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+PortOpt [Portfolio Optimizer] is an open-source (LGPLed) C++ program (with Python binding) implementing the Markowitz(1952) [[http://en.wikipedia.org/wiki/Modern_portfolio_theory|mean-variance model]] with agent's linear indifference curves toward risk in order to find the optimal assets portfolio under risk.
+You have to provide PortOpt (in text files or - if you use the api- using your own code) the variance/covariance matrix of the assets, their average returns and the agent risk preference.
+It returns the vector of assets' shares that compose the optimal portfolio.
+In order to minimise the variance it internally uses [[http://quadprog.sourceforge.net/|QuadProg++]], a library that implement the algorithm of Goldfarb and Idnani for the solution of a (convex) Quadratic Programming problem by means of an active-set dual method.
+{{ :personal:portfolio:windows_portopt_screenshot.png?direct | Screenshot on Windows}}
+===== Download it =====
+Windows executable (command line tool!), linux (x64) executable and source code (for C++/Python) are available from [[https://sourceforge.net/projects/portopt |SourceForge]].
+===== Bugs and support =====
+If you find a bug, request a feature or need support open a ticket or discuss it in the [[https://sourceforge.net/projects/portopt |SourceForge]] pages.
+===== Theorical Background =====
+In portfolio theory agents attempts to maximise portfolio expected return for a given amount of portfolio risk, or equivalently to minimise risk for a given level of expected return.
+{{ :personal:portfolio:portfolio_model.png?nolink |Theoretical framework}}
+The portfolio management can be portrayed graphically as in the above Figure, where the feasible set of variance-profitability combinations in enclosed by the blue curve and the B-D segment represents the efficient frontier, where no variance can be lowered at productivity's price or equivalently no productivity can be increased at price of increasing variance.
+In order to simplify computations, forest managers are assumed to have risk aversion with simple linear preferences, that is they are willing to trade off variance with productivity proportionally.
+In such case the indifference curves can be drawn like a bundle of straight lines having equation  $prod = \alpha * var + \beta$ , where  $\alpha$  is the linear risk aversion coefficient and both  $prod$  and  $var$  refer to the overall portfolio's productivity and variance.
+Point  $B$  represents the point having the lowest possible portfolio variance.  Agents with  $\alpha$  risk aversion will choose however the tangent point  $C$  that can be obtained by solving the following quadratic problem:
+\begin{equation}
+\begin{array}{rrrll}
+\max_{x_i, \beta} & Y                & =         & \beta                                                   & \\
+s.t.              &                  &           &                                                         & \\
+                  & x_i              & \geqslant & 0                                                       & \forall i\\
+                  & \sum_i x_i       & =         & 1                                                       & \\
+                  & \sum_i {x_i p_i} & =         & \alpha \sum_i { \sum_j { x_i x_j \sigma_{i,j}}} + \beta & \\
+\end{array}
+\label{eq:optimisation_problem1}
+\end{equation}
+that by substitution become:
+\begin{equation}
+\begin{array}{rrrll}
+\min_{x_i} & Y          & =         &  \alpha \sum_i { \sum_j { x_i x_j \sigma_{i,j}}} - \sum_i {x_i p_i} & \\
+s.t.       &            &           &                                                                     & \\
+           & x_i        & \geqslant & 0                                                                   & \forall i\\
+           & \sum_i x_i & =         & 1                                                                   & \\
+\end{array}
+\label{eq:optimisation_problem2}
+\end{equation}
+where  $x_i$  is the share of the asset  $i$ ,  $p_i$  is its productivity,  $\sigma_{i,j}$  is the covariance between assets  $i$  and  $j$  and hence  $\sum_i {x_i p_i}$  is the overall portfolio productivity and  $\sum_i { \sum_j { x_i x_j \sigma_{i,j}}}$  is its variance.
+As the only quadratic term arises when  $i=j$  and  $\sigma_{i,j}$  being the variance is always positive, the problem is convex and hence easily numerically solved.
