[GSoC-PortA] Mean-mETL objective?

[Doug Martin]

The LP formulation, as well as the intrinsic convexity of the basic CVaR/ETL
problem was established by Rockafellar and Uryasev (2000).  With mETL none
of those results follow.    

Doug

P.S. I don't know if you noticed that Zhang was my Ph.D. student.   



-----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 6:36 AM
To: gsoc-porta at r-forge.wu-wien.ac.at
Subject: Re: [GSoC-PortA] Mean-mETL objective?

Doug,

Per my other emails in this thread, I'd love to know how to formulate the
mean/ETL problem as an LP.

This UW dissertation is one of the early links on Google:

https://digital.lib.washington.edu/researchworks/bitstream/handle/1773/21869
/Zhang_washington_0250E_10711.pdf?sequence=1

page 26 of the document (p38 of the pdf) constructs the mean/ETL problem as
a linear programming problem.

I haven't followed it further than this, but it appears that we just need to
sort out the formulation, and we should be good.

The Cornish Fisher solution will be locally convex over much of its feasible
space.  It is often not globally convext across variations in probability
'p' (or 'alpha', though I dislike the alpha notation since alpha is such a
loaded word in finance).  It is not guaranteed to be convex, of course, and
will not be convex if skewness or kurtosis are sufficiently large and the
'p' setting is sufficiently large.

so, based on what I've been able to read this morning, it seems we just need
to get the formulation correct, and we should be able to treat mean/ETL
optimization as an LP problem.

Brian

On 10/05/2013 11:06 AM, Doug Martin wrote:
> -----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: Friday, October 04, 2013 12:59 PM
> To: gsoc-porta at r-forge.wu-wien.ac.at
> Subject: Re: [GSoC-PortA] Mean-mETL objective?
>
> If it is an LP problem, I think you can only minimize subject to 
> constraints.
>
> */[Doug] Although I have never check this, it does not sound right.  
> The inner product in the LP formulation of ETL supports that 
> formulation of ETL as an LP, but there should be no problem to adding 
> another piece representing the inner product of mean return forecasts 
> and portfolio weights (mean portfolio return estimate).  I will check 
> it out, as I had intended to add this in the ETL chapter./*
>
> If it is a QP problem, can't you do the mean/ETL portfolio?
>
> That assumes the space is convex, which it will be for Gaussian ETL,
>
> */[Doug] But that case is not interesting, does not add value relative 
> to MVO./*
>
> *//*
>
> and may not be for modified Cornish Fisher ETL, but will be most of 
> the time, at most reasonable confidence levels.
>
> */[Doug] For both standard and modified ETL, the problem is in general 
> non-convex.  I guess you are saying from your experience the problem 
> with modified ETL usually appears to be convex.  I'm curious about how
> you ascertain that?   E.g., because on multiple runs with DeOptim you
> seldom find more than one local minimum?  That would certainly be
> reassuring./*
>
> *//*
>
> Brian
>
> On 10/04/2013 02:42 PM, Ross Bennett wrote:
>
>  > Peter,
>
>  >
>
>  > Unfortunately, with ROI we are only able to minimize ETL with ETL 
> as
>
>  > an objective. If you have mean and ETL as an objective using ROI,
>
>  > unless there is a target in the mean return objective, we just
>
>  > minimize ETL. If you have both mean and ETL as objectives, you 
> could
>
>  > add a target to the mean objective and this will minimize ETL 
> subject to the target return.
>
>  >
>
>  > We can do the following with ETL as an objective using ROI:
>
>  >   - Minimize ETL subject to leverage, box, group, exposure, position
>
>  > limit, and target return.
>
>  >
>
>  > Multipliers are ignored with ROI since the problems are formulated
>
>  > into an LP/QP problem. I'll take a look at the documentation in
>
>  > optimize.portfolio and make sure this is clear.
>
>  >
>
>  > I hope that helps clear it up.
>
>  >
>
>  > Ross
>
>  >
>
>  >
>
>  > On Fri, Oct 4, 2013 at 11:49 AM, Peter Carl <peter at braverock.com
>
>  > <mailto:peter at braverock.com>> wrote:
>
>  >
>
>  >     Hey Ross,
>
>  >
>
>  >     I can't seem to get the Mean-mETL objective to select anything
other
>
>  >     than
>
>  >     the Min mETL portfolio using ROI.  It looks like there should be
good
>
>  >     convexity, but I think there's a substantial imbalance between the
>
>  >     size of
>
>  >     the monthly mean return and the loss indicated by the ETL.  I've
> tried
>
>  >     modifying the multiplier on the mean, but it doesn't seem to have
an
>
>  >     effect.
>
>  >
>
>  >     Any thoughts?
>
>  >
>
>  >     pcc
>
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--
Brian G. Peterson
http://braverock.com/brian/
Ph: 773-459-4973
IM: bgpbraverock
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