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In essence, this approach was very appealing in terms of performance, development time, and cost (essentially free). Although faster and more efficient implementations are possible (e.g. C/C++ and Fortran with open-MPI , the aforementioned implementation was sufficient for our purposes).

The code utilized was initially developed for sequential execution (in SAS ) and then converted to R with similar performance. It was subsequently converted from sequential to parallel to exploit the benefits of a parallel R -implementation. The standard steps for this conversion process are pretty standard, essentially:

  1. We identify the loops which carry independent computations. we have two main loops. Firstly, simulating J portfolios can be regarded as J independent operations, which we can execute concurrently. Secondly, running the algorithm over a number of N years, can be regarded as N independent computational efforts.
  2. Vectorize loops ( Workhorse Functions).
  3. Gather results ( Combine/Gather Functions).
  4. Distribute Execution (Call functions with snow ).

Several 64 processor jobs were submitted to Rice's Cray XD1 Research Cluster (ADA) - occupying 16 nodes, each with a total of 4 processors. The jobs would take less than 20 hours to complete, for about 64 simulated tracks of 40 years each.

Results

Preliminary results

Several simulations were run with observed, above average performance (number of portfolios inspected per simulation was in the range of J = 25 , 000 to J = 50 , 000 ). Figure 1 shows a simulation of J = 50 , 000 portfolios per year over a period of 43 years. Several interesting features can be noted through this figure. We can appreciate that any investor that made up a portfolio with an initial investment of $100,000 in 1970 and selected the same stocks chosen by our algorithm would have allowed his or her portfolio to compound to a total of $3.7M (by the end of 2008), which performed better than both an equal-investment strategy in the S&P 500 Index (about $2.7M) or a market-cap weighted investment strategy in the S&P 500 Index (slightly below $1M). Of course, we can imagine that the computational power that was used was not available in the early seventies, but moving forward it will be and to an extent this is what matters. Also it is clearly seen that the Coordinated Max-Median Rule is inherently a more volatile rule (as compared to the S&P 500). Next, Figure 2 describes 1 of 3 pilot runs that were evaluated with various measures suggesting the superiority of the max-median (as opposed to, say for instance the mean, as well as the benefit of using the “max” rather than the “min”). This seems plausible, at least heuristically, as the median is most robust (the mean is least robust), and in some sense the previous years “best” performing companies are more likely to perform better next year than the previous years “worst” performing companies (in terms of returns).

Coordinated Max-Median Rule (Single Run) 50,000 Portfolios Evaluated per Year
Coordinated Max-Median Rule (Single Run) 25,000 Portfolios Evaluated per Year with additional evaluations

Questions & Answers

what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, The art of the pfug. OpenStax CNX. Jun 05, 2013 Download for free at http://cnx.org/content/col10523/1.34
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