BUSF_A01.qxd

Capital asset pricing model

Table 7.2Betas of three leading UK businesses in January 2008

Rolls-Royce Group plc (engine and generator manufacturing business) 0.99

Tesco plc (supermarket business) 0.85

Wolseley plc (supplier of construction equipment) 1.22

Source: http://www.digitallook.com (Digital Look Ltd website)

Beta: a measure of risk

CAPM tells us that the capital market prices securities so that no higher returns are

expected for bearing specific risk. Bearing systematic risk is expected to be rewarded

by a risk premium (over the risk-free rate) of:

[E(rm) −rf]×Cov(i,M)/σ^2 m

The last term is usually known as beta (ββ), so CAPM is typically written as:

E(ri) =rf+[E(rm) −rf]βi

The greater the beta that characterises a particular security, in theory, the higher are

that security’s expected returns.

Note that CAPM does not assert that securities with a high beta are guaranteed high

returns. It is in the nature of risk that nothing is guaranteed. However, before the event,

high-beta securities are, in theory, expected to have higher returns than low-beta ones.

If the generality of investment in securities (the market portfolio) does well, then port-

folios containing high-beta securities should prosper: the higher the beta, the more

they should prosper. On the other hand, should securities generally fare badly, high-beta

securities should fare particularly badly. In other words, beta is a measure of volatility

of returns relative to those of the market portfolio. Betas above 1.0 are regarded as

high and those below 1.0 as low. High-beta securities are sometimes referred to as

aggressive, and low-beta ones as defensive. In real life, equity shares can be found having

betas of up to about 2.0; they can also be found with betas as low as around 0.4. The

betas of three leading UK businesses in January 2008 are shown in Table 7.2.

Security market line

Figure 7.8 shows CAPM represented diagrammatically. Here risk is measured by beta.

The risk/return profile of all assets should lie somewhere along the line rfT, which is

known as the security market line(SML).

It is important to recognise the difference between the capital market line and the

security market line. The CML shows expected returns plotted against risk, where risk

is measured in terms of standard deviation of returns. This is appropriate because the

CML represents the risk/return trade-off for efficient portfolios, that is, the risk is all

systematic risk. The SML, on the other hand, shows the risk/return trade-off where

risk is measured by beta, that is, only by the systematic risk element of the individual

security. No individual security’s risk/return profile is shown by the CML because all

individual securities have an element of specific risk, that is, they are all inefficient.

Thus all individual securities (and indeed all inefficient portfolios) lie to the bottom-

right of the efficient frontier (Figure 7.6).

‘

‘