Principles of Managerial Finance

226 PART 2 Important Financial Concepts

12. The portfolio of a firm, which would consist of its total assets, is not differentiated from the portfolio of an
    owner, which would probably contain a variety of different investment vehicles (i.e., assets). The differing character-
    istics of these two types of portfolios should become clear upon completion of Chapter 10.

efficient portfolio
A portfolio that maximizes return
for a given level of risk or
minimizes risk for a given level
of return.

portfolioof assets.^12 The financial manager’s goal is to create an efficient portfo-

lio,one that maximizes return for a given level of risk or minimizes risk for a

given level of return. We therefore need a way to measure the return and the stan-

dard deviation of a portfolio of assets. Once we can do that, we will look at the

statistical concept of correlation,which underlies the process of diversification

that is used to develop an efficient portfolio.

Portfolio Return and Standard Deviation

The return on a portfoliois a weighted average of the returns on the individual

assets from which it is formed. We can use Equation 5.5 to find the portfolio

return, kp:

kp(w 1 k 1 )(w 2 k 2 ).. .(wnkn)

n

j 1

wjkj (5.5)

where

wjproportion of the portfolio’s total dollar value represented by asset j

kjreturn on asset j

Of course, nj=1wj1, which means that 100 percent of the portfolio’s assets

must be included in this computation.

The standard deviation of a portfolio’s returnsis found by applying the for-

mula for the standard deviation of a single asset. Specifically, Equation 5.3 is

used when the probabilities of the returns are known, and Equation 5.3a (from

footnote 10) is applied when the outcomes are known and their related probabil-

ities of occurrence are assumed to be equal.

EXAMPLE Assume that we wish to determine the expected value and standard deviation of

returns for portfolio XY, created by combining equal portions (50%) of assets X

and Y. The forecasted returns of assets X and Y for each of the next 5 years

(2004–2008) are given in columns 1 and 2, respectively, in part A of Table 5.7. In

column 3, the weights of 50% for both assets X and Y along with their respective

returns from columns 1 and 2 are substituted into Equation 5.5. Column 4 shows

the results of the calculation—an expected portfolio return of 12% for each year,

2004 to 2008.

Furthermore, as shown in part B of Table 5.7, the expected value of these

portfolio returns over the 5-year period is also 12% (calculated by using Equa-

tion 5.2a, in footnote 9). In part C of Table 5.7, portfolio XY’s standard devia-

tion is calculated to be 0% (using Equation 5.3a, in footnote 10). This value

should not be surprising because the expected return each year is the same—

12%. No variability is exhibited in the expected returns from year to year.