mvnrnd and positive semidefinite covariance matrices

Hi. Newbie question here.

Does anyone know why Matlab's mvnrnd function requires that the
covariance matrix be positive semidefinite? Is it possible to
generate random numbers from a multivariate normal distribution whose
covariance matrix is not positive semidefinite?

As context: I'm currently using the mvnrnd function to generate
random portfolio returns based off of random asset class
performances. Because the covariance matrix of the asset classes is
not positive semidefinite, I've had to use a conversion, which leads
to the portfolio not quite having the distribution that I expected.

Thanks!
.

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