Capital asset pricing model

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1 Introduction

In the previous chapter we looked at the effect of gearing and Modigliani and Millers’ hypothesis.

In this chapter we will ignore gearing and look at the effect of changes in business risk on the shareholder.

Please note that for the whole of this chapter we will ignore the effect of gearing and therefore assume throughout that we are dealing with companies that are financed entirely from equity.

2 What is business risk?

Why is it that some shares in some companies are viewed as inherently more risky than shares in other companies? It is because the nature of their business is more risky. As a result, the potential fluctuations in profits (and hence dividends) in the future are greater. If things go well shareholders may well receive much higher dividends, but the risk is that things may go badly in which case they will receive much lower dividends. The greater the potential fluctuations in returns, the greater we say that the risk is.

3 Two types of business risk

There are two different reasons why one company may be more risky than another.

1. Unsystematic risk (or company specific risk)

This is risk due to factors within the particular company, such as poor labour relations or the appointment of a new management director.

1. Systematic risk (or market risk)

This is risk due to general economic factors, such as the level of inflation or changes in the exchange rate.

A shareholder can ‘remove’ the unsystematic risk by creating a portfolio of shares on the basis that although each share individually has unsystematic risk, it ‘cancels out’ with the risk of other shares in the portfolio. We say that a well-diversified portfolio is one where the unsystematic risk has been completely removed. (i.e. diversified away)

Systematic risk exists in all companies and cannot be removed – all companies will be affected by, for example, the level of inflation. However, the level of systematic risk depends on the type of business and will be different for different types of business.

Although each individual shareholder may not hold a well-diversified portfolio of shares, we assume that shareholders overall are well-diversified and that it is shareholders overall who determine the return given by a share (because it is they who determine the market value of the share). Capital Asset Pricing Model assumes therefore that it is the level of systematic risk that determines the required return from an investment.

4 Measurement of systematic risk

There are several ways in which we could attempt to measure the systematic risk of an investment, but the standard way is to measure it relative to the risk of the stock exchange as a whole. The stock exchange index is the average of all the shares on the stock exchange, and is risky (in that it fluctuates). Some shares fluctuate more than the average, whereas some fluctuate less than the average.

We use β to measure the systematic risk, and β is defined as being the systematic risk of the investment as a proportion of the risk of the market (or stock exchange) as a whole.

(Calculating β’s is not examined in Paper F9 – where needed, the β will be given. In practice the β’s for large companies are regularly published in financial management journals.)

If an investment has a β of 1,   it has 1 times the risk of the market – i.e. it has the same risk as the market.

If an investment has a β > 1,   then it is more risky than the market.

If an investment has a β < 1,   then it is less risky than the market.

If an investment has a β of 0,   then it has zero risk, or we say that it is risk-free.

In practice, no investment is completely without risk, but we assume that short-term government securities are effectively risk-free.

5 The determination of the required return from an investment

As stated earlier, we assume that investors overall are well-diversified, and that therefore it is the level of systematic risk that will determine the required return.

The following formula is given to you in the examination:

  E(r_i)=R_f + β_i (E(r_m) – R_f )

    where:

    R_f = the risk-free rate, and

    E(r_m) = the return from the market

6 Using CAPM for investment appraisal

If the financial manager is considering an investment in a new project, then since it is shareholders money that is being invested, he should appraise the investment in the same way as would shareholders if they were investing their money directly.

As a result the required return from the project (and hence the discount rate) should be calculated from the β of the project.

7 The limitations of CAPM

7.1 The two main limitations of CAPM are as follows:

• it is difficult to estimate the β of a project accurately. Generally we use the β of a company operating in the same type of business as the project, which restricts it to large projects

• the theory of CAPM was developed as just a single period model, whereas in practice most investment projects will be expected to continue for more than one year.