<html xmlns:v="urn:schemas-microsoft-com:vml" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns:m="http://schemas.microsoft.com/office/2004/12/omml" xmlns="http://www.w3.org/TR/REC-html40"><head><META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=us-ascii"><meta name=Generator content="Microsoft Word 14 (filtered medium)"><style><!--
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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link=blue vlink=purple><div class=WordSection1><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><b><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'>From:</span></b><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'> gsoc-porta-bounces@lists.r-forge.r-project.org [mailto:gsoc-porta-bounces@lists.r-forge.r-project.org] <b>On Behalf Of </b>Ross Bennett<br><b>Sent:</b> Monday, June 24, 2013 7:02 AM<br><b>To:</b> PortfolioAnalytics<br><b>Subject:</b> [GSoC-PortA] Question on quadratic constraint specification<o:p></o:p></span></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Hi All,<o:p></o:p></p><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>I have a quick question on quadratic constraint specification. One of the bullet points under constraints is "provide quadratic constraint specification". I did some digging for the ROI solvers and found that quadprog and glpk only handle linear constraints. The ROI plugin for cplex can handle a quadratic constraint, but this is a commercial product so I am not sure if we want to go down that road and add support for the cplex plugin for optimize_method="ROI". Are there workarounds to handle quadratic constraints in quadprog or glpk?<o:p></o:p></p><p class=MsoNormal><b><i><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>[Doug] I have thought very about the desirability of a chapter on cplex in view of the extensive use of the product. But there is so much else to do that this probably won’t happen this go around</span></i></b><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p></o:p></span></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>Is the intent of providing quadratic constraint specification to allow the user to specify or define any function?<o:p></o:p></p><p class=MsoNormal><b><i><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>[Doug] A generic quadratic constraint capability would be ideal. But just adding the two you list below would be a good first step. With regard to the second below, I note that Jorion showed that adding an absolute volatility risk constraint to TEV portfolios improves their performance.</span></i></b><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p></o:p></span></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>Or should we limit it to pre-defined constraint types and functions that I can add?<o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>A couple use cases for a quadratic constraint that I thought of are:<o:p></o:p></p></div><div><p class=MsoNormal>- Diversification (Allows the user to specify a diversification limit as a constraint).<o:p></o:p></p></div><div><p class=MsoNormal>- Volatility (Allows the user to specify a target volatility (or min or max) as a constraint. (e.g. see Peter Carl's email with a portfolio specific limit to target volatility of > 10%)<o:p></o:p></p></div><div><p class=MsoNormal>- Other use cases for quadratic constraints?<o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>I can add constraint functions for diversification, volatility, etc. and then this could be implemented in constrained_objective or with the mapping function that I will work on in the next section.<o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>Thanks,<o:p></o:p></p></div><div><p class=MsoNormal>Ross Bennett<o:p></o:p></p></div></div></body></html>