%This case study is conducted with the portfolio retail
%loans dataset provided by the Kukmin Bank, Korea.
%Default scenarios of bonds are generated at the 
%Kukmin Bank with the CreditMetrix software from the RiskMetrics Group.
%Scenarios data are imported to PSG by the Converter_VaR_Optimizaion
%intended for processing the outputs from the CreditMetrix.
%For a portfolio of clusters of retail loans the expected return
%is maximized subject to the constraint on VaR deviation.
%It is assumed that weights for clusters can be rebalanced
%within 10% and 20% of the original weights.
%This example implements Problem 2 of case study,
%where portfolio VaR DEVIATION is minimized subject to
%constraint on the portfolio rate of return.
%Weights for clusters can be rebalanced within 10% of the original weights.

clear;
format long;

%Convert the problem from File Format files into the riskprog function run format.
%Input data is stored in the MAT-file.

%Load the problem:
load('problem_2_Korea_retail_bound_0_1_data.mat');

%Read current portfolio weights:
load('point_current_portfolio_weights.mat');

%Turn off displaying messages posted by calculating process 
stroptions.Display = 'Off';

risk='var_dev';

%Solve the optimization problem for specified  values of the parameter
[xout, fval, status, output] = riskprog(risk, w, H, c, p, [], A, b, ...
                                        [], [], lb, ub, [], stroptions);
                                    
%Change constraint sign to compensate >= instead of <= in riskprog constraint statement
fAval = -1*output.fAval;

%Display the solution
fprintf('Minimum of portfolio VaR DEVIATION = %f\n', fval);
fprintf('Constraint on the portfolio rate of return = %f\n', fAval);
fprintf('Component Name  Value\n');
for i=1:1:length(xout)
fprintf('%6s\t', component_name_arr{i}); fprintf('%14f\n', xout(i));
end
   

%Build graph showing contributions to VaR Deviation of individual clusters
%in the Optimal Portfolio (Increment). The Increment is calculated as the 
%difference between the VaR Deviation of the portfolio and 
%the VaR Deviation of the portfolio without this cluster. 

%Set number of points to be shown on the graph. The graph shows
%n_plot maximal absolute values of increments. 
n_plot = 10;
if n_plot > size(xout,1)
    n_plot > size(xout,1);
end

%Calculate increments for all clusters in the Optimal Portfolio
[Increment_Opt] = functionincrement(risk, w, H, c, p, xout);
u = sort(abs(Increment_Opt), 'descend');
i = 0;
for j=1:1:size(xout,1)
    if abs(Increment_Opt(j)) >= u(n_plot)
         i = i + 1;
         point_variables(i) = component_name_arr(j);
         Point1(i) = Increment_Opt(j);
     end
end

figure
plot(Point1,'.', 'MarkerSize',20)
set(gca,'XTick',1:1:size(point_variables',1));
hAxes = gca;
set(hAxes, 'XTickLabel', point_variables');
grid on;
xlabel('Clusters');
ylabel('Contributions to VaR Deviation');
title(sprintf('%0.f%s',n_plot,' Significant Values of Contributions to VaR Deviation of Individual Clusters in Optimal Portfolio'));


%Build graph showing ratio of the contributions to the VaR Deviation
%of individual clusters to the VaR_DEV of the Optimal Portfolio
%(Relative Contribution)

%Extract value of the VaR_DEV for the Optimal Portfolio from the 
%solution of the problem

risk_opt = fval;
figure
plot(Point1/risk_opt,'.', 'MarkerSize',20)
set(gca,'XTick',1:1:size(point_variables',1));
hAxes = gca;
set(hAxes, 'XTickLabel', point_variables');
grid on;
xlabel('Clusters');
ylabel('Relative Contributions to VaR Deviation');
title(sprintf('%0.f%s',n_plot,' Significant Values of Relative Contributions to VaR Deviation'));

%Build graph showing difference between weights of the Optimal
%Portfolio and the current portfolio 
%The graph shows n_plot maximal absolute values of the difference. 

%Calculate the difference
z = xout - current_point';
clear u;
clear point_variables;
clear Point1;
u = sort(abs(z), 'descend');
i = 0;
for j=1:1:size(xout,1)
    if abs(z(j)) >= u(n_plot)
         i = i + 1;
         point_variables(i) = component_name_arr(j);
         Point1(i) = z(j);
     end
end
figure
plot(Point1,'.', 'MarkerSize',20)
set(gca,'XTick',1:1:size(point_variables',1));
hAxes = gca;
set(hAxes, 'XTickLabel', point_variables');
grid on;
xlabel('Clusters');
ylabel('Values of the Difference');
title(sprintf('%0.f%s',n_plot,' Significant Values of Difference Between Components of Optimal and Current Points'));


%Build graph showing difference between contributions to VaR Deviation 
%(increments) of individual clusters in the Optimal Portfolio and the
% Current Portfolio.

