[R-SIG-Finance] Sharpe's algorithm for portfolio improvement
Enrico Schumann
enricoschumann at yahoo.de
Tue Aug 2 07:31:13 CEST 2011
With 120 observations and 30 assets and a smooth objective function and
relatively simple constraints, the running time should be *seconds*. One
potential problem with DE is how the constraints are implemented, more
specifically the lower/upper limits. When DE creates new solutions, it does
not observe any constraints except for such that one "implicitly" adds (eg,
like you did with the budget constraint). Thus, one typically repairs the
constraints after new solutions are created, or penalises solutions that
violate constraints. If you penalise too strongly, the algorithm will in
effect throw away many candidate solutions, and so the algorithm may indeed
have a hard time to find a solution, since in portfolio optimisation
problems the solution is often on the boundary.
Regarding the installation error: the \title in one Rd-file uses quotation
marks (via \sQuote), which should be supported (according to R-exts since R
2.12.0). R CMD check never complained to me on Win XP or Ubuntu. Could you
please send me (off-list) the R-version/OS you work on? But I will remove
the quotation marks later today, so the new version should be available from
R-Forge tomorrow. Please let me know if this doesn't work either.
Regards,
Enrico
> -----Ursprüngliche Nachricht-----
> Von: r-sig-finance-bounces at r-project.org
> [mailto:r-sig-finance-bounces at r-project.org] Im Auftrag von
> John P. Burkett
> Gesendet: Montag, 1. August 2011 23:08
> An: Enrico Schumann; R-SIG-Finance at r-project.org
> Betreff: Re: [R-SIG-Finance] Sharpe's algorithm for portfolio
> improvement
>
> Enrico Schumann wrote:
> > what kind of "difficulty" did you encounter? If you would give more
> > details on what you tried, and how, then people should be
> better able to help you.
> Thank you, Enrico, for your prompt and helpful response.
> Focusing on Sharpe's algorithm, I originally omitted
> specifics about difficulties I have encountered with packages
> based on other algorithms. However, in case it is of
> interest, I will now outline my project and difficulties.
> I have about 120 monthly observations on gross real
> returns for about 30 assets. [Trying to mitigate estimation
> error, I've shrunk observed returns toward a common value as
> proposed by Philippe Jorion, "Bayes-Stein Estimation for
> Portfolio Analysis", Journal of Financial and Quantitative
> Analysis, v. 21, n. 3 (Sept.,
> 1986), pp. 279-92.] I initially specified the utility
> function as U =
> R/(0.5 + R) where R is R is the gross return on a portfolio
> and specified long-only constraints. The restriction that
> portfolio shares sum to 1 is handled by specifying n-1
> variables (where n is the nubmer of assets) and making the
> share asset n be 1 minus the sum of other shares. If I apply
> DEoptim to a sufficiently small subset of the assets, it
> converges and selects a plausible portfolio. Yet if I ask
> DEoptim to analyze as many as 30 assets, it fails to converge
> in any number of iterations that I've tried. Given the same
> problem, Rgenoud converged after 44 hours (more than 2
> million generation, if memory serves). I subsequently tried
> changing the utility function to ln(R) and asking Rgenoud to
> maximize that. Thus far it has run for over 1.5 million
> generations without converging. The portfolio shares have
> barely changed over many recent generations. Perhaps I could
> just relax the default convergence criteria and declare the
> problem solved for practical purposes. However, that might
> result in mistaking a local for a global maximum. These
> experiences may just indicate that a 30 asset portfolio is
> hard to optimize using general purpose algorithms. Kris Boudt
> et al. note that "portfolio problems encountered in practice
> may require days to optimize on a personal computer"
> ("Large-scale portfolio optimization with DEoptim," p. 1).
> These experiences motivated my interest in trying an
> algorithm, such as that of Sharpe, designed specifically for
> portfolio optimization.
>
> > I don't know the paper you mentioned, but I know a paper of
> W. Sharpe
> > in which he suggests to do repeated zero-sum changes to the
> portfolio,
> > like "increase one asset by x%, and decrease another one by x%". If
> > that is what you mean, this can be done with a local search.
> The algorithm you describe sounds very much like that covered
> in the articles I cited in my previous note. It's probably
> the same algorithm.
>
> (But actually, other
> > functions like DEoptim should work just as well. The
> DEoptim package
> > even comes with a vignette that adresses portfolio optimisation.)
