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M.Sc. Finance

M.Sc. International Banking and

Finance and

M.Sc. International Accounting and

Finance

FINANCE II

UNIT 2

CAPITAL MARKET THEORY

 - Aims Page - Objectives 

• INTRODUCTION
• PORTFOLIOS WITH RISKLESS ASSETS
  • CAPITAL MARKET THEORY - Basic Assumptions - Capital Market Line - Separation Theorem
  • CAPITAL ASSET PRICING MODEL - The Security Market Line - Beta as a Measure of Risk - Expected and Actual Returns - Characteristic Lines - Estimating Beta
  • DETERMINANTS OF BETA - Cyclical Demand - Operating Gearing - Debt and Financial Gearing
  • EMPIRICAL STUDIES OF CAPM
  • CAPM AND COST OF CAPITAL
  • CONCLUSION
  • APPENDIX 2.1: Scope Of The Capital Market Line
• APPENDIX 2.2: Capital Asset Pricing Model: Sharpe’s Approach
• APPENDIX 2.3: Decomposing Risk
• APPENDIX 2.4: Portfolio Betas And Covariances
• APPENDIX 2.5: LBA Risk measurement Service
• ANSWERS TO SELF ASSESSMENT QUESTIONS

PREVIEW

Aims

The aims of this unit are to develop the basic elements of capital market theory and to explain the relationship between risk and return.

Objectives

After completing this unit you should be able to

• determine the implications for portfolio theory of the extending choice of investments to include risk free as well as risky assets;
• specify the risk-return trade off implied by the capital market line;
• determine the expected rate of return on assets held as part of a well diversified

portfolio;

• develop the capital asset pricing model;
• explain the role of "beta" as a measure of risk;
• specify the primary determinants of beta; and
• consider the role of beta and the capital asset pricing model in determining the cost

of capital.

INTRODUCTIO

N

In this unit we will first of all consider the implications for portfolio theory of extending the

range of investments to include a risk free asset. The introduction of a risk free asset into the analysis, along with a number of assumptions about the nature of investors and the capital market, provides the basis for developing propositions about the risk-return trade off to be found in an efficient and competitive capital market. In developing the analysis we will make considerable use of the ideas underlying portfolio theory. However, our objective will be different from our discussion of portfolio theory in unit one. Portfolio theory is primarily concerned with the possibilities of reducing risk through diversification, and the development of guidelines on risk management for investors who are assumed to be risk averse. Capital market theory on the other hand attempts to explain the nature of the risk-return relationship that we can expect to observe when assets are traded in highly competitive and efficient markets investors are rational, well informed, and fully exploit the opportunities identified by portfolio theory to manage their risk exposure.

linked government securities, but we will avoid the problem of inflation in this unit by simply

assuming that prices are constant.

The introduction of a risk free asset has a significant impact on the set of efficient portfolios, as is illustrated in Figure 2.1. The risk-return combination for the risk free asset is simply shown as a point on the vertical axis. This asset can be included in a portfolio along with any efficient risky portfolio to extend the choice available to investors. Whilst it is possible to develop the analysis with any of the portfolios on the efficiency frontier, such as A, B, C or M, as illustrated in Figure

2.1, there is one particular portfolio which will provide the optimal set of possibilities for

investors.

This is identified by the line drawn from R F

which is tangential to the efficient frontier for

the

risky portfolios. This line dominates the risk-return possibilities defined by the risk free asset and risky portfolios A, B and C, and, indeed, any other possible portfolio. Once the risk free asset is introduced into the analysis, portfolios such as A, B, and C are no longer included in the efficient set. The risk-return combinations for the portfolios that include the risk free asset are drawn to fall on straightlines, and the rationale for this is discussed below.

Figure 2.1: Portfolios With Investment in a Riskless Asset

Expected

Return

M

C

R F B

A

0 SD(RP)

The expected return and risk of a portfolio consisting of a risk free asset and a risky portfolio can be considered using the standard two asset portfolio model. Assume that the proportion of the

portfolio;

is the expected

return on the

riskless asset;

and is the expected return

on the risky

portfolio M

The variance of return on this portfolio may be written initially in the standard form for a two asset

portfolio:

VAR( R ) = (1 - W ) 2 VAR( R ) + W

2

VAR( R M ) + 2W(1 - W) COV ( RF R M )

but we can recognise that for a risk free asset:

• the variance of the expected return is zero; and
• the covariance of its return with the return on portfolio of risky assets is zero.

