Wednesday, June 8, 2016
Pachamanova & Fabozzi, Portfolio Construction and Analytics
The book is divided into six parts: statistical models of risk and uncertainty, simulation and optimization modeling, portfolio theory, equity portfolio management, fixed income portfolio management, and derivatives and their application to portfolio management. The authors assume that the reader has practically no knowledge of financial markets or quantitative concepts; everything is described from scratch. The reader does, however, have to be quite mathematically literate. The authors’ only concession on this score is an appendix explaining basic linear algebra concepts.
Many of the problems the book introduces can be addressed, although often with severe limitations, using either R or Excel (for instance, basic optimization with Excel Solver, a task the authors explain in step-by-step detail). Although most portfolio managers will undoubtedly opt for more user-friendly specialized software packages, for teaching purposes it makes sense to rely on readily available free (or nearly free) software.
Just to give a taste of the book, let’s look briefly at the problem of optimization under uncertainty. There are three approaches to dealing with this problem: dynamic programming, stochastic programming, and robust optimization.
With dynamic programming, “the optimization problem is solved recursively, going backwards from the last state, and computing the optimal solution for each possible state of the system at a particular stage. In finance, dynamic programming is used in the context of pricing of some derivative instruments, in investment strategies such as statistical arbitrage, and in long-term corporate financial planning.”
Stochastic methods “rely on representing the uncertain data with scenarios and focus on finding a strategy so that the expected value of the objective function over all scenarios (sometimes, penalized for some measure of risk) is optimal. Stochastic algorithms have been successfully applied in a variety of financial contexts, such as management of portfolios of fixed income securities, corporate risk management, security selection, and asset/liability management….”
The problem with both of these methods is that, in most real-world applications, “the dimensions … are too large, and the problems are difficult to handle computationally. Often, approximation algorithms are used; some such algorithms employ Monte Carlo simulation and sample the state space efficiently.”
Robust optimization, introduced to the world of finance more recently, “takes a worst-case approach to optimization formulations.” It “makes optimization models robust with respect to uncertainty in the input data of optimization problems by solving so-called robust counterparts of these problems for appropriately defined uncertainty sets for the random parameters. The robust counterparts contain no uncertain coefficients; they are deterministic optimization problems.”
As you can see from these snippets, Portfolio Construction and Analytics isn’t exactly a James Patterson thriller, but for the quantitatively oriented student of finance or portfolio manager it is a useful text.