[GSoC-PortA] Mean-mETL objective?

Mon Oct 7 21:02:19 CEST 2013

see comments inline

On Mon, Oct 7, 2013 at 8:51 AM, Doug Martin <martinrd at comcast.net> wrote:

> Ross,****
>
> ** **
>
> OK, I see what you mean.   Do keep in mind the following:****
>
> ** **
>
> **1)      **Before a search is done the code should check that the mean
> return of the global minimum ETL (under constraints) – I call this GMETL is
> less than the risk free rate (which may be zero by default).  Otherwise the
> search is useless as there is no tangent portfolio (well I have to be a
> little careful, this is definitely the case for the MVO efficient frontier
> without constraints and most likely with most constraints, and ditto for
> the mean-ETL efficient frontier).  By this ratio is known as the STARR
> ratio in the literature.
>
 Thanks for the suggestion, I'll add the check. To clarify, I think you
mean that the mean return of the GMETL portfolio should be greater than the
risk-free rate, correct?

> ****
>
> ** **
>
> **2)      **If in your second paragraph do you mean that is the default
> behavior?  If so there should be a default argument whose default is
> “maxSTARR”, but the user should also be able to choose GMETL.
>
 Correct. If the portfolio has two objectives, mean and ES, then the
optimal portfolio will be the max STARR portfolio. If the user just wants
the GMETL portfolio, the portfolio should only have a single objective for
ETL.

I did make it possible to pass in maxSTARR=TRUE or maxSTARR=FALSE in the
dots in optimize.portfolio. I did the same for max sharpe ratio (maxSR).
This is important to have for the quadratic utility case because the user
may want to specify a risk_aversion parameter and get the optimal portfolio
at the given risk_aversion parameter. Setting maxSR=TRUE would override any
risk_aversion parameter and find the max sharpe ratio portfolio, so I made
maxSR=FALSE the default.

> ****
>
> ** **
>
> Doug****
>
> ** **
>
> ** **
>
> *From:* gsoc-porta-bounces at lists.r-forge.r-project.org [mailto:
> gsoc-porta-bounces at lists.r-forge.r-project.org] *On Behalf Of *Ross
> Bennett
> *Sent:* Monday, October 07, 2013 8:30 AM
>
> *To:* PortfolioAnalytics
> *Subject:* Re: [GSoC-PortA] Mean-mETL objective?****
>
> ** **
>
> Doug,****
>
> ** **
>
> 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.
> ****
>
> ** **
>
> 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.****
>
> ** **
>
> Ross****
>
> ** **
>
> ** **
>
> On Sun, Oct 6, 2013 at 6:11 PM, Doug Martin <martinrd at comcast.net> wrote:*
> ***
>
> 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???     ****
>
>  ****
>
> 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.  ****
>
>  ****
>
> Am I missing something?****
>
>  ****
>
> Doug****
>
>  ****
>
>  ****
>
> *From:* gsoc-porta-bounces at lists.r-forge.r-project.org [mailto:
> gsoc-porta-bounces at lists.r-forge.r-project.org] *On Behalf Of *Ross
> Bennett
> *Sent:* Sunday, October 06, 2013 5:56 PM
> *To:* PortfolioAnalytics****
>
>
> *Subject:* Re: [GSoC-PortA] Mean-mETL objective?****
>
>  ****
>
> 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.****
>
>  ****
>
> Step 1: Calculate the minimum ETL portfolio given the constraints. This is
> the minimum possible mean return.****
>
>  ****
>
> Step 2: Calculate the maximum return portfolio given the constraints. This
> is the maximum possible mean return.****
>
>  ****
>
> Step 3: Increase or decrease the target return constraint and run the
> optimization.****
>
>  ****
>
> Repeat step 3 until we get convergence within a specified tolerance or
> reach the maximum number of iterations.****
>
>  ****
>
> 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. ****
>
>  ****
>
> Am I on the right track here? Any thoughts on how to do step 3?****
>
>  ****
>
> Thanks,****
>
> Ross****
>
>  ****
>
> On Sun, Oct 6, 2013 at 8:44 AM, Doug Martin <martinrd at comcast.net> wrote:*
> ***
>
> Will need to do an in-depth comparison of Rglpk versus Symphony LP
> (withMIP)
> solvers.
>
> I think you mentioned a project for evaluating the various solvers against
> commonly used benchmark problems? What is the status and timing of that?**
> **
>
>
> Doug
>
>
>
> -----Original Message-----
> From: gsoc-porta-bounces at lists.r-forge.r-project.org
> [mailto:gsoc-porta-bounces at lists.r-forge.r-project.org] On Behalf Of Brian
> G. Peterson****
>
> Sent: Sunday, October 06, 2013 8:19 AM
> To: gsoc-porta at r-forge.wu-wien.ac.at
> Subject: Re: [GSoC-PortA] Mean-mETL objective?****
>
> On 10/06/2013 10:00 AM, Doug Martin wrote:
> > P.S. Chapter 4 in the 2nd edition on mean-ETL optimization via LP with
> > Rglpk, with some nice examples (will send when available).   I will also
> use
> > this for the MIP examples in an advanced constraints chapter (since we
> > don't have a QP solver available with MIP capability, unless I can
> > find time to do a chapter using CPLEX via PortfolioAnalytics via ROI).
>
> there is also a ROI front end to the MILP Symphony solver.
>
> I'm not sure iof the Symphony solver includes QP constraints.
>
> --
> Brian G. Peterson
> http://braverock.com/brian/
> Ph: 773-459-4973
> IM: bgpbraverock
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