Introduction to Corporate Finance

PART 2: VALUATION, RISK AND RETURN

With two points identified on the line, the Treasury note and the market portfolio, we can calculate

the line’s slope by taking the rise over the run, just as we did in the example on page 236:

Slope

1

==

Er r

Er r

mf

mf

()–

()–

0

The difference in returns between a portfolio of risky securities and a risk-free asset is the market risk

premium. The market risk premium indicates the reward that investors receive if they hold the market

portfolio.^10

The intercept of the line in Figure 7.4 equals rf. From elementary algebra we know that the equation

for a straight line is y = b + mx where b is the intercept and m is the slope. In Figure 7.4, the variable

we measure on the y-axis is the expected return on some portfolio of Treasury notes and the market

portfolio. The variable we measure on the x-axis is the beta of this portfolio. Therefore, the equation of

the line plotted in this figure is

E(rp) = rf + βp[E(rm) – rf]

The equation says that the expected return on any portfolio consisting of Treasury notes and the

market portfolio depends on three things: the risk-free rate, the portfolio beta and the market risk

premium. It’s easy to verify that this equation works with a numerical illustration.

What if an investor is willing to hold a position that is even more risky than the market portfolio? One

option is to borrow money. When investors buy Treasury notes, they are essentially lending money to the

government. Suppose investors also borrow money at the risk-free rate. To be more precise, suppose a

certain investor has $10,000 to invest, but raises an additional $5,000 by borrowing. The investor then

puts all $15,000 in the market portfolio. The portfolio weight on Treasury notes becomes –0.50, and the

weight invested in the market portfolio increases to 1.50. The investor now holds a portfolio with a beta

greater than 1 and an expected return greater than 10%, as confirmed in the following calculations:

βp = –(0.5)(0) + (1.5)(1.0) = 1.5

E(rp) = 4% + (1.5)[10% – 4%] = 13%

10 Conceptually, the market portfolio invests in every risky asset available in the market. No such portfolio exists in practice, so to estimate the

market risk premium, analysts typically use the risk premium on a well-diversified share portfolio.

Suppose the risk-free rate is 4% and the expected

return on the market portfolio is 10%. This implies

that the market risk premium is 6%. What is the

expected return on a portfolio invested equally

in Treasury notes and shares? There are actually

several ways to get the answer. First, we know that

the expected return on the portfolio is simply the

weighted average of the expected returns of the

assets in the portfolio, so we have:

E(rp) = (0.5)(4%) + (0.5)(10%) = 7%

Alternatively, we could begin by calculating

the beta of this portfolio. The portfolio beta is a

weighted average of the betas of Treasury notes and

the market portfolio, so we obtain:

βp = (0.5)( Treasury note beta) + (0.5)(Market beta)

= (0.5)(0) + (0.5)(1.0) = 0.5

Now, using the equation of the line in Figure 7.4,

we calculate the portfolio’s expected return as

follows:

E(rp) = 4% + (0.5)[10% – 4%] = 7%

The position of this portfolio appears as point A

in Figure 7.4.

example

market risk premium
The additional return earned
(or expected) on the market
portfolio over and above the
risk-free rate