Code covered by the BSD License

# Risk and Asset Allocation

### Attilio Meucci (view profile)

16 Nov 2005 (Updated )

Software for quantitative portfolio and risk management

S_LogT.m
```% this script simulates a bivariate log-t distribution
% it shows its pdf as proxied by the 3-D histogram
% it shows the distribution of a generic linear combination (portfolio) of the two variables
% see "Risk and Asset Allocation"-Springer (2005), by A. Meucci

clc; clear; close all
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% input parameters

Mu=[0 0]';
s=[0.3 0.2]';
r=-.99;
Nu=7;

LinCombination=[1 -2]';

NumSimulations=100000;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Sigma=[s(1)^2     r*s(1)*s(2)
r*s(1)*s(2)    s(2)^2];

Ones=ones(NumSimulations,1);
% generate sample by rescaling the built-in generator
Y = Ones*Mu' + (Ones*s').*mvtrnd([1 r;r 1],Nu,NumSimulations);
X = exp(Y);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% plots

figure
% marginals
NumBins=round(10*log(NumSimulations));

subplot('Position',[.05 .3 .2 .6])
[n,D]=hist(X(:,2),NumBins);
barh(D,n,1);
[y_lim]=get(gca,'ylim')
set(gca,'xtick',[])
grid on

subplot('Position',[.3 .05 .6 .2])
[n,D]=hist(X(:,1),NumBins);
bar(D,n,1);
[x_lim]=get(gca,'xlim')
set(gca,'ytick',[])
grid on

% scatter plot
subplot('Position',[.3 .3 .6 .6])
h=plot(X(:,1),X(:,2),'.');
set(gca,'xlim',x_lim,'ylim',y_lim)
grid on

% histogram (~rescaled pdf)
NumBins3d=round(sqrt(NumSimulations)/5);
figure
hist3(X,[NumBins3d NumBins3d]);

```