Institutional features and investment policy specifications often lead to more complicated requirements than simple minimization of risk (whatever the definition of risk may be) or maximization of expected portfolio return. For instance, there can be constraints that limit the number of trades, the exposure to a specific industry, or the number of stocks to be kept in the portfolio. Some of these constraints are imposed by the clients, while others are imposed by regulators. For example, in the case of regulated investment companies, restrictions on asset allocation are set forth in the prospectus and may be changed only with the approval of the fund's board of directors. Pension funds must comply with Employee Retirement Income Security Act (ERISA) requirements. The objective of the portfolio optimization problem can also be modified to consider specifically the trade-off between risk and return, transactions costs, or taxes.

In this section, we take a single-period view of investing, in the sense that the goal of the portfolio allocation procedure will be to invest optimally over a single pre-determined period of interest, such as one month.3 We use w0 to denote the vector array of stock weights in the portfolio at the beginning of the period, and w to denote the weights at the end of the period (to be determined).

Many investment companies, especially institutional investors, have a long investment horizon. However, in reality, ...

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