> Perhaps I should just be more patient with DEoptim or buy a
> faster computer!
>
> > An example for a local search procedure is given in one of the
> > vignettes of the NMOF package (which is available from
> > https://r-forge.r-project.org/R/?group_id=1128 ), even
> though I am not
> > sure how self-explanatory the vignette is.
> Thank you for the NMOF reference. I've printed "Examples and
> Extensions for the NMOF package" and tried the command
> install.packages("NMOF", repos =
> "http://R-Forge.R-project.org") That command elicited the
> following messages:
> Warning in install.packages("NMOF", repos =
> "http://R-Forge.R-project.org") :
> argument 'lib' is missing: using
> '/home/john/R/i486-pc-linux-gnu-library/2.8'
> trying URL
> 'http://R-Forge.R-project.org/src/contrib/NMOF_0.14-2.tar.gz'
> Content type 'application/x-gzip' length 1352123 bytes (1.3
> Mb) opened URL ==================================================
> downloaded 1.3 Mb
>
> * Installing *source* package 'NMOF' ...
> ** R
> ** data
> ** moving datasets to lazyload DB
> ** inst
> ** preparing package for lazy loading
> ** help
> >>> Building/Updating help pages for package 'NMOF'
> Formats: text html latex example
> DEopt text html latex example
> EuropeanCall text html latex example
> GAopt text html latex example
> LSopt text html latex example
> MA text html latex example
> NMOF-package text html latex example
> NS text html latex example
> NSf text html latex example
> PSopt text html latex example
> TAopt text html latex example
> bundData text html latex example
> callHestoncf text html latex example
> fundData text html latex example
> gridSearch text html latex example
> qTable text html latex example
>
> ERROR in file 'repairMatrix.Rd': Environment (text enclosed
> in {}) found in \title{...}.
> The title must be plain text!
>
> ERROR: building help failed for package 'NMOF'
> ** Removing '/home/john/R/i486-pc-linux-gnu-library/2.8/NMOF'
>
> The downloaded packages are in
> /tmp/RtmpNAuDvf/downloaded_packages
> Warning message:
> In install.packages("NMOF", repos = "http://R-Forge.R-project.org") :
> installation of package 'NMOF' had non-zero exit status
>
> ***************************************
>
> Any suggestions for how to successfully install NMOF would be
> greatly appreciated.
>
> Best regards,
> John
>
>
>
> >
> >
> > Regards,
> > Enrico
> >
> >
> >
> >
> >> -----Ursprüngliche Nachricht-----
> >> Von: r-sig-finance-bounces at r-project.org
> >> [mailto:r-sig-finance-bounces at r-project.org] Im Auftrag
> von John P.
> >> Burkett
> >> Gesendet: Montag, 1. August 2011 18:49
> >> An: R-SIG-Finance at r-project.org
> >> Betreff: [R-SIG-Finance] Sharpe's algorithm for portfolio
> improvement
> >>
> >> An attractive sounding algorithm for maximizing the
> expected utility
> >> of of a portfolio was proposed by William F. Sharpe in "An
> algorithm
> >> for portfolio improvement," Advances in Mathematical
> Programming and
> >> Financial Planning, 1987, pp.
> >> 155-170 and summarized by the same author in "Expected
> utility asset
> >> allocation," Financial Analysts Journal, vol.
> >> 63, no. 5 (Sep.-Oct., 2007), pp. 18-30.
> >>
> >> Has this algorithm been implemented in R?
> >>
> >> If not, is there a substitute that is likely to work well for a
> >> user-specified concave utility function? I've tried
> optim, DEoptim,
> >> and Rgenoud but encountered difficulty in getting them to converge
> >> for a long-only portfolio of around 30 assets.
> >>
> >> Best regards,
> >> John
> >>
> >> --
> >> John P. Burkett
> >> Department of Economics
> >> University of Rhode Island
> >> Kingston, RI 02881-0808
> >> USA
> >>
> >> _______________________________________________
> >> R-SIG-Finance at r-project.org mailing list
> >> https://stat.ethz.ch/mailman/listinfo/r-sig-finance
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> >> -- Also note that this is not the r-help list where general R
> >> questions should go.
> >
> >
>
>
> --
> John P. Burkett
> Department of Economics
> University of Rhode Island
> Kingston, RI 02881-0808
> USA
>
> phone (401) 874-9195
>
> _______________________________________________
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