New Markowitz / Matlab

[Vic Norton]

We are currently working on a paper

   New Markowitz: a package to aid in portfolio selection

   ABSTRACT
   We present a GNU Octave package to aid in financial portfolio
   selection, with examples of its use on current data. Our minnormy
   function, at the core of the package, is a variation on Harry
   Markowitz’s critical line algorithm.

to be published in the Portfolio Management section of "The Archives"
<http://arxiv.org>. An example in the paper uses the 2014 performance of
243 exchange traded funds, each of which had at least $1 billion in
assets under managemnt at the end of 2014. In that example we compute
the efficient portfolio of these funds that had a total return of
exactly 15% in 2014. (Efficient here means least standard deviation of
return.)

For your curiosity the 243 funds and their 2014 statistics are listed
at
  http://vic.norton.name/finance-math/stats243_2014.pdf
in decreasing order of assets under management at the end of 2014. The
efficient portfolio descibed above is
  0.00018  XLP  - Consumer Staples Select Sector SPDR ETF
  0.08359  TLT  - iShares 20+ Year Treasury Bond
  0.04336  ICF  - iShares Cohen & Steers REIT
  0.08937  BNDX - Vanguard Total Intl Bd Idx ETF
  0.16371  PGX  - PowerShares Preferred
  0.02371  IYT  - iShares Transportation Average
  0.00894  FXG  - First Trust Consumer Staples AlphaDEX
  0.01587  EPI  - WisdomTree India Earnings
  0.00555  FBT  - First Trust NYSE Arca Biotech Index
  0.08274  HYD  - Market Vectors High-Yield Muni ETF
  0.07932  PGF  - PowerShares Financial Preferred
  0.22353  TFI  - SPDR Nuveen Barclays Capital Muni Bond
  0.00842  EMLP - First Trust North American Energy Infras
  0.17171  UUP  - PowerShares DB US Dollar Index Bullish
at 2014-12-31 closing prices.

Apparently Matlab/MathWorks has routine(s) that accomplish the same task.
  
http://www.mathworks.com/help/finance/mean-variance-portfolio-optimization.html
We are not aware of any such Octave packages. We expect that Matlab
might have a problem with our data since the corresponding covariance of
returns matrix has L2-condition-number over 100,000,000.

We do not have access to Matlab, but we would be very much interested in
how it performs on our data. Our package (with data) is available for
testing at
  http://vic.norton.name/finance-math/newmarkowitz-tests.tar.gz
Any information on Matlab performance would be greatly appreciated.

Regards,

Vic Norton

P.S. The rtndecomp function is part of the New Markowitz package. This
function is described at <http://arxiv.org/abs/1206.2333>.

P.P.S. Our New Markowitz package requires at least Octave 3.8 since it
has functions nested inside of a function.