inducing correlation with contraints

Hi, I'm busy doing my thesis but I keep running into this problem: I'm trying to generate several series that are correlated. One must be able to specify this correlation though (as a function input). However, there is the additional constraint that no value in any of the series can be less than -1. I need to also be able to specify the mean and variance of each series as a function input. Oh and the values should be drawn from a normal distribution. Can anyone help me? This has been holding me up for days! Thanks!! This is my code so far:

function [Returns,Z,C]= cholesky1(numberShares,numberReturns,varMatrixInput,inducedCorrInput,meanInput)
var_matrix = diag(varMatrixInput);
inducedCorr_matrix = inducedCorrInput;
A = randn(length(var_matrix),length(var_matrix));
%Creates a matrix that has a size determined by the number of shares. This
%matrix is used to create the variance-covariance matrix.
B = tril(A,-1);
%This creates a lower triangular matrix (the function tril does this)
%without the diagonals (the minus one does this).
for i = 2:length(var_matrix)
  B(i,1) = inducedCorr_matrix(1,i)*sqrt(var_matrix(i,i))*sqrt(var_matrix(1,1));
end
var_cov_matrix = B+ B' + var_matrix;
C = chol(var_cov_matrix);
Z = randn(numberReturns,numberShares);
Returns = Z*C;
end
This does everything perfectly, inducing the correlation,, mean and variance, but allows values to be less than -1. Does anyone have any idea how to fix this without affecting the correlation etc? Any input would be appreciated!

[Walter Roberson]

This is at least your fourth question asking the same thing. Please do not create duplicate questions. You can edit previous questions to add new information.

Answer 1

[Sean de Wolski]

Add a scalar to your mean. It's impossible to fix a variance and a mean on a normal distribution and then constrain it to not include values that would appear under the bell curve.

E.g.

the_mean = 2;
the_var = 11;

You can't have a normal distribution without values less than negative one.