% This case study maximizes annualized portfolio return on multiple sample
% paths subject to constraint on Drawdown Deviation Maxinun Multiple. 
% It solves the optimization problem for several values of 
% upper bound on the Drawdown Deviation Maxinun Multiple by running 
% multiple times the mpsg-solver.
% The program buillds tables with optimal points; builds efficient frontier
% "Return vs. Drawdown Deviation Maximum Multiple"; 
% builds graph showing components of the optimal solution corresponding to
% the first value of upper bound on the Drawdown Deviation Maxinun Multiple. 

clc
clear

%Generate list of matrices names:
str_ = ['matrix_average_annualized_returns ' 'matrix_1 ' 'matrix_2 '...
                  'matrix_3 ' 'matrix_4 '  'matrix_5 ' 'matrix_6 ' ...
                  'matrix_7 ' 'matrix_8 '  'matrix_9 ' 'matrix_10 ' 'matrix_11'];
matrices_names = strread(str_, '%s');

%Read and pack all matrices to PSG Toolbox format:
clear toolboxstruc_arr;
count = 1;

for j=1:1:size(matrices_names,1)
    clear header_matrix;
    clear matrix_arr;
    [header_matrix, matrix_arr] = read_matrix([matrices_names{j} '.txt']);
    toolboxstruc_arr(count) = tbpsg_matrix_pack(matrices_names{j}, matrix_arr, header_matrix);
    count = count+1;
end

%Read and pack all points to PSG Toolbox format:
clear header_point;
clear point_arr;
[header_point, lb] = read_point('point_lb.txt');
toolboxstruc_arr(count) = tbpsg_point_pack('point_lowerbounds', lb, header_point);
count = count+1;

clear header_point;
clear point_arr;
[header_point, ub] = read_point('point_ub.txt');
toolboxstruc_arr(count) = tbpsg_point_pack('point_upperbounds', ub, header_point);
count = count+1;

% Specifies a set of values of parameter (upper bound on risk) for which
% runs should be conducted:
Parameters = [0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.2 0.21 0.22];

%Generate fragments of the problem description common for all parameters: 
 str1 = sprintf('maximize');
 str2 = sprintf('  linear(matrix_average_annualized_returns)');
 str4 = sprintf('  drawdownmulti_dev_max(matrix_1,...,matrix_11)');
 str5 = sprintf('Box: >= point_lowerbounds, <= point_upperbounds');
 str6 = sprintf('Solver: VAN, precision = 9');
  
 for i=1:size(Parameters,2)
  
%Generate parameter-specific fragment of the problem description
    str3 = sprintf('%s%.3f','Constraint: <= ', Parameters(i));

%Generate problem statement
    clear problem_statement;
    problem_statement = sprintf('%s\n', str1, str2, str3, str4, str5, str6);

% Uncomment the following line to open the problem in Toolbox Window
% tbpsg_toolbox(problem_statement,toolboxstruc_arr);

%Optimize the problem      
    [solution_str, outargstruc_arr] = tbpsg_run(problem_statement, toolboxstruc_arr);

%Extract optimal solution   
     point_variables = tbpsg_optimal_point_vars(solution_str, outargstruc_arr);
     Points(:,i) = tbpsg_optimal_point_data(solution_str, outargstruc_arr)';          
     returns(i) = tbpsg_objective(solution_str, outargstruc_arr); 
     risk(i) = tbpsg_constraints_data(solution_str, outargstruc_arr);
     
 end
 
 warning('on', 'all');

% output solution
fprintf('Points: %d\n', length(risk));
str__ = ['Poin_1 ' 'Poin_2 ' 'Poin_3 ' 'Poin_4 ' 'Poin_5 ' 'Poin_6 ' 'Poin_7 ' 'Poin_8 ' 'Poin_9 ' 'Poin_10 ' 'Poin_11 ' 'Poin_12 ' 'Poin_13 ' 'Poin_14 '];
Point_N = strread(str__, '%s');
fprintf(' Point #   Drawdown Deviation Maxinun Multiple  Return\n');
for j=1:1: length(risk)
  fprintf('%7s%25f\t%19f\n', Point_N{j}, risk(j), returns(j));  
end
fprintf('\nOptimal Points:\n');
fprintf('\nComponent    Point_1     Point_2     Point_3     Point_4     Point_5     Point_6     Point_7\n');
for i=1:1:length(point_variables)
 fprintf('%8s',point_variables{i});
 for j=1:1: 7
  fprintf('%12f', Points(i,j));  
 end
 fprintf('\n');
end

fprintf('\nComponent    Point_8     Point_9    Point_10    Point_11    Point_12    Point_13    Point_14\n');
for i=1:1:length(point_variables)
 fprintf('%8s',point_variables{i});
 for j=8:1: 14
  fprintf('%12f', Points(i,j));  
 end
 fprintf('\n');
end
% display efficient frontier
figure
plot(risk,returns);
grid on;
xlabel('Drawdown Deviation Maximum Multiple');
ylabel('Return');
title('Efficient Frontier. Return vs. Drawdown Deviation Maximum Multiple ');

% build graph showing components of the optimal solution corresponding to
% the first value of the parameter. Only components exceeding lower bounds
% are shown
clear x;
clear y;
i = 0;
for j=1:1:size(point_variables,2)
    if Points(j,1)> lb(j)
        i = i+1;
        x(i) = point_variables(j);
        y(i) = Points(j,1);
    end  
end
figure
 bar(y,0.1,'c');
  set(gca,'XTick',1:1:length(x));
hAxes = gca;
set(hAxes, 'XTickLabel', x);
grid on;
xlabel('Components of Optimal Solution Exceeding Lower Bounds');
ylabel('Components Values');
title('Point 1: Drawdown Deviation Maximum Multiple = 0.05. Components of Optimal Solution Exceeding Lower Bounds');

%=======================================================================|
%American Optimal Decisions, Inc. Copyright                             |
%Copyright ©American Optimal Decisions, Inc. 2007-2016.                 |
%American Optimal Decisions (AOD) retains copyrights to this material.  |
%                                                                       |
%Permission to reproduce this document and to prepare derivative works  |
%from this document for internal use is granted, provided the copyright |
%and “No Warranty”  statements are included with all reproductions       |
%and derivative works.                                                  |
%                                                                       |
%For information regarding external or commercial use of copyrighted    |
%materials owned by AOD, contact AOD at support@aorda.com.              |
%=======================================================================|