Optimization

Abstract

Consider the problem of finding the best asset allocation strategy across thousands of investments so that the highest return is achieved with the smallest amount of risk. The methodology for coming up with the answer to such a question requires us to select parameters that will maximize/minimize our objective function subject to constraints. In our case, a plausible objective function might be the total return of a strategy divided by the maximum drawdown of the strategy over a predefined period. The constraints might be the total amount of capital devoted to each asset within the portfolio. Many interesting problems in finance, computer science, and the physical sciences rely on the specification and use of models. These mathematical formulations typically include one or more parameters as part of their input specifications. Optimization is a branch of mathematics that provides techniques for finding the best values for these parameters under constraints. R has a slew of packages that deal with optimization, and we will look at a few of them in this chapter.