[R-SIG-Finance] Sharpe's algorithm for portfolio improvement

[alexios]

I've found the cmaes (Covariance Matrix Adapting Evolutionary Strategy) 
solver on CRAN to be quite robust to some nonconvex portfolio
problems which required a global optimizer. Like other such global 
solvers which do not accept explicit constraint functions, you would 
need to create a sort of penalty barrier function i.e

-obj(x) + 100*(1-sum(x))^2

For state of the art global solvers you'll probably need to look outside 
R to a commercial implementation or try submitting your problem to the 
NEOS server (http://www.neos-server.org/neos/solvers/index.html...see in 
particular the Branch and Bound type solver BARON).

Regards,

Alexios

On 01/08/2011 22:07, John P. Burkett wrote:
> 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
>>>
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>>> -- Also note that this is not the r-help list where general R
>>> questions should go.
>>
>>
>
>