The Mathematics of Financial Modelingand Investment Management

16-Port Selection Mean Var Page 504 Wednesday, February 4, 2004 1:09 PM

504 The Mathematics of Financial Modeling and Investment Management

all four asset classes in the optimization. The inclusion of U.S. small cap

and EAFE international equity into the mix makes the opportunity set

bigger (i.e., the frontier covers a larger risk/return spectrum). It also

moves the efficient frontier outwards (i.e., the frontier results in a larger

expected return at any given level of risk, or conversely, results in a

lower risk for any given level of expected return). The frontier also

highlights portfolios A′ and B′—the portfolios with the same standard

deviation as portfolios A and B, respectively.

Exhibit 16.14 shows the composition of the underlying portfolios

that make up the frontier. Interestingly, U.S. small cap and EAFE inter-

national equity—the more aggressive asset classes—are included in all

the portfolios. Even, the least risky portfolio has a small allocation to

these two asset classes. On the other hand, U.S. large cap equity—an

asset class that is thought of as the backbone of a domestic portfolio—

gets excluded from the more aggressive portfolios.

Exhibit 16.15 compares the composition of portfolios A and B to A′

and B′, respectively. Both the new portfolios, A′ and B′, find U.S. small

EXHIBIT 16.14 Composition of the Efficient Frontier

Source: Exhibit 3.11 in Frank J. Fabozzi, Francis Gupta, and Harry M. Markow-

itz, “Applying Mean-Variance,” Chapter 3 in Frank J. Fabozzi and Harry M.

Markowitz (eds.), The Theory and Practice of Investment Management (Hobo-

ken, NJ: John Wiley & Sons, 2002), p. 55.