This implies that the first and third terms in the equation are equal to zero and drop out of the

equation, leaving the variance for this particular type of portfolio to be given by:

VAR( R P ) = W 2

VAR( R M )

Taking square roots to determine the standard deviation gives

SD( R P )= W SD( RM )

The risk of the portfolio depends simply on the standard deviation of the risky portfolio, and proportion invested in this asset.

Recognising that

implies

SD( R P

) = W

SD( R M

) W =

SD( R P

)/ SD( R

M )

and substituting this expression for W in the equation for the expected return allows us to define the expected rate of return on a portfolio made up of a riskless asset and a risky portfolio in the following way:

E ( R P

) = RF (^) + [ E ( R M ) − RF (^) ] SD ( RP )

SD ( R M^ )

This can be written in a way which we will find easier to interpret:

[ E ( RM ) − RF

]

E ( R P ) = R F +

SD ( R M^ SD ( R^ P^ )

The expected return on the portfolio is a linear function of the portfolio's risk. This is illustrated in

Figure 2.2. The intercept term is given by

R F , the slope of the line by [E( Rm

- R F )/ SD( R M )]

and the risk of the portfolio, [SD( R P )] , is the independent variable. (See Appendix 2.1 for a

more formal proof of this linear relationship.)

Figure 2.2: Efficient Frontier with Riskless Asset

Expected Return

E( R P ) = R F + [E( R M ) - R F ]

SD

( R P^ ) SD( R^ M^ )

M

R F

SAQ 2.

The return on the risk free asset is 6 per cent and the expected rate of return on a risky portfolio

is 15 per cent with a standard deviation of 20 per cent. What will be the expected return and risk of a portfolio made up of 40 per cent of the risk free asset and 60 per cent of the risky portfolio?

CAPITAL MARKET THEORY

Portfolio theory considers the principles underlying the use of diversification to reduce risk

exposure. It demonstrates that as long as the returns on assets are not perfectly positively correlated diversification provides scope for reducing risk. Portfolio theory is developed on the assumption that the returns and risk of different assets are given, and does not explain the expected risk-return combination offered by different assets. We will now build on portfolio theory to develop a model of the capital market that attempts to explain the relationship between expected return and risk.

To develop a model of the interrelationship between risk and return requires an understanding of the decision taking of investors and the functioning of the capital markets in which securities are traded. We need to be able to identify the critical features of investor behaviour and the nature of a competitive capital market, and capture elements in the form of some simple assumptions. The implications of the assumptions can then be explored to develop propositions about the risk - return relationship.

Basic Assumptions

Investors are assumed

• to be risk averse, and prefer portfolios with a lower dispersion of outcomes, all else being equal;
• to prefer higher returns all else being equal;
• to take decisions on the basis of the expected return and risk over a one period time

horizon; and

• to have developed identical expectations regarding the anticipated returns, standard

deviations, and covariances of all securities.

These investors are assumed to take their decisions in the context of perfectly competitive capital markets in which

• information is instantly and costlessly available to all investors;
• there are no taxes or transactions costs;
• investors can borrow or lend at the risk free rate of interest; and
• no market participant can exercise any market power.

These assumptions may appear to be rather demanding, and possibly unrealistic. However, most

of

the assumptions can be relaxed without this changing the broad nature of the predictions derived

Price of risk =

E( R M ) - RF

= SD( R M )

Standard Risk Premium

Standard Risk Exposure

This implies we can interpret the capital market line as producing a basis for breaking down the return required by investors into two components, a reward for waiting or postponing consumption, and compensation for risk.

E( R P ) = R F

E( R M ) - R F

+ [

] SD( R P^ )

SD( R M^ )

E( R P^ ) = Reward for Waiting + Price of Risk x Risk Exposure

where the risk free rate of interest constitutes the reward for waiting, the compensation required by investors for delaying consumption.

Let's consider an arithmetic illustration

R F = .06, E( R M ) = .18, and SD( R M ) =.

Market Price of Risk =

E( R M ) - RF

SD( R M )

The data we have employed implies a slope of the market line of 1.5: for every one per cent increase in the standard deviation of expected returns a 1.5 per cent increase in expected return can be anticipated.

Figure 2.