Introduction to Corporate Finance

7: Risk, Return and the Capital Asset Pricing Model

7-3 PULLING IT ALL TOGETHER: THE

CAPM

Now we are ready to tie together the concepts of risk and return for portfolios as well as for individual

securities. Once again, we will begin by considering a portfolio consisting of just two assets. One asset

pays a risk-free return equal to rf. We already know that the beta of the risk-free asset equals zero. The

other asset is a broadly diversified portfolio. Imagine a portfolio that is so diversified that it invests in

every available risky asset in the economy. Because such a portfolio represents the overall market, we

refer to it as the market portfolio. Designate the expected return on the market portfolio as E(rm).

The beta of the market portfolio must equal 1.0. To see why, reconsider the definition of beta. An

asset’s beta describes how the asset moves in relation to the overall market. The market portfolio will

mimic the overall market perfectly. Because the portfolio’s return moves exactly in sync with the market,

its beta must be 1.0. Figure 7.4 plots the beta and the expected return of the risk-free asset and the

market portfolio.

Suppose we combine the risk-free asset – let’s call it a Treasury note – and the market portfolio

to create a new portfolio. We know that the expected return on this new portfolio must be a weighted

average of the expected returns of the assets in the portfolio. Similarly, we know that the beta of the

portfolio must be a weighted average of the betas of a Treasury note and the market. This implies that the

new portfolio we’ve created must lie along the line connecting the risk-free asset and the market portfolio

in Figure 7.4. What are the properties of this line?

LO7.3

FIGURE 7.4 THE SECURITY MARKET LINE

The security market line plots the relationship between an asset’s beta and its expected return. The line shows how an

investor can construct a portfolio of Treasury notes and the market portfolio to achieve the desired level of risk and

return. One investor might choose a relatively conservative portfolio, mixing Treasury notes and the market portfolio in

equal proportions (see point A). Another investor could construct a very risky portfolio by investing his own money and

borrowing more to invest in the market (see point B).

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2.0

Beta

Expected return

Market portfolio

B

rf = 4%

E(rm) =10%

Treasury note

7%

13%

D

C

A

market portfolio

A portfolio that invests in

every asset in the economy