Nonparametric Finance

Chapter 12Dynamic Portfolio Selection

Dynamic portfolio selection means here such portfolio selection in a multiperiod model where the portfolio weights are repeatedly rebalanced at the beginning of every period, using information available at the beginning of each period. We apply the methods of Chapter 6, where prediction of asset returns is studied, and the methods of Chapter 7, where prediction of volatility is studied.

The return of a portfolio is a linear combination of the returns of the portfolio components. Let us exclude the risk-free rate for a moment, so that the return of the portfolio is given by

where is the gross return the portfolio, is the vector of portfolio weights, and is the vector of the gross returns of the risky assets. We can consider the following approaches to choose the portfolio weights .

1. 1. Maximize the expected return
   12.1
2. where .
3. 2. Maximize the variance ...