Introduction to Corporate Finance

PART 2: VALUATION, RISK AND RETURN

The second asset plotted in Figure 7.3 is an average share. The term average share means that this

security’s sensitivity to market movements is neither especially high, like OrotonGroup, nor especially

low, like AGL Energy. By definition, the beta of the average share equals 1.0. On average, its return goes up

or down by 1% when the market return goes up or down by 1%. Assume for a moment that the expected

return on this share equals 10%.

By drawing a straight line connecting the two points in Figure 7.3, we gain some insight into the

relationship between beta and expected returns. An investor who is unwilling to accept any systematic

risk at all can hold the risk-free asset and earn 4%. An investor who is willing to bear an average degree of

systematic risk, by investing in a share with a beta equal to 1.0, expects to earn 10%. In general, investors

may expect higher or lower returns based on the betas of the shares they hold, as the following example

illustrates.

example

We can derive an algebraic expression for the line

in Figure 7.3. Recognise that the vertical (y-) axis

in the figure is measuring the expected return of

some investment, which we will denote as E(r). The

horizontal (x-) axis is measuring the investment’s

beta (β ). The y-intercept is the risk-free rate, which

we assume to be 4%. Because we have plotted two

points on the line, we can use the ‘rise over run’

formula to calculate the line’s slope.

Slope=

Rise

Run

(10% 4%)

(1.0 0.0)

= 6%

−

−

=

Because we now know both the intercept (4%)

and the slope (6%) of the line, we can express the

relation between an investment’s expected return and

its beta as follows:

E(r) = 4% + (6% × β )

Now consider an investor who wants to take an

intermediate level of risk by holding a share with a

beta of 0.5. The expected return on this share

is 7%:

E(r) = 4% + (6% × 0.5) = 7%

On the other hand, an investor who is willing to

take a lot of risk by holding a share with a beta of 1.5

can expect a much higher return:

E(r) = 4% + (6% × 1.5) = 13%

The line in Figure 7.3 plays a very important role in finance, and we will return to it later in this

chapter. For now, the important lesson is that beta measures an asset’s systematic risk, a risk that has a direct

relationship with expected returns.

1 What is the difference between an asset’s expected return and its actual return?

Why are expected returns so important to investors and managers?

2 Contrast the historical approach to estimating expected returns with the probabilistic approach.

3 Why should share betas and expected returns be related, while no such relationship exists between

share standard deviations and expected returns?

4 Why is the risk-based approach the best method for estimating a share’s expected return?

CONCEPT REVIEW QUESTIONS 7-1