This is machine translation

Translated by Microsoft
Mouseover text to see original. Click the button below to return to the English version of the page.

Note: This page has been translated by MathWorks. Please click here
To view all translated materials including this page, select Japan from the country navigator on the bottom of this page.

Compare Concentration Indices for Random Portfolios

This example shows how to simulate random portfolios with different distributions and compare their concentration indices. For illustration purposes, a lognormal and Weibull distribution are used. The distribution parameters are chosen arbitrarily to get a similar range of values for both random portfolios.

Generate random portfolios with different distributions.

rng('default'); % for reproducibility
PLgn = lognrnd(1,1,1,300);
PWbl = wblrnd(2,0.5,1,300);

Display largest simulated loan value.

fprintf('\nLargest loan Lognormal: %g\n',max(PLgn));
fprintf('Largest loan Weibull: %g\n',max(PWbl));
Largest loan Lognormal: 97.3582
Largest loan Weibull: 91.5866

Plot the portfolio histograms.

hold on
hold off
title('Random Loan Histograms')
xlabel('Loan Amount')

Compute and display the concentration measures.

ciLgn = concentrationIndices(PLgn,'ID','Lognormal');
ciWbl = concentrationIndices(PWbl,'ID','Weibull');

ProportionLoans = 0:0.1:1;
area(ProportionLoans',[ciWbl.Deciles; ciLgn.Deciles-ciWbl.Deciles; ProportionLoans-ciLgn.Deciles]')
axis([0 1 0 1])
title('Lorenz Curve (by Deciles)')
xlabel('Proportion of Loans')
ylabel('Proportion of Value')
        ID            CR          Deciles        Gini         HH          HK           HT          TE   
    ___________    ________    _____________    _______    ________    _________    _________    _______

    "Lognormal"    0.066363    [1x11 double]     0.5686    0.013298    0.0045765    0.0077267    0.66735
    "Weibull"      0.090152    [1x11 double]    0.72876    0.020197    0.0062594     0.012289     1.0944

See Also

Related Examples

More About

Was this topic helpful?