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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 5:45 PM<br><b>To:</b> PortfolioAnalytics<br><b>Subject:</b> Re: [GSoC-PortA] Question on quadratic constraint specification<o:p></o:p></span></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal style='margin-bottom:12.0pt'>See comments below<o:p></o:p></p><div><p class=MsoNormal>On Mon, Jun 24, 2013 at 10:27 AM, Doug Martin <<a href="mailto:martinrd@comcast.net" target="_blank">martinrd@comcast.net</a>> wrote:<o:p></o:p></p><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><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"'> <a href="mailto:gsoc-porta-bounces@lists.r-forge.r-project.org" target="_blank">gsoc-porta-bounces@lists.r-forge.r-project.org</a> [mailto:<a href="mailto:gsoc-porta-bounces@lists.r-forge.r-project.org" target="_blank">gsoc-porta-bounces@lists.r-forge.r-project.org</a>] <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</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Hi All,<o:p></o:p></p><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p></div><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>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></div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><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><o:p></o:p></p></div></div></div><div><p class=MsoNormal>[Ross] It looks like the IBM CPLEX suite is free for academic use. I might be able to work on this in the fall after GSOC is complete.<o:p></o:p></p><p class=MsoNormal><b><i><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>[Doug] Well, that would be serious incentive.</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><blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;padding:0in 0in 0in 6.0pt;margin-left:4.8pt;margin-right:0in'><div><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p></div><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Is the intent of providing quadratic constraint specification to allow the user to specify or define any function?<o:p></o:p></p></div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><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><o:p></o:p></p></div></div></div></blockquote><div><p class=MsoNormal>[Ross] Sounds good, I'll work on adding constraint types for diversification and volatility.<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 briefly describe the Jorion 2003 result in the appendix of LSS4 attached, and have attached the paper.<o:p></o:p></span></i></b></p><p class=MsoNormal><b><i><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>We did something similar with ETL based optimization in FinAnalytica’s Cognity product.</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><blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;padding:0in 0in 0in 6.0pt;margin-left:4.8pt;margin-right:0in'><div><div><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>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 style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>A couple use cases for a quadratic constraint that I thought of are:<o:p></o:p></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>- Diversification (Allows the user to specify a diversification limit as a constraint).<o:p></o:p></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>- 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 style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>- Other use cases for quadratic constraints?<o:p></o:p></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>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 style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Thanks,<o:p></o:p></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Ross Bennett<o:p></o:p></p></div></div></div></div><p class=MsoNormal style='margin-bottom:12.0pt'><br>_______________________________________________<br>GSoC-PortA mailing list<br><a href="mailto:GSoC-PortA@lists.r-forge.r-project.org">GSoC-PortA@lists.r-forge.r-project.org</a><br><a href="http://lists.r-forge.r-project.org/cgi-bin/mailman/listinfo/gsoc-porta" target="_blank">http://lists.r-forge.r-project.org/cgi-bin/mailman/listinfo/gsoc-porta</a><o:p></o:p></p></blockquote></div><p class=MsoNormal><o:p> </o:p></p></div></body></html>