Nonparametric Finance

Chapter 11Markowitz Portfolios

Portfolio choice with mean–variance preferences was proposed by Markowitz (1952 1959). The approach introduced the idea of balancing risk and return to find an optimal portfolio.

Markowitz approach can be used in the single period portfolio selection. Let be the portfolio return. In the Markowitz approach there exists three ways to choose the portfolio:

1. 1. Maximize the variance penalized expected return
   
2. where is the risk aversion coefficient. Parameter measures the investor's relative risk aversion, as defined in (9.31).
3. 2. Minimize the variance under a minimal requirement for the expected return: , where is the minimal requirement for the expected return.
4. 3. Maximize the expected return under a condition that the variance is not too large: where ...