected returns and the market risk premium

in the South African stock market (Raputsoane, 2009:3-13).

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

mean-variance analysis was used .The mean-variance analysis

focused on short-term expected returns and risks and was extended


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to take into account multi-horizon setting (Campbell and Viceira,

2002:34-44). 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 risk-return trade-off. 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: 20-30), based on their

return-forecasting model, have concluded that long-horizon returns

on stocks were significantly less volatile than their short-horizon

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: 20-30) and (Campbell, 1987: 373-399).

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, 1993:27-33).

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, 2004:25-46).

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 risk-free rates and that the

capital market is in equilibrium (Fama and French, 2004:25-46).

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,

1986:347-368).

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, 1980:739-743).

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 risk-return

relationship of each asset and the covariance.

Documents

Modern Portfolio Theory Handin-monday