Introduction to Corporate Finance

Ross et al.: Fundamentals

of Corporate Finance, Sixth

Edition, Alternate Edition

V. Risk and Return 13. Return, Risk, and the

Security Market Line

© The McGraw−Hill^449

Companies, 2002

This is the same portfolio expected return we calculated previously.
This method of calculating the expected return on a portfolio works no matter how
many assets there are in the portfolio. Suppose we had nassets in our portfolio, where n
is any number. If we let xistand for the percentage of our money in Asset i,then the ex-
pected return would be:

E(RP) x 1 E(R 1 ) x 2 E(R 2 ) ... xnE(Rn) [13.2]

This says that the expected return on a portfolio is a straightforward combination of the
expected returns on the assets in that portfolio. This seems somewhat obvious, but, as
we will examine next, the obvious approach is not always the right one.

CHAPTER 13 Return, Risk, and the Security Market Line 421

TABLE 13.5

Expected Return on an

Equally Weighted

Portfolio of Stock L and

Stock U

(1) (2)

State Probability (4)

of of State of (3) Product

Economy Economy Portfolio Return if State Occurs (2) (3)

Recession .50 .50 
20%.50 30% 5% .025

Boom .50 .50  70%.50 10%40% .200

E(RP) 22.5%

Portfolio Expected Return

Suppose we have the following projections on three stocks:

We want to calculate portfolio expected returns in two cases. First, what would be the ex-

pected return on a portfolio with equal amounts invested in each of the three stocks? Second,

what would be the expected return if half of the portfolio were in A, with the remainder equally

divided between B and C?

Based on what we’ve learned from our earlier discussions, we can determine that the ex-

pected returns on the individual stocks are (check these for practice):

E(RA) 8.8%

E(RB) 8.4%

E(RC) 8.0%

If a portfolio has equal investments in each asset, the portfolio weights are all the same. Such

a portfolio is said to be equally weighted.Because there are three stocks in this case, the

weights are all equal to^1 ⁄ 3. The portfolio expected return is thus:

E(RP) (^1 ⁄ 3 ) 8.8% (^1 ⁄ 3 ) 8.4% (^1 ⁄ 3 ) 8% 8.4%

In the second case, verify that the portfolio expected return is 8.5 percent.

Returns if State Occurs

State of Probability of

Economy State of Economy Stock A Stock B Stock C

Boom .40 10% 15% 20%

Bust .60 8 4 0

EXAMPLE 13.3