+===== Compilation (not needed if using a pre-compiled version) =====
+===   Option 1 - as a stand-alone program ===
+  g++ -std=c++0x -O -o portopt_executable QuadProg++.cpp Array.cpp anyoption.cpp portopt.cpp  main.cpp
+=== Option 2 - as a library to be used in your C/C++ program ===
+  g++ -fPIC -std=c++0x -O -c QuadProg++.cpp Array.cpp anyoption.cpp portopt.cpp main.cpp
+  g++ -std=c++0x -O -shared -Wl,-soname,portopt.so -o portopt.so QuadProg++.o Array.o anyoption.o portopt.o
+Then link your program e.g. with:
+  g++ -std=c++0x -O -o portopt_executable main.o -Wl,-rpath,'$ORIGIN' -L . portopt.so
+  ./portopt_executable
+===  Option 3 - as a lib to be used in python, using swig ===
+  swig -c++ -python portopt.i
+  g++ -fPIC -std=c++0x -O -c QuadProg++.cpp Array.cpp anyoption.cpp portopt.cpp portopt_wrap.cxx main.cpp -I/usr/include/python2.7 -I/usr/lib/python2.7
+  g++ -std=c++0x -O -shared -Wl,-soname,_portopt.so -o _portopt.so QuadProg++.o Array.o anyoption.o portopt.o portopt_wrap.o
+(then please refer to the python example for usage)
+If you want to change the output library name (e.g. you want to create _portopt_p3.so for python3 alongside _portopt.so for python2), do it in the %module variable of portopt.i and in the -soname and -o options of the linking command (and don't forget to use the right python included directory in the compilation command).\\
+You can then load the correct module in your script with something like:
+  import sys
+  if sys.version_info < (3, 0):
+    import portopt
+  else:
+    import portopt_p3 as portopt
+===== Usage =====
+:!: Please notice that the API changed from version 1.1, with the introduction of the ''port_opt_mean'' and ''port_opt_var'' parameters (both by reference). For the old 1.1 call instructions see [[https://lobianco.org/antonello/personal:portfolio:portopt?rev=1441891152|here]].
+== Linux ==
+  ./portopt [options]
+== Windows ==
+  portopt.exe [options]
+(from a DOS prompt: (a) START->run->"cmd"; (b) cd \path\to\portopt )
+== As a lib from C++: ==
+Call:
+  double solveport (const vector< vector <double> > &VAR, const vector<double> &MEANS, const double &alpha, vector<double> &x_h, int &errorcode, string &errormessage, double &port_opt_mean, double &port_opt_var, const double tollerance = 0.000001)
+== As a lib using Python: ==
+  import portopt
+  results = portopt.solveport(var,means,alpha,tolerance) # tolerance is optional, default to 0.000001
+  functioncost = results[0]
+  shares       = results[1]
+  errorcode    = results[2]
+  errormessage = results[3]
+  opt_mean     = results[4]
+  opt_var      = results[5]
+=== Options ===
+<code>
+  -h  --help                                   Prints this help
+  -v  --var-file [input_var_file_name]         Input file containing the variance/covariance matrix (relative path)
+  -m  --means-file [input_means_file_name]     Input file containing the means vector (relative path)
+  -a  --alpha [alpha_coefficient]              Coefficient between production and risk in the linear indifference curves
+  -f  --field-delimiter [field_delimiter]      Character to use as field delimiter (default: ';')
+  -s  --decimal-separator [decimal-separator]  Character to use as decimal delimiter (default: '.')
+  -t  --tollerance [tolerance]                 A tolerance level to distinguish from zero (default: 0.000001)
+</code>
+=== Notes ===
+  * Higher the alpha, lower the agent risk aversion;
+  * Set a negative alpha to retrieve the portfolio with the lowest possible variance;
+  * Set alpha to zero to retrieve the portfolio with the highest mean, independently from variance (solution not guaranteed to be unique);
+  * Assets shares are returned in the x_h vector, eventual error code (0: all fine, 1: input data error, 2: no solutions, 3: didn't solve, 4: solver internal error) in the errorcode parameter.
+  * Use option "tollerance" with two l up to version 1.1 included
+===== Copyright and licence =====
+Copyright (C) 2014 Antonello Lobianco.
+PortOpt is free software: you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
+PortOpt is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
+You should have received a copy of the GNU Lesser General Public License along with PortOpt.  If not, see [[http://www.gnu.org/licenses]].
+===== Citations =====
+If you use this program or a derivative of it in an academic framework, please cite it!\\
+Please cite as:
+  * A. Dragicevic, A. Lobianco,  A. Leblois (2016), "[[http://dx.doi.org/10.1016/j.forpol.2015.12.010|Forest planning and productivity-risk trade-off through the Markowitz mean-variance model]]", Forest Policy and Economics, Volume 64, March 2016, Pages 25–34.
+===== Acknowledgements =====
+This work was supported by:
+  * a grant overseen by Office National des Forêts through the [[http://www.foretspourdemain.fr |Forêts pour Demain International Teaching and Research Chair]];
+  * the French National Research Agency through the [[http://mycor.nancy.inra.fr/ARBRE/ |Laboratory of Excellence ARBRE]], a part of the "Investissements d'Avenir" Program (ANR 11 -- LABX-0002-01).