16-Port Selection Mean Var Page 509 Wednesday, February 4, 2004 1:09 PM
Portfolio Selection Using Mean-Variance Analysis 509SUMMARY
■ The principles of financial optimization were established by Markowitz
in 1952.
■ The key idea of Markowitz is that financial decision-making should be
based on an optimal trade-off between risk and returns.
■ Markowitz’s seminal work proposed optimizing a trade-off between
variance and the expected returns of a portfolio under the assumption
of joint normality of returns.
■ The key principle behind mean-variance optimization is diversification.
■ Markowitz’s work had a lasting influence on the investment manage-
ment community; investment management principles are still deeply
influenced by these ideas.
■ Portfolios that achieve the minimum variance for a given expected
return are called minimum-variance portfolios.
■ Minimum-variance portfolios are called mean-variance efficient portfo-
lios; the set of mean-variance efficient portfolios form the efficient fron-
tier.
■ The theoretical problem of finding mean-variance efficient portfolios
leads to an optimization problem solvable in closed form with the tech-
nique of Lagrange multipliers.
■ Sharpe, Tobin, and Lintner extended the portfolio selection model in
the presence of a risk-free asset; the mean-variance portfolios are those
that are a combination of the tangency portfolio and the risk-free asset.
■ In the presence of a risk-free asset the efficient frontier becomes the
Capital Market Line which is the straight line tangent to the Market
Portfolio.
■ If realistic constraints are added, namely sector exposure and tradabil-
ity constraints, the problem becomes one of quadratic programming or
a mixed-integer programming to be solved with numerical techniques.
■ Markowitz’s mean-variance formulation can be used for portfolio
selection as well as asset allocation.
■ Risk-of-loss-analysis is an extension of the basic model. It considers the
risk of not achieving a portfolio’s expected return.
■ The basic mean-variance analysis can also be extended to cover the lia-
bilities of pension funds.
■ The theory of Markowitz can be extended in a one-period setting as
maximization of expected utility.
■ In a multiperiod setting agents maximize utility defined on consump-
tion.
■ In a multiperiod setting agents determine at each step the optimal
trade-off between investment and consumption.