calculation time in the vicinity of the finalbestport-folio. Note that we are not looking for the tangencyportfolio; simple mean/CVaR optimization can beachieved with standard optimizers. We are lookinghere for the best balance between return and risk con-centration.We have utilized the mean return/CVaR concen-tration examples here as more realistic, but still styl-ized, examples of non-convex objectives and con-straints in portfolio optimization; other non-convexobjectives, such as drawdown minimization, are alsocommon in real portfolios, and are likewise suitableto application of Differential Evolution. One of thekey issues in practice with real portfolios is that aportfolio manager rarely has only a single objectiveor only a few simple objectives combined. For manycombinations of objectives, there is no unique globaloptimum, and the constraints and objectives formedlead to a non-convex search space. It may take sev-eral hours on very fast machines to get the best an-swers, and the best answers may not be a true globaloptimum, they are justas close as feasiblegiven poten-tially competing and contradictory objectives.When the constraints and objectives are relativelysimple, and may be reduced to quadratic, linear, orconical forms, a simpler optimization solver will pro-duce answers more quickly.When the objectivesare more layered, complex, and potentially contra-dictory, as those in real portfolios tend to be,DE-optimor other global optimization algorithms suchas those integrated intoPortfolioAnalyticsprovidea portfolio manager with a feasible option for opti-mizing their portfolio under real-world non-convexconstraints and objectives.ThePortfolioAnalyticsframework allows any ar-bitrary R function to be part of the objective set, andallows the user to set the relative weighting that theywant on any specific objective, and use the appropri-ately tuned optimization solver algorithm to locateportfolios that most closely match those objectives.SummaryIn this note we have introduced DE andDEoptim.The packageDEoptimprovides a means of applyingthe DE algorithm in the R language and environmentfor statistical computing. DE and the packageDE-optimhave proven themselves to be powerful toolsfor the solution of global optimization problems ina wide variety of fields. We have referred interestedusers toPrice et al.(2006) andMullen et al.(2011) fora more extensive introduction, and further pointersto the literature on DE. The utility of usingDEoptimwas further demonstrated with a simple example of astylized non-convex portfolio risk contribution allo-cation, with users referred toPortfolioAnalyticsforportfolio optimization using DE with real portfoliosunder non-convex constraints and objectives.
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- Summer '17
- K B
- Optimization, Modern portfolio theory, objective function, diﬀerential evolution, DEoptim