<div dir="ltr">Doug,<div><br></div><div>I don't think you were missing anything, perhaps I misunderstood. From previous emails in this thread, I thought that there was a way to formulate the mean/ETL as an LP problem that would avoid having to do a search for the maximum mean/ETL portfolio. There is no need to do this for DEoptim or random portfolios, I was just referring to maximizing mean/ETL using ROI. </div>
<div><br></div><div>I implemented this as of commit r3212. If mean and ETL (also ES or CVaR) are objectives and optimize_method="ROI", the optimal portfolio returned is one that maximizes mean/ETL. I use a bisection search to find the portfolio that maximizes mean/ETL.</div>
<div><br></div><div style>Ross</div><div><br></div></div><div class="gmail_extra"><br><br><div class="gmail_quote">On Sun, Oct 6, 2013 at 6:11 PM, Doug Martin <span dir="ltr"><<a href="mailto:martinrd@comcast.net" target="_blank">martinrd@comcast.net</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div lang="EN-US" link="blue" vlink="purple"><div><p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d">Maybe I’m missing something, and you are concerned about something more than just mean-ETL optimization, i.e., using random portfolios or DeOptim due to constraints??? <u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d"><u></u> <u></u></span></p><p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d">As for the STARR ratio Step 3 is fine, and can also be used for max Sharpe ratio. As long as the efficient frontier is concave both ratios increase until the maximum and then decrease, so a simple line search will work and converge pretty rapidly. I have a placeholder for a max SR section in Chapter 2 and will do soon. <u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d"><u></u> <u></u></span></p><p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d">Am I missing something?<u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d"><u></u> <u></u></span></p><p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d">Doug<u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d"><u></u> <u></u></span></p><p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d"><u></u> <u></u></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""> <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> Sunday, October 06, 2013 5:56 PM<br><b>To:</b> PortfolioAnalytics</span></p><div><div class="h5"><br><b>Subject:</b> Re: [GSoC-PortA] Mean-mETL objective?<u></u><u></u></div></div><p></p><div><div class="h5">
<p class="MsoNormal"><u></u> <u></u></p><div><p class="MsoNormal">It will be nice if there is a simple way to formulate this as an LP problem to maximize mean/ETL. If there is not a simple formulation, one way to approach this would be similar to finding the tangency portfolio on the efficient frontier. Generating a finite number of portfolios along the frontier and finding the portfolio with the highest mean/ETL will find the approximate tangency portfolio and is what I do for the efficient frontier code.<u></u><u></u></p>
<div><p class="MsoNormal"><u></u> <u></u></p></div><div><p class="MsoNormal">Step 1: Calculate the minimum ETL portfolio given the constraints. This is the minimum possible mean return.<u></u><u></u></p></div><div><p class="MsoNormal">
<u></u> <u></u></p></div><div><p class="MsoNormal">Step 2: Calculate the maximum return portfolio given the constraints. This is the maximum possible mean return.<u></u><u></u></p></div><div><p class="MsoNormal"><u></u> <u></u></p>
</div><div><p class="MsoNormal">Step 3: Increase or decrease the target return constraint and run the optimization.<u></u><u></u></p></div><div><div><p class="MsoNormal"><u></u> <u></u></p></div><div><p class="MsoNormal">
Repeat step 3 until we get convergence within a specified tolerance or reach the maximum number of iterations.<u></u><u></u></p></div></div><div><p class="MsoNormal"><u></u> <u></u></p></div><div><p class="MsoNormal">I'm not sure what the right approach or method would be for step 3. Maybe split the frontier in two equal spaces and iteratively shrink the search space until we find a solution. <u></u><u></u></p>
</div><div><p class="MsoNormal"><u></u> <u></u></p></div><div><p class="MsoNormal">Am I on the right track here? Any thoughts on how to do step 3?<u></u><u></u></p></div><div><p class="MsoNormal"><u></u> <u></u></p></div>
<div><p class="MsoNormal">Thanks,<u></u><u></u></p></div><div><p class="MsoNormal">Ross<u></u><u></u></p></div></div><div><p class="MsoNormal" style="margin-bottom:12.0pt"><u></u> <u></u></p><div><p class="MsoNormal">On Sun, Oct 6, 2013 at 8:44 AM, Doug Martin <<a href="mailto:martinrd@comcast.net" target="_blank">martinrd@comcast.net</a>> wrote:<u></u><u></u></p>
<p class="MsoNormal">Will need to do an in-depth comparison of Rglpk versus Symphony LP (withMIP)<br>solvers.<br><br>I think you mentioned a project for evaluating the various solvers against<br>commonly used benchmark problems? What is the status and timing of that?<u></u><u></u></p>
<div><p class="MsoNormal"><br>Doug<br><br><br><br>-----Original Message-----<br>From: <a href="mailto:gsoc-porta-bounces@lists.r-forge.r-project.org" target="_blank">gsoc-porta-bounces@lists.r-forge.r-project.org</a><br>[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>] On Behalf Of Brian<br>
G. Peterson<u></u><u></u></p></div><div><p class="MsoNormal" style="margin-bottom:12.0pt">Sent: Sunday, October 06, 2013 8:19 AM<br>To: <a href="mailto:gsoc-porta@r-forge.wu-wien.ac.at" target="_blank">gsoc-porta@r-forge.wu-wien.ac.at</a><br>
Subject: Re: [GSoC-PortA] Mean-mETL objective?<u></u><u></u></p></div><div><div><p class="MsoNormal">On 10/06/2013 10:00 AM, Doug Martin wrote:<br>> P.S. Chapter 4 in the 2nd edition on mean-ETL optimization via LP with<br>
> Rglpk, with some nice examples (will send when available). I will also<br>use<br>> this for the MIP examples in an advanced constraints chapter (since we<br>> don't have a QP solver available with MIP capability, unless I can<br>
> find time to do a chapter using CPLEX via PortfolioAnalytics via ROI).<br><br>there is also a ROI front end to the MILP Symphony solver.<br><br>I'm not sure iof the Symphony solver includes QP constraints.<br><br>
--<br>Brian G. Peterson<br><a href="http://braverock.com/brian/" target="_blank">http://braverock.com/brian/</a><br>Ph: <a href="tel:773-459-4973" target="_blank">773-459-4973</a><br>IM: bgpbraverock<br>_______________________________________________<br>
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