%Calculate increments for all clusters in the Current Portfolio
[Increment_Curr] = functionincrement(risk, w, H, c, p, current_point');

%Calculate the difference
Increment_Dif = Increment_Opt - Increment_Curr;

clear u;
clear point_variables;
clear Point1;
u = sort(abs(Increment_Dif), 'descend');
i = 0;
for j=1:1:size(xout,1)
    if abs(Increment_Dif(j)) >= u(n_plot)
         i = i + 1;
         point_variables(i) = component_name_arr(j);
         Point1(i) = Increment_Dif(j);
     end
end

figure
plot(Point1,'.', 'MarkerSize',20)
set(gca,'XTick',1:1:size(point_variables',1));
hAxes = gca;
set(hAxes, 'XTickLabel', point_variables');
grid on;
xlabel('Clusters');
ylabel('Values of the Difference');
title(sprintf('%0.f%s',n_plot,' Values of Difference Between Contributions to VaR Deviation of Optimal and Current Points'));

%Build graph showing difference between 
%the ratio of the contributions to the VaR Deviation of individual clusters
%to the VaR_DEV of the Optimal Portfolio(Relative Contribution in the 
%Optimal Portfolio)
%and
%the ratio of the contributions to the VaR Deviation of individual clusters
%to the VaR_DEV of the Current Portfolio(Relative Contribution in the 
%Current Portfolio)

%Culculate value of the VaR_DEV for the Current Portfolio
[risk_current] = functionvalue(risk, w, H, c, p, current_point');

clear u;
clear point_variables;
clear Point1;
clear Increment_Dif;

%Calculate the difference
Increment_Dif = Increment_Opt/risk_opt - Increment_Curr/risk_current;
u = sort(abs(Increment_Dif), 'descend');
i = 0;
for j=1:1:size(xout,1)
    if abs(Increment_Dif(j)) >= u(n_plot)
         i = i + 1;
         point_variables(i) = component_name_arr(j);
         Point1(i) = Increment_Dif(j);
     end
end

figure
plot(Point1,'.', 'MarkerSize',20)
set(gca,'XTick',1:1:size(point_variables',1));
hAxes = gca;
set(hAxes, 'XTickLabel', point_variables');
grid on;
xlabel('Clusters');
ylabel('Values of the Difference');
title(sprintf('%0.f%s',n_plot,' Values of Difference Between Relative Contribution to VaR Deviation of the Optimal and Current Portfolios'));


% Build the graph showing the exposures of  the current portfolio.  
% The graph shows n_plot maximal values of the exposures. 
% Exposures with less values are combined into category "Others".

u = sort(abs(current_point), 'descend');
i = 0;
other = 0;
for j=1:1:size(xout,1)
    if abs(current_point(j)) >= u(n_plot)
         i = i + 1;
         point_variables(i) = component_name_arr(j);
         Point1(i) = current_point(j);
    else
        other = other + current_point(j);
    end
end

Point1(n_plot+1) = other;
point_variables(n_plot+1)={'other'};
figure;
pie(Point1);
legend(point_variables, 'Location','EastOutside');
title(sprintf('%0.f%s',n_plot,' Largest Exposures of  the Current Portfolio'));

% Build the graph showing the exposures of  the optimal portfolio.  
% The graph shows n_plot maximal values of the exposures. 
% Exposures with less values are combined into category "Others".

u = sort(abs(xout), 'descend');
i = 0;
other = 0;
for j=1:1:size(xout,1)
    if abs(xout(j)) >= u(n_plot)
         i = i + 1;
         point_variables(i) = component_name_arr(j);
         Point1(i) = xout(j);
    else
        other = other + xout(j);
    end
end

Point1(n_plot+1) = other;
point_variables(n_plot+1)={'other'};
figure;
pie(Point1);
legend(point_variables, 'Location','EastOutside');
title(sprintf('%0.f%s',n_plot,' Largest Exposures of  the Optimal Portfolio'));


% Build the histogram of losses for the optimal portfolio
losses = -H*xout; % Calculate losses
[L, IX] = sort(losses); %Order losses
n_bins = 25;   % number of bins

%Calculate the bin locations and frequencies
delta = (L(size(L,1)) - L(1))/n_bins;  
Y(1) = L(1) + delta/2;
n(1) = 0;
for j=2:1:n_bins
   n(j) = 0; 
   Y(j) = Y(j-1) + delta;
end
i = 1;
for j=1:1:size(L,1)
   if  L(j) < Y(i) + delta/2
       n(i) = n(i) + p(IX(j));
   else
       i = i+1;
   end
end

figure;
bar(Y,n);
xlabel('Losses');
title('Histogram of Losses for the Optimal Portfolio');

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