16-Port Selection Mean Var Page 484 Wednesday, February 4, 2004 1:09 PM
484 The Mathematics of Financial Modeling and Investment ManagementEXHIBIT 16.4 Indifference CurvesSelection of the Optimal Portfolio
A reasonable assumption is that investors are risk averse. A risk-averse
investor is an investor who, when faced with choosing between two
investments with the same expected return but two different risks, pre-
fers the one with the lower risk.
In selecting portfolios, an investor seeks to maximize the expected
portfolio return given his tolerance for risk. Given a choice from the set
of efficient portfolios, the optimal portfolio is the one that is preferred
by the investor. In terms of utility functions, the optimal portfolio is the
efficient portfolio which has the maximum utility.
The particular efficient portfolio on the CML that the investor will
select will depend on the investor’s risk preference. This can be seen in
Exhibit 16.5, which is the same as Exhibit 16.2 but has the investor’s
indifference curves included. The investor will select the portfolio on the
CML that is tangent to the highest indifference curve, u 3 in the exhibit.
Notice that without the risk-free asset, an investor could only get to
u 2 , which is the indifference curve that is tangent to the Markowitz effi-
cient frontier. Thus, the opportunity to borrow or lend at the risk-free
rate results in a capital market where risk-averse investors will prefer to