[GSoC-PortA] Mean-mETL objective?

[Brian G. Peterson]

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