The Mathematics of Financial Modelingand Investment Management

16-Port Selection Mean Var Page 479 Wednesday, February 4, 2004 1:09 PM

Portfolio Selection Using Mean-Variance Analysis 479

return and variance, with the optimal portfolio being the one portfolio

selected based on the investor’s preference (which later we will see is quan-

tified by the investor’s utility function). The efficient frontier changes, how-

ever, once a risk-free asset is introduced and assuming that investors can

borrow and lend at the risk-free rate. This is illustrated in Exhibit 16.3.

Every combination of the risk-free asset and the efficient portfolio

M, which we referred to as the tangency portfolio in the previous sec-

tion, is shown on the line drawn from the vertical axis at the risk-free

rate tangent to the Markowitz efficient frontier. All the portfolios on the

line are feasible for the investor to construct. Portfolios to the left of

portfolio M represent combinations of risky assets and the risk-free

asset. Portfolios to the right of portfolio M include purchases of risky

assets made with funds borrowed at the risk-free rate. Such a portfolio

is called a leveraged portfolio because it involves the use of borrowed

funds. The line from the risk-free rate that is tangent to the efficient

frontier of risky assets is called the capital market line (CML).

Let’s compare a portfolio on the CML to a portfolio on the

Markowitz efficient frontier with the same risk in Exhibit 16.3. For

EXHIBIT 16.3 Capital Market Line and the Markowitz Efficient